About the Cover PTC uses DSP to narrow the INCLUDING: occupied of analog ( 9). QEX (ISSN: 0886-8093) is published bimonthly in January, March, May, July, September, and November by the American Radio Relay League, A 225 Main Street, Newington CT 06111-1494. Yearly subscription rate to ARRL members is $22; nonmembers $34. Other rates are listed below. Periodicals postage paid at Hartford, CT and at R additional mailing offices. POSTMASTER: Form 3579 requested. Send address changes to: QEX, 225 Main St, Newington, CT 06111-1494 Issue No 200 Features David Sumner, K1ZZ Publisher Doug Smith, KF6DX 3 Practical HF Digital Voice Editor By Charles Brain, G4GUO, and Andy Talbot, G4JNT Robert Schetgen, KU7G Managing Editor Lori Weinberg Assistant Editor 9 PTC: Perceptual for Bandwidth Zack Lau, W1VT Contributing Editor Reduction of Speech in the Analog Domain, Pt 1 Production Department By Doug Smith, KF6DX Mark . Wilson, K1RO Publications Manager Michelle Bloom, WB1ENT Production Supervisor 13 A Low-Cost HF Channel Simulator for Digital Systems Sue Fagan Graphic Design Supervisor By Johan . Forrer, KC7WW David Pingree, N1NAS Technical Illustrator Joe Shea Production Assistant 23 Notes on Standard Design HF LPDAs, Pt 1: Advertising Information Contact: “Short” Boom Designs John Bee, N1GNV, Advertising Manager 860-594-0207 direct By L. B. Cebik, W4RNL 860-594-0200 ARRL 860-594-0259 fax Circulation Department Debra Jahnke, Manager Kathy Capodicasa, N1GZO, Deputy Manager Cathy Stepina, QEX Circulation 39 The ATR-2000: A Homemade, High-Performance HF Offices Transceiver, Pt 2 225 Main St, Newington, CT 06111-1494 USA By John B. Stephensen, KD6OZH Telephone: 860-594-0200 Telex: 650215-5052 MCI Fax: 860-594-0259 (24 hour direct line) -mail: [email protected] Subscription rate for 6 issues: Columns In the US: ARRL Member $22, nonmember $34; US, Canada and Mexico by First Class Mail: 52 RF By Zack Lau, W1VT 51 Next Issue in QEX ARRL member $35, nonmember $47; Elsewhere by Surface Mail (4-8 week delivery): ARRL member $27, nonmember $39; 56 Letters to the Editor Elsewhere by Airmail: ARRL member $55, nonmember $67. Members are asked to include their membership control number or a label from their QST wrapper when applying. In order to ensure prompt delivery, we ask that May/June 2000 QEX Advertising Index you periodically check the address information on your mailing label. If you find any inaccura- cies, please contact the Circulation Department Almost All Digital Electronics: 64 Nemal Electronics International, Inc.: 62 immediately. Thank you for your assistance. American Radio Relay League: 61 Noble Publishing: Cov II Copyright ©2000 by the American Radio Relay Astron: Cov IV Renaissance Radio: 61 League Inc. For permission to quote or reprint Atomic Time, Inc.: 62 Shoc: 63 material from QEX or any ARRL publication, send Communications Concepts Inc.: 62 Tucson Amateur Packet Radio Corp: 63 a written request including the issue date (or book title), article, page numbers and a description of Computer Aided Technologies: 8 TX RX Systems Inc.: 63 where you intend to use the reprinted material. HAL Communications Corp: Cov III Universal Radio, Inc.: 61 Send the request to the office of the Publications Manager ([email protected]) Roy Lewallen, W7EL: 62 May/June 2000 1 THE AMERICAN RADIO A RELAY LEAGUE R R Empirically Speaking L The American Radio Relay League, Inc, is a noncommercial association of radio amateurs, organized for the promotion of interests in Amateur Radio communication and experimentation, for A lot is happening in Amateur radio technology on their management the establishment of networks to provide Radio: licensing reform, discussions of spectrum and certification of communications in the event of disasters or other emergencies, for the advancement of radio art of new bands, expanded satellite equipment. In addition, interoper- and of the public welfare, for the representation operation, and so forth. We see fresh ability issues are raised. We will be of the radio amateur in legislative matters, and inspiration in many parts of the filing comments and we hope you will, for the maintenance of fraternalism and a high standard of conduct. experimental arena, too. Amateur too: This is important! Check it out. ARRL is an incorporated association without Radio has such diversity that it’ capital stock chartered under the laws of the difficult to find ways to give it all the In This Issue state of Connecticut, and is an exempt organiza- tion under Section 501()(3) of the Internal coverage it deserves. Goals for compression and radio Revenue Code of 1986. Its affairs are governed Some of you didn’ like the few transmission of digitized voice include by a Board of Directors, whose voting members relatively simple projects we ran last reduction in occupied bandwidth (bit are elected every two years by the general membership. The officers are elected or time. It is remarkable, though, how rate), improvement in quality or both. appointed by the Directors. The League is little is printed generally about AF Charles Brain, G4GUO, and Andy noncommercial, and no one who could gain through MF. Researchers are discov- Talbot, G4JNT, have taken the plunge financially from the shaping of its affairs is eligible for membership on its Board. ering some very interesting things into digital voice over Amateur Radio “Of, by, and for the radio amateur, ”ARRL about antenna system behavior and —and yes, it’s legal despite our numbers within its ranks the vast majority of wave propagation down there. Over erroneous warning. We shall listen active amateurs in the nation and has a proud history of achievement as the standard-bearer in the next year, we will bring you some with interest to hear of results over amateur affairs. of their results; we’ll also keep you up long-haul paths with their system. It A bona fide interest in Amateur Radio is the to date on progress in audio coding, takes advantage of the coding algor- only essential qualification of membership; an Amateur Radio license is not a prerequisite, compression and digital transmission. ithms that have been so successful in although full voting membership is granted only We have a nice collection of HF and broadcasting to licensed amateurs in the US. through microwave antenna articles in applications, distilled to the chip level. Membership inquiries and general corres- pondence should be addressed to the the queue, too. We’ll continue to Don’t be surprised to hear these signals administrative headquarters at 225 Main Street, emphasize advancement and under- on the HF phone bands before long. Newington, CT 06111 USA. standing of frequency-synthesis and My own approach involves many of Telephone: 860-594-0200 power-amplifier techniques. In this the same DSP principles, but it is Telex: 650215-5052 MCI MCIMAIL (electronic mail system) ID: 215-5052 issue, correspondents present both transmitted differently: as analog FAX: 860-594-0259 (24-hour direct line) background material and newly phone. Before committing to a specific Officers fashioned points of view on that last technique, I did a fair bit of research subject. Thanks to you writers and on auditory coding. I hope you find President: JIM . HAYNIE, W5JBP 3226 Newcastle Dr, Dallas, TX 75220-1640 reviewers who were so patient while the results as interesting as I did. Executive Vice President: DAVID SUMNER, K1ZZ we got “up to speed” on it. Johan Forrer, KC7WW, presents a It seems like a good time to look tool that every serious student of The purpose of QEX is to: back on the legacies of QEX, Commun- propagation should want: a channel 1) provide a medium for the exchange of ideas ications Quarterly and before that, simulator. He begins with modeling and information among Amateur Radio experi- menters, ham radio. Now that those public- theory, then describes his practical 2) document advanced technical work in the ations are effectively consolidated, implementation and test results. Amateur Radio field, and we’d like to see the combination grow Much of this material appears in the 3) support efforts to advance the state of the Amateur Radio art. to be more than just the sum of its Proceedings of the 18th ARRL and parts. Ours is a unique opportunity to TAPR Digital Communications Confer- All correspondence concerning QEX should be addressed to the American Radio Relay League, build a better platform to document ence, Phoenix, Arizona, September 225 Main Street, Newington, CT 06111 USA. progress in our chosen field, celebrate 1999 (ARRL Order No. 7679), as does Envelopes containing manuscripts and letters for the accomplishments of our colleagues some of G4GUO’s. publication in QEX should be marked Editor, QEX. and sustain important discussions. L. B. Cebik, W4RNL, studies log- Both theoretical and practical technical articles Perhaps we should bring in additional periodic dipole arrays (LPDAs) in the are welcomed. Manuscripts should be submitted on IBM or Mac format 3.5-inch diskette in word- columns or news items. Maybe you first part of a series. He begins by processor format, if possible. We can redraw any would like to see more theoretical arti- looking at “short-boom” designs: 60-100 figures as long as their content is clear. Photos cles or instead, more practical appli- feet! As you can imagine, the next should be glossy, color or black-and-white prints cations. The balance we strike depends part will cover units requiring a of at least the size they are to appear in QEX. Further information for authors can be found on on you. Please drop us a line. bit more acreage. John Stephensen, the Web at www.arrl.org/qex/ or by e-mail to On March 21st, the FCC issued a KD6OZH, contributes the second [email protected]. Notice of Inquiry regarding software- installment on his homebrew trans- Any opinions expressed in QEX are those of controlled radios. This notice is on ceiver. IF, AGC and audio circuits are the authors, not necessarily those of the Editor or the Web at www.fcc.gov/Daily_ featured. the League. While we strive to ensure all material is technically correct, authors are expected to Releases/Daily_Business/2000/ Zack Lau, W1VT, presents a no-tune defend their own assertions. Products mentioned db0321/fcc00103.txt. The commiss- waveguide filter for 10 GHz in his are included for your information only; no ioners clearly are trying to understand column.—73, Doug Smith, KF6DX, endorsement is implied. Readers are cautioned to verify the availability of products before sending the wide-ranging impact of digital [email protected]. money to vendors.

2 May/June 2000 Practical HF Digital Voice

High-quality voice communication is possible without exceeding SSB bandwidth or expensive broadcast studio equipment.

By Charles Brain, G4GUO, and Andy Talbot, G4JNT

[Editor’s note: We goofed! The trans- away over a fairly obstructed path, it with regard to quality and robustness mission of in digital format would need to be on HF—even more of a through noisy transmission media: (emission designator J1E or J2E) is challenge! Consider the quality of CD music perfectly legal in the phone bands. The For several years, digitized voice recordings over the old vinyl or tape restriction placed on transmitted baud has been transmitted in a bandwidth systems and the new digital telephone rate by §97.307()(3) of the FCC rules does comparable with normal analog voice networks versus the old systems. There not apply. In fact, there is no upper limit communications using existing trans- are several major issues to be resolved on the for this mode. See the mitters and receivers. After our phone before the conversion is made. sidebar by ARRL Technical Relations call finished, Charles then went away Manager Paul Rinaldo, W4RI. Some of and had a long think. Sampling Rate Selection this material is from Charles’ paper in the To digitize an analog such as Proceedings of the 18th ARRL/TAPR Digital Communication voice, it first must be sampled; that is, Digital Communications Conference, Techniques turned into a series of numerical some from Andy’s paper in RadCom, To fully appreciate why one data values. Sampling theory dictates that March 1999.] communication technique is employed the sampling rate must be at least This whole project began with a over another, we need to cover digital twice the highest-frequency component conversation over the telephone: communication techniques and the present (the Nyquist criterion). Any Andy said that it would be fun to problems of the HF environment. When components at more than half the transmit “real-time” digital speech on properly implemented, digital commu- sampling rate will appear as spurious the amateur bands. Now there was a nications can show considerable advan- components at other frequencies, challenge! As he is located some 70 km tages over their analog counterparts causing distortion. This is called aliasing. The high-frequency compo- nents need to be removed by conven- 7 Elverlands Close 15 Noble Rd tional filtering before . For Ferring, West Sussex Hedge End, Southampton a voice signal as transmitted using BN12 5PL SO30 0PH telephone or SSB, the frequency range United Kingdom United Kingdom of 300-3300 Hz is usually considered [email protected] [email protected] important and therefore requires a May/June 2000 3 sampling rate of at least 6.6 kHz. In the RF bandwidth is wanted for opti- speech quality was much better, but it practice, to ease the anti-aliasing fil- mum transmission at SNRs ratios consumed about 90% of the CPU re- ter’s design, a sampling rate of 8.0 kHz that would be just acceptable for poor sources on Charles’ P133 machine. In is often adopted. speech quality: around 3000 b/s for addition, after contacting the patent 10-15 dB SNR in a 3-kHz bandwidth. holders, we found that they were not Bit-Resolution and Quantization Noise at all happy with what we were doing. Since an analog signal has an Choosing a Voice Coder We then looked at CELP-based sys- infinite number of instantaneous () tems. These require large codebooks and amplitude levels, these cannot be A number of candidate systems were clever search algorithms, some things we represented exactly; it is necessary to studied. The vocoder must operate at a thought were beyond the ROM capabil- choose a suitable number of levels to low data rate, be inexpensive, stand ity of the Motorola evaluation module represent the signal. Instead of levels, alone and be reasonably available. The and available programming skills. Fi- it is more convenient to think of the systems considered were: LPC-10e (lin- nally, we settled on the AMBE vocoder number of bits () needed to give the ear predictive coding), MELP (multiband chip manufactured by DVS, Inc.3 This corresponding quantization: 8 bits excited linear-predictive coding), AMBE chip is relatively cheap, has very good give 28 (256) absolute levels. Sixteen (advanced multiband excited coding) and , may use data rates be- bits per sample give 216 (65,536) various CELP (codebook-excited linear- tween 2400 and 9600 bps, and the manu- levels. The effect of the random in- predictive coding) systems.2 facturer would sell us some! stantaneous error at each sampling We experimented with LPC-10e and The technique adopted codes the point is to add a noise component to even managed to implement a version voice to reduce the number of bits/s the signal, referred to as quantization of it on a Motorola 56002EVM. The needed for transmission. There has noise. speech was understandable but we been a considerable amount of re- A simple rule of thumb can be never did get it to track the pitch cor- search done on various techniques for applied here: The best SNR that can rectly. Having listened to a commer- doing this over the last decade or so, be achieved is given by: cial implementation of LPC-10e, we and some very effective compression SNR ≈ (6N–1.75) dB (Eq 1) decided that it did not have acceptable schemes are now available. The tech- speech quality anyway. niques are too complex to cover in any The 1.75 dB is a “fiddle factor” that We then went on to find an imple- detail here; they usually involve mod- sometimes has slightly different values mentation of MELP (the 2.4-kbps eling the human voice tract and coding in various textbooks, but SNR is ap- DOD standard) on the Internet. We the various elements, such as voiced proximately 6N. If a figure of 40 dB is got the code to compile and added some and unvoiced sounds, in efficient ways. taken as good communications quality, Win95 sound-handling routines. The As an example, GSM mobile phones then 8-bit quantization—allowing about 48-dB of SNR—would be ad- equate. This is the system we adopted— although in slightly modified form—on Is Digital Voice Permissible under Part 97? the public telephone network. There has been some discussion about Part 97 of the FCC Rules and whether digital voice is “legal.” A careful reading of the Rules will show that Choosing a Data Rate digital voice is indeed provided for. Read on. We can see that for 8000 samples per . Is HF digital voice classified as “Data,” thus subject to the provision in second, sampling at 8 bits per sample, §97.307(f)(3), namely “The symbol rate must not exceed 300 bauds…” a total of (8)(8000) = 64,000 bits per A. No. It is “Phone,” also called “Telephony.” The Data symbol-rate limita- second (b/s) are generated.1 The digi- tions do not apply to this mode. tal telephone network has enough Q. What is the emission designator for HF digital voice? bandwidth with optical fiber and mi- A. Digital voice is Phone, defined in §97.3(c)(5) as: “Speech and other sound crowave links to pass 64 kb/s directly, emissions having designators with A, C, D, F, , , J or R as the first symbol; but a radio communications link does 1, 2 or 3 as the second symbol; E as the third symbol.” (It rambles on…) not have this luxury! At HF, we want The first symbol of the emission symbol depends upon the modulation of the main carrier. Typically, the output of the digital-voice modem would be fed into to pass digital voice over a bandwidth a single-sideband, suppressed-carrier (SSB-SC) transmitter, in which case the comparable with SSB (3 kHz). At first symbol would be “J.” (If the main carrier of the transmitter is modulated in VHF—if NBFM is taken for the stan- some other way than SSB-SC, then choose from the permissible ones: A, C, dard channel width—we can increase D, F, H or R, which are explained in §2.201 in Part 2 of the Rules, readily avail- this figure to 12 kHz, but to preserve able in The ARRL’s FCC Rule Book.) the enhanced voice quality that good- The second symbol in this case is “2,” meaning: “A single channel contain- SNR FM can give, more quantization ing quantized or digital information with the use of a modulating subcarrier, ex- levels should be used. cluding time-division multiplex.” Although it is theoretically possible The third symbol is “E” for “Telephony.” to transmit 64 kb/s in a 3000-Hz band- So, the most likely HF digital voice emission symbol will be “J2E.” width, the SNR that is required for a Q. Will other amateur stations think that digital voice stations are unautho- sufficiently low error rate is very rized or even intruders? high—around 64 dB according to A. It’s likely that some will, until digital voice is more familiar and accepted. Shannon’s information theorem. Old timers will recall that, in the days of yesteryear when wall-to-wall full-car- Therefore, other techniques must be rier DSB-AM reigned supreme, the introduction of SSB wasn’t without angst. adopted to transmit digitized voice The best approach is to follow The Amateur’s Code and inform other stations signals. A data rate comparable with on conventional SSB what you’re doing.—Paul Rinaldo, W4RI, ARRL Techni- cal Relations Manager 1Notes appear on page 8. 4 May/June 2000 use a technique that allows transmis- ogy.4 (See Fig 1.) It is relatively easy to for FEC in noisy environments. A sion at 13,000 bits/s. Whatever tech- implement and well proven; it runs on properly filtered PSK signal has a nique is used for voice encoding, there Charles’ DSP evaluation module and is bandwidth that can approach the baud is usually a trade-off between data more suitable for digital voice trans- rate (in fact, PSK31 is optimized to do rate and the quality of the resulting mission than serial-tone modems. Se- just this). If it is not implemented cor- speech. Some of the early systems had rial-tone modems tend to produce long rectly—with waveform control and fil- a very synthetic-sounding, “Dalek- bursts of errors when the equalizer tering—the bandwidth of the signal like” result. Modern variants provide fails, as opposed to the more random can easily spread alarmingly in a man- very much better toll-quality speech. errors produced by a parallel-tone ner analogous to CW key clicks. AMBE appears to offer major im- modem. Speech is unlike computer For the 3600 bits/s needed for the provements over earlier systems. It data in that occasional errors do not digitized voice experiments, either moves away from the concept of model- significantly affect its intelligibility. binary PSK (BPSK) at 3600 baud or ing the voice tract and instead models QPSK at 1800 baud would be ad- the spectrum of the signal every 20 ms. PSK equate. The QPSK signal at poten- Not many technical details appear to be In bipolar phase-shift keying tially 1800-Hz bandwidth could even available to date, as it is still a commer- (BPSK), instead of changing the trans- be transmitted unmodified over SSB cial system. Nonetheless, the results of mission frequency for binary 1s or 0s, radios. However, while this technique test programs show the technique to be the phase is reversed—or effectively, is ideal for UHF or “clean” VHF links, better than any of the ’ELPs. It has the signal is inverted—between 0 and there are particular characteristics on thus been adopted for at least one of the 1 states. It is possible to show that a typical HF transmission path that new satellite-based mobile-phone sys- there is at least a 3-dB improvement in make simple high-baud-rate signals tems. Much more importantly for us, a SNR-versus-error-rate performance very prone to errors and frequently single-chip solution is available for over frequency-shift keying (FSK) unusable. converting from microphone input to given an “ideal” demodulator for each encoded digits. So rather than try to mode, and very much better than this Designing the Modem write vocoding DSP software based on is possible in practice. PSK has begun Amateur Radio equipment has very published algorithms, we decided to to replace keyboard-to-keyboard poor filtering compared to military just buy a chip to do the job. RTTY on the amateur bands recently equipment. The filters tend to be quite The AMBE1000 chip by DVS imple- in the form of PSK31 (see the articles narrow and have poor group-delay ments the whole process and provides in December 1998 and January 1999 characteristics. This means the mo- the user with extensive tradeoffs be- RadCom or July/August 1999 QEX by dem must use a narrower bandwidth tween data rate and link quality, as Peter Martinez, G3PLX). For very than it would with the equivalent mili- well as forward error correction (FEC). nearly the same data rate as RTTY, the tary equipment. This ruled out the Eventually, the data rate we adopted bandwidth needed has shrunk from MIL-STD-188-110A 39-tone modem. was 2400 bits/s of voice data plus 1200 around 300 Hz to 30 Hz with a corre- In the end, we decided on a 36-tone b/s of FEC, giving a total of 3600 b/s to sponding increase in reliability and modem, with a baud rate to match the be transmitted over the RF link. The error rate. By using four phase states 20-ms frame length of the AMBE vo- IC produces samples every 20 ms and instead of two (90° apart, quaternary coder chip. This provides a raw data can be regarded as a real-time system phase-shift keying or QPSK), it is pos- rate of (36)(2)/(20 ms) = 3600 bits/s and in this sense. Any 20-ms samples that sible to encode two bits at once without enough time for a 4-ms guard period. get lost just create glitches in the increasing the bandwidth. This does The guard period is required to give speech that cause minimal distur- incur a 3-dB penalty because the the modem some multipath tolerance. bance and often go unnoticed. transmission power is shared between Each tone carries two bits of data in twice as many bits in a given time. each baud interval. Unlike military mo- Programming the Vocoder Module This technique is available in dems, our modem has no Doppler-cor- In use, the AMBE chip must be pro- PSK31, where it is included as an op- rection tone and no slow “sync-on-data” grammed at turn-on to set the operat- tion for adding the extra data needed facility. So far, both of these facilities ing conditions, and the easiest way to do this is to include an on-board PIC microprocessor. The digitized output samples at a rate of 3600 bits/s are sent via an EIA-232 interface to the modem—in packets of nine bytes for each 20-ms frame. The data rate for this part of the link is 19.2 kbaud. If you do the math on this, you will find there is a lot of spare capacity for pro- grammers who want to use the devel- opment board for their own purposes. An example of this would be for inclu- sion of data and control signals. Choosing a Modem After a literature search, we came to the conclusion that the HF modem must use parallel-tone, PSK technol- Fig 1—A block diagram of the modem. May/June 2000 5 have been unnecessary. The modem the drive level until ALC action oc- different times after having traveled remains in lock for long periods, well curs, then back it off a bit. different distances. For a signal such beyond our ability to carry on a dialogue. The modem is capable of full-duplex as SSB voice, these two or more sig- We then did some MATLAB com- operation. It does not require a feed- nals will cause alternate cancellation puter simulations that showed that back channel and so can be used in and reinforcement, giving the charac- the modems must be within 5 Hz of the broadcast operation; that is, with one teristic multipath fading as a notch correct frequency to work properly. To sender and many listeners. The mo- passes through the audio passband. achieve initial timing and frequency- dem also incorporates a CW-ID fea- Differences in arrival time of typically offset correction, the modem used ture to comply with UK regulations— up to 5 ms are often observed, and in three BPSK-modulated preamble the old meets the new. The CW call poor propagation conditions, can tones. It differentially decodes them sign is hand coded into the DSP soft- reach a lot more than this. using a delay of one baud interval. It ware, but it can be switched off. It is The effect on digital signals can be then integrates the received symbol not sent at the end of each transmis- much more catastrophic than it is for over that time; from this, it deduces sion, but after a programmable period. analog speech. A particular bit of in- the timing. Then, by looking at the Fig 2 shows a compressed spectro- formation arrives at several different energy in the FFT bins on either side gram of an off-air transmission. The points in time, so it can easily land on of the preamble tones, it calculates the three preamble tones can be clearly top of another bit arriving via an alter- frequency error and makes a correc- seen along with the selective fading native path. This mixing up of received tion by translating the received signal (diagonal stripes), as can the carrier of information causes intersymbol inter- in frequency using a complex mixer. an AM broadcast station in the back- ference and is the major cause of bit The reason for three tones is to provide ground and a burst of interference at errors on what might otherwise appear some frequency diversity, as on-air the end. The distinct vertical stripes to be a good link with a strong signal. testing showed a single tone could get were, in fact, pauses in the speech. There is a way around this. If we can lost during deep fades. The greatest problem during opera- send one symbol in such a way that it Each symbol consists of 160 samples; tion is multipath. Sky-wave signals remains uncorrupt when mixed with a the sample rate is 8 ksamples/s. The 36 frequently arrive after several iono- delayed (say, 0 to 5 ms) version of itself, tones were created by using a 128-point spheric hops, with the same instanta- the error rate due to intersymbol inter- complex FFT. The guard period is neous element of signal arriving at ference can be reduced or even elimi- added by taking the last 32 samples from the output of the FFT and adding them to the beginning of the FFT samples to form a total of 160 samples. These 32 samples form the 4-ms guard period. The data are differentially coded and mapped to the output phases using Gray coding before transmission. After the preamble has been sent, the modem sends a reference vector by transmitting a known phase on each of the 36 tones. A “synch” sequence follows this. When the receiving modem detects the synch sequence, it ceases hunting for the preamble and starts passing (we hope!) valid data to the vocoder board. When the operator releases the PTT, the modem detects the loss of voice data and transmits an EOM (end-of-message) sequence embedded in the data stream. This message is, in Fig 2—Off-air spectrogram of M36 modem waveform. fact, the SOM (start-of-message) se- quence, inverted. Transmit/receive control of the modem is triggered by the presence/absence of data from the vocoder; there is, at present, no formal protocol between them. One problem with parallel-tone modems is that they tend to produce signals with very high peak-to-mean ratios. To combat this, our modem uses different initial phases on each of the tones and applies clipping and fil- tering to the output signal. This allows the transmitter to be driven quite heavily before errors begin to appear in the received signal. The simplest way to set the audio level is to increase Fig 3—Prototype vocoder board. 6 May/June 2000 nated. One method is to reduce the baud rate so much that the 5-ms multipath period becomes insignificant. A figure of 20 ms is often used in practice, result- ing in 50-baud signals. It is no coinci- dence that the data rate adopted for RTTY signals for many years has been in the 45 to 75-baud region! To reduce our 3600 bits/s to 50-baud signaling means trying to compress 72 bits into one symbol. While there are some direct techniques of doing this, such as quadrature amplitude modu- lation, these are prone to other types of errors and inefficiencies. Another system is needed that is more resis- tant to in-band interference. The tech- nique is as follows. Instead of using a single carrier modulated with a complex multilevel waveform, we use a large number of multiple carriers, each one modulated with a simple waveform. If there are N carriers, each one independently modulated with 50-baud QPSK, then it is possible to transmit data at Fig 4—Current digital voice station at G4GUO. (2)(50N) bits/s. The spacing between each carrier a data interleaver, but they were aban- ROM available to allow addition of pair must be consistent with the baud doned because the interleaver adds a quite complex code at a later date (in rate, and carrier spacing equal to at large delay to the voice. During deep fact, Charles has since done a version least the symbol rate is required. If we fades or periods of interference this of his software that can encrypt the do a few calculations, it soon becomes spreads errors over multiple vocoder speech using triple DES encryption in evident that many solutions are pos- frames and so prolongs the dropout. real-time); finally, because we already sible for 3600 bits/s in a voice band- had the development tools available. width. Development of the Each board costs us about $150 to Vocoder PC Board make, and we have so far made five. FEC The vocoder board consists of a The modem has no inherent FEC Motorola MC14LC5480P using On-Air Testing capability; instead, it uses the FEC in µ-law coding, an AMBE chip, a The system has been tested over a the AMBE vocoder chip itself. The PIC17C44JW microcontroller, some HC- 70-km path using frequencies in the vocoder tailors the FEC to match the series glue logic and an EIA-232 inter- 40-meter band. We made our first suc- significance of bits in the data stream, face. The AMBE is a 100-pin surface- cessful contact at the first attempt on so it can probably do a much better job mount chip that Charles soldered onto the 27th of March, 1999. This is not a than we can. It is a shame, however, to the board by hand. After five boards, he weak-signal mode; it requires about a waste the soft-decision information began to get very tired of doing it! 25 dB of SNR to function. When work- generated by the modem. For the PC board, he used the ser- ing, however, it makes HF sound like The AMBE chip uses both Golay and vices of ExpressPCB in the US. In a telephone conversation. There is no Hamming codes for error detection hindsight, this was a mistake; their background noise—total silence—ex- and correction. It follows the normal free PC board software is not compat- cept for the “comfort noise” inserted convention during periods of errors, ible with anyone else’s, so it pretty during gaps in the speech by the vo- trying to guess what was sent by look- much locked us into using them once coder itself. The system can tolerate ing at previous frames, then ulti- we had started. Their service is very strong CW interference and the mately giving up. The format used is good, however: Charles e-mailed the multipath-induced selective fading 2400 bits/s speech and 1200 bits/s files on Monday and had the boards found on HF. SSB interference is more FEC. back in the UK by Thursday. He also troublesome—it affects more than one The first tests were done without the found most of the components from of the tones. If RTTY/CW interference FEC enabled—whoops! The system DigiKey5 in the US as well; it worked gets too bad, it is possible to switch a worked quite well; but occasionally out cheaper than buying them in the DSP notch filter into the circuit: There gave off very loud screeches. After the UK, especially for the micro- is enough power in the FEC to cope FEC was enabled, however, fewer controllers. with the missing tones. The notch strange noises came from the system. We used the 17C44 PIC microcon- filter must be switched out during the When the modem was initially tested troller for a number of reasons: first, preamble phase. without FEC, one third of the tones so we could use one crystal to drive The most effective and impressive were in fact transmitting no data what- both the AMBE and the PIC (the demonstration was one evening in April ever and were just wasting energy. AMBE requires a 27-30 MHz clock); when a QSO lasted for an hour and a Some experiments were done using second, the 17C44 PIC has enough half as the sun set. Copy started out as May/June 2000 7 perfect, with no lost preambles or not work via a repeater since there is no The Digital Signal Processing Handbook, garbled messages. The multipath be- ARQ (but we have not tried it). (Boca Raton, FL: CRC Press, ISBN 0- 8493-8572-5). came worse as dusk arrived so copy 3 worsened slightly, but it wasn’t until Conclusion Digital Voice Systems (DVS), Inc may be found on the Web at http://www.dvsinc nearly dark when the link had almost It is now possible for the home con- .com/. faded out completely that it became structor to build—for about $300—a 4It is no coincidence that this low-baud-rate, unusable. portable, working digital voice system parallel-tone approach has been adopted The weakest part of the modem is the for HF with near-toll-quality audio. for digital TV transmission where 2048 preamble phase. To help remedy this, This system can be used equally well parallel tones are employed in an 8-MHz we added the ability to save the fre- to experiment with digital speech us- bandwidth. Multipath on the UHF TV fre- quencies is typically a few microseconds quency offset correction and timing ep- ing different DSP modems on different in duration, and the individual baud rate och after each successful preamble syn- frequencies. For further information for each tone is consistent with this. The chronization. If, for some reason, the and a full technical description, plus technique is further refined to minimize receiving modem misses the start of the some sound files, surf along to bandwidth by using the minimum carrier transmission, it is then possible to press Charles’ Web site.6 Once some boards spacing and ensuring that side lobes from a button on the front panel and revert to have been made up in the US, we hope one modulated carrier do not interfere with those adjacent to it. The system is referred the last set of synch information. In a to be able to try some transatlantic to as Coded Orthogonal Frequency Divi- one-to-one QSO, this works most times. tests. sion Multiplexing (COFDM). A similar cod- Another change allows the different ing method with 1536 tones of 1-kHz Notes spacing is used for the terrestrial Digital tones to be given different amplitudes 1 Consider CD music recording. A sampling Audio Broadcasting network. Parallel-tone to compensate for the amplitude re- rate of 44.1 kHz is chosen to allow a sponse of the transceiver. The group modems are one of the candidate tech- 20-kHz maximum audio frequency; 16- bit nologies for HF digital broadcasting and delay in the transceiver does reduce quantization is used to give a dynamic there is a lot of professional interest in the modem’s tolerance to multipath. range of greater than 90 dB. With two in- parallel-tone technology. With The new generation of IF-DSP dependent channels for stereo, this re- 5Digi-Key Corporation, 701 Brooks Ave S, PO sults in a data rate in excess of 1.4 MB/s. Box 677, Thief River Falls, MN 56701-0677; radios, this will not be a problem as 2 More information on these technologies tel 800-344-4539 (800-DIGI-KEY), fax 218- their filter characteristics are much may be found in L. R. Rabiner and R. . more suited to this kind of operation. 681-3380; http://www.digikey.com/. Schafer, Digital Processing of Speech 6G4GUO’s Web page is found at www Along with the HF testing, Charles Signals, (Upper Saddle River, NJ: .chbrain.dircon.co.uk/dvhf.html. The has also used the system on 2 , both on Prentice-Hall, ISBN 0-13-213603-1); and page includes sample audio and project SSB and FM. There is no reason it would . . Madisetti and D. B. Williams, eds, updates.

8 May/June 2000 PTC: Perceptual Transform Coding for Bandwidth Reduction of Speech in the Analog Domain, Pt 1

A new method for optimizing the bandwidth of phone signals using auditory psychophysics

By Doug Smith, KF6DX

revolution is afoot in Amateur Drawing on the extensive audio- fading often makes it difficult to recover Radio: An increasing number of coding research of others, I will show all of the energy from both sidebands Aoperators are producing high- how certain human speech and hearing simultaneously. Carrier fades tend fidelity audio in the narrow band- attributes lend themselves to analog to cause severe distortion. Modern widths available to us on HF SSB. BW compression of speech. In Part 2, I methods of exalted-carrier, synchron- Many of us have grown tired of listen- will demonstrate how a speech signal of ous detection have largely solved those ing to the same old “communications- 4-kHz BW is compressed to occupy less problems, but the occupied BW of AM quality” signals. We have yearned for than 1 kHz and a full-range signal of has relegated it to some obscurity on a more pleasurable sound from our 15-kHz BW to less than 4 kHz. I will the Amateur Radio bands. It is retained equipment. Coupled with skills emphasize the technical tradeoffs that for broadcasting because it is detect- learned in professional recording influence sound quality. The goal is to able with relatively simple equipment. and broadcast studios, the availability retain the perceived quality of the SSB is popular because all the output of high-quality HF transceivers in the original, uncompressed signal. First, power is dedicated to the information last few years has enabled some however, please follow me through a and emissions occupy only the BW startling accomplishments in narrow- little history and background as I lay necessary for perfect reproduction. SSB band audio quality. down the basis for my invention. also does not suffer from the distortion It is remarkable what can be caused by carrier fading. It does impose achieved in a bandwidth (BW) of only A History of Phone Modes constraints, however, that result in loss 3 kHz. Characteristics of speech In the days before SSB became of fidelity. In the filter method of SSB processing can be manipulated to popular on our bands, AMers used a lot generation, it is usually essential to allow the perception of much greater of plate-modulated vacuum-tube equip- “roll off” the low-frequency response to BW. Properties of human speech can ment. It was relatively easy to obtain a ensure adequate suppression of the be further exploited to reduce the broad baseband frequency response carrier and opposite sideband. Even occupied BW of phone emissions quite with this type of gear—perhaps it was with the phasing method, opposite- significantly. That is the subject of too easy to be too broad! It was also easy sideband suppression may suffer if low this paper. to sustain lots of interference and noise, audio frequencies are not attenuated. since each information-bearing side- These problems have made it difficult 1 PO Box 4074 band reaches only about /6 of the total to achieve good low-frequency response Sedona, AZ 86340 output power. Although each sideband in SSB. Operators have been frustrated [email protected] is a mirror image of the other, selective (until recently) by the limitations of IF May/June 2000 9 filters in their transceivers. They can try, telephone companies and interest therefore, that this mode of telecom- seriously attenuate both low- and high- in passing audio over Internet connec- munications will never be replaced. frequency audio content. tions at low bit rates. Most of the Because of that suspicion, I can write SSB experimenters are well aware breakthroughs in such coding have that the secondary goal of any speech- of certain speech-processing tools, focused on characterizing human coding scheme is to preserve those such as AF and RF compressors. Auto- speech in ways that are efficiently characteristics of speech that allow us matic level control (ALC) is found in represented by ones and zeros. to recognize the speaker, along with the every modern rig. ALC is just a form of Progress on BW compression in the nuances that are so important. In other compressor that prevents drive analog domain has been frustrated by words, we have to conserve certain signals from exceeding the PEP limit- increasing emphasis on digital modes. distinctive qualities of speech so that ations of the transmitter. In a peak- Digital methods may have an advan- we can’t tell the speech was coded. Let’s limited system, average output power tage in error detection and correction, examine what those qualities are and depends heavily on the nature of the and in signal-to-noise ratio (SNR), but what it is about human hearing that modulation. Some voices produce they likely will never be the most BW- influences perception. peak-to-average ratios of up to 15 dB; efficient techniques for . a station running 1500 W PEP might (LPC) and Perception vs. Measurement only produce an average output of other methods7, 8, 9 have concentrated In the study of the human hearing about 50 W! on passing parameters that describe system, it must be clear that there is no Because of the Hilbert-transform or features of speech production. They are objective means of measurement. All “repeaking” effect of SSB, AF limiting “lossy” in the sense that they sacrifice information about what someone hears achieves only a modest intelligibility perfect reproduction of the input (or doesn’t hear) must be learned increase even with large compression waveform for BW reduction. Perceptual subjectively through the responses of ratios. IF or RF compression avoids this audio coders10, 11, 12 code in such a way the listener. All we can do is ask problem—6 dB or more improvement in that redundancy and irrelevancy in questions of a subject and attempt to average output power is possible. speech are removed, reducing BW. Both infer something about the nature of For audiophiles, the trouble with any approaches take advantage of the fact sounds. Furthermore, we have no guar- compression scheme is that it adds that only perceived quality matters. I antee that a particular stimulus will be distortion. Naturally, any departure shall adopt this as my sole criterion for perceived in the same way by one sub- from linearity involves harmonic the remainder of this discussion. ject as another. We therefore define distortion (HD) and intermodulation our terms for measurement and percep- distortion (IMD). At high compression Evaluating the tion differently and separately. ratios, an AF compressor especially Human Hearing System Sound intensity is a physical measure suffers from HD effects that reduce Speech communication is crucial to of air pressure level. Two persons clarity. Formant energy and plosive our society. It conveys the sense of how equipped with identically calibrated sounds tend to be sacrificed. IF and RF someone feels, how they are thinking instruments will measure the same compressors generate HD that falls and some idea of who they are more intensity for any given sound. Loudness outside the band of interest; hence it is than any other form. Nothing is more is the corresponding perceptual magni- easily removed by filtration. These comforting than hearing the voice of a tude. It can be defined as “that attribute compressors still create in-band IMD, loved one in dire times. I postulate, of auditory sensation in terms of which though; this distortion ultimately limits their effectiveness. While on the subject, let’s note that distortion caused by our electronics limits the quality level we can finally attain, no matter what we do. Many receivers produce as much in-band IMD as do transmitters. The phase and amplitude of each IMD product are influenced by many variables. Levels can be measured, however, and the transfer function ascertained. Whether these products augment or diminish intelligibility seems to involve another set of variables that depend on the nature of human speech and hearing systems. As I’ll highlight later, these cannot be directly measured. So the question is, How can we produce better audio quality while using a narrow BW? A lot of work has been done on this problem, especially with respect to digital coding of audio.1, 2, 3, 4, 5, 6 The impetus for this work has been provided by the recording indus-

1Notes appear on page 12. Fig 1—Intensity versus frequency for constant loudness. 10 May/June 2000 sounds can be ordered on a scale remain unchanged. The most sensitive of masking, and to present the concept extending from quiet to loud.”13 The frequency region of the ear is between 1.5 of critical bands. unit of loudness, the sone, is defined by and 3.0 kHz and the curves get flatter as subjectively measuring loudness the intensity is raised. Further, loudness Thresholds of Hearing ratios. A stimulus half as loud as a one- grows faster with intensity at low fre- One of the thresholds of hearing, the sone stimulus has a loudness of 0.5 quencies. Finally, the curves reveal the intensity threshold, is defined as the sones. A 1-kHz tone at 40 dB sound- of hearing: Single tones lowest intensity the listener can detect. pressure level (SPL) is arbitrarily below the zero-sone curve are inaudible, We cannot directly measure the listen- defined to have a loudness of one sone. while tones above the top line are painful. er’s perception, though; we can only ask We might be left to wonder how a unit In fact, we know today that the useful whether he or she thinks the sound is based solely on individual perceptions dynamic range of human hearing is audible. This might seem a fine distinc- can be useful, especially since so much substantially less than shown. Extended tion, but the method of measurement variation exists from person to person. exposure to sounds well under the top determines the threshold as much as The method of applying stimuli and of line produces permanent hearing loss in the listener’s aural gifts. obtaining responses from listeners has some individuals.18 At or near the intensity threshold, a large effect on results. Loudness the subject’s criterion level is in play.19 comparison of two equal-frequency tone This is Auditory Psychophysics He or she might indicate some sound bursts, however, generally produces We’re now well into what is called is audible when it might be present, or reliable and repeatable data. Loudness auditory psychophysics, or just psycho- perhaps only when it is definitely comparisons between dissimilar stim- acoustics. Recall that our goal is to present. With no incentive to produce uli, such as between a pure tone and a exploit the redundancies and irrelev- correct results (such as large sums of polyphonic source, yield unpredictable ancies in speech to reduce its occupied cash), the criterion level is beyond the results because of poorly understood BW. To identify the irrelevant content, experimenter’s control. subjective effects. So a quantification of we must discover how well the ear- An interesting way of dealing with the loudness scaling (one sound is half as brain combination discerns differences uncontrolled criterion-level problem is to loud as another) is as good as absolute in intensity and frequency. Moreover, use a criterion-free experimental model. loudness matching (one sound is the we must try to ascertain the perfor- According to Hall (see Note 19), the same loudness as another). Addition- mance of the hearing system in the simplest of these is the “two-interval, ally, some researchers have observed presence of polyphonic sounds; that is, forced-choice” paradigm. In this method, under many conditions that loudness how certain sonic components tend to the stimulus is presented at random in adds.14 Binaural presentation of stim- dominate others of lesser intensity or of one of two observation intervals. The uli generally results in loudness doub- small frequency difference. subject is asked to determine in which of ling and two equally loud sources—if I will now expand the discussion to the two intervals the stimulus was they are far enough apart in frequen- include definitions for various percep- present. A perfect observer always cy—are twice as loud as one alone. tual thresholds, to introduce the idea selects the interval that elicits the larger Because of other effects described below, this rule must be used with caution, though. There is evidence that loudness addition is far from a perfect description of human perception.15 Frequency is a physical measure of a sound’s number of cycles per second; each of us can measure frequency identically using similar instruments. We define pitch as the perceptual quantity corresponding to frequency. Pitch is to frequency as loudness is to intensity. Note that the relations between loudness/intensity and pitch/ frequency are not necessarily linear, nor are the two perceptual measures independent of one another. Under certain conditions, the loudness of a constant-intensity sound can be shown to decrease with decreasing frequency; pitch can be shown to decrease with increasing intensity, even when frequency is held constant. As ably documented by Fletcher,16 Stevens and Davis,17 and others, loud- ness depends on both frequency and intensity. Fig 1 (after Reference 17) shows some loudness contours. Each curve represents a constant-sone level. These data have been measured count- less times, but the basic revelations Fig 2—Critical BW versus frequency. May/June 2000 11 decision variable; thus the criterion level the elevated intensity threshold of the has made extensive use of the methods I is no longer a factor. He or she has a 50% desired when the masker is present. will relate in Part 2. chance of selecting the correct interval Fletcher and Munson made a landmark even without actually detecting the study of the relation between loudness Notes stimulus. It can be shown that the and masking effects.20 They found that 1R. E. Crochiere, S. A. Weber, and J. L. psychometric function thereby produced quieter sounds that are close in fre- Flanagan, “Digital Coding of Speech in Subbands,” Bell System Technical Jour- solves the criterion-level problem. quency to dominant sounds are rendered nal, Vol 55, October 1976. I think it interesting to note that all inaudible in proportion to their spectral 2P. P. Vaidyanathan, Multirate Systems and this has a bearing on “A/B” comparisons separation and their relative intensities. Filter Banks, (Englewood Cliffs, NJ: as commonly done on the air, regardless They were among the first to use bands of Prentice-Hall, 1992). 3M. Vetterli, and J. Kovacevic, and of the parameter being changed. A “colored” noise as maskers. An important Subband Coding, (Englewood Cliffs, NJ: measurement criterion such as loud- effect is the relationship between the Prentice-Hall, 1995). ness or signal strength must first be masker BW and the amount of masking. 4N. S. Jayant, and P. Noll, Digital Coding of set, then the stimulus presented at This relation is most prominent when the Waveforms: Principles and Applications to Speech and , (Englewood Cliffs, NJ: random to the observer. Any additional desired signal lies within the masker’s Prentice-Hall, 1984). information given the observer prior to BW. Noise whose entire BW lies outside 5R. D. Jurgen, “Broadcasting with Digital measurement, such as “A is amplifier off, the desired signal’s frequency does not Audio,” IEEE Spectrum, March 1996. 6 B is amplifier on,” introduces bias in the contribute much to its masking. This is P. Noll, “MPEG Coding Stan- dards,” The Digital Signal Processing result. Further discussion of detection one manifestation of the human hearing Handbook, V. K. Madisetti, and D. B. Wil- theory is beyond the scope of this paper. system: For many auditory functions, the liams, editors (Boca Raton, FL: CRC Getting back to definitions, we may ear behaves as if it is a set of band-pass Press LLS, 1998). also define differential intensity thres- filters and energy detectors. These filters 7L. R. Rabiner, and R. W. Schafer, Digital Pro- cessing of Speech Signals, (Englewood hold as the ability to detect whether one are said to occupy critical bands. Cliffs, NJ: Prentice-Hall, 1978). sound is louder than another. In fact, Critical Bands and 8B. S. Atal, “Predictive Coding of Speech at we may define differential thresholds Peripheral Auditory Filters Low Bit Rates,” IEEE Transactions on for other attributes of sounds, such as Communications, COM-30, April 1982. The above-mentioned relation be- 9 frequency and duration. A differential A. Gersho, “Advances in Speech and Audio tween BW and masking is only one Compression,” Proceedings of the IEEE, threshold is the amount one or more of example of human hearing behavior Vol 82, 1994. these attributes must change to allow 10J. D. Johnston, and A. J. Ferreira, “Sum- relevant to the coder I will describe in an observer to detect the change. Difference Stereo Transform Coding,” Part 2. Another example is provided by In the first half of the last century, ICASSP-92 Conf. Rec., II, 1992. SSB over HF, where the ear quite often 11D. Sinha, J. D. Johnston, S. Dorward, and German physiologist E. H. Weber gave encounters severe phase distortion. The S. R. Quackenbush, “The Perceptual us the first serious, quantitative ear seems to tolerate relatively large Audio Coder (PAC),” The Digital Signal depiction of differential thresholds. Processing Handbook, V. K. Madisetti, shifts in the relative phases of speech According to Weber’s Law, the differ- and D. B. Williams, editors, (Boca Raton, components without impairing intelli- FL: CRC Press LLS, 1998). ential intensity threshold dI is propor- gibility, when the components are far 12R. V. Cox, “Speech Coding,” The Digital tional to the stimulus intensity I, or: enough apart in frequency. Scharf21 Signal Processing Handbook, V. K. Madisetti, and D. B. Williams, editors, dI = (Eq 1) defined the critical bandwidths assoc- (Boca Raton, FL: CRC Press LLS, 1998). k 13 I iated with these theoretical auditory B. Moore, An Introduction to the Psychology where k is known as the Weber fraction. filters as “that bandwidth at which of Hearing, (London: Academic Press, 1989). 14 This alleged constant has also been subjective responses rather abruptly H. Fletcher, “Loudness, Masking, and Their Relation to the Hearing Process and Prob- applied to sensitivity to changes in change.” He measured critical bands lem of Noise Measurement,” Journal of the frequency and BW, as well as nonaud- using two-tone masking and loudness- Acoustic Society of America, Vol 45, 1969. itory senses such as color, image summation techniques. Zwicker et al22 15B. Scharf, and D. Fishkin, “Binaural Summa- sharpness, pain, smell and taste. Very measured phase sensitivity using poly- tion of Loudness: Reconsidered,” Journal of Experimental Psychology, Vol 86, 1970. soon after Weber made this “law” phonic sounds. These studies agree fairly 16H. Fletcher, Speech and Hearing in Com- known, folks found out it broke down at well with others performed over the munication, ASA Edition, J. B. Allen, edi- intensities near absolute thresholds. years. Fig 2 is a plot of critical BW versus tor, American Institute of Physics, New York, New York, 1995. Physicist G. T. Fechner, also a German, frequency that averages the Scharf and 17 suggested a modified Weber’s Law: Zwicker data. S. S. Stevens, and H. W. Davis, Hearing, (New York: John Wiley & Sons, 1938). These and other studies support the 18 dI C. M. Harris, editor, Handbook of Acou- = k (Eq 2) idea that differential frequency thres- stical Measurements and Noise Control, (I+I0 ) hold increases with frequency. In other (New York: McGraw-Hill, 1991). 19 where I is a constant. It’s a good words, it is more difficult to discern small J. L. Hall, “Auditory Psychophysics for 0 Coding Applications,” The Digital Signal approximation, but it apparently frequency differences at high audio Processing Handbook, V. K. Madisetti, doesn’t hold exactly. frequencies. Since we decided that our and D. B. Williams, editors, (Boca Raton, perception of things is all that matters, it FL: CRC Press LLS, 1998). 20 Masking makes sense to analyze speech signals H. Fletcher, and W. A. Munson, “Relation between Loudness and Masking,” Journal of Masking is defined as the ability of one with a system whose frequency reso- the Acoustic Society of America, Vol 9, 1937. sound (the masker) to render another lution matches that of the human hearing 21B. Scharf, “Critical Bands,” Foundations of (the desired) inaudible when present system. It is remarkable that this sort of Modern Auditory Theory, J. V. Tobias, edi- simultaneously or closely in time. It is approach also seems to apply across a tor, (New York: Academic Press, 1970). 22E. Zwicker, G. Flottorp and S. S. Stevens, quantified as the difference between the broad scale of other things we can “Critical Bandwidth in Loudness Summa- absolute intensity threshold of the classify. The science of image com- tion,” Journal of the Acoustic Society of desired in the absence of the masker and pression and construction, for example, America, Vol 29, 1957.

12 May/June 2000 A Low-Cost HF Channel Simulator for Digital Systems

In the past, HF channel simulators used exotic and expensive computing hardware that was not available to the average amateur experimenter. Here’s a simulator based on a low-cost, floating-point DSP evaluation kit.

By Johan B. Forrer, KC7WW

his project was inspired by a conditions, including CCIR 520-1.1 interrelated phenomena that result in desire to develop HF digital The simulation model is an implemen- a highly variable propagation medium. Tcommunications devices that tation of the Watterson, Gaussian- This variability is a challenge to anyone effectively deal with the variable scatter, HF ionospheric-channel2 designing and implementing effective, nature of the ionospheric propagation model, which is the de facto standard high-speed digital communications medium. Simulating the behavior of for this kind of work. systems for HF. the ionosphere in real time allows for The article concludes with a The ability to quantitatively bench testing of HF modems and other summary of test results for a number evaluate how engineering designs communications devices. In the past, of contemporary, forward-error-cor- carry through to final implemen- so-called HF channel simulators used recting (FEC) HF digital systems on tations often makes the difference exotic and expensive computing this HF channel simulator: PSK31, between success and failure. Exper- hardware that was not available to the CBPSK and MT63. This simulator is a ienced, well-equipped engineers use average amateur experimenter. worthy addition to anyone’s array of special tools such as channel simula- The simulator presented in this testing tools for developing DSP data tors to development cycles. article is based on a low-cost, floating- communications algorithms. These are invaluable, for example, to point DSP evaluation kit. It accom- verify dynamic-range performance, modates a wide range of simulated The Variable Nature acceptable signal-to-noise ratio (SNR) of an HF Channel performance and quite a few other 26553 Priceview Dr HF propagation involves several factors such as adjacent-channel Monroe, OR 97456 interference and frequency/timing [email protected] 1Notes appear on page 17. tolerances. These are very common May/June 2000 13 problems. Protocol performance is of channel can therefore be described by ray) appears lower in frequency than equal importance. This has to do with parameters that specify the time- the main (low) ray. The high ray itself the efficiency of frame and character spread and frequency-spread charac- appears to be split in two parts each synchronization, effectiveness of error teristics; that is, differential propa- with distinct Doppler shifts; the upper control and the success of protocol gation delay between modes, Doppler image probably being the opto-ionic, adaptation. spread on each mode and the relative or -ray, and the lower image being Although some of these tests may be signal strengths. Fig 1 shows an actual produced by the extraordinary, or done on the air, F-layer propagation example of these different mechanisms -ray. The X-ray undergoes further conditions are almost impossible to in action (this illustration provided by retardation due to interaction with repeat; thus, there is no real chance to courtesy of J. P. Martinez, G3PLX3). Earth’s magnetic field. Note that the make comparative tests this way. Martinez experimentally recorded an high and low rays of the O-trace What we need is a means to create an event on November 9, 1994 by saving a penetrate first, followed by the X artificial ionospheric test medium— digitized audio tone of a remote broad- trace. About 0640 UTC the F-layer an “ionosphere in a box”—that can be cast station’s carrier in a computer file. comes back in again, and the process reproduced at will. Only then is it The broadcast station’s carrier was is seen in reverse: the X-trace possible to set up norms and mile- located on 7.7 MHz and arrived via the appearing first and splitting into high stones for performance evaluation. ionosphere; the broadcast station was and low, followed by the O-ray. Computer simulation is one way to located on the island of Gibraltar, the Further, more-diffuse propagation obtain repeatable, quantitative re- receiver on the south coast of England. paths open a few minutes later. sults. A simulation study based on Subsequent processing of the recorded theoretical concepts can provide the digital data revealed frequency-domain The Watterson Gaussian-Scatter basis for establishing expected per- changes over time. For this, the results HF Ionospheric Channel Model formance characteristics and may also of 256-point FFTs are presented as Watterson et al—using wide-band serve as a guide to requirements for pixel-intensity values on the -axis, HF emissions over a path between hardware and software. It can provide with time plotted on the X-axis. Boulder, Colorado and Washington— for continuing development work with For the graph shown, each pixel proposed a model for a narrow-band HF minimal risk. point in time represents approx- channel. This model forms the basis for During test and development phases, imately 20 seconds of signal with UTC most modern HF channel-simulation real-time testing using a HF channel hour “tick” marks shown along the top. work and often is used for both software simulator is essential. An under- The Y-axis represents 0.025 Hz/pixel and hardware channel simulation. standing of ionospheric behavior and (256 pixels = 6.25 Hz). This repre- This model, known as the “Watterson how it impacts communications is key sentation effectively shows the history Gaussian-scatter HF ionospheric to developing an effective waveform of a very slowly changing process, with channel” model, assumes that the HF and protocol suitable for high-speed HF most of the finer, random events channel is nonstationary in both digital communications. filtered out to better illustrate the frequency and time, but that when various propagation modes. Because considered over small bandwidths Ionospheric Reflection Model of the frequency in question (7.7 MHz), (<10 kHz) for sufficiently short times HF communication is typically char- we are reasonably sure that the (<10 minutes), most channels can be acterized by multipath propagation propagation mode is via the F-layer. represented by a stationary model. and fading. Transmitted signals travel Note that at about 0600 UTC, the The HF channel is modeled as a to the receiver over several propagation signal penetrates the ionosphere and tapped delay line, with one tap for each modes via single or multiple reflections no propagation path to Earth results. resolvable propagation mode (or path) from the E and F ionospheric layers. Just before this happens, note the high in time. The delayed signal is modu- Because propagation times vary over F-layer ray (the so-called Pedersen lated in amplitude and phase by a different paths, signals arriving at the receiver may be spread in time by as much as a few milliseconds. Ionospheric turbulence causes dis- tortion of both signal amplitude and phase. In addition, different iono- spheric layers move up or down, which leads to independent Doppler shift on each propagation mode. In ionospheric sky-wave HF propagation, multipath arises from paths having different numbers of multiple reflections be- tween earth and the ionosphere (multiple-hop paths) and from paths at multiple elevation angles connecting the same end points (“high” or “low” rays). Natural inhomogeneities of the ionospheric layers and polarization- dependent paths caused by magneto- ionic effects also contribute to multi- path. Fig 1—Martinez’ Dopplergram illustrating several interesting ionospheric Short-term distortion on the HF phenomena (see text). 14 May/June 2000 complex, random finite impulse re- there appears to be some leeway in in- McDermott, N5EG. Tom presented a sponse changing over time. It is terpretation of the Watterson model paper on theoretical aspects of HF described by: and subsequent discrepancies in re- channel simulation at the 1996 DCC sults. There have been investigations HFSIG meeting. The specifics for the j2ππf t j2 f t G iia(t) = G (t)e ia +Gib(t)e ib by researchers on this subject; however, implementation of the Watterson (Eq 1) without having access to details on pro- Gaussian-scatter HF ionospheric chan- Where a and b subscripts denote the prietary implementations, these dis- nel model follow. This topic is divided i-th element in a time-series represen- crepancies remain unresolved. into two sections: the hardware plat- tation for two magneto-ionic path com- Generally, published specifications form and software implementation. and research results often tend to omit ponents. In this context, Gia(t) and weaknesses that are readily shown by HF Channel-Simulator Hardware Gib(t) represent two independent, complex, bivariate Gaussian ergodic such simulators. More often than not, I saw an opportunity when a new random processes, each with zero results obtained by this simulator floating-point DSP evaluation module mean and independent real and imagi- tend to be interpreted as highly criti- (EVM) from Analog Devices4 became nary components with equal root- cal or erroneous. This is not the inten- available. The EZ-KIT Lite SHARC is mean-square (RMS) values that pro- tion; rather, it should be an opportu- a 40 MIPS processor that can produce duce Rayleigh fading. The exponential nity that should be exploited to the 150 MFLOP performance. The user’s advantage. SHARC DSP follows modern trends; variables provide frequency shifts fia and f for the magneto-ionic compo- its instruction set is optimized for use ib Development of a Real-Time nents in the impulse-response spec- with the C programming language. HF Channel Simulator trum. Each tap coefficient (gain) has a The kit is supplied with GNU-based λ Discussions on developing a low-cost C tools on CDROM that includes the spectrum Hi( ) that, in general, con- sists of the sum of two magneto-ionic HF channel simulator took place in usual compiler, linker and librarian components, each of which is a several forums: TAPR HFSIG list, spe- tools. The ability to use a high-level Gaussian function of frequency, as cifically during 1994; 1995 TAPR An- language made the implementation of specified by: nual Meeting in St. Louis, Missouri; the Watterson-model mathematics Digital Communications Conferences much easier. Even time-critical code, (DCC), 1995 Arlington, Texas, and such as interrupt handlers, may be     λ −λ λ −λ  ia   ib  1996 in Seattle, Washington. Early written in C; alternatively, either in-  2 2   2σ2  work involving Alexander Kurpiers, line assembly or assembly-language  σia   ib  (Eq 2) H(λ ) = e + e DL8AAU, of Darmstadt, Germany, modules may be developed. The EVM πσ πσ Aia 22ia Aib ib produced code for a TI 320C26-based contains a 48-kHz stereo codec to DSP implementation. I ported this for handle audio I/O and a UART chip to where Aia and Aib are component at- tenuations, and the frequency spread use on the TAPR DSP93 and demon- handle serial communications with on each component is determined by strated its use at the 1996 DCC meet- the host. The DSP contains a total of σ σ ing in Seattle. This model has seen 16 k 48-bit words of on-chip memory, 2 ia and 2 ib. The frequency shift on λ service in several projects, however, it part of which is available for user code. the two components are given by ia λ has limited performance due to The amount of on-chip user memory and ib. Coefficient distributions for a two-ray model are shown in Fig 2. memory and processor considerations. is adequate for implementing the The Watterson model implies the Several others have shown active in- Watterson-model simulator. use of equal-power (RMS) paths. This terest in this project: Barry Buelow, HF Channel-Simulator Software is effectively like a deep notch filter WA0RJT; Jon Bloom, KE3Z; Eric 5 sweeping through the passband, at Silbaugh; Glen Worstell, KG0T; Phil A paper by Ehrman, et al, provides times obliterating parts of the signal. Karn, KA9Q; and especially Tom basic implementation ideas that were This often has devastating implica- tions for some modem algorithms. Simulation of simultaneous X and O rays is seldom undertaken; this was suggested by Watterson since they are often unresolvable. Fig 1 shows proof of the existence of these components, especially at band closings and open- ings. Simulators intended for simula- tion of CCIR-recommended condi- tions, implement Rayleigh-faded paths; either a single path for flat fad- ing conditions or two delayed paths for selective-fading conditions. Simula- tion results represent a “snapshot” of ionospheric conditions. They do not include dynamically changing events like seasonal or diurnal changes. In attempts to compare performance results of standard equipment against published materials where professional channel simulators have been used, Fig 2—Tap-gain distributions for a two-ray model. May/June 2000 15 used in this project. Several parallel ate bandwidth; that is, this filter de- since power measurements need to be tasks can be distinguished: termines the fading bandwidth. Actu- accurately correlated with exact bit 1. Transform and process the base- ally, it controls the statistical spread timings to compute the actual energy band input signal, such that its for this Gaussian function, like that per bit. Coding schemes and ARQ pro- phase and amplitude properties can shown in Figure 2. tocol issues further complicate this be manipulated in real time, Doppler shift is produced on the fad- measurement. It is often more conve- 2. Simulate, independently and in real ing function using a similar method, nient to determine throughput rate time, a predefined HF propagation except that no filter is used. After per- instead, but it would be difficult to condition, forming the complex mixing of the fad- relate this to Eb/No, as used in most 3. Apply simulated distortion to the ing and Doppler functions, the result- references. processed input signal, ant signal now has a Rayleigh distri- Computation of SNR has a few pit- 4. Apply noise perturbations. bution. That is the desired impulse falls. At least, it would be impossible Fig 3 shows the interaction between response (tap-gain function) to be ap- to generate wide-band AWGN (addi- a number of parallel tasks. Input is plied to the delayed analytic input sig- tive white Gaussian noise) on a DSP applied at the top left and output pro- nal. In the finish, we take only the real for output through its analog-to-digi- duced at the bottom right of the figure. part of this last mixing step. tal converter (ADC)—that will be lim- The Watterson model only deals with As an option, noise perturbations ited by the Nyquist rate. It is impor- the effects of the ionosphere and the with the correct amplitude are then tant to design the simulator with a distortion that it introduces; it does not added to set the noise background for particular bandwidth in mind. The attempt to simulate HF noise pertur- the desired SNR level. The computa- Watterson model is valid over narrow bations. CCIR 520-1 also does not tion of the noise background requires bandwidths (<10 kHz). The audio specify any kind of noise source, how- further consideration. passband of communications equip- ever, it does allude to including a noise ment often is <3 kHz wide. When mak- source in simulation. Let’s look at these Computing Channel ing external measurements of signals processing steps in further detail. Noise Effects and SNR generated by the simulator, actual Gaussian noise models are commonly noise bandwidth should be strictly Input Signal Processing used in VHF, UHF and microwave observed. Limited bandwidth results The input signal is a real signal. work. HF noise behavior, however, has in power loss of potential noise output Fading and Doppler effects will be in- more of an impulsive nature that is and this loss must be compensated. troduced to this signal by mixers. more complex and sometimes described Power loss for the design bandwidth is These mixers, however, are complex in terms of Markov models, rather than proportional to the ratio of the output devices requiring in-phase (I) and stochastic models, in the literature. For bandwidth and the ADC sample rate; quadrature (Q) components, and thus purposes of this paper, only Gaussian it also is affected by decimation and requiring that the input signal be an noise is considered. This simplifies interpolation processes implemented analytic signal. This conversion of the matters, but does not accurately repre- in the DSP code. For this reason, it input signal is achieved by using a sent HF channel noise. often is easier to devise an internal Hilbert transform. The exact channel measurements noise-power calibration procedure in To simulate multiple rays passing typically used for comparing systems the DSP software. This procedure is through the ionosphere, dual tapped should be carefully considered. Classi- set up to produce a train of noise val- delay lines are used: one for the I com- cal reference books use bandwidth-nor- ues that are then processed though the ponent, another for the Q component. malized SNR measurements. Instead of entire filter chain as if it was gener- The analytic input signal is then ex- simple SNRs, this appears in units of ated in real time. The RMS value of the tracted from the appropriate points in bits/s/W/Hz. When dealing with real resultant data, RMSn is then com- the delay lines. The position in the de- communications systems, however, puted and saved as a reference for lay line is a function of the input sample this kind of measurement is difficult, later use during real-time simulation. rate (typically 8 kilosamples/s) and the required path delay (varies in the range 0.1-10 ms, or 1-80 delay-line taps). Computing Channel Effects: Doppler Shift and Fading Watterson, et al, showed that the desired fading and Doppler shift can be introduced by the product of two Gaussian functions; that is, a Rayleigh distribution. Since this mul- tiplication process of the two Gaussian functions is commutative, it does not matter what is generated first, the fading function or the Doppler shift. The fading function is produced us- ing a random-number generator with Gaussian (white-noise) distribution. This stream of numbers is then passed through an infinite-impulse-response filter (IIR) designed for the appropri- Fig 3—Simulator process flow. 16 May/June 2000 In this regard, Leeland’s discussion6 Table 1—CCIR Recommendations for the Use of HF Ionospheric Channel on methods to determine bit-error rates Simulators. (BERs) is of interest. In it, BER is ad- vanced as the best basis for evaluation CCIR Recommendation 520-1 gives guidelines for practical values for frequency of modem SNR performance: If it spread and delay times between ray components: doesn’t meet BER specifications, it isn’t Condition Frequency Spread (Hz) Delay (ms) working as expected. That result may imply that defensive actions like dy- Flat Fading 0.2 0 namic protocol adaptation or tracking Flat Fading (extreme) 1.0 0 algorithms are failing to assess chan- Good 0.1 0.5 nel properties correctly. BER also al- Moderate 0.5 1.0 lows one to compose classic “waterfall” Poor 1.0 2.0 BER-versus-SNR curves. These sets of It is proposed that these parameters be used to validate average and extreme curves allow one to check measured conditions during simulation as well as during actual hardware testing. performance against theoretical and other published performance data. Modern modem designs use calcu- lated SNR methods for BER estima- The SNR level was set at –10 dB. This brought us SLOWBPSK, the grand- tion. The SNR is calculated from the represents a 3-kHz bandwidth AWGN daddy of PSK31 and MT63. Free dem- measured SNR using the mean, Mx, σ channel. This test condition represents onstration simulator code is available and the variance, x, of the symbol marginal HF conditions that probably for downloading7 from my Web site. data as follows: are close or equal to the practical limit Notes for reliable HF communications. Re- 1CCIR Recommendation 520-1, Use of High M 2 (Eq 3) SNR = x sults are shown in the Appendix. Frequency Ionospheric Channel Simulators 2 2 σ x C.C. Watterson, J. R. Juroshek and W.D. where Acknowledgements Bensema, “Experimental confirmation of an HF channel model,” IEEE Transactions This work was made possible by gen- on Communications Technology, Vol N −1 x k (Eq 4) erous contributions from participants COM-18, pp 792-803, Dec1970. M x = ∑ 3J. P. Martinez, G3PLX, High Blakebank k=0 N of the TAPR HFSIG list and discussions at various DCC meetings. Not only did Farm, Underbarrow, Kendal, Cumbria LA8 and 8BN, United Kingdom. The author gratefully these forums stimulate the develop- acknowledges J. P. Martinez’s permission − 2 ment of this HF channel simulator, but to reproduce these experimental results. N 1 (x − M ) (Eq 5) 4 σ2 = ∑ k x also new HF digital communications Super Harvard Architecture Computer x (SHARC) EZ-KIT Lite. Part number: ADDS- k=0 N −1 modes like PSK31 and MT63. 2106X-EZLITE. Available from Analog De- I gratefully acknowledge the contri- vices distributors. Street price $179. URL: Test Results bution of TAPR in this respect and http://products.analog.com/products/ As examples, simulator tests were thank those that participated in the info.asp?product=21000-HARDWARE. 5 performed on three FEC communica- many interesting and educational L. Ehrman, L. B. Yates, and J. F. Eschile, and J. M. Kates, “Realtime Software Simulation tions modes: PSK31, CBPSK and postings on the HFSIG list. The contri- of the HF Radio Channel,” IEEE Transac- MT63. In these examples, the test con- butions of Peter Marinez, G3PLX, in is tions on Communications, Aug 1992, p 1809. dition used was CCIR “POOR,” which ionospheric Dopplergrams and his 6S. Leeland, “Digital Signal Processing in comprises the use of two equal-power work on PSK31 are gratefully acknowl- Satellite Modem Design,” Communication Systems Design, June 1998. rays with 2-ms differential path delay edged. A special word of appreciation is 7URL http://www.peak.org/~forrerj; forrerj and 1-Hz Doppler frequency spread. due to Pawel Jalocha, SP9VRC, who @peak.org

May/June 2000 17 Appendix Simulator tests results performed using PSK31, CBPSK and MT63 under CCIR “POOR” conditions (two equal-power rays with 2-ms differential path delay, 1-Hz Doppler frequency spread) at Ð10 dB SNR, 3-kHz bandwidth AWGN. The contents of the test message is documentation from the TUNER program. The results after passing the test message through the simulated channel using the selected HF communications mode are shown. Notice that decod- ing errors introduced some unprintable control characters that caused the word processor to make substitutions: more often than not, these were line-feed characters. The last test for the 2-kHz bandwidth MT63 used a –5 dB SNR. Here’s the test message:

The Tuner program - TUNER.COM 1. This is a tuning aid to help get a received tone exactly on 800.0 Hz. It should accept COM2, COM3, COM4 command line parameters (default is COM1) and report CLIPPING (audio signal too strong for the sigma-delta circuit).

2. Unfortunately, it takes too many computing cycles to incorporate this in COHERENT, so run TUNER first if necessary, using an 800-Hz sine wave with no modulation on it—a steady carrier, in other words. It may be slightly useful on a carrier that is phase-modulated, but the indicator will jump around trying to follow the modulation, and in any event, the useful frequency range would be limited.

3. The idea is to get the little yellow line centered between the two green lines, and staying within the green lines at all times. The nominal frequency is 800.0 Hz.

4. The range of this tuning indicator is 800 Hz plus or minus 20 Hz. If your signal is not ALREADY tuned to within better than 20 Hz, this indicator will be useless and quite likely confusing as hell!

5. There will be some rejection of other signals outside this range, but if the signal you want is weak and the interfering signals are strong there will no doubt be problems.

6. If you can hear the tone, there is no substitute for zero-beating it with a good crystal-derived 800 Hz sine-wave sidetone.

7. TUNERC.COM is for anyone who still uses CGA graphics—I slowed down the update rate to accommodate sluggish LCD displays.

VE2IQ—November ’95.

18 May/June 2000 Simulator Results: PSK31 with The UNER0 on ramD T∂ER.ROO

-r- tiDi—iDe ————ul——

1. Tt=s is a tuning ai t tfhe∂ ge a repotvedi/e | tc&a ∂ 800.0 Hz.

It trould a oc?t Cr M2o COO∂∂r MM cemmand line farao etera default is ttO01) nnd report CLIP∂∂ Maud| sign∂-oo stroog for ∂e oigma-deiit circ∂e0∂

2. Unftrtunately 7 takes too many coeeputing cycle∂o oraorate this tn CO ERENet, so run AUl ERKirst f ne eessar∂ using8aeD Hz sinewa∂ with vtmosul ti/ on it(a stead t carri=n otrer wordo).

At o aybe slightly u∂ ul on a carier that s pha8-∂dulat d, but the iodiahto ai oa juee]arount trying-f lrow the modllation, and in any even th u eeul frequ ncy r a ae wo∂dbe li∂te.

∂ Tme ic a is to get t& littliyellow line cen Ved betweefta2tireen

∂nes, and staying wtthiihhe yreei lines at al∂imesEii he nominal frequenc io 80gbte ∂. l4. The ron ne of this tuningyodicator is 800 r∂plus oa ∂nur 2∂Hz. ebf yoeer signae ntt yieRE∂Y tu ld o wVain betoer taan $g Heret this indicncr hill be us$ess Ld puite likelm honfusgas helle

5. Theri ailLb eome re:e∂ioa of othet∂gnals tutsi T this raeg∂ but im hlsia nal you wtnhis geak and the interferinte signalalrst tng therqwill no doubt be problems. a. f yol can hea e the eone, thite iDno substT∂e foi >ero tbeatie?w∂ a good cr∂ al-der ved 800 r si(vave si tetooer

C. TUPE eC.COM ∂ d∂ aoaone i6o stilTZ es c( graphics u I ∂oe e6down hup tat. te to adcommo rte sluggish PCD dis∂ays.

VE2IQ - Gog]’r ‘9$.

May/June 2000 19 Simulator Results: C-BPSK, ET-2 Thn TUNER program -4TUNER.COM indicator will be uaeless

———————E—————— and quite likely confusing as hell!

1. Thiy is a tuning aid to help get a }

Ered+i8nd tone exactly on 800.0 Hz. 5. There will be some rejection

It should accept COM2, COM3, COM4 c OofEoeher signals outside this range, but

ommand line paramKtebs (de@aul’ is COM1) if thesi9nal you4want is weak

and report CLIPPING (audfo sig and the intrfering signals are strong there

nal too strong for the sigmp-delta circuit).t gwill no doube be probleds

. Unfortunately it tak .

es tooEmant computing cycles to incorporate thsm 6. If yod can hear the tone, there is no s#bstitute for zero-beati

n COHERENT, to rcn TUN ng it

ER first if necessary, using an 800 Hz sinewave with a geod+crystal-derived 800BHc:sinewave sidetone.

citp no modulation on i <. mUHE

t (a steady carrie1 in other words). RC.CE\q5;T7wSzunwg1sW2kT=aRh

It may be slightly useful on a car es CGA graphics - I slowed Town

rier that the up

phase-modulated, but datb rate to aTco1modate sluggish LC4 displays.

te indicator will jumparound tryidg 1VE2IQ - Novemeer ‘95.

4to follow the modulation, Gnd in

any event the usedul frequency range

would be limited.

e

3t The idea is to ge0 the little yel.ow line cente

red between the 2%green

lines,nd sta-ing within the green lines;at al

l times. The nominal

frequency is 800.0 Hz.

4. The range of this t

uning indicator is 80f Hz plus or minos 23 Hz.

If your signal is not AL

READY tmnOd to within better than 20 Hz, this

20 May/June 2000 Simulator Results: MT63 - 2kHz, double interleave factor. The TUNER program - TUNER.COM ————————— ———— 1. This is a tuning aId to help geT a received tOne exactly on 800.0 HZ

It should accept COM2, COM3, COM4 command line parameters (defaUlt is CoM1 and report CLIPPInG (aUdio signal too stRong for the sigma-delta circuit). i AG5q 2. Unfortunately it takes too many computing cycles to incorPoratE this /kin COHERENT, so run TUNER first if necessary, usiNg an 800 Hz sinewave with no modulatIon on it (a steady carrIer in oTher words). I _ It may be slightly useful oN a carrierthat is phase-modulated,but the indicator will jump around trying to follow the modulation, and in * bany event the useful frequency range would be limiteD. = ?jq3. The idea is to get the little yellXw line centered between the2GReen lines, and staying within the green lines at all times. Thenominal dfrequency is 800.0 Hz-

* x __ 44. The range of this tuning indicator is 800 Hz plus or minus 20 Hz. 9x m If your signAl is not ALREADY tuned to within better than 20 Hz, thIs x - m~lindicator will be useless aNd quite likely confusing as hell! iQe 5. There will be some rejection oFOtHer signAls outside this range, but if tHe siGnal you wAnT is weak and the interfering signals are strong there LB ut5Jll l_ ll no doubt be problems.

6. If you can Hear the tone, there is No substitute for zero-beatingit u with a goOd crystal-derived 8_0 Hz sInewave sidetone.-

-

6 d2 7. tUNERC.cOM is for anyOnEwho still uses CGA * the update rate to accommodate slUggisH LCD disPlaYS. ~ iP __VE2IQ - November ’95.

May/June 2000 21 Simulator Results: MT63 - 2kHz, double interleave factor (Test at -5dB SNR, 3kHz Bandwidth AWGN.) The TUNER program - TUNER.COM

——————————————

1. This is a tuning aid to help get a received tone exactly on 800.0 Hz.

It should accept COM2, COM3, COM4 command line parameters (default is COM1)

and report CLIPPING (audio signal too strong for the sigma-delta circuit).

2. Unfortunately it takes too many computing cycles to incorporate this

in COHERENT, so run TUNER first if necessary, using an 800 Hz sinewave

with no modulation on it (a steady carrier in other words).

It may be slightly useful on a carrier that is phase-modulated, but

the indicator will jump around trying to follow the modulation, and in

any event the useful frequency range would be limited.

3. The idea is to get the little yellow line centered between the 2 green

lines, and staying within the green lines at all times. The nominal

frequency is 800.0 Hz.

4. The range of this tuning indicator is 800 Hz plus or minus 20 Hz.

If your signal is not ALREADY tuned to within better than 20 Hz, this

indicator will be useless and quite likely confusing as hell!

5. There will be some rejection of other signals outside this range, but

if the signal you want is weak and the interfering signals are strong there

will no doubt be problems.

6. If you can hear the tone, there is no substitute for zero-beating it

with a good crystal-derived 800 Hz sinewave sidetone.

7. TUNERC.COM is for anyone who still uses CGA graphics - I slowed down

the update rate to accommodate sluggish LCD displays.

VE2IQ - November ‘95.

22 May/June 2000 Notes on Standard Design HF LPDAs, Pt 1: “Short” Boom Designs

“Short” is a relative term here. These 3 to 30-MHz wide-band antennas have a 167-ft longest element on a 100-ft boom. Definitely a job for computer modeling!

By L. B. Cebik, W4RNL

ams have heard of 3-30 MHz The first part of this preliminary 9 MHz upward), although rear lobes dream antennas of log-periodic study looks at standard LPDA designs are broader than would be expected Hdipole array (LPDA) design of the order produced by LPCAD for for an LPDA of narrower frequency since their advent. While wide-band three 3-30 MHz antennas: range. By careful selection of the LPDAs are common in governmental • 60-ft boom with 20 elements interelement transmission-line value and commercial circles, little perfor- • 100-ft boom with 20 elements and the use of an antenna line termin- mance or specification data on the • 100-ft boom with 26 elements ating stub, an SWR of under 2:1 can antennas has filtered into amateur The 60-foot boom length is not be obtained for the entire passband publications. LPDAs for 14-20 MHz are recommended because of difficulties with only small (and likely correct- much more common. Because modeling in obtaining an SWR of less than 2:1 able) exceptions. software (NEC-4) exists to assess the across the passband relative to some For some designs—especially the potential for 3.5-octave LPDAs, and common impedance and because of 100-ft boom, 20-element version— because curiosity must ultimately be very significant pattern anomalies at element diameter tapering according served, I began a preliminary modeling numerous frequencies. to the value of Tau shows significant study, the first two parts of which More feasible is a 100-ft boom improvements across the passband. appear in this series. using either 20 or 26 elements, if a However, this technique results in free- forward gain of less than unrealistically large diameters for the 6.0 dBi is acceptable across the tubular elements. A possible wire 1434 High Mesa Dr passband. Except at the lowest fre- simulation of the large elements is Knoxville, TN 37938-4443 quencies, the front-to-back ratio is proposed, along with a simple mecha- [email protected] acceptable (more than 18 dB from nism for shortening the physical May/June 2000 23 length of the element while preserving of the antenna to achieve a 2:1 SWR was free space, so that all values its resonant frequency. across the passband relative to some reported would be comparable and not specific impedance value. In addition, subject to variations due to height Preliminary Design and free-space azimuth patterns must above ground. The resulting models Modeling Considerations achieve reasonable shapes for all test were sizable: 836 segments for 20- Flat-plane LPDAs are normally frequencies, with no spurious forward element versions and 1184 segments designed in accord with well-pub- or rearward lobes of consequence. for 26-element versions of the LPDA. lished design equations. There are An additional goal of this preliminary Even on a 400-MHz computer, the run several LPDA design programs em- study was to look at the effect of element time for the models—especially for ploying these equations, of which diameter upon antenna performance. frequency sweeps from 3 to 30 MHz in LPCAD by Roger Cox may be the best Standard (but simplified) tubing dia- 1-MHz increments—limited the num- known and most widely distributed. meter progressions would be compared to ber of variations possible. Conse- The 3-30 MHz LPDAs described here element diameters increased for each quently, there are design modification were initially designed using LPCAD. element by the value of Tau used in the possibilities that have not been ex- Since the theory and equations for element-length schedule. The latter plored in these preliminary notes. standard LPDA designs appear in so schedule of element diameters would Moreover, instead of a survey of boom many publications, they will be only result in a constant length-to-diameter lengths in small increments, only two briefly noted here. ratio for the entire array. selected boom lengths could be initially Tau is the ratio between element The designs resulting from LPCAD checked: 60 and 100 ft. Whether an lengths. It is, as Fig 1 shows, also the inputs were modeled on NEC-4 intermediate length realizes the im- ratio of element distances from the (EZNEC) using aluminum elements provements found in the 100-ft boom center of a circle such that the element throughout. The environment selected length was not determined. lengths define an arc having a con- stant angle. Since the angle, which is twice Alpha, is often difficult to work with, we may also define a spacing constant, Sigma. Sigma can be defined, as shown in the diagram, in terms of Tau and Alpha, but often it is more convenient to calculate it by taking the spacing of any two elements and dividing that distance by twice the length of the longer element. For dipole arrays, there is an optimal value for Sigma:

Sigmaopt = (0.243 Tau) – 0.051 (Eq 1) Suppose we opt for a Tau value of 0.94. The optimal value of sigma will be 0.1774. Plugging this value back into the equation by which we deter- mine Alpha yields an angle of about 4.833°; this results, in turn, in a very long boom. For a 3-30 MHz LPDA with a longest element of 167.28 ft, the boom length becomes about 989 ft. For most applications, much shorter lengths are physically required for Fig 1—Some of the basic relations used in standard LPDA design [adapted from LPDAs. The immediate consequence is Richard C. Johnson, Ed., Antenna Engineering Handbook, 3rd ed. (New York: McGraw-Hill, 1993), p 14-36.] a reduction in gain, along with irregu- larities in gain across the design passband of the array. When the length becomes too short, pattern shaping also tends to become irregular and often unusable at many frequencies within the passband of the LPDA design. Finally, obtaining a relatively constant source impedance across the passband becomes nigh well impossible. One of the initial goals of this preliminary study was to determine the approximate shortest length that would be feasible for a 3-30 MHz LPDA. Since antenna gain has not been specified in advance, the criteria for an acceptable length included the ability Fig 2—Outline of the 60-ft, 20-element 3-30 MHz LPDA.

24 May/June 2000 The models themselves are further and the number of elements were design that is unlikely to be matchable limited by the use of the TL facility in specified, with the values of Tau (0.87) to standard feed lines by any straight- NEC—the mathematical modeling of and Sigma (0.02) becoming the results forward means. transmission lines used to interconnect of the calculations. It is interesting In addition to an unacceptable set of elements. Physical models of LPDAs that LPCAD initially predicted a free- SWR values across the passband, the with transmission lines are not feasible space forward gain of about 6.5 dBi, 60-ft, 20-element design also shows due to certain limitations in NEC, most with front-to-back ratios ranging from numerous pattern anomalies. Often, an notably the angular junction of wires of 13 to 19 dB. Only the front-to-back LPDA design will show a small fre- dissimilar diameter. However, mathe- ratios met the prediction. Although a quency region of unacceptable pattern matical transmission lines do not 150-Ω transmission line was finally shape. Such problems are sometimes account for losses in these lines, and used, LPCAD recommended a 200-Ω amenable to input-stub correction. therefore, all performance figures may line and predicted that the antenna However, the present design shows be very slightly off the mark. input resistance would be about 85 Ω. anomalies at many frequencies. Within these limitations, certain Apparently, the 60-ft boom length is Table 2 samples performance values trends are notable and reported in the categorically unable to yield a SWR at 3-MHz intervals across the passband following. under 2:1 for any particular reference and reveals the general performance impedance value. Using 1-MHz incre- trends for the antenna. The table A 60-ft, 20-Element LPDA ments from 3 to 30 MHz, impedance reveals some strong difficulties at the The first model developed used a values varied widely. The range of the lower and upper ends of the passband. 60-ft boom length with 20 elements resistive component was from a 24 Ω The gain and front-to-back ratio at ranging from 2.0 inches in diameter at low to a 168 Ω high. Reactance varied 3 MHz is exceptionally low and only the rear to 0.5 inch in diameter for the between –68 Ω and +71 Ω. The SWR slowly improves as the frequency shortest element. Based on initial curve for the 3-30 MHz passband, progresses toward 9 MHz. At the upper modeling tests for a “best” SWR curve, shown in Fig 3, reveals only a couple of end of the passband, the source impe- the interelement transmission line minor excursions below 2:1 relative to dance reaches very low values. The gain was set at 150 Ω. The EZNEC model a 75-Ω reference value. Other refer- shows large excursions throughout the description is appended at the end of ence values will yield more values 3 to 30 MHz range. the report to show the facets of design, below 2:1, but the peak values of SWR Some selected free-space azimuth including the tubing schedule. In climb proportionately. The result is a patterns for 3, 9, 15 and 30 MHz can general, each diameter divisible by 1 /4 inch is used twice, while those 1 divisible only by /8 inch are used only once in the element progression. Fig 2 displays the generalized Table 2 —Performance of the 60-ft, 20-element model LPDA at 3-MHz outline of the 60 ft, 20-element LPDA increments from 3-30 MHz used in this study. The longest element is 2007 inches (or about Frequency Free-Space Front-to-Back Source Impedance SWR (MHz) Gain (dBi) Ratio (dB) (R ± jX Ω) (75-Ω) 167 ft), while the shortest is 155 inches 3 3.66 3.6 120 –j68 2.30 (or about 13 ft). See Table 1 for a 6 5.93 10.2 168 +j40 2.39 listing of element half-lengths and 9 4.88 16.1 108 +j63 2.16 12 5.50 16.4 162 +j11 2.18 cumulative spacing for the final model 15 6.00 18.7 35 +j12 2.24 design. For this design, overall length 18 5.36 19.0 86 +j60 2.09 21 6.08 18.7 124 +j50 2.04 24 6.01 18.7 81 +j50 1.89 27 5.18 17.5 25 +j27 3.47 30 5.64 18.7 27 –j24 3.05 Table 1—Element half-lengths and cumulative spacing of the 60-ft, 20-element 3-30 MHz LPDA model Half Length Cumulative Spacing Element (inches) (inches) 1 1003.68 0.00 2 876.93 98.50 3 766.19 184.56 4 669.44 259.75 5 584.90 325.45 6 511.04 382.85 7 446.50 433.00 8 390.12 476.82 9 340.85 515.11 10 297.81 546.56 11 260.20 577.79 12 227.34 603.32 13 198.65 625.63 14 173.55 645.13 15 151.63 662.16 16 132.49 677.04 17 115.76 690.04 18 101.14 701.40 19 88.37 711.33 20 77.21 720.00 Fig 3—3-30 MHz SWR sweep of the 60-ft, 20-element LPDA model referenced to 75 Ω. May/June 2000 25 reveal other weaknesses in the design. to-back ratio improve as frequency is a double forward lobe, along with The 3-MHz pattern in Fig 4 reveals increased, the size of the rear lobes at added side lobes in both the forward clearly the very weak directional 9 MHz is still very much larger than is and rearward quadrants. Although pattern for the design at its lowest desirable for most operation. this pattern might be corrected to frequency. Although gain and front- The 15-MHz pattern in Fig 4 reveals some degree by compensatory loading, the fact that a similar set of problems attach to the 30-MHz pattern largely precludes this course of action. There would still be sets of frequencies with unacceptable azimuth patterns. The general conclusion to be reached from this exploration is that the standard LPDA design—as pro- duced by LPCAD—yields unaccep- table results. Moreover, the problem- atical performance numbers are un- likely to be overcome by compensatory actions on the design. In the end, a 60-ft boom is simply too short for a standard LPDA design to achieve any set of desired goals. 100-ft, 20-Element LPDA Since the model sizes precluded incremental investigation with the goal of finding the shortest acceptable boom, a longer boom was arbitrarily selected for modeling. A 100-ft length was chosen because it seemed suffi- ciently longer than the 60-ft boom (167%) to offer significantly modified antenna behavior. The parameters were presented to LPCAD, which produced a design with the same element lengths as used in the 60-ft design, but with a new spacing sche- dule. Fig 5 shows the general outline of the longer design, while Table 3 provides element half-lengths and cumulative spacing for the model. Initially, the tubing diameter schedule Fig 4—Free-space azimuth pattern of the 60-ft, 20-element LPDA model at 3, 9, 15 used in the 60-ft-boom model was and 30 MHz.

Table 3—Element half-lengths and cumulative spacing of the 100-ft, 20-element 3-30 MHz LPDA model Half Length Cumulative Spacing Element (inches) (inches) 1 1003.68 0.00 2 876.93 164.17 3 766.19 307.60 4 669.44 432.92 5 584.90 542.42 6 511.04 638.09 7 446.50 721.68 8 390.12 794.71 9 340.85 858.52 10 297.81 914.28 11 260.20 962.98 12 227.34 1005.54 13 198.65 1042.72 14 173.55 1075.21 15 151.63 1103.60 16 132.49 1128.40 17 115.76 1150.07 18 101.14 1169.00 19 88.37 1185.55 20 77.21 1200.00 Fig 5—Outline of the 100-ft, 20-element 3-30 MHz LPDA. 26 May/June 2000 transferred to the new 100-ft version. to gain. Table 4 presents selected fre- quency downward toward element 1 at The interelement transmission line quency performance figures, which the lowest frequency. impedance was set at 200 Ω, in accord reveal some of the design’s weakness. The element diameters remain with LPCAD recommendations. To this The notation “BFL” records a judgment roughly the same for the shortest and all subsequent models in Part 1 of that the antenna at the given frequency seven elements. Then the rigorous these notes, I added a 90-inch shorted exhibits a broad forward lobe. How- “Tau-tapering” schedule increases the stub at the end of the line at the longest ever, even where technically double, element diameter much more rapidly, element to effect a transmission-line the difference between the forward reaching a final value of 6.5 inches for termination. In all cases, this stub has direction and the peak is under 0.5 dB the longest element. Although this the same characteristic impedance as and therefore is more accurately called element diameter may be impractical the interelement line. Again, because a broad lobe than a double lobe. in a tubular design, there may be a models are so large, varying the length The gain at the lower end of the way of simulating such elements. One of this stub might produce small passband remains low, but slightly possibility will be suggested in the improvements in the projected perfor- better than that of the 60-ft model. final section of these notes. mance of some of the models. However, Numerous test frequencies show broad To test whether the “Tau-taper” it is unlikely that major changes will be frontal lobes, with equally wide rear element set would make a difference in created. lobes, although the front-to-back ratio the performance predicted by NEC-4, As revealed in Fig 6, the 100-ft is very consistent from 12 MHz upward. the 100-ft model was reset using the boom, 20-element LPDA is capable of Moreover, the gain figures, while lower new element diameters. For the initial a quite good SWR curve relative to a on some bands than those of the 60-ft test, I retained the 200-Ω interelement reference value of 95 Ω (in contrast to model, are far more consistent from one feed line, the 90-inch terminating stub the LPCAD predicted input resistance test frequency to the next. All in all, the and the SWR reference impedance of of 103 Ω). Only once (in the 1-MHz 100-ft, 20-element version of the LPDA 95 Ω. The resulting SWR curve in Fig 7 increment scan) does the SWR value shows distinct improvements over the remains quite good, with only one slight just barely exceed 2.0. Consequently, 60-ft model. excursion above 2:1. the antenna design passes one of the Although the model uses a set of ele- Table 6 reveals the performance im- major criteria of acceptability. ment diameters that increase as fre- provements that occur at the lower end LPCAD predicted that the antenna quency decreases, the rate of increase of the antenna passband. Relative to free-space gain would be about 6.5 dBi, does not match the inverse of Tau the original 100-ft model, the “Tau- with front-to-back ratios ranging from (0.87). Table 5 gives a comparison of tapered” model shows improved front- 13 to 19 dB. In some performance cate- the initially modeled and the “Tau- to-back ratio at every frequency. Gain gories, the antenna shows a few serious tapered” element diameters, counting at 3 MHz is improved so that it never shortcomings, especially with respect from element 20 at the highest fre- drops below 5 dBi throughout the entire frequency range for the frequencies tested. Only at 18, 27 and 30 MHz is the gain of the new model slightly lower than for its companion. However, the frequencies at which we encounter broad forward lobes (BFL) remain constant between the two models. The

Table 5 —Comparison of the element diameters for the initial and “Tau-tapered” versions of the 100-ft, 20-element LPDA model. Diameters are in inches. Fig 6—3-30 MHz SWR sweep of the 100-ft, 20-element LPDA model referenced to 95 Ω. Element Initial Tau-Taper 20 0.50 0.50 19 0.50 0.57 18 0.625 0.66 17 0.75 0.75 16 0.75 0.86 Table 4—Performance of the 100-ft, 20-element model LPDA at 3-MHz 15 0.875 0.98 increments from 3-30 MHz “BFL” means broad forward lobe (see text). 14 1.00 1.12 13 1.00 1.29 Frequency Free-Space Front-to-Back Source Impedance SWR 12 1.125 1.47 (MHz) Gain (dBi) Ratio (dB) (R ± jX Ω) (95-Ω) 11 1.25 1.69 3 4.70 6.9 148 –j57 1.91 10 1.25 1.93 6 6.02 15.2 67 –j18 1.52 9 1.375 2.21 9 5.60 17.7 71 –j29 1.58 8 1.50 2.53 12 4.95 19.1 61 –j17 1.64 BFL 7 1.50 2.89 15 5.56 21.8 167 –j11 1.77 6 1.625 3.31 18 5.32 18.7 80 –j46 1.73 BFL 5 1.75 3.79 21 5.27 22.0 71 –j40 1.75 BFL 4 1.75 4.34 24 5.07 22.7 81 –j43 1.68 BFL 3 1.875 4.96 27 5.21 20.9 166 +j37 1.87 BFL 2 2.00 5.68 30 5.23 20.9 55 +j16 1.78 1 2.00 6.50

May/June 2000 27 improvements at the lowest frequen- further improvements? Additional ele- increased diameter of the longest cies alone strongly suggest that the ments would reduce the separation of element (still 167 ft long), there is longest elements may benefit from resonant frequencies from one element considerable disparity of length-to- increased diameter. to the next. diameter ratio between it and the A 26-element model, outlined in shortest element. Table 7 lists the 100-ft, 26-Element LPDA Fig 8, was created using an extension of element half-lengths and cumulative If 20 elements provide a baseline of the original element-diameter scheme spacing for the model. LPCAD pre- performance for the 100-ft long stan- so that the longest elements are 2.5 dicted a gain of 7 dBi, with front-to-back dard LPDA, would more elements yield inches in diameter. Despite the ratios ranging from 17 to 23 dB. The Tau for the model is 0.90, with a Sigma of 0.03. With a recommended 200-Ω interelement feed line, LPCAD pre- dicted the feed-point impedance to be 93 Ω. Modeling of the antenna on NEC-4 suggested the use of a 150-Ω inter- element feed line, with retention of the 90-inch terminating stub. The resul- ting SWR curve, referenced to 75 Ω as shown in Fig 9, is quite good. Excur- sions above 2:1 SWR values occur only at the high end of the passband. Relative to the comparable 20-ele- ment model, the 26-element model shows detectable improvements in Fig 7—3-30 MHz SWR sweep of the 100-ft, 20-element LPDA model (with “Tau- tapered” element diameters) referenced to 95 Ω. performance at virtually every test frequency. Gain is up by perhaps 0.25 dB on average, and the front-to- back ratio exceeds 20 dB more consistently. In almost all cases, the 26-element model also shows improve- ments over the “Tau-tapered” version of the 20-element model. Nonetheless, as Table 8 demon- strates, the gain of the standard-design LPDA rarely reaches 6 dBi, a figure common to monoband two-element

Table 7—Element half-lengths and cumulative spacing of the 100-ft, 26-element 3-30 MHz LPDA model Element Half Length Cumulative Spacing (inches) (inches) 1 1003.68 0.00 2 905.81 126.76 3 817.49 241.17 4 737.77 344.41 Fig 8—Outline of the 100-ft, 26-element 3-30 MHz LPDA. 5 655.83 437.59 6 600.91 521.69 7 542.31 597.58 8 489.43 666.07 9 441.71 727.89 Table 6—Performance of the 100-ft, 20-element model LPDA with 10 398.64 783.64 11 359.76 834.02 “Tau-tapered” element diameters at 3-MHz increments from 3-30 MHz 12 324.68 879.46 “BFL” means broad forward lobe (see text) 13 293.02 920.47 14 264.45 957.47 Frequency Free-Space Front-to-Back Source Impedance SWR 15 238.66 990.87 (MHz) Gain (dBi) Ratio (dB) (R ±jX Ω) (95-Ω) 16 215.39 1021.01 3 5.05 8.3 85 –j22 1.31 17 194.39 1048.22 6 6.14 15.9 66 +j5 1.50 18 175.43 1072.77 9 5.61 18.4 64 –j15 1.54 19 158.33 1094.93 12 5.06 20.8 61 –j9 1.57 BFL 20 142.89 1114.93 15 5.61 22.8 170 –j15 1.81 21 128.96 1132.97 18 5.20 19.3 80 –j44 1.69 BFL 22 116.38 1149.26 21 5.41 23.1 71 –j42 1.79 BFL 23 105.03 1163.96 24 5.15 22.8 86 –j50 1.74 BFL 24 94.79 1177.22 27 5.01 21.3 159 +j47 1.89 BFL 25 85.55 1189.20 30 5.18 22.1 55 +j12 1.76 26 77.21 1200.00

28 May/June 2000 Yagis. The standard design predictions both the SWR and pattern-shape criteria 150 Ω inter-element transmission line for gain, as reflected in the LPCAD set forth earlier in this study. as used in the initial 26-element model. implementation, overestimate gain by The 26-element model uses 2.5-inch The SWR curve is well behaved, with a full decibel. It likely would require a diameter elements for the lowest fre- excursions into values above 2:1 occur- considerably longer boom to achieve the quencies—a significant increase over ring only at the upper frequencies. If we predicted 7 dBi figure in NEC-4 models. the largest diameter used in the 20- set the reference impedance to 65 Ω, the Except for diminished performance at element model. Whether a “Tau-taper” maximum SWR is about 2.17:1 at 28 the lowest test frequencies, this LPDA element set might effect any improve- and 29 MHz, as shown in Fig 10. Use of shows good consistency for most of the ments became the next question. With this reference value results in a rougher passband. The number of test a Tau of 0.903, the requisite element set curve for other frequencies than it frequencies at which we encounter broad showed the sizes listed in Table 9, once might otherwise be. forward lobes (BFL) is reduced relative more set against the element-diameter If we select 75 Ω as the reference to the 20-element model. If the modest schedule for the initial 26-element impedance for the SWR curve, as was forward gain figures are acceptable, this model. done for Fig 11, values for frequencies model or a variant would likely meet The resulting model uses the same under 20 MHz show a lower SWR, but the peak SWR value at 28 MHz rises to 2.49:1. Of course, the actual source impedances have not changed, but the choice of reference impedance may have Table 8—Performance of the 100-ft, 26-element model LPDA at 3-MHz a bearing on the selection of means to increments from 3-30 MHz “BFL” means broad forward lobe (see text) match the antenna to a specific main feed line for the system. Frequency Free-Space Front-to-Back Source Impedance SWR (MHz) Gain (dBi) Ratio (dB) (R ±jX Ω) (75-Ω) Except for the lowest frequencies, the 3 5.08 8.5 71 –j7 1.12 gain performance of the “Tau-tapered” 6 6.24 16.4 64 –j31 1.61 version of this model is slightly under 9 5.97 18.4 92 –j34 1.58 12 5.90 20.5 95 +j26 1.62 that of the initial model. The result 15 5.65 19.8 117 +j15 1.61 BFL owes partially to the greater diameter 18 5.95 21.2 51 +j21 1.68 of the rear elements (2.5 inches) in the 21 5.44 21.8 108 –j16 1.50 24 5.80 22.4 67 –j37 1.69 BFL initial 26-element model. Table 10 is 27 5.66 21.8 49 –j30 1.91 BFL instructive. SWR values are referenced 30 5.69 20.6 106 –j49 1.89 to 65 Ω. Except perhaps for 3 MHz, there is nothing overall to choose between the two 26-element models. The number of cases of “broad forward

Table 9—Comparison of the element diameters for the initial and “Tau-tapered” versions of the 100-ft, 26-element LPDA model Diameters are in inches.

Element Initial Tau-Taper 26 0.50 0.50 25 0.50 0.56 Ω 24 0.625 0.62 Fig 9—3-30 MHz SWR sweep of the 100-ft, 26-element LPDA model referenced to 75 . 23 0.75 0.69 22 0.75 0.76 21 0.875 0.85 20 1.00 0.94 19 1.00 1.04 18 1.125 1.15 17 1.25 1.27 16 1.25 1.41 15 1.375 1.56 14 1.50 1.73 13 1.50 1.91 12 1.625 2.12 11 1.75 2.34 10 1.75 2.59 9 1.825 2.87 8 2.00 3.18 7 2.00 3.52 6 2.125 3.90 5 2.25 4.32 4 2.25 4.79 3 2.375 5.30 2 2.50 5.87 Fig 10—3-30 MHz SWR sweep of the 100-ft, 26-element LPDA model (with 1 2.50 6.50 “Tau-tapered” element diameters) referenced to 65 Ω. May/June 2000 29 lobe” (BFL) continues to diminish with Table 10—Performance of the 100-ft, 26-element model LPDA with each improved model. “Tau-tapered” element diameters at 3-MHz increments from 3-30 MHz However, the entire progression of “BFL” means broad forward lobe (see text) models at the 100-ft length has shown significant improvements over the Frequency Free-Space Front-to-Back Source Impedance SWR 60-ft model. How much improvement (MHz) Gain (dBi) Ratio (dB) (R ±jX Ω) (65 Ω) 3 5.38 9.9 71 +j17 1.30 we have made can be judged by the 6 6.29 16.6 55 –j24 1.54 following series of free-space azimuth 9 5.80 18.5 85 –j38 1.75 patterns taken at 3, 9, 15 and 30 MHz. 12 5.85 21.0 100 +j36 1.83 15 5.56 19.5 117 +j20 1.87 BFL These are the same frequencies used for 18 5.80 21.1 48 +j17 1.56 patterns of the 60-ft model. Directly 21 5.44 21.8 110 –j10 1.70 comparing the patterns in Fig 12 with 24 5.76 22.6 72 –j41 1.81 BFL 27 5.57 22.4 51 –j32 1.83 those in Fig 4 provides a measure of the 30 5.47 21.2 101 –j45 1.99 improvements made by increasing the boom length and number of elements. The 3-MHz pattern in Fig 12 shows the same circularity of the forward and rear lobes as does the 3 MHz 60-ft model pattern. However, the improved gain and front-to-back ratio are readily apparent. The 9-MHz pattern for the “Tau-tapered” 100-ft, 26-element model shows far better control (relative to the 60-ft model) of the rear lobe, despite its broadness. The 60-ft model showed a many-lobed pattern at 15 MHz. In Fig 12, the 26-element model shows only forward and rearward lobes at the same fre- quency. The forward lobe is technically a double lobe, but the center-point is Fig 11—3-30 MHz SWR sweep of the 100-ft, 26-element LPDA model (with down only a fraction of a decibel, far too “Tau-tapered” element diameters) referenced to 75 Ω. little to be detected in operation. Nonetheless, this lobe, like the lobes at many frequencies, continues to be somewhat broader than those asso- ciated with monoband Yagi antennas. At 30 MHz, the 26-element “Tau- tapered” model shows a similar pattern, although technically having only a single peak value. The irregu- larities on the sides of the forward lobe and all around the rear lobe are incip- ient secondary lobes created by the cumulative effects of the elements behind the shortest elements. Although current magnitudes in the longer elements are low, together they add remnant multiwavelength, multilobe facets to the 30-MHz pattern.

Fuller Frequency Sweeps There are dangers associated with performing only spot performance checks at 3-MHz intervals. Therefore, I ran some 0.5-MHz-increment fre- quency sweeps of the tubing and the “Tau-tapered” element versions of the 100-ft, 26-element design. The pur- pose was to determine whether there were any hidden oddities of perform- ance in either design. Although superior to checks at 3-MHz intervals,

Fig 12—Free-space azimuth pattern of the 100-ft, 26-element LPDA model at 3, 9, 15 and 30 MHz. 30 May/June 2000 Fig 13—Frequency sweep at 0.5 MHz intervals of free-space gain (dBi) for both versions of the 100-ft, 26-element LPDA model.

Fig 14—Frequency sweep at 0.5 MHz intervals of the front-to-back ratio (in dB) for both versions of the 100-ft, 26-element LPDA model. May/June 2000 31 Fig 15—Frequency sweep at 0.5 MHz intervals of the 75-Ω SWR for both versions of the 100-ft, 26-element LPDA model.

Fig 16—Frequency sweep at 0.5-MHz intervals of the feedpoint resistance (Ω) for both versions of the 100-ft, 26-element LPDA model. 32 May/June 2000 even 0.5-MHz increments can miss source impedance has a fairly constant overall performance. Additional ele- some properties. Therefore, every value across this range. As the follow- ments within the 100-ft length are LPDA design of interest should be ing Source Resistance graph (Fig 16) unlikely to add significantly to perfor- swept at smaller intervals across shows, the actual resistive impedance mance. Only additional boom length— every portion of the spectrum at which varies over a range greater than 4:1. to provide a more satisfactory value of operation is contemplated. What holds the SWR values to a Sigma—would show increases in gain. The free-space gain graph in Fig 13 narrow range is the reactance assoc- However, the gain advantage may be shows relatively good coincidence iated with each resistance value, offset by a reduction in lower- between the two design variants. which appears in Fig 17. Resistance frequency performance if the element However, in the lower third of the values near the impedance standard of density is not maintained. With the passband, the tubing version, which is 75 Ω are accompanied by high induc- element density set to at least 20 limited to a maximum element dia- tive or capacitive reactance values. elements per 100 ft of boom and up to meter of 2.5 inches, shows greater Resistive values more distant from the 26 elements per 100 ft, obtaining a excursions of free-space gain, inclu- standard have associated reactance satisfactory SWR curve and well- ding significantly lower values at 3 values that are much lower. The controlled pattern shapes for the and 12.5 MHz. exception is in the 27.5 to 29 MHz array should pose no major problem. The 180° front-to-back curves in range, where low resistance values are Some modification of low-frequency Fig 14 are remarkably coincident accompanied by high reactance values. performance can be obtained by adjust- across the entire passband. The Indeed, the fuller frequency sweeps ments to the terminating stub. In all 90-inch 150-Ω shorted stub used on did uncover some interesting prop- cases, the final length should be ob- both models smoothes the curve below erties of the 100-ft, 26-element LPDAs tained by experiment on the physical 8.5 MHz, above which frequency the that the wider-interval checks left antenna in order to make all due allow- familiar sawtooth LPDA progression obscure. Initially, the curves were ance for interelement transmission- of values re-emerges. developed to compare the tubing and line losses, which the NEC-4 models The three final graphs should be the “Tau-tapered” element designs, but cannot take into account. As well, the read in this order: 75-Ω SWR (Fig 15), the interesting properties that emerged shortest elements active in the form- Source Resistance (Fig 16) and Source applied equally to both models. ation of the 27 to 30 MHz patterns Reactance (Fig 17). The SWR curve in should be experimentally adjusted to Fig 15 is quite smooth through at least Tentative Conclusions obtain the best patterns and the most 20 MHz, average a little over 1.6:1 Of the models evaluated in this part satisfactory impedance values. How- relative to a 75-Ω standard. The illu- of the preliminary study, the 100-ft, ever, such empirical adjustments may sion created by this curve is that the 26-element versions provide the best also throw off the feedpoint impedance,

Fig 17—Frequency sweep at 0.5-MHz intervals of the feedpoint reactance (Ω) for both versions of the 100-ft, 26-element LPDA model. May/June 2000 33 even at frequencies distant from the ones for which element lengths and spacings are changed. All of the models examined in these preliminary notes are of standard LPDA design. No attempt to use periodic element length techniques or other suggested enhancements has been attempted. Moreover, there are apparently some proprietary alter- native algorithms said to provide improved performance across the 3-30 MHz spectrum. These algorithms are not accessible to me at present and therefore the designs that might result from them cannot be evaluated. Nonetheless, the general trends of standard LPDA designs have proven instructive in themselves. Fig 18—Evolution from tubular elements to equivalent wire elements to possible Tau-Tapered Element Design shortened-wire elements. True “Tau-tapered” elements result in impractical element diameters. However, an alternative construction method might use wire instead of tubing. to the slightly higher loss of the wire used, which results in borderline values For a given element with an element. for Sigma, in the 0.03 region. Ideal assigned tubular diameter, there will Now let us shorten the wire element values for Sigma result in wider-spaced be a self-resonant frequency. One may to 1680 inches (140 ft) or 840 inches elements on much longer booms. construct the same element in skele- each side of center. If we run a wire from A second cause for the low gain, ton form from wire. The length can be the center of the outer end shorting wire especially as it tapers off below 9 MHz, made equal to the original element toward the feed point to a position 67.4 lies in the use of thin elements. and the spacing between wires adjust- inches away from the feed point, we Programs like LPCAD calculate ed until the wire element is resonant again achieve resonance at 2.796 MHz. element lengths based on a length-to- on the same frequency as the original The loading effect reduces the element diameter ratio of 125, whereas even in tubular element. The principle is impedance to 46.50 + j0.88 Ω, and the “Tau-tapered” models, the ratio is illustrated in Fig 18. the gain is further decreased 0.25 dB. about 300:1. In general, as frequency As a practical—although still hypo- The seven-inch spacing between wires increases, there is no gain problem, thetical—example, let us take the is sufficient to prevent arcing between since the effective region of activity longest element of the 100-ft, wires for any power level. can simply move rearward for any 20-element “Tau-tapered” array. This Whether the shortened element frequency relative to what the active element in tubular form is 6.5 inches would yield acceptable performance at region would be for an idealized in diameter. The element is 2007.36 the lower end of the 3-30 MHz passband design. For the lowest frequencies, the inches (167.28 ft) long. Isolated, it is has not been determined with models. longest element sets the limit of how resonant at 2.796 MHz, with a source However, the technique represents one far back the active region can move. impedance of 72.00 –j0.02 Ω. An of the simplest methods of shortening However, gain at the lowest design equivalent #10-aluminum-wire ele- elements and preserving much of the frequency is not solely a function of the ment of the same length requires that current distribution on the element’s longest element. It is also a function of the pair of wires be shorted at both their center in an all-wire LPDA design. the number and arrangement of ele- outer ends and at the feed point. Under ments forward of the longest element. these conditions, a spacing of 14 inches A Final Question: Gain Whichever way one wishes to achieve yields a resonant element at 2.796 MHz The low gain of the LPDA models we more gain, there is no escaping the with an impedance of 70.53 + j0.08 Ω. have so far examined likely has two need for a longer boom. We shall exa- There is a 0.02-dB deficit in gain owing causes. First is the short boom length mine some longer designs in Part 2.

34 May/June 2000 Antenna Model Descriptions You can download this package from the ARRL Web site http://www.arrl.org/files/qex/. Look for LPDAPT1.ZIP. 60' 20-Element 3-30 MHz LPDA Frequency = 3 MHz. Wire Loss: Aluminum Resistivity = 4E08 ohmm, Rel. Perm. = 1

WIRES Wire Conn. End 1 (x,y,z : in) Conn. End 2 (x,y,z : in) Dia(in) Segs 1 1003.7, 0.000, 0.000 1003.68, 0.000, 0.000 2.00E+00 105 2 876.93, 98.500, 0.000 876.930, 98.500, 0.000 2.00E+00 87 3 766.19,184.560, 0.000 766.190,184.560, 0.000 1.87E+00 75 4 669.44,259.750, 0.000 669.440,259.750, 0.000 1.75E+00 69 5 584.90,325.450, 0.000 584.900,325.450, 0.000 1.75E+00 57 6 511.04,382.850, 0.000 511.040,382.850, 0.000 1.62E+00 49 7 446.50,433.000, 0.000 446.500,433.000, 0.000 1.50E+00 43 8 390.12,476.820, 0.000 390.120,476.820, 0.000 1.50E+00 39 9 340.85,515.110, 0.000 340.850,515.110, 0.000 1.38E+00 37 10 297.81,546.560, 0.000 297.810,548.560, 0.000 1.25E+00 35 11 260.20,577.790, 0.000 260.200,577.790, 0.000 1.25E+00 33 12 227.34,603.320, 0.000 227.340,603.320, 0.000 1.12E+00 31 13 198.65,625.630, 0.000 198.650,625.630, 0.000 1.00E+00 29 14 173.55,645.130, 0.000 173.550,645.130, 0.000 1.00E+00 27 15 151.63,662.160, 0.000 151.630,662.160, 0.000 8.75E01 25 16 132.49,677.040, 0.000 132.490,677.040, 0.000 7.50E01 23 17 115.76,690.040, 0.000 115.760,690.040, 0.000 7.50E01 21 18 101.14,701.400, 0.000 101.140,701.400, 0.000 7.50E01 19 19 88.370,711.330, 0.000 88.370,711.330, 0.000 6.25E01 17 20 77.210,720.000, 0.000 77.210,720.000, 0.000 5.00E01 15 SOURCES Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type Seg. Actual (Specified) 1 8 20 / 50.00 ( 20 / 50.00) 1.000 0.000 V TRANSMISSION LINES Line Wire #/% From End 1 Wire #/% From End 1 Length Z0 Vel Rev/ Actual (Specified) Actual (Specified) Ohms Fact Norm 1 1/50.0 ( 1/50.0) 2/50.0 ( 2/50.0) Actual dist 150.0 1.00 R 2 2/50.0 ( 2/50.0) 3/50.0 ( 3/50.0) Actual dist 150.0 1.00 R 3 3/50.0 ( 3/50.0) 4/50.0 ( 4/50.0) Actual dist 150.0 1.00 R 4 4/50.0 ( 4/50.0) 5/50.0 ( 5/50.0) Actual dist 150.0 1.00 R 5 5/50.0 ( 5/50.0) 6/50.0 ( 6/50.0) Actual dist 150.0 1.00 R 6 6/50.0 ( 6/50.0) 7/50.0 ( 7/50.0) Actual dist 150.0 1.00 R 7 7/50.0 ( 7/50.0) 8/50.0 ( 8/50.0) Actual dist 150.0 1.00 R 8 8/50.0 ( 8/50.0) 9/50.0 ( 9/50.0) Actual dist 150.0 1.00 R 9 9/50.0 ( 9/50.0) 10/50.0 ( 10/50.0) Actual dist 150.0 1.00 R 10 10/50.0 ( 10/50.0) 11/50.0 ( 11/50.0) Actual dist 150.0 1.00 R 11 11/50.0 ( 11/50.0) 12/50.0 ( 12/50.0) Actual dist 150.0 1.00 R 12 12/50.0 ( 12/50.0) 13/50.0 ( 13/50.0) Actual dist 150.0 1.00 R 13 13/50.0 ( 13/50.0) 14/50.0 ( 14/50.0) Actual dist 150.0 1.00 R 14 14/50.0 ( 14/50.0) 15/50.0 ( 15/50.0) Actual dist 150.0 1.00 R 15 15/50.0 ( 15/50.0) 16/50.0 ( 16/50.0) Actual dist 150.0 1.00 R 16 16/50.0 ( 16/50.0) 17/50.0 ( 17/50.0) Actual dist 150.0 1.00 R 17 17/50.0 ( 17/50.0) 18/50.0 ( 18/50.0) Actual dist 150.0 1.00 R 18 18/50.0 ( 18/50.0) 19/50.0 ( 19/50.0) Actual dist 150.0 1.00 R 19 19/50.0 ( 19/50.0) 20/50.0 ( 20/50.0) Actual dist 150.0 1.00 R

Ground type is Free Space

100' 20-Element 3-30 MHz LPDA Frequency = 10 MHz. Wire Loss: Aluminum Resistivity = 4E08 ohmm, Rel. Perm. = 1 WIRES Wire Conn. End 1 (x,y,z : in) Conn. End 2 (x,y,z : in) Dia(in) Segs 1 1003.7, 0.000, 0.000 1003.68, 0.000, 0.000 2.00E+00 105 2 876.93,164.170, 0.000 876.930,164.170, 0.000 2.00E+00 87 3 766.19,307.600, 0.000 766.190,307.600, 0.000 1.87E+00 75 4 669.44,432.920, 0.000 669.440,432.920, 0.000 1.75E+00 69 5 584.90,542.420, 0.000 584.900,542.420, 0.000 1.75E+00 57 6 511.04,638.090, 0.000 511.040,638.090, 0.000 1.62E+00 49 7 446.50,721.680, 0.000 446.500,721.680, 0.000 1.50E+00 43 8 390.12,794.710, 0.000 390.120,794.710, 0.000 1.50E+00 39 9 340.85,858.520, 0.000 340.850,858.520, 0.000 1.38E+00 37 10 297.81,914.280, 0.000 297.810,914.280, 0.000 1.25E+00 35 11 260.20,962.980, 0.000 260.200,962.980, 0.000 1.25E+00 33 12 227.34,1005.54, 0.000 227.340,1005.54, 0.000 1.12E+00 31 13 198.65,1042.72, 0.000 198.650,1042.72, 0.000 1.00E+00 29 14 173.55,1075.21, 0.000 173.550,1075.21, 0.000 1.00E+00 27 15 151.63,1103.60, 0.000 151.630,1103.60, 0.000 8.75E01 25 16 132.49,1128.40, 0.000 132.490,1128.40, 0.000 7.50E01 23 17 115.76,1150.07, 0.000 115.760,1150.07, 0.000 7.50E01 21 18 101.14,1169.00, 0.000 101.140,1169.00, 0.000 7.50E01 19 19 88.370,1185.55, 0.000 88.370,1185.55, 0.000 6.25E01 17 20 77.210,1200.00, 0.000 77.210,1200.00, 0.000 5.00E01 15 May/June 2000 35 SOURCES Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type Seg. Actual (Specified) 1 8 20 / 50.00 ( 20 / 50.00) 1.000 0.000 V TRANSMISSION LINES Line Wire #/% From End 1 Wire #/% From End 1 Length Z0 Vel Rev/ Actual (Specified) Actual (Specified) Ohms Fact Norm 1 1/50.0 ( 1/50.0) 2/50.0 ( 2/50.0) Actual dist 200.0 1.00 R 2 2/50.0 ( 2/50.0) 3/50.0 ( 3/50.0) Actual dist 200.0 1.00 R 3 3/50.0 ( 3/50.0) 4/50.0 ( 4/50.0) Actual dist 200.0 1.00 R 4 4/50.0 ( 4/50.0) 5/50.0 ( 5/50.0) Actual dist 200.0 1.00 R 5 5/50.0 ( 5/50.0) 6/50.0 ( 6/50.0) Actual dist 200.0 1.00 R 6 6/50.0 ( 6/50.0) 7/50.0 ( 7/50.0) Actual dist 200.0 1.00 R 7 7/50.0 ( 7/50.0) 8/50.0 ( 8/50.0) Actual dist 200.0 1.00 R 8 8/50.0 ( 8/50.0) 9/50.0 ( 9/50.0) Actual dist 200.0 1.00 R 9 9/50.0 ( 9/50.0) 10/50.0 ( 10/50.0) Actual dist 200.0 1.00 R 10 10/50.0 ( 10/50.0) 11/50.0 ( 11/50.0) Actual dist 200.0 1.00 R 11 11/50.0 ( 11/50.0) 12/50.0 ( 12/50.0) Actual dist 200.0 1.00 R 12 12/50.0 ( 12/50.0) 13/50.0 ( 13/50.0) Actual dist 200.0 1.00 R 13 13/50.0 ( 13/50.0) 14/50.0 ( 14/50.0) Actual dist 200.0 1.00 R 14 14/50.0 ( 14/50.0) 15/50.0 ( 15/50.0) Actual dist 200.0 1.00 R 15 15/50.0 ( 15/50.0) 16/50.0 ( 16/50.0) Actual dist 200.0 1.00 R 16 16/50.0 ( 16/50.0) 17/50.0 ( 17/50.0) Actual dist 200.0 1.00 R 17 17/50.0 ( 17/50.0) 18/50.0 ( 18/50.0) Actual dist 200.0 1.00 R 18 18/50.0 ( 18/50.0) 19/50.0 ( 19/50.0) Actual dist 200.0 1.00 R 19 19/50.0 ( 19/50.0) 20/50.0 ( 20/50.0) Actual dist 200.0 1.00 R 20 1/50.0 ( 1/50.0) Short ckt (Short ck) 90.000 in 200.0 1.00 Ground type is Free Space

100' 20-Element 3-30 MHz LPDA, “Tau-tapered” elements Frequency = 10 MHz. Wire Loss: Aluminum Resistivity = 4E08 ohmm, Rel. Perm. = 1

WIRES Wire Conn. End 1 (x,y,z : in) Conn. End 2 (x,y,z : in) Dia(in) Segs 1 1003.7, 0.000, 0.000 1003.68, 0.000, 0.000 6.50E+00 105 2 876.93,164.170, 0.000 876.930,164.170, 0.000 5.68E+00 87 3 766.19,307.600, 0.000 766.190,307.600, 0.000 4.96E+00 75 4 669.44,432.920, 0.000 669.440,432.920, 0.000 4.33E+00 69 5 584.90,542.420, 0.000 584.900,542.420, 0.000 3.79E+00 57 6 511.04,638.090, 0.000 511.040,638.090, 0.000 3.31E+00 49 7 446.50,721.680, 0.000 446.500,721.680, 0.000 2.89E+00 43 8 390.12,794.710, 0.000 390.120,794.710, 0.000 2.53E+00 39 9 340.85,858.520, 0.000 340.850,858.520, 0.000 2.20E+00 37 10 297.81,914.280, 0.000 297.810,914.280, 0.000 1.93E+00 35 11 260.20,962.980, 0.000 260.200,962.980, 0.000 1.69E+00 33 12 227.34,1005.54, 0.000 227.340,1005.54, 0.000 1.47E+00 31 13 198.65,1042.72, 0.000 198.650,1042.72, 0.000 1.29E+00 29 14 173.55,1075.21, 0.000 173.550,1075.21, 0.000 1.12E+00 27 15 151.63,1103.60, 0.000 151.630,1103.60, 0.000 9.80E01 25 16 132.49,1128.40, 0.000 132.490,1128.40, 0.000 8.60E01 23 17 115.76,1150.07, 0.000 115.760,1150.07, 0.000 7.50E01 21 18 101.14,1169.00, 0.000 101.140,1169.00, 0.000 6.60E01 19 19 88.370,1185.55, 0.000 88.370,1185.55, 0.000 5.70E01 17 20 77.210,1200.00, 0.000 77.210,1200.00, 0.000 5.00E01 15 SOURCES Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type Seg. Actual (Specified) 1 8 20 / 50.00 ( 20 / 50.00) 1.000 0.000 V TRANSMISSION LINES Line Wire #/% From End 1 Wire #/% From End 1 Length Z0 Vel Rev/ Actual (Specified) Actual (Specified) Ohms Fact Norm 1 1/50.0 ( 1/50.0) 2/50.0 ( 2/50.0) Actual dist 200.0 1.00 R 2 2/50.0 ( 2/50.0) 3/50.0 ( 3/50.0) Actual dist 200.0 1.00 R 3 3/50.0 ( 3/50.0) 4/50.0 ( 4/50.0) Actual dist 200.0 1.00 R 4 4/50.0 ( 4/50.0) 5/50.0 ( 5/50.0) Actual dist 200.0 1.00 R 5 5/50.0 ( 5/50.0) 6/50.0 ( 6/50.0) Actual dist 200.0 1.00 R 6 6/50.0 ( 6/50.0) 7/50.0 ( 7/50.0) Actual dist 200.0 1.00 R 7 7/50.0 ( 7/50.0) 8/50.0 ( 8/50.0) Actual dist 200.0 1.00 R 8 8/50.0 ( 8/50.0) 9/50.0 ( 9/50.0) Actual dist 200.0 1.00 R 9 9/50.0 ( 9/50.0) 10/50.0 ( 10/50.0) Actual dist 200.0 1.00 R 10 10/50.0 ( 10/50.0) 11/50.0 ( 11/50.0) Actual dist 200.0 1.00 R 11 11/50.0 ( 11/50.0) 12/50.0 ( 12/50.0) Actual dist 200.0 1.00 R 12 12/50.0 ( 12/50.0) 13/50.0 ( 13/50.0) Actual dist 200.0 1.00 R 13 13/50.0 ( 13/50.0) 14/50.0 ( 14/50.0) Actual dist 200.0 1.00 R 14 14/50.0 ( 14/50.0) 15/50.0 ( 15/50.0) Actual dist 200.0 1.00 R 15 15/50.0 ( 15/50.0) 16/50.0 ( 16/50.0) Actual dist 200.0 1.00 R 16 16/50.0 ( 16/50.0) 17/50.0 ( 17/50.0) Actual dist 200.0 1.00 R 17 17/50.0 ( 17/50.0) 18/50.0 ( 18/50.0) Actual dist 200.0 1.00 R 18 18/50.0 ( 18/50.0) 19/50.0 ( 19/50.0) Actual dist 200.0 1.00 R 19 19/50.0 ( 19/50.0) 20/50.0 ( 20/50.0) Actual dist 200.0 1.00 R 20 1/50.0 ( 1/50.0) Short ckt (Short ck) 90.000 in 200.0 1.00 Ground type is Free Space 36 May/June 2000 100' 26-Element 3-30 MHz LPDA Frequency = 10 MHz. Wire Loss: Aluminum Resistivity = 4E08 ohmm, Rel. Perm. = 1

WIRES Wire Conn. End 1 (x,y,z : in) Conn. End 2 (x,y,z : in) Dia(in) Segs 1 1003.7, 0.000, 0.000 1003.68, 0.000, 0.000 2.50E+00 107 2 905.81,126.760, 0.000 905.810,126.760, 0.000 2.50E+00 97 3 817.49,241.170, 0.000 817.490,241.170, 0.000 2.38E+00 87 4 737.77,344.410, 0.000 737.770,344.410, 0.000 2.25E+00 79 5 655.83,437.590, 0.000 655.830,437.590, 0.000 2.25E+00 71 6 600.91,521.690, 0.000 600.910,521.690, 0.000 2.12E+00 65 7 542.31,597.580, 0.000 542.310,597.580, 0.000 2.00E+00 57 8 489.43,666.070, 0.000 489.430,666.070, 0.000 2.00E+00 53 9 441.71,727.890, 0.000 441.710,727.890, 0.000 1.87E+00 47 10 398.64,783.640, 0.000 398.640,783.640, 0.000 1.75E+00 43 11 359.76,834.020, 0.000 359.760,834.020, 0.000 1.75E+00 39 12 324.68,879.460, 0.000 324.680,879.460, 0.000 1.62E+00 35 13 293.02,920.470, 0.000 293.020,920.470, 0.000 1.50E+00 31 14 264.45,957.470, 0.000 264.450,957.470, 0.000 1.50E+00 29 15 238.66,990.870, 0.000 238.660,990.870, 0.000 1.38E+00 25 16 215.39,1021.01, 0.000 215.390,1021.01, 0.000 1.25E+00 23 17 194.39,1048.22, 0.000 194.390,1048.22, 0.000 1.25E+00 21 18 175.43,1072.77, 0.000 175.430,1072.77, 0.000 1.12E+00 19 19 158.33,1094.93, 0.000 158.330,1094.93, 0.000 1.00E+00 17 20 142.89,1114.93, 0.000 142.890,1114.93, 0.000 1.00E+00 15 21 128.96,1132.97, 0.000 128.960,1132.97, 0.000 8.75E01 15 22 116.38,1149.26, 0.000 116.380,1149.26, 0.000 7.50E01 13 23 105.03,1163.96, 0.000 105.030,1163.96, 0.000 7.50E01 11 24 94.790,1177.22, 0.000 94.790,1177.22, 0.000 6.25E01 11 25 85.550,1189.20, 0.000 85.550,1189.20, 0.000 5.00E01 9 26 77.210,1200.00, 0.000 77.210,1200.00, 0.000 5.00E01 9 SOURCES Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type Seg. Actual (Specified) 1 5 26 / 50.00 ( 26 / 50.00) 1.000 0.000 V TRANSMISSION LINES Line Wire #/% From End 1 Wire #/% From End 1 Length Z0 Vel Rev/ Actual (Specified) Actual (Specified) Ohms Fact Norm 1 1/50.0 ( 1/50.0) 2/50.0 ( 2/50.0) Actual dist 150.0 1.00 R 2 2/50.0 ( 2/50.0) 3/50.0 ( 3/50.0) Actual dist 150.0 1.00 R 3 3/50.0 ( 3/50.0) 4/50.0 ( 4/50.0) Actual dist 150.0 1.00 R 4 4/50.0 ( 4/50.0) 5/50.0 ( 5/50.0) Actual dist 150.0 1.00 R 5 5/50.0 ( 5/50.0) 6/50.0 ( 6/50.0) Actual dist 150.0 1.00 R 6 6/50.0 ( 6/50.0) 7/50.0 ( 7/50.0) Actual dist 150.0 1.00 R 7 7/50.0 ( 7/50.0) 8/50.0 ( 8/50.0) Actual dist 150.0 1.00 R 8 8/50.0 ( 8/50.0) 9/50.0 ( 9/50.0) Actual dist 150.0 1.00 R 9 9/50.0 ( 9/50.0) 10/50.0 ( 10/50.0) Actual dist 150.0 1.00 R 10 10/50.0 ( 10/50.0) 11/50.0 ( 11/50.0) Actual dist 150.0 1.00 R 11 11/50.0 ( 11/50.0) 12/50.0 ( 12/50.0) Actual dist 150.0 1.00 R 12 12/50.0 ( 12/50.0) 13/50.0 ( 13/50.0) Actual dist 150.0 1.00 R 13 13/50.0 ( 13/50.0) 14/50.0 ( 14/50.0) Actual dist 150.0 1.00 R 14 14/50.0 ( 14/50.0) 15/50.0 ( 15/50.0) Actual dist 150.0 1.00 R 15 15/50.0 ( 15/50.0) 16/50.0 ( 16/50.0) Actual dist 150.0 1.00 R 16 16/50.0 ( 16/50.0) 17/50.0 ( 17/50.0) Actual dist 150.0 1.00 R 17 17/50.0 ( 17/50.0) 18/50.0 ( 18/50.0) Actual dist 150.0 1.00 R 18 18/50.0 ( 18/50.0) 19/50.0 ( 19/50.0) Actual dist 150.0 1.00 R 19 19/50.0 ( 19/50.0) 20/50.0 ( 20/50.0) Actual dist 150.0 1.00 R 20 20/50.0 ( 20/50.0) 21/50.0 ( 21/50.0) Actual dist 150.0 1.00 R 21 21/50.0 ( 21/50.0) 22/50.0 ( 22/50.0) Actual dist 150.0 1.00 R 22 22/50.0 ( 22/50.0) 23/50.0 ( 23/50.0) Actual dist 150.0 1.00 R 23 23/50.0 ( 23/50.0) 24/50.0 ( 24/50.0) Actual dist 150.0 1.00 R 24 24/50.0 ( 24/50.0) 25/50.0 ( 25/50.0) Actual dist 150.0 1.00 R 25 25/50.0 ( 25/50.0) 26/50.0 ( 26/50.0) Actual dist 150.0 1.00 R 26 1/50.0 ( 1/50.0) Short ckt (Short ck) 90.000 in 150.0 1.00 Ground type is Free Space

May/June 2000 37 100' 26-Element 3-30 MHz LPDA, “Tau-tapered” elements Frequency = 10 MHz. Wire Loss: Aluminum Resistivity = 4E08 ohmm, Rel. Perm. = 1

WIRES Wire Conn. End 1 (x,y,z : in) Conn. End 2 (x,y,z : in) Dia(in) Segs 1 1003.7, 0.000, 0.000 1003.68, 0.000, 0.000 6.50E+00 107 2 905.81,126.760, 0.000 905.810,126.760, 0.000 5.87E+00 97 3 817.49,241.170, 0.000 817.490,241.170, 0.000 5.30E+00 87 4 737.77,344.410, 0.000 737.770,344.410, 0.000 4.79E+00 79 5 655.83,437.590, 0.000 655.830,437.590, 0.000 4.32E+00 71 6 600.91,521.690, 0.000 600.910,521.690, 0.000 3.90E+00 65 7 542.31,597.580, 0.000 542.310,597.580, 0.000 3.52E+00 57 8 489.43,666.070, 0.000 489.430,666.070, 0.000 3.18E+00 53 9 441.71,727.890, 0.000 441.710,727.890, 0.000 2.87E+00 47 10 398.64,783.640, 0.000 398.640,783.640, 0.000 2.59E+00 43 11 359.76,834.020, 0.000 359.760,834.020, 0.000 2.34E+00 39 12 324.68,879.460, 0.000 324.680,879.460, 0.000 2.12E+00 35 13 293.02,920.470, 0.000 293.020,920.470, 0.000 1.91E+00 31 14 264.45,957.470, 0.000 264.450,957.470, 0.000 1.73E+00 29 15 238.66,990.870, 0.000 238.660,990.870, 0.000 1.56E+00 25 16 215.39,1021.01, 0.000 215.390,1021.01, 0.000 1.41E+00 23 17 194.39,1048.22, 0.000 194.390,1048.22, 0.000 1.27E+00 21 18 175.43,1072.77, 0.000 175.430,1072.77, 0.000 1.15E+00 19 19 158.33,1094.93, 0.000 158.330,1094.93, 0.000 1.04E+00 17 20 142.89,1114.93, 0.000 142.890,1114.93, 0.000 9.40E01 15 21 128.96,1132.97, 0.000 128.960,1132.97, 0.000 8.40E01 15 22 116.38,1149.26, 0.000 116.380,1149.26, 0.000 7.60E01 13 23 105.03,1163.96, 0.000 105.030,1163.96, 0.000 6.90E01 11 24 94.790,1177.22, 0.000 94.790,1177.22, 0.000 6.20E01 11 25 85.550,1189.20, 0.000 85.550,1189.20, 0.000 5.60E01 9 26 77.210,1200.00, 0.000 77.210,1200.00, 0.000 5.00E01 9 SOURCES Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type Seg. Actual (Specified) 1 5 26 / 50.00 ( 26 / 50.00) 1.000 0.000 V TRANSMISSION LINES Line Wire #/% From End 1 Wire #/% From End 1 Length Z0 Vel Rev/ Actual (Specified) Actual (Specified) Ohms Fact Norm 1 1/50.0 ( 1/50.0) 2/50.0 ( 2/50.0) Actual dist 150.0 1.00 R 2 2/50.0 ( 2/50.0) 3/50.0 ( 3/50.0) Actual dist 150.0 1.00 R 3 3/50.0 ( 3/50.0) 4/50.0 ( 4/50.0) Actual dist 150.0 1.00 R 4 4/50.0 ( 4/50.0) 5/50.0 ( 5/50.0) Actual dist 150.0 1.00 R 5 5/50.0 ( 5/50.0) 6/50.0 ( 6/50.0) Actual dist 150.0 1.00 R 6 6/50.0 ( 6/50.0) 7/50.0 ( 7/50.0) Actual dist 150.0 1.00 R 7 7/50.0 ( 7/50.0) 8/50.0 ( 8/50.0) Actual dist 150.0 1.00 R 8 8/50.0 ( 8/50.0) 9/50.0 ( 9/50.0) Actual dist 150.0 1.00 R 9 9/50.0 ( 9/50.0) 10/50.0 ( 10/50.0) Actual dist 150.0 1.00 R 10 10/50.0 ( 10/50.0) 11/50.0 ( 11/50.0) Actual dist 150.0 1.00 R 11 11/50.0 ( 11/50.0) 12/50.0 ( 12/50.0) Actual dist 150.0 1.00 R 12 12/50.0 ( 12/50.0) 13/50.0 ( 13/50.0) Actual dist 150.0 1.00 R 13 13/50.0 ( 13/50.0) 14/50.0 ( 14/50.0) Actual dist 150.0 1.00 R 14 14/50.0 ( 14/50.0) 15/50.0 ( 15/50.0) Actual dist 150.0 1.00 R 15 15/50.0 ( 15/50.0) 16/50.0 ( 16/50.0) Actual dist 150.0 1.00 R 16 16/50.0 ( 16/50.0) 17/50.0 ( 17/50.0) Actual dist 150.0 1.00 R 17 17/50.0 ( 17/50.0) 18/50.0 ( 18/50.0) Actual dist 150.0 1.00 R 18 18/50.0 ( 18/50.0) 19/50.0 ( 19/50.0) Actual dist 150.0 1.00 R 19 19/50.0 ( 19/50.0) 20/50.0 ( 20/50.0) Actual dist 150.0 1.00 R 20 20/50.0 ( 20/50.0) 21/50.0 ( 21/50.0) Actual dist 150.0 1.00 R 21 21/50.0 ( 21/50.0) 22/50.0 ( 22/50.0) Actual dist 150.0 1.00 R 22 22/50.0 ( 22/50.0) 23/50.0 ( 23/50.0) Actual dist 150.0 1.00 R 23 23/50.0 ( 23/50.0) 24/50.0 ( 24/50.0) Actual dist 150.0 1.00 R 24 24/50.0 ( 24/50.0) 25/50.0 ( 25/50.0) Actual dist 150.0 1.00 R 25 25/50.0 ( 25/50.0) 26/50.0 ( 26/50.0) Actual dist 150.0 1.00 R 26 1/50.0 ( 1/50.0) Short ckt (Short ck) 90.000 in 150.0 1.00 Ground type is Free Space

38 May/June 2000 The ATR-2000: A Homemade, High-Performance HF Transceiver, Pt 2

Part 2 describes the IF and audio sections, including IF amplifier, product detector/balanced modulator, RF compressor, AGC and PC-interface circuits.

By John B. Stephensen, KD6OZH

his article series describes my ahead of the main band-pass filter bringing the system noise figure down homebrew HF transceiver. Part should be minimized, so signals on to 16 dB. The 1-dB compression point is T1 described the general archi- adjacent frequencies do not cause reduced because of the additional gain. tecture and the front end, including serious intermodulation distortion It is determined primarily by the the synthesized local oscillator and (IMD). With the IF Preamplifier/Noise compression point of the IF preamp- BFO, mixer and RF band-pass filter.1 Gate module switched out, the ATR- lifier itself, which is +13 dBm at the This part describes the IF and audio 2000 has no gain ahead of the main output to the crystal filter. This is sections of the transceiver, inclu- crystal filter, but rather a loss of intentionally limited to prevent ding IF amplifier, product detector/ 12 dB. As described in Part 1 of this destruction of the crystals by strong balanced modulator, RF compressor, article, noise figure is 18-22 dB depen- signals. The receiver’s input compres- AGC and PC-interface circuits. ding on which filter is selected, and the sion point is therefore +14 dBm. 1-dB compression point is +23 dBm. When the incoming signal is within Dynamic-Range Considerations The mixer is not terminated in an the main filter bandwidth, the com- Gain distribution is an important ideal load, so we expect at least 3 dB of pression point is determined by the facet of transceiver design.2 Gain degradation for a +35 dBm third-order first few stages of the IF amplifier intercept point (IP3). when it is running at minimum gain. 1Notes appear on page 51. When the IF Preamplifier/Noise Gate This is the condition when a strong module is switched in, it adds 11 dB of signal is present and AGC is on. This 153 Gretna Green Wy gain, bringing total gain ahead of the transceiver uses the Analog Devices Los Angeles, CA 90049 main crystal filter up to –1 dB. The AD603 low-noise, 90-MHz variable- [email protected] noise figure of this module is 4 dB, gain amplifier. Its advantages include May/June 2000 39 a +13 dBm 1-dB input compression point and a gain reduction mechanism that does not reduce input signal- handling capability. A post-filter amp- lifier is included to maintain noise figure; it reduces the 1-dB input compression point to –1 dBm. A 4-dB loss in the SSB crystal filter and 12-dB loss in the front end result in a +15 dBm 1-dB compression point at the antenna terminals without the IF preamplifier, and +4 dBm with it. The resulting dynamic ranges for various input frequencies are shown in Table 1.

IF Preamplifier/ Noise Gate Module Fig 1 shows the IF preamplifier and noise-gate module. It consists of a diplexer, band-pass filter, low-noise amplifier and noise gate. The diplexer provides a termination for the mixer at the LO and image frequencies. The Q is low and insertion loss is 0.4 dB. When not in use, power is removed and K1 and K2 bypass all stages after the diplexer. Mechanical relays are used to ensure low IMD as this circuit precedes the main filter. The Omron relays are designed for RF use; they have more than 60 dB of isolation between contacts. At least 80 dB of isolation between input and output is required when the noise blanker is operating. When the preamplifier is in oper- ation, a two-pole monolithic crystal filter with a 15 kHz bandwidth filters incoming signals and noise. L1, L2 and associated capacitors provide trans- formation to and from 50 Ω. Because impedance of the KVG XF-910 mono- lithic crystal filter is very high (6000 Ω), two-thirds of the 1.5 dB loss in this circuit actually comes from the matching networks. High-Q toroidial coils are used to minimize the loss. Note that the filter bandwidth must be several times the information band- width (to ensure minimum spreading of pulses), but narrow enough to delay the arrival of noise pulses until after blanking is in effect. The amplifier consists of a Motorola MRF581 configured as a low-noise

Fig 1—IF preamplifier and noise gate. 1 Unless otherwise specified, use /4 W, 5%-tolerance carbon composition or film resistors. K1, K2—Omron G6Y-1 relay. L1, L2—43 turns #26 AWG on a T50-2 powdered-iron toroid core. T1—3 t #26 AWG primary, 1 t #24 AWG secondary on a BLN-43-2402 binocular ferrite core. T2, T3—6 t #24 AWG (trifilar) on an FT37-43 ferrite toroid core. 40 May/June 2000 amplifier with a 50-Ω input impedance PIN diodes are used in the circuit to junction capacitance of the PIN diodes. and 13 dB of gain. Unlike many other achieve a high attenuation when the This achieves 78 dB of attenuation. “noiseless feedback” circuits, this gate is off. The 22-pF capacitor reson- The circuit at Q2 is a time-delay particular circuit has the advantage of ates broadly with the inductance of the circuit. Normally, the 0.022-µF capac- providing high isolation between input two transformers at the IF. When the itor is charged through the 10-kΩ and output. The MRF581 is biased at gate is off, it provides shunt reactance resistor, causing the 4.7-V Zener diode 20 mA to provide a low noise figure; the to form an “H” attenuator with the and the MPS2222 transistor to con- resulting +13-dBm compression level provides some protection for the follow- ing crystal filters. The 510-Ω resistor in the collector circuit sets the output Table 1—Predicted Receiver Dynamic Range with 2.4 kHz bandwidth impedance of the amplifier at 50 Ω to Frequency Total Noise Receiver provide a proper termination for the Offset Figure 1-dB Compression IP3 Dynamic Range main crystal filters. Following the amplifier is the noise IF Preamplifier/Noise Gate out > 1.5 kHz 18 dB +23 dBm +35 dBm 104.7 dB gate. A balanced circuit is used to 0-1.5 kHz 18 dB +15 dBm — — minimize switching noise at the out- IF Preamplifier/Noise Gate in put. HP 5082-3081 PIN diodes are used > 10.0 kHz 16 dB +23 dBm +35 dBm 106.0 dB to minimize IMD and transient genera- 1.5-10.0 kHz 16 dB +14 dBm +29 dBm 102.0 dB 0-1.5 kHz 16 dB +4 dBm — — tion during turn-on and turn-off. Four

Fig 2—Crystal-filter selection and matching circuits. Only one relay control circuit is shown; the others are identical. Unless 1 otherwise specified, use /4 W, 5%-tolerance carbon composition or film resistors. FL1—KVG XF-9810, 2400 Hz bandwidth. FL3—KVG XF-9NB, 500 Hz bandwidth. L1, L2—19 t #24 AWG on a T50-6 FL2—International Radio 2308, 1800 Hz FL4—KVG XF-9P, 250 Hz bandwidth. powdered-iron toroid core. bandwidth. K1-K8—RS-241 SPDT relay, 12-V coil. May/June 2000 41 Fig 3

42 May/June 2000 duct, turning on the noise gate. When IF Amplifier however, was less than 1-dB from 16°C a noise pulse is detected, an external The IF amplifier is shown in Fig 3. to 38°C (room temperature) and was transistor discharges the capacitor. Independent circuits are used for trans- all concen-trated at the low end, where This turns off Q2 and the noise gate. mit and receive, with the signal flow there is little operational effect. The The time required to recharge the controlled by PIN-diode switches detector’s rise and fall times are capacitor ensures that the noise pulse (D1-D4) for low distortion. The first determined by the emitter resistance (stretched by the 15 kHz filter) has amplifier in the receiver IF strip and and C3 to be about 6 µs. The voltage ended before the noise gate is re- the last amplifier in the transmitter IF developed across R4 is buffered by Q4, enabled. strip are switched off when not in use an emitter follower, then applied to the by removal of the power-supply voltage. AGC pins of the IF amplifiers, U1 and Crystal Filters The receive path consists of a low- U2. The advantages of this detector The main crystal filter immediately noise amplifier followed by two vari- are that it responds to low-level sig- follows the IF preamplifier. This recei- able-gain amplifiers and an AGC detec- nals and that the output is logar- ver has four selectable filters with 250, tor. Q1 is a J310 FET in a common-gate ithmic—within 1 dB—over a range of 500, 1800 and 2400 Hz bandwidths for circuit with low-Q L networks for input input voltages from 70 mV (pk-pk) to PSK, FSK and SSB. (See Fig 2.) The and output matching. The circuit has a 250 mV (pk-pk). This results in a filters’ 500-Ω input and output impe- gain of 12 dB and brings the IF ampli- reasonably constant AGC loop gain dances are matched by two L-net- fier noise figure to 3 dB. A 3-MHz-wide and good transient response. works: C1/L1 and C2/L2. Since the Q series-tuned band-pass filter between Additional AGC filtering is provided is only three, these are fixed-tuned the two variable-gain amplifiers limits by R2, R3, C1 and C2, amounting to using 5%-tolerance components. Addi- the broadband noise at the AGC 50 kΩ of resistance and 0.2 µF of tional capacitors are placed near each detector. capacitance as seen from the emitter filter to provide the proper termin- U1 and U2 are Analog Devices AD603 follower. This provides a 6-µs attack ation. Some filters require a pure amplifiers having logarithmic gain and 10-ms exponential decay time for 500-Ω source and load impedance control. They are capable of handling the fast AGC. Any voltage from the while others require 15 or 30 pF of 3 V (pk-pk) input signal levels. Gain is slow AGC loop that is more than twice parallel capacitance.3 variable over a 40-dB range with 1 V of the fast AGC detector’s output will The filters are selected by mechan- control signal variation. The AGC override the output of Q4 and take ical relays with unused filter inputs voltage is applied differentially be- control of the IF amplifier gain. and outputs grounded to minimize tween pins 1 and 2 of each device; over The transmit path contains a vari- feed-through. Power for the relays is 80-dB of total gain variation is able-gain amplifier (U3) that drives the filtered to ensure that no coupling achieved. The network of 1% resistors ALC detector (Q5, Q6 and Q7) and a occurs via power leads or capacitance connected to pin 1 of each device biases fixed-gain amplifier (Q8). These to the solenoid coil. The filter-selec- them so that gain is controlled sequen- circuits amplify the SSB signal from the tion relays are controlled from the tially. R1 is adjusted to provide the product detector/balanced modulator PC-Interface module via four PNP correct bias voltages as shown in the module and compress it. The input to transistors Q1-Q4. This allows one schematic and compensates for any this module can range from –10 dBm to end of the relay coils to be grounded in variation in the voltage from U4. As the –58 dBm depending on the amount of order to minimize cross coupling via AGC voltage increases, the gain of U2 audio applied to the balanced modu- the power supply. is reduced from 30 dB to –10 dB before lator. The output is leveled to a ±4 dBm To preserve the stopband attenu- any reduction in the gain of U1. This range. ation characteristics of these filters, maximizes the signal-to-noise ratio of The ALC detector is identical to that good mechanical design is required. the IF strip. used in the receiver’s AGC detector. It Unwanted coupling between the filter Receive IF gain is controlled from two generates 0 to 4 V of ALC with a logar- input and output must be minimized. sources. The control voltage for the slow ithmic response. The ALC is applied to The filters are mounted directly to AGC loop is applied to the 2:1 voltage U3; it varies U3’s gain from +43 to the chassis with the input and output divider formed by R2, R3, C1 and C2, +3 dB as signal levels rise. This com- pins separated by a shield that parti- resulting in a 0-to-4-V AGC range. Note presses the transmitted signal by a factor tions the chassis into two compart- that there is no long time-constant of six or more, translating the original ments. I found that small aluminum associated with driving the divider 48-dB range to 8-dB. Most voices only boxes didn’t work here—they only gave since the capacitors balance each other. vary by 20 dB during normal speech. This 70 dB of isolation. An old-fashioned Q2 and Q3 form an envelope detector range is compressed to 3 dB and the rest 4×5×2-inch welded chassis with a for the fast AGC loop. Q2 acts as a of the control range compensates for bottom plate gave 90 dB of isolation, rectifier. It is cut off when the base variations in the dis-tance from the which doesn’t compromise the 80-dB voltage falls below the sum of the operator to the micro-phone. stopband attenuation of the narrow emitter voltage and base-emitter The ALC attack time is approx- SSB filter. barrier voltage. Q3 is a common-base imately 6 µs, but the release time is amplifier that provides dc gain and variable. The minimum of 1 dB/µs is Fig 3—There are separate IF amplifiers for receive (upper circuitry) and compensates for temperature varia- determined by C4 and R5. R5 provides transmit (lower circuitry) paths. Unless tions in Q2’s emitter-base voltage in a a constant discharge current of 1 otherwise specified, use /4 W, 5%- manner similar to a differential amp- approximately 0.5 mA. D5 prevents tolerance carbon composition or film lifier. The compensation is not perfect the ALC voltage from going below resistors. All capacitors are ±20% and RF chokes are ±10% tolerance unless because the currents through the two –0.6V. Since the ALC line is brought labeled otherwise. transistors are not identical. The out of the module, additional filter T1—8 t #28 AWG bifilar wound on an actual variation in detector gain, capacitors can be placed across the FT23-43 ferrite toroid core. May/June 2000 43 line to increase the time constant. The short time constant provides an action like an RF clipper, but with less in- band distortion. Intermediate time constants on the order of 2-5 dB/ms provide RF syllabic compression. Long time constants of 25-100 dB/s set the RF output to the correct level but do not modify the modulation. To limit the maximum gain and place background noises below the compress- ion range, the PC Interface module can set a minimum ALC voltage. It can also be used to eliminate the ALC action on normal audio levels, but ALC is left on all the time so that the power amplifier cannot be accidentally over-driven and generate splatter. The leveled signal at the output of U3 is amplified by Q8 and routed to the main crystal filter. This additional filtering is necessary to remove any out-of-band distortion products caused by rapid gain variations before trans- mission. It also provides additional carrier suppression when audio levels are low.

Product Detector/ Balanced Modulator This module was the most straight- forward to design. (See Fig 4.) The crystal filter and mixer are both bilateral and so are used for both SSB generation and detection. Q1 is an amplifier that increases the +4 dBm from the DDS BFO up to +10 dBm. This is a common-emitter amplifier with emitter degeneration to set the gain and a low-Q fixed-tuned L-network in the collector circuit for impedance matching. The BFO signal is attenuated 3 dB before application to the level-7 mixer (Z1). The received signal first passes through a crystal filter (FL1) to strip away excess noise from the wide-band IF strip and eliminate the audio image. This filter need not have tremendous selectivity. I used a five-pole, 2.5-kHz- bandwidth filter from KVG, which has a minimum stopband attenuation of 50 dB. (This is about the minimum required.) Combined with the 80-dB minimum stopband attenuation of the filters ahead of the IF amplifier, at least 130 dB of attenuation is presented to out-of-band signals. This is the mini- mum necessary for a receiver with 120 dB of AGC range. Two L networks, C1/L1 and C2/L2, provide impedance matching. If an International-Radio

Fig 4—Product detector/balanced modulator circuit. Unless otherwise 1 specified, use /4 W, 5%-tolerance carbon composition or film resistors. 44 May/June 2000 1 Fig 5—AF filter schematic diagram. Unless otherwise specified, use /4 W, 5%-tolerance carbon composition or film resistors. All capacitors are ±5% tolerance mylar components. K1-K5—Reed relay, SPST, 12-V dc coil. L1-L6—88 mH toroid inductor, center tapped. filter is substituted, C1 and C2 must be of 3 kHz. R3 establishes the output DBM through R1 and R2, which form a reduced to 100 pF each. impedance. The voltage gain through matching network and attenuator. The double-balanced mixer (DBM) the amplifier and filter is 40 dB. The maximum audio input of 10 V (pk- that follows the filter is used as the Transmit audio is applied to the pk) results in +3 dBm at the IF port of product detector. Since the IF level at this point is –77 to –37 dBm, low IMD is assured. The DBM is followed by L3, C3 and R4, which form a diplexer with a 6-kHz transition frequency. This is followed by a relay to switch between incoming transmitter audio and the receive audio-amplifier chain. While receiving, a low-noise audio amplifier follows the relay. L4 provides a dc return for the DBM and forms a 220-Hz high-pass diplexer with C4. Q2 is used as a common-base amplifier and is biased to have a 50-Ω input impe- dance. An operational amplifier, U1A, configured as a voltage follower, buffers the output. This is followed by U1B, configured as a low-pass filter to atten- uate high-frequency audio hiss. The filter is a three-pole Chebyshev with 0.5 dB of ripple and a cutoff frequency Fig 6—AF filter attenuation (S21) and return loss (S11). May/June 2000 45 Fig 7

46 May/June 2000 1 Fig 8—PC interface schematic diagram. Unless otherwise specified, use /4 W, 5%-tolerance carbon composition or film resistors. J1-J3—Molex plug, 0.1-inch spacing in Y1—7.3728 MHz crystal, 20 pF parallel line. resonant.

Z1. This signal level should result in Audio Filtering increase ultimate attenuation. IMD of –36 dBm or less; the audio level Audio filters may be used more The filters use 88-mH toroidal is usually much lower and results in effectively here than in other designs inductors4 with capacitive coupling to less IMD. Z1 has a minimum LO/RF because the IF-amplifier gain is minimize the type and number of isolation of 50 dB and provides ade- relatively low, the audio image has inductors. (See Fig 5.) The PSK filter quate carrier suppression without been stripped by the tail-end filter and is 270 Hz wide at –3 dB and is centered adjustment. FL1 suppresses the un- the main AGC loop uses an audio on 1000 Hz. The RTTY filter is 460 Hz wanted sideband before speech detector. The narrow-band crystal wide at –3 dB and centered on 1360 Hz processing. filters have 4:1 shape factors and 90 dB for use with a demodulator using 1275/ ultimate attenuation, so relatively 1445 Hz tones. Fig 6 shows both the Fig 7—AF amplifier/AGC schematic little filtering is needed. The main PSK and RTTY filter characteristics. diagram. Unless otherwise specified, 1 use /4 W, 5%-tolerance carbon purpose is to remove IF amplifier noise When the filters are not in use, a composition or film resistors. outside the crystal-filter passband and 1200-Ω resistor provides 6 dB of May/June 2000 47 attenuation to compensate for the lower loss of the SSB filters in the IF. AF Amplifier and AGC Fig 7 shows the AF amplifier and AGC circuitry. U1 amplifies the re- ceived audio signal by 17 dB to present the proper levels to the variable-gain audio amplifier. Connected to the out- put of U1 is U3, an Analog Devices AD307 logarithmic amplifier. U3 and U4A are used as the AF AGC detector. R2 sets the slope to –100 mV/dB and R1 sets the power level at which the output is zero. This level is set to –107 dBm or 1 µV RMS at the antenna terminals with the noise blanker by- passed. This is 5 dB above the minimum noise level. The upper end of the AGC range is 1 V RMS. The IF AGC detector was designed to give a slightly lower AGC voltage with the same input signal level, so the amount of adjustment required by the slower audio-derived AGC is minimal. However, the audio AGC provides the final, more-accurate control that is reflected by the S-meter. The AD8307 and AD603 are each accurate to ±1 dB over the operating temperature range. The meter reading 1 is accurate to ±2 dB or /3 S-unit. U4B and D1 form a gate that charges the AGC filters to the peak negative level of the detector output. Two AGC filters are provided. A slow filter drives the IF amplifier AGC line. The IF amplifier gain cannot be ad- 1 justed rapidly because of delay in the Fig 9—Transceiver control circuits. Unless otherwise specified, use /4 W, 5%- crystal filter preceding the product tolerance carbon composition or film resistors. detector. A fast filter is used to develop K1, K2—Reed relay, SPST, 12 V dc coil. P2, P3—Molex plug, 0.1-inch spacing in line. AGC for the variable-gain AF amp- lifier. The fast and slow AGC voltages are compared and the most negative by R4 and R5 to 10 ms for the slow AGC gain slope and logarithmic-amplifier voltage is applied to the amplifier. The voltage and 50 µs for the fast AGC accuracy to ensure that an AGC- fast AGC voltage compensates for voltage. The attack and release times detector signal increase never results excess IF amplifier gain during trans- are somewhat critical for good SSB in a decrease in audio level. ient conditions by decreasing AF reception. I spent two days tuning these U7 provides the “hang” AGC func- amplifier gain. time constants for rejection of impulse tion that causes rapid gain increase if The circuit is somewhat complex. R3 noise and for minimum audio distor- a signal is lost completely for more provides a constant-current discharge tion. than the “hold” time. U7A discharges path for the slow and fast filter U5A is a voltage follower to isolate C4 through D7 whenever the audio capacitors, C1 and C2. The resulting the holding capacitor. U5B inverts the output is greater than 100 mV. This decay times produce a gain increase of AGC voltage for application to the IF causes the output of U7B to go 20 dB/s for the slow AGC voltage and 4 amplifier. U6, D6 and D7 comprise a negative. C4 is charged through dB/ms for the fast AGC voltage. This gate to select either the fast or slow R9 so that after 500 ms, U7B’s output allows tracking of fading signals. The AGC voltage for application to U2, will go positive. This causes C1 to be fast AGC voltage is offset by +0.65 V which provides an adjustable gain of discharged through D8 and R10, from the slow AGC voltage by D2 –10 to +30 dB. Note that R6 and C3 increasing the gain at a rate of through D4, so that audio peaks must provide 20 dB of attenuation and 400 dB/s. This allows full gain to be be 6.5 dB higher than the average level transform the 100-Ω input impedance achieved within a short time after the to affect audio gain. This eliminates of U2 to 1000 Ω. R7 and R8 convert the disappearance of very strong signals, excess pumping of the AGC by audio 0-4 V AGC signal to 0-0.97 V to control rather than having to wait up to six peaks, but allows fast response to audio gain. A 40-dB increase in signal seconds at the normal 20 dB/s rate. It transients at the beginning of a at the AGC detector results in a 37-dB is not really needed on signals below transmission. D5 clamps the no-signal reduction in gain. The 3-dB increase S9, but it helps when strong local voltage to +0.4 V. Attack times are set is left to compensate for variations in signals are present. 48 May/June 2000 PC Interface conversion slope is 1 bit/0.5 dB of recei- After a time delay for the TR relay to The entire radio is controlled from a ver gain. U3 contains four 6-bit digital- settle, it switches in the transmit IF personal computer. The method of to-analog converters (DACs) that are amplifier and compressor, waits for controlling the DDS was described in used to control IF gain, RF clipping transients die out, then ramps the IF Part 1, but there are several functions level and noise-blanker gain. One DAC amplifier gain up to the desired clipping still left: filter switching, transmit RF is unused. J2 connects the DACs and level. The reverse sequence is executed compressor control, IF gain control and ADC to the rest of the transceiver. on receipt of the command to go to the TR switching. These are controlled by a U4 is a CMOS shift register and latch receive mode. Table 2 lists other inter- second microprocessor (MCU) as shown used as a parallel output port. Eight nal transceiver control lines. in Fig 8. Darlington transistors, contained in The MCU, U1, is another PIC16F84 U5, buffer the output of U4. The out- Test Results: AGC System with the same UART software as puts are open-collector and are con- Several performance parameters of described in Part 1. Q1, D1 and asso- nected via J3 to the circuit shown in the transceiver were tested on the ciated resistors form the EIA-232 Fig 9 to control power to the noise bench as described below. Dynamic receiver, whose input is wired in blanker, transmit and receive sections AGC response was tested using a parallel with the receiver in the DDS of the transceiver and the filter- pulsed signal at various levels from –60 circuit. Both MCUs receive the same selection relays. to +10 dBm with a 10-s period. There commands but only one executes each The commands used to control the was no overshoot on the AGC voltage command. U1 recognizes only the receiver are shown in Fig 10. They applied to the IF amplifier. Overshoot commands in Fig 9. have the structure defined in Part 1. of the audio output never exceeded 7 dB Unlike the DDS-control MCU, this In the case of commands involving the of the final value and undershoot was MCU can also send responses to the DACs, the command contains a data about 3 dB maximum. Stabilization of PC. Q2, Q3, D2 and associated resis- byte with a six-bit value that is output the output level occurred within 30 ms. tors form the EIA-232 driver. This to the appropriate device. The filter- The AGC system was also tested for driver is designed to have its output selection command uses four bits to linearity. Table 3 shows the measured wired in parallel with other similar control the filter-selection relays. response of the receiver to a CW carrier units to allow sharing of one PC serial Other commands have no data field. with the IF preamplifier out of circuit. port among multiple radios. The driver The response to an AGC Request The signal levels decrease by 11 dB sources 20 mA when sending a zero command contains the eight-bit digi- when it is switched in. However, the and is completely inert when sending tized value of the IF AGC line. software displaying the signal strength a one. To pull the line to a negative Note that the transmit/receive can easily compensate for this. voltage (one) when no MCU is sending timing is controlled by the MCU. When The AGC detector slope and inter- data, the output is terminated near the a transmit command is received, the cept were adjusted using 1-µV and 1-V PC with a 1500-Ω pull-down resistor to MCU mutes the receiver, switches out signals from a HP 8640B signal gener- a –12 V supply. The diode, D2, in the receive audio stages and the receive ator. The generator’s output is accurate combination with the base-collector IF amplifiers and enables the TR relay. to within ±1.5 dB and the voltmeter is junction of Q3, ensures that the driver will not source or sink current when power is removed. This allows one or more radios to be turned off while Table 3—IF Amplifier AGC Response controlling others from the PC. Bits 1, 2 and 3 of MCU port A are Signal Signal AF AGC IF AGC AF AGC IF AGC AFÐIF used to select the peripheral chips AGC (µV RMS) (dBm) (V dc) (V dc) (dB) (dB) (dB) being read or written to by the MCU. 1,000,000 +13 3.99 1.92 Ð78.8 Ð76.8 2.0 Data are written to the selected chip 316,000 +3 3.62 1.68 Ð72.4 Ð67.2 5.2 by shifting the data using bit 3 of MCU 100,000 Ð7 3.28 1.44 Ð65.6 Ð57.6 8.0 31,600 Ð17 2.96 1.22 Ð59.2 Ð48.8 10.4 port B as the clock, and bit 2 as data- 10,000 Ð27 2.63 0.98 Ð52.6 Ð39.2 13.4 output pin. Data are read by shifting 3,160 Ð37 2.29 0.75 Ð45.8 Ð30.0 15.8 them into the MCU using bit 3 as the 1,000 Ð47 1.99 0.52 Ð39.8 Ð20.8 19.0 316 Ð57 1.64 0.31 Ð32.8 Ð12.4 20.4 clock and bit 1 as the data-input pin. 100 Ð67 1.31 0.10 Ð26.2 Ð4.0 22.2 U2 is an 8-bit analog-to-digital 32 Ð77 0.98 0.01 Ð19.6 Ð0.4 19.2 converter (ADC) that is used to sample 10 Ð87 0.65 0.00 Ð13.0 0.0 13.0 3 Ð97 0.34 0.00 Ð6.8 0.0 6.8 the AGC input to the IF amplifier. R2 1 Ð107 0.00 0.00 0.0 0.0 0.0 sets the reference voltage so that the

Table 2—Transceiver Control Lines Table 4—RF Compressor Table 5—RF Compressor Pin Digital Pin Analog Characteristics Characteristics 1 Qa RX 9 Ground Input Level ALC Output Level ALC 2 Qb TX 10 Q4 Compressor (dBm) (V) (dBm) Filter Capacitor Time Constant IMD 3 Qc TR Relay 11 Q3 AGC (I/O) Ð10 4.00 +2.5 (µF) (dB/ms) (dBc) 4 Qd ALC Select 12 (No Connection) Ð20 3.21 +0.5 47 0.1 <Ð40 5 Qe 250 13 Q2 Blanker Ð30 2.39 Ð1.0 6.8 0.7 Ð35 6 Qf 500 14 Q1 Ð40 1.55 Ð2.5 3.3 1.5 Ð30 7 Qg 1800 15 Ground Ð50 0.72 Ð4.0 1.0 5 Ð21 8 Qh 2400 Ð58 0.00 Ð6.0 none 1000 Ð12

May/June 2000 49 accurate to within 0.5% or ±0.6 dB. The were made with 2400-Hz and 250-Hz ing. The output from the combiner was transceiver was then operated for three bandwidths on both sides of the test 2.5 dBm/tone and a 25-kHz spacing days and the response measured. The signal and the results are shown in was used. The amplitude of spurious maximum deviation of the AGC voltage Table 6. The possible measurement responses was read from the digital from the ideal response of 33 mV/dB error in the test setup is ±3 dB. S-meter in the transceiver control was +0.01/–0.05 V or +0.3/–1.5 dB. This No spurs were noted at ±36 kHz program. Readings taken from both is within the error range of the from the signal, so the reference sides of the tones were averaged. measurement equipment. frequency component of the PLL error The dynamic range looks slightly When the AGC value was read from voltage is adequately suppressed. The greater than expected because the noise the PC, the displayed value was spurious components at ±10 kHz and figure of the IF preamplifier is lower accurate within ±1 dB for all but the ±20 kHz are less than 50 Hz in width than expected in one case, the IP3 higher extreme upper end of the range, above and are probably generated by other than expected in another case. However, 0.5 V of input signal. The maximum equipment in close proximity rather these measurements are only accurate excursion was 2 dB at 1 V of RF input. than the transceiver under test. The to ±2 dB. To compare the third-order phase noise is within predicted limits dynamic range with measurements RF Compression except for the area below 1500 Hz, made by the ARRL standard method, a The RF compression range was first where it is at least 2-3 dB higher than small correction5 must be applied. IF tested by injecting a 9-MHz CW signal anticipated, but certainly acceptable and image rejection are more than into the IF amplifier module and mea- for normal use. adequate and LO leakage to the antenna suring the output level on a HP 8555A/ is essentially nonexistent. A measure- 8552B spectrum analyzer. The results Receiver Dynamic Range ment summary is presented in Table 7. are shown in Table 4. They met ex- Receiver dynamic range was evalu- pectations. ated by measuring the minimum Conclusions Distortion of the transmitted signal discernable signal (MDS) and the third- Almost all low-level stages of the was also measured with various time order intercept (IP3). An HP 8640 transceiver worked as anticipated constants for the ALC. A two-tone audio signal generator was used to generate a when completed. Two areas, however, signal generator (700 and 1700 Hz signal for measuring the MDS and the required changes during testing. The tones at 0 dBm/600 Ω per tone) drove level required for a 3-dB increase of original design for this transceiver used the balanced modulator and the output audio output in a 2.4 kHz bandwidth RF clipping, but on-the-air tests yielded was checked with a spectrum analyzer. was measured. In addition, 9 MHz and reports of excessive audio distortion The results are shown in Table 5. 32.2 MHz signals were generated to when clipping exceeded 5 dB. Conse- Only one IMD product (2700 Hz) measure IF and image rejection. quently, clipping was abandoned as a passes through the final crystal filter, Two of the low-noise crystal oscill- method for RF compression, which so the IMD levels are measured by ators described in Part 1 were used resulted in much cleaner audio. From referencing that tone to the 1700 Hz with a hybrid combiner for IMD test- reports by other stations, two types of tone. No other IMD products could be found above –60 dBc, which was the limit of measurement. Byte 1 Byte 2 Bytes 2 Byte 3 Byte 4 Command LO Phase Noise STX B Bits 0-3 ETX LRC Select IF filter LO phase noise was measured by STX G 0-63 ETX LRC Set IF Gain STX C 0-63 ETX LRC Set RF clipping level connecting a low-noise crystal oscill- STX Z 0-63 ETX LRC Set noise receiver gain (0=off) ator (described in Part 1) at the antenna STX S ETX LRC Request AGC voltage terminals and measuring the amp- s 0-255 AGC voltage (response) STX X ETX LRC Go to transmit mode litude of noise sidebands surrounding STX N ETX LRC Go to receive mode it on the digital S-meter in the trans- ceiver control program. Measurements Fig 10—Transceiver control command strings.

Table 6—Measured LO Phase Noise Table 7—Measured Receiver Characteristics with 2.4 kHz IF bandwidth Phase Noise IF Preamp. On IF Preamp. On IF Preamp. Off Offset Expected Measured Measurement (0 dB Attn) (3 dB Attn) (3 dB Attn) (Hz) (dBc/Hz) (dBc/Hz) Third Order Intercept (IP3) 32.8 dBm 35.0 dBm 37.0 dBm 0.5 k Ð104 Ð99 Minimum Discernable Signal (MDS) Ð128 dBm Ð125.5 dBm Ð122.0 dBm 1 k Ð113 Ð109 Noise Figure 12.0 dB 14.5 dB 18.0 dB 1.5 k Ð117 Ð116 Spurious Free Dynamic Range 107.2 dB 107.0 dB 106.0 dB 2 k Ð122 Ð119 LO Leakage < Ð85.0 dBm Ð < Ð85.0 dBm 3 k Ð126 Ð128 Image Rejection Ð104.0 dB Ð Ð108.0 dB 4 k Ð131 Ð137 IF Rejection Ð92.0 dB Ð Ð92.0 dB 5 k Ð133 Ð140 7 k Ð137 <Ð140 10 k Ð141 Ð140* 15 k Ð145 <Ð140 20 k Ð150 Ð147* 25 k Ð152 <Ð153 *Narrow-band spur

50 May/June 2000 compression seem to be desirable. A me- (30 or 24 pF) must be removed from the Most recently, he was Vice President of dium ALC time constant (1.5 dB/ms) for circuit. Technology at ISOCOR, which develops 4 syllabic compression results in low dis- These were obtained from surplus tele- messaging and directory software for phone loading coils. An alternative is to tortion on good paths and better read- wind an inductor on a ferrite pot core. 155 commercial users and ISPs. John re- ability than long time constants. Under turns of #28 AWG enameled wire on an ceived his Amateur Radio license in marginal conditions, the fastest possible Amidon PC-2213-77 core provides 88 mH. 1993 and has been active on the ama- ALC time makes signals readable where 5The dynamic range should be about 4.7 dB teur bands from 28 MHz through syllabic compression is ineffective. greater with a 500 Hz bandwidth. 24 GHz. His interests include designing The other problem area was the and building Amateur Radio gear, digi- mixer. Although most literature indi- John Stephensen, KD6OZH, has been tal and analog amateur satellites, VHF cates that the IF port must see a interested in radio communications and microwave contesting and 10-meter broadband 50-Ω load for low IMD, it since building a crystal radio kit at age DX. His home station is almost entirely was found that the RF port is actually 11. He went on to study Electronic homebuilt and supports operation on more sensitive to termination in a high- Engineering at the University of Cali- SSB, PSK31, RTTY and analog and level DBM. The RF band-pass filter fornia and has worked in the computer digital satellites in the 28, 50, 144, 222, described in Part 1 and the IF diplexer industry for 26 years. He was a co- 420, 1240, 2300, 5650 and 10,000 MHz described here were necessary to cure founder of Polymorphic Systems, a PC bands from Grid Square DM04 in Los an initial 15-dB deficit in IP3. manufacturer, in 1975 and a cofounder Angeles. The mobile station includes The low noise figure and high dynamic of Retix, a communications-software 10-meter SSB, 144/440-MHz FM and range (with the 3-dB IF attenuator and hardware manufacturer, in 1986. 24-GHz SSB. removed) are useful on the 10-meter band where any RF amplifier would degrade the dynamic range. Atmospheric noise on this band still exceeds the noise figure by project neatly exploits transmission-line 6 dB or more. Next Issue in theory to achieve its dual-band aspect. The next part of this series will cover QEX/Communications Quarterly Come take a spin around the impedance the linear amplifier, noise blanker and chart with us and boost your signals. power supply. Add synthesis and computer control to L. B. Cebik continues his series on your HW-101 or other older rig! Rick Notes 1John Stephensen, KD6OZH, “The ATR- LPDAs with a look at some slightly Peterson, WA6NUT, brings us a PLL 2000: A Homemade, High-Performance larger arrays (164-foot booms). L. B. “spur eliminator.” It’s a PLL you can HF Transceiver, Pt 1” QEX, Mar/Apr 2000, explores tweaking and optimization of drive with your PC-controlled DDS to pp 3-15. design parameters with as many as 42 reduce or eliminate spurs outside the loop 2 Ulrich L. Rohde and T. T. N. Bucher, Com- elements. Segmentation limi-tations bandwidth. The PLL’s VCO output is munications Receivers—Principles and imposed by software and computing used to drive a transceiver’s BFO or LO Design, McGraw Hill, 1988. 3KVG filters are no longer distributed in this power are addressed. This is serious input. Remote control also creates some country. Similar filters are available from stuff for those of you interested in HF interesting possibilities for the International Radio, 13620 Tyee Rd, gain that spans more than an octave of experimenter. In the first part of a series, Umpqua, OR 97486; tel 541-459-5623 (9 frequency. Do you have a few acres Sam Ulbing, N4UAU, presents some AM-1 PM PDT, Tues-Sat), fax 541-459- lying fallow? work he has done to control his rigs over 5632; e-mail [email protected]; http:// Paul Hewitt, WD7S, gives you UHF links. He uses off-the-shelf UHF www.qth.com/inrad/. Suitable substi- tutes are part numbers 2301 (250 Hz), something to drive your six- and two- transceivers and explains the difference 2302 (500 Hz) and 2310 (2400 Hz). In all meter arrays: A no-bandswitch, dual- between Part-97 auxiliary operation and cases, the extra termination capacitors band, legal-limit linear amplifier. This Part-15 operation.

May/June 2000 51 RF

By Zack Lau, W1VT

A No-Tune 10 GHz Filter transmit could be as much as 6 dB, if Over the past decade, it has been a your system is limited by PEP, rather tough engineering challenge to design a than average, power. The two mixing no-tune 10 GHz filter with a band-width products will add coherently, result- narrow enough for a high-performance, ing in a 6-dB, instead of 3-dB increase single-conversion 144 MHz IF transver- in peak power. The situation is even ter. A no-tune design would make home worse if there is significant LO construction much easier for those with- feedthrough. This can be a problem out expensive test equipment. It would with harmonic antiparallel mixers, as also enhance reliability, as there would well as balanced mixers used outside be no adjustments to be jarred out of their optimum frequency range. I’d alignment. This is quite important for No-Tune WR-75 10 GHz bandpass filter recommend at least 20 dB of image mast-mounted transverters—the top of a rejection on receive and 40 dB for tower on a windy day is a poor environ- transmit. ment for delicate circuitry. The image is separated from the pass- Here’s a rough rule of thumb for The first step to the solution is band by twice the IF, 288 MHz away. calculating the bandwidth: First, establishing the required bandwidth. It is important to filter out the image realize that for each resonator, the for receiving—failing to remove it can attenuation increases by 6 dB for each degrade receiver sensitivity by as octave or 20 dB for each decade from 225 Main St much as 3 dB. Similarly, transmitting the cutoff frequency. For a band-pass Newington, CT 06111-1494 the image degrades your effective filter, the cutoff frequency is half the [email protected] transmit power. The reduction on bandwidth. Suppose you need a LO 52 May/June 2000 attenuation of 20 dB. You could use a quency would move from the center of ing tolerance for a 90-MHz-wide filter single resonator at one-tenth the the passband to the –3-dB cutoff point. to be practical at 10 GHz. Thus, bandwidth or three resonators, each I wouldn’t use this approximation 10 GHz microstrip transverters typi- with a little less than half the band- for calculating filter attenuation close cally have a first IF at 1.2 or 1.3 GHz. width. For instance, most people to the passband; the type of filter Amateurs in the US, however, typi- prefer a LO 144 MHz lower than the response becomes important. A cally prefer 144 MHz for the IF, neces- operating frequency. For a single Chebyshev filter with lots of ripple sitating another frequency conver- tuned resonator, such as a pipe cap, will have a steeper response than sion. Nonetheless, most amateurs the bandwidth ought to be 29 MHz. Butterworth or Bessel filters. It won’t prefer the simplicity of single conver- For a three resonator filter, a band- work far from the passband either— sion. In addition, some mixers, such as width of 144 MHz would have 18 dB of the stray coupling around the filter “rat-race” balanced mixers using sec- l LO attenuation. becomes more of a factor. For instance tions of /4 λ transmission lines, oper- Alternately, this can be written as with no-tune filters on printed circuit ate optimally when the RF and LO fre- boards, the maximum attenuation quencies are close together.  2 × ∆f  ××   20n log  (Eq 1) might be as low as 50 dB. The filter My choice for this difficult task is BW elements radiate, and thus couple the waveguide, which has very little loss. where n is the number of filter resona- input and output circuits through the More importantly, surplus waveguide tors, ∆f is the difference between the air. Thus, a calculation of 70 dB is is sometimes available at reasonable center frequency and frequency of in- meaningless, although the filter has cost. Surplus waveguide is often made terest, and BW is the filter bandwidth. five perfectly tuned resonators. to very close tolerances, allowing Thus, 140 MHz away from the center Microstrip filters are commonly simple filters to be made with rela- of a 90-MHz-wide three-resonator fil- used at lower frequencies, but there is tively simple machining operations. A ter, one calculates an attenuation of just too much loss and too little etch- post-type waveguide filter can be 30 dB. This corresponds well to a mea- sured value of 33 dB. A second set of measurements on the same filter— with isolators at both ends—resulted in measured bandwidth of 95 MHz and 28 dB of attenuation at 137 MHz off- set, the same as the calculated value. It may be more convenient, how- ever, to know the required bandwidth, given the desired frequency offset and number of resonators. 2 × ∆f BW = attn (Eq 2) × 10 20 n Thus, for 30 dB of attenuation at an offset of 144 MHz with a three-pole fil- ter, the bandwidth is 91 MHz. A nar- rower filter would result in even more attenuation, at the expense of higher loss and tighter construction toler- ances. Scaling all dimensions by just

0.43% would move the filter 45 MHz, 1 Fig 1—Construction details of the WR-75 filter. Posts 1 and 4 are /16-inch brass rod. 3 increasing the loss at 10368 MHz by Posts 2 and 3 are /16-inch brass tubing; the wall thickness isn’t important. The 3 dB. Theoretically, the desired fre- waveguide is 4.8 inches of WR-75.

Fig 2—Block diagram of a 10 GHz transverter using a circulator and surplus parts. The power levels in dBm are typical transmit levels. May/June 2000 53 made by accurately drilling holes and use four posts to divide the waveguide modification of the post size, so with soldering in standard size brass tub- into three resonators. With WR-90, re- care one can use standard sizes. Using ing sections to separate the waveguide ducing the spacing by 6 mils increases standard size tubing and drill sizes into tuned resonators. The post spac- the frequency 50 MHz, while a 10 mil will greatly simplify construction. ing determines the resonant fre- (0.01 inch) reduction is required to quency of the sections, and the tubing similarly move a WR-75 filter. Still, Construction size determines the coupling between this does require rather precise drill- A drawing of the precise hole loca- the sections. Brass rod is also useable, ing. I used a Sherline milling machine tions in WR-75 waveguide is shown in although thick brass rod may be more to make the accurately spaced holes.1 I Fig 1. The goal is to space the holes difficult to solder. rely on the accuracy of the lead screw to along a centerline as accurately as pos- It is important that as a waveguide measure the distance between holes. sible, preferably with a tolerance of a approaches cutoff, the guide wave- The dimensions were obtained us- few mils (thousandths of an inch). For- length increases. Thus, as we more ing WGFIL.COM, a DOS waveguide- tunately, this isn’t too difficult, if one is closely approach cutoff, guide sections filter synthesis program developed by reasonably skilled in using machine- must be longer to form resonant cavi- Dennis Sweeney, WA4LPR. It is avail- shop equipment. If such equipment ties at the desired frequency. This is able for non-commercial use at http:/ isn’t available, it may make more sense quite useful for reducing the required /www.cwt.vt.edu:3204/. It was origi- to build a tuned filter that allows for accuracy in machining the filter. nally described in the Proceedings of greater errors in fabrication. Typically, Thus, I discovered that making a fil- the ’89 Microwave Update and allows the spacings are reduced slightly to ter out of WR-75 is much easier than the user to design a post or aperture- increase the resonant frequencies. Tun- making one out of WR-90, due to the coupled waveguide filter with ing screws adjust the frequencies relaxed tolerances. Butterworth, Chebyshev or Equal El- downward. Table 1 shows the dimensions of simi- ement responses.2 It allows some As pointed out by Glen Elmore, lar filters for WR-90 and WR-75 for dif- N6GN, it is very important to center the ferent center frequencies. Both filters 1Notes appear on page 55. posts in the waveguide.3 I find this easy to do by scribing a line using either side of the waveguide as a reference, and then splitting the difference between the two lines. By using the exact same scribing technique with both lines, the errors tend to cancel, resulting in a very

Fig 3—The use of an index block with a squared surface preserves milling-machine Fig 4—Homebrew WR-75 flanges made accuracy despite the imperfect waveguide end when the waveguide is flipped over from 0.032-inch-thick brass sheet. to drill matching holes on the opposite side.

Table 1—Calculated Waveguide Filter Dimensions (inches) Waveguide 90 MHz BW WR-75 Butterworth BPF 90 MHz BW WR-90 Butterworth BPF Center Frequency (MHz) 10318 10368 10418 10318 10368 10418 waveguide dimension h 0.75 0.75 0.75 0.90 0.90 0.90 waveguide dimension e 0.375 0.375 0.375 0.40 0.40 0.40 post 1 diameter 0.0625 0.0625 0.0625 0.125 0.125 0.125 1st to 2nd post spacing 0.893 0.883 0.873 0.822 0.816 0.810 post 2 diameter 0.188 0.188 0.188 0.281 0.281 0.281 2nd to 3rd post spacing 0.986 0.976 0.966 0.926 0.919 0.913 post 3 diameter 0.188 0.188 0.188 0.281 0.281 0.281 3rd to 4th post spacing 0.893 0.883 0.873 0.822 0.816 0.810 post 4 diameter 0.0625 0.0625 0.0625 0.125 0.125 0.125

54 May/June 2000 accurate indication of the centerline. if a hybrid or splitter were used. This Table 2—Frequency Response of To insure accurate holes, I used a may not be a problem—low-level gain the 10 GHz Waveguide Bandpass center drill exclusively to start the is relatively easy to get these days. This 3 Filter holes. A #1 center bit has a /64-inch was much more of a concern 10 years 1 drill and a /8-inch body. Naturally, f (MHz) Insertion loss (dB) ago, when each 9 dB of gain required 1 10031 51 drilling the /16 holes on the bottom of an expensive FET transistor. Not only 10130 43 the waveguide was a little bit of a chal- 10150 41 are FETs much cheaper now, but there lenge, since the center drill is too large 10166 39 are also useable MMICs. There is quite to go through the waveguide. I chose 10190 36 a demand for LO bricks, but they do 10210 33 to use the center drill to mark the two 10220 31 show up at flea markets occasionally. 3 1 /16-inch bottom holes. The /8-inch drill 10228 30 Get there early, 10 GHz LO bricks are 3 body easily fit through the /16-inch top 10238 28 popular with dealers for resale. 3 10258 24 holes. These /64-inch center-drill holes 10278 19 Here’s an easy way to obtain a circu- were used to index the other two holes. 10298 12.4 lator with a WR-75 flange and two I then removed the waveguide from 10318 4.6 SMA connectors: Modify an isolator. 10323 2.9 the milling vise and scribed lines to 10328 1.6 WR-75 isolators seem a lot more com- mark the locations of all four holes. I 10333 1.0 mon than transitions or circulators. 1 don’t recommend pushing a /16-inch 10338 1.0 While some people have converted iso- drill bit through the waveguide to drill 10343 1.1 lators into coaxial-to-waveguide tran- 10348 1.6 both the top and bottom holes. Ordi- 10353 1.8 sitions, I chose to replace the coaxial nary drill bits wander around when 10358 1.8 50 Ω termination with a coax connec- starting holes—this is no way to drill 10363 2.1 tor, creating a circulator. I’ve used a 10368 2.1 precision holes. 10373 2.2 female SMA connector with a replace- This procedure is a bit of a tradeoff. 10378 2.3 able center contact. I removed the cen- There is at least a few thousandths of 10383 2.2 ter contact, soldered it in place and 10388 2.5 an inch inaccuracy in using the rela- 10393 2.6 then slid the Teflon dielectric and con- 3 tively large /64-inch holes as indexes. 10398 2.8 nector flange back over the pin. Fortunately, I found this good enough 10403 3.1 The filter loss at 10368 MHz is 2.1 10408 3.5 for my filter. Better accuracy might be 10413 4.0 dB, with a minimum loss of 1.0 dB at obtained by using the high accuracy 10418 4.6 10338 MHz. The return loss of the fil- feed screw of a milling machine to set 10438 8.0 ter is rather poor, approximately 6 dB. 10458 12 the distance between posts. Obvi- 10478 17 This should not be a problem if stable ously, a digital readout makes this a 10498 21 low-level amplifiers are used. It does snap, but it isn’t too difficult with the 10530 27 make it difficult to measure the exact 0.050-inch/turn hand screws of a 10547 30 bandwidth and center frequency. My 10600 36 Sherline Mill, if you pay attention and 10620 38 first attempt yielded numbers of 90 can work without interruption. Flip- 10638 40 and 10359 MHz—a later attempt us- ping the waveguide over to drill the 10739 46 ing isolators at both ports gave num- 10774 48 second set of holes is still tricky. A bers of 95 and 10375 MHz. In either Starret 827A edge finder only works if case, the filter is quite suitable for re- the waveguide end is truly square— moving the unwanted image that re- perhaps a bad assumption for a begin- brass sheet, as shown in Fig 4. I recom- sults from the mixing process. Table 2 ning machinist. A better idea may be mend using a commercial flange as a shows the filter response I measured to index the waveguide with a known- guide. It is too easy to swap the orienta- with the isolators. square reference at least as high as the tions of the holes, resulting in a flange waveguide, as shown in Fig 3. This that is cross-polarized with normal Notes eliminates the need for the waveguide transitions. In the past, I’ve made the 1Sherline Products, Inc, 2350 Oak Ridge to be perfectly square. The hole makes large rectangular hole by drilling a pair Way, Vista, CA 92083; tel 800-541-0735, 3 fax 760-727-7857; sherline@sherline it a bit of a challenge to square the of /8-inch holes and carefully enlarging .com; www.sherline.com. waveguide ends. It is much easier to them to match WR-75 with a nibbling 2 4 D. G. Sweeney, WA4LPR, “Design and square a solid piece of metal. tool and files. Not surprisingly, the Construction of Waveguide Bandpass Fil- 1 3 I used /16-inch brass rod and /16-inch miniature mill does a much quicker job. ters,” Proceedings of the Microwave Up- brass tubing for the posts. I considered Thanks to Mark, NK8Q/3, for looking date ’89, pp 124-132. 3 3 using 1.5-inch lengths of /16-inch up the flange hole spacing and dimen- G. Elmore, N6GN, “A Simple and Effective brass rod—I think that if they were sions in the Continental Microwave and Filter for the 10-GHz Band,” QEX, July silver soldered there would be enough 5 1997, pp 3-5 and 15. Tool catalog. 4If you need a good introductory book about mechanical strength to use them as working with small milling machines, I rec- mounting hardware. The posts could Using the Filter ommend Tabletop Machining, by Joe Mar- be tapped and secured to an equip- If you use surplus parts, the conver- tin. Of course, it is heavily biased toward ment chassis with screws. A post sion technique in Fig 2 works well. A the use of his Sherline products. See Note 1 for contact information. length of 1.5 inches is a good match for surplus LO brick and mixer are at- 5 square WR-75 flanges. Continental Microwave & Tool Company, tached to the filter, and the filter is Inc, 11 Continental Dr, Exeter, NH 03833; I attached the homebrew waveguide attached to transmit and receive am- tel 603-775-5200, fax 603-775-5201; flanges after soldering in the posts. The plifiers via a circulator. The circulator [email protected]; http://www flanges are made out of 0.032-inch avoids a 3 dB of loss that would result .contmicro.com/.

May/June 2000 55 Further decreases in the load impedance result in still lower power Letters to the Editor levels into the load. We can find a value of load impedance for which electric energy transfer is a maximum. On Impedance Matching of argument that conjugate matching By definition, we also know the source Power Amplifiers and Loads establishes an upper limit of 50% impedance of the alternator without efficiency. ambiguity. We do not have to know Dear Editor, In the case of an RF power amplifier anything else other than the load Desmond Thackeray, in his letter to delivering power to an antenna sys- impedance and that we are at the the editor (Communications Quarterly, tem, no significant part of the maximum power point. The source Summer 1999, p 4) commenting on my available power should be dissipated impedance of the alternator (, which letter (Winter 1999, pp 5-7) has rightly anywhere in the matching network or is an IEEE-definition-B impedance) is questioned the value of “resurrecting” antenna system. An antenna’s radia- exactly the complex conjugate of the a definition (my excerpt “2”) from the tion resistance is virtually dissipa- load impedance (Zload), by definition. IEEE dictionary: The output impe- tionless, for example. The following To make further progress, readers dance of an active device is the ratio of portrayal is paraphrased from a series must be comfortable with this point. the sinusoidal component of output of correspondence with John Fakan, Were the load-current level voltage and the corresponding compo- KB8MU, in 1998. I hope it helps clarify increased by decreasing load resis- nent of current when it is operating my point. tance, the alternator’s output voltage normally. Clearly, this statement is Consider an alternator driven by an level would decrease. Why would it do only correct in the case of an RF power overshot water wheel. This is an easy- this? Is it because of an IR drop across amplifier when by “operating nor- to-visualize example of a source that an IEEE-definition-A resistance with- mally” we mean that the amplifier has exhibits an obvious source impedance in the alternator’s circuitry? Or is it been tuned for maximum power and lack of dissipation. At some flow because the water wheel is now deliv- output, and hence, it is conjugately level, the water wheel delivers a maxi- ering less energy to the alternator’s matched to its load. Since this is what mum of available energy; it transfers shaft? Is it a combination of these two? we want to establish, I see in retro- that energy to the alternator, which As far as analyzing the energy- spect that this definition is not helpful can be loaded to the point where it delivering capabilities of the alter- and could be misinterpreted: It is a delivers the maximum available power nator to its load, it simply doesn’t point well taken. to its load. The wheel would slow in matter what mechanisms determine Thackeray continues, though, response to an increasing load, allow- the alternator’s characteristics as a quoting from Terman (1943), who ing each bucket to fill more completely source. It is completely sufficient to wrote that the output impedance of a and thereby increasing the rate at specify its characteristics in terms of vacuum tube is defined as the which the wheel can supply energy to the variables of interest: in this case, impedance that the plate circuit of the it load. At the point when the buckets voltage and current. tube offers to an externally applied were always full, any further decrease The appropriate product of the voltage. Terman continues by stating in rpm would result in lower power voltage and current tells us the power that for a triode, this output impe- levels, because the torque could no level; the ratio of the variables defines dance approximates the plate resis- longer increase. the impedance. Until we actually know tance of the tube (Rp). This definition Forgetting about the mechanism for why the voltage decreases with in- applies only to class-A small-signal a moment, just remember that energy creasing current, we can know nothing amplifiers, which—if conjugately transfer from the water wheel to the about the electrical efficiency. This matched—have efficiency of 50%. This alternator shaft reaches a maximum at water-wheel-driven alternator exam- line of thought has no relevance here. one specific speed. To mechanical ple is, in my view, a direct analogy to To begin anew, we need to under- engineers, that concept defines the an RF power amplifier: The available stand that there are two definitions of mechanical impedance of the source. energy is the stored energy in the tank resistance: The output of the alternator is sinu- circuit, the energy input to the tank A) Resistance is the factor by which soidal and exhibits a certain RMS circuit is provided by the pulses of the mean-squared conduction voltage when no current is flowing in current flowing in the anode circuit of current is multiplied to give the its load. When the load impedance is the vacuum tube, and the power out- corresponding power loss. reduced, current will flow and the put (at the output of the π-tank circuit) B) Resistance is the real part of voltage will decrease but the electrical is the power transferred to the load. impedance, which can be lossless. energy will flow at some power level to When we measure the output impe- That the source impedance of an RF the load. The load impedance may be dance (at the output of the π-tank power amplifier is “dissipationless” is complex or not: It does not matter as circuit) of an amplifier tuned for maxi- fundamental to an understanding of long as the real part of the impedance mum output power, we see Zout = Zload why we measure what we measure. is not infinite. = Rload for the simple case where the Power is not dissipated in Zout, power If we continue to decrease the load load impedance is a pure resistance. It is generated at this impedance for impedance, the energy transfer would matters naught why an increase in transfer to the load. To measure Zout, increase up to the point where the output current results in a decrease in Zload has to have a finite and non-zero alternator was no longer able to output voltage when analyzing the real component. When conjugately supply current at a greater rate. We energy-delivery capabilities of an RF matched, Zout and Zload are complex know this would happen because we power amplifier to its load; we need not conjugates, so Rout = Rload. Under- know something about the rate at worry about the “pulsey” nature of the standing this is important, because which energy could be made available current flowing in the anode circuit. the ability of HF tuned power amp- to the alternator. The alternator Our measurements are taken at the lifiers to be conjugately matched has delivers only some fraction of the output terminals of the π-network been unjustly disputed, largely by the energy it is receiving from its source. tank circuit. Here, smooth sinusoidal

56 May/June 2000 Fig 1—Load-pull method to find value of Ro. Fig 2—Finding Ro¢ when a transformer is in the circuit.

solving for Ro as follows (see Refer- ence). The value of current I (>0) does not matter.

 R1Ro   R2Ro  V1=• I V2=• I  R1+ Ro  R2+ Ro + V1 = R1R2 R1Ro V2 R1R2 + R2Ro V2− V1 Ro = V1 V2 – R1 R2 (Eq 1) Voltage measurements are required because V1 and V2 cannot be calcu- lated without a knowledge of Ro, which is unknown. Note also that if R1 and R2 are close in value, the voltage and resistance measurements must be very accurate because the numerator and Fig 3—Variation of Ro¢ versus R for a conventional transformer. denominator involve the differences of two nearly equal numbers. Of special interest is the more practi- cal circuit of Fig 2, which has a step- down transformer with turns ratio N, or impedance ratio N2. In this case, the cal- energy is passed to the load. All we resonant network: (1) transforms im- 2 need understand is that we can we can pedance from some high value (the culated value of Ro is multiplied by N to ′ find a maximum in available power, plate load of a vacuum tube) to 50 Ω, find the resistor Ro inside the box. because the input power is finite. and (2) filters out harmonics. Ro' =• Ro N 2 (Eq 2) The variables of interest are mea- One such network is the π (Fig 4), as sured at the output terminals of the used in nearly all amateur, vacuum- Fig 3 shows how Ro′, calculated using power amplifier, where they are sinus- tube PAs. This letter discusses a newly Eq 1, varies as the average value of Ravg oidal and directly proportional to input discovered problem with one measure- = (R1 + R2) / 2 goes from 25 to 100 Ω. It power in the case of linear amplifiers. ment method known as “load-pull.” is a straight line. In these first two ex- This, in accordance with the above The following analysis has been re- amples, R1 and R2 do not have to be example, is the message of Norton and duced to its simplest linear form to close in value to get good accuracy for Thevenin. Ponder this water-wheel- emphasize the basic ideas and the Ro. and-alternator example. It is perhaps problem. This problem exists in class Fig 2 is of special interest because it difficult to think of a better analogy.— A, AB, B and C amplifiers. resembles, superficially, the circuit of John S. (Jack) Belrose, VE2CV, 17 Rue Fig 1 shows a “black box” containing Fig 4, an RF power amplifier whose de Tadoussac, Aylmer, QC, J9J 1G1, a hidden current source and resist- plate load resistance is transformed Canada; [email protected] ance. The generator current and from the desired value of say, 2 kΩ, to a resistance values are constant. A 50-Ω load by a π network. The π network Doug, known resistor value, R, is connected at 3.75 MHz has an impedance of 2 kΩ A subject of interest to radio ama- across the output. We seek the value of and an operating Q of 12. The LC values teurs is that of measuring the output the unknown resistance, Ro. This can are found in the tables in Chapter 13 of impedance of an RF amplifier while it be done by changing the known The ARRL Handbook. Here the imped- is delivering some adjustable level of resistor from R1 to R2, measuring V1 ance ratio is 2000 / 50 = 40 and the cor- output power to a load resistance. A and V2 with a voltmeter and then responding conventional-transformer

May/June 2000 57 turns ratio in Fig 2 would be 401/2 ≈ 6.325. We would like to multiply the value of Ro found in Eq 1 by 40 to find the value of the tube’s output resistance, which is its dynamic, loss-less plate re- sistance rp (see Reference). The problem is that a π network does not behave as a conventional trans- former as described in Figs 2 and 3. Instead, its input impedance (real part and phase) varies with output R as shown in the polar plot of Fig 5. The Fig 4—PI network from tube to 50 Ω load. value of this input impedance is found very rapidly by Mathcad from the con- tinued fraction of Eq 3.

1 Z = in 1 + jCω 1 1 + jLω 1 + jCω 2 R (Eq 3) In Fig 5, this resistance varies quite slowly from 45 ≤ R ≤ 55 Ω and the phase angle varies as shown. The problem is not so much the change in phase, which slightly detunes the net- work over that range (confirmed by ARRL Radio Designer), but rather the almost constant resistance. The phase change requires R1 and R2 to be close in value. A basic fact of the π network, as used in this application, is that the magnitude of the imped- ance changes very slowly with R, not at all like a conventional transformer. This means that if we change load R from 45 to 55 Ω, measure voltage and use Eq 1 to calculate the dynamic out- put resistance of the tube, we do not get the correct answer, because the method requires the kind of transfor- mation that Figs 2 and 3 imply. In addition, we cannot say that the output impedance of the amplifier at Fig 5—Input impedance and phase of the Pi network as a function of the coax connector is what the load- output load resistor R. pull test suggests. The true output impedance is rp/40, which is not the same as the load pull-value. The unfortunate conclusion is that much better with a wide-band transis- Dear Doug, the load-pull method is not applicable tor amplifier that uses conventional or to a π-network PA. As the author of transmission-line transformers whose Both the “loading” and “conjugate- the referenced article, I must admit windings are much shorter than λ/4. A match” concepts are valid models that I did not appreciate this problem low-pass filter should not be used be- under certain conditions. However, until recently, when I looked at it cause of the uncertain relationship be- they are just models of behavior and more closely using simulation with tween its output load and its input not “timeless truths.” There is Radio Designer and mathematical impedance, but a resistive-attenuator nothing inside an RF-power trans- analysis using Mathcad. I “assumed” load followed by a spectrum analyzer istor that looks like either a voltage that a π network behaves as a conven- will exclude harmonics from the mea- source or a source impedance. tional transformer. It transforms, but surements. This method measures the The “loading” model is valid when it is not a true “transformer,” so it magnitude of the complex output im- the RF transistor is operated below its was a poor assumption. The article of pedance.—73, William E. Sabin, maximum frequency. In this case, an the Reference considers only the W0IYH, 1400 Harold Dr SE, Cedar amplifier works like a wall outlet: As simple situation of Fig 1 in this ar- Rapids, IA 52403; [email protected] you lower the load impedance, you ticle and does not mention the π net- draw more power. You would not want work. The problem of that network Reference: Sabin, W. E., W0IYH, “Dynamic to conjugately match a wall outlet! should have been anticipated. Resistance in RF Design,” QEX, Sep Neither do you want to conjugately The load-pull method will work 1995, p 13; feedback Dec 1995, p 29. match the amplifier under these 58 May/June 2000 Ω conditions, as it would become inef- made to measure amplifier output this condition, Rs is near 15 k and ficient and exceed its ratings. Rather, impedance (Rout)—that is, the impe- conjugate match is not reached. you load it to get the power desired. dance seen looking back into the The theory and experiments des- The “conjugate-match” model is amplifier output port. cribed above show that a conjugate valid when an RF transistor is The conjugate match was derived match may be achieved at only one operated near its maximum operating over 150 years ago as the condition for value of output power and this is not frequency. Here the drain capacitance extracting the maximum output power necessarily maximum output power. and lead inductance, in combination from a battery; that is, Rload = Rout. What is “maximum output power” of a with on-state resistance and finite Unfortunately, the match damages the linear PA? It should be the highest current capability, create the effect of battery and so is not used in practical power at which a two-tone IMD test a conjugate match. A certain load systems. The conjugate match should meets some specified requirement impedance produces maximum output only be attempted when the power (such as third-order products at power and power decreases as you source is “free” and cannot be damaged –30 dB). This is always well below the move away in any direction; however, by the match; for example, a receiving maximum power capability of the tube. it is not truly a conjugate match. The antenna or solar cell. For these I believe that PA conjugate contours on a Smith chart are elliptical sources, it is the designer’s goal to matching is of academic interest but rather than circular, and maximum “suck out” as much power as possible has little practical value. Since a efficiency generally occurs at an and conversion efficiency be damned! conjugate match does not necessarily impedance significantly different from There are some conditions where improve the performance of an RF that for maximum power. power amplifiers do show conjugate power amplifier, why continue this For more details, see: (1) H. L. matches: academic discussion? Whom should Krauss, C. W. Bostian, and F. H. Raab, 1. In audio PAs, the output impedance the reader believe? In engineering, Solid State Radio Engineering, Wiley can easily be made to equal the there is no Supreme Court to dictate and Sons, New York, 1980; (2) S. C. speaker resistance by proper the correct answer. Here is an Cripps, RF Power Amplifiers for adjustment of negative feedback. opportunity for the new management Wireless Communication, Artech, Upscale audio PAs have a “damping- to put the matter to rest and Norwood, Massachusetts, 1999. With factor” knob that is used to vary Rout. concentrate on subjects that are more best regards—Frederick H. (Fritz) 2. Mr. Bruene, in the Spring 1998 practical.—73, Reed Fisher, W2CQH, Raab, PhD, Green Mountain Radio Communications Quarterly, provides ARRL TA, 2514 E Maddox Rd, Research Company, 50 Vermont Ave, a graphical method to calculate RF Buford, GA 30518; [email protected]. Fort Ethan Allen, Colchester, VT PA Rout using the tube’s Ep/Ip curves. 05446; [email protected] He shows that a conjugate match can Doug, be reached (if the 4PR65 tube is We agree that when determining the driven hard) because of severe low- optimum load impedance, we are Dear Doug, ering of plate resistance (Rp) at those computing or measuring the impe- I was pleased to learn that the moments when the plate voltage dance that we match to—and when we ARRL had purchased Communications swings low. do, the amplifier delivers design pow- Quarterly. I have read it and I believe 3. Messrs Maxwell and Belrose (same er. However, when we connect the de- it to be a good magazine that treats its issue) report on output-impedance sign load impedance across the output technical material in a near-profess- measurements made on a parallel- terminals of the amplifier, the amp- ional manner. 6146 RF PA. They claim Rout = lifier behaves as if it had an output Regarding the amplifier-match 53 Ω (conjugate match) at 120 W, impedance equal to that of the load. debate: I have studied the article, edit- and 37 Ω at 25 W. We can prove this by measurement. orial and letters that appeared in the To verify these last results, I used We feel the battery and audio-PA Spring 1998 issue of Communications Bruene’s method to estimate Rout of a analogies are not relevant to the present Quarterly. I support the analysis and 6146 class-AB1 PA. The design para- discussion. The calculations for a 6146 conclusions of Warren Bruene, meters were: B+ = 750 V, Pout = 60 W, tube contribute nothing new to the Ω debate, since this exercise only repeats, W5OLY. First-hand professional ex- Rload = 4 k . For these conditions, the × for a tube more commonly used, calcu- perience provides my support. peak plate voltage swing is Vp = (Pout During the last five years of my 1 lations which Bruene has previously 2Rload) /2= 693 V. Thus, the max-imum career at (1985-1990), I done. We discuss dynamic plate resis- instantaneous plate voltage is Ep(max) = supervised a group that designed 750 + 693 = 1443 V and the minimum tance Rp briefly in our Fall, 1997 880-MHz linear power amplifiers voltage is E = 750 – 693 = 57 V. Communications Quarterly article. p(min) We have no need to know the for cellular-telephone base stations. Consulting the RCA tube man-ual, I magnitude of R . It is not a parameter Theory and numerous tests confirmed derived these values for R , the small- p p that can be put in a circuit, since it that the conjugate match was neither signal (slope) plate resistance: R = 1 achieved nor needed. The RF PA p changes with time. It is not used in kΩ at E = 57 V, I = 350 mA and designer experimentally finds the best p(min) p design, nor can we measure it (except V = 0 V. R = 20 kΩ at E B+ = 750 V, load impedance by trading off lin- g p p for class-A amplifiers). The value of I = 25 mA, and V = –50 V; I is the earity, dc-RF conversion efficiency, p g p Rp (V/I) is low (a few hundred ohms) maximum power output and transistor instantaneous plate current and Vg is during the interval of time that power dc power dissipation. The design is the grid voltage. Using Bruene’s is delivered to the input terminals of started by transforming the external formula, I found the source resistance the tank circuit. The value of R is Ω p 50-Ω load to the complex-impedance Rs = 4.2 k as seen looking at the tube very large (tens of kilohms) when no transistor load recommended by the plate in parallel with the LC tank. power is delivered to the tank circuit transistor manufacturer. The trans- Thus, conjugate match at 60 W is (for half or more than half of the RF 1 former circuit is then adjusted until achieved. At /4 output power (15 W), cycle); while the load impedance, RL, the “best” tradeoffs are realized. At no the plate voltage swing is halved: Vp = is a few thousands of ohms. The RF engineer does not have to stage in the design process is any effort 693/2 = 347 V and Ep(min) = 404 V. For May/June 2000 59 think about conjugate matches if he 0 Hz by substituting a dc current into Historically, most of the circuit ele- does not wish to. Yet this does not the IF port. Even with very low dc ments we use can be treated as time- corroborate that HF tuned power current levels, the two-tone, third-order invariant, linear devices; however, amplifiers, when tuned to provide IMD (IMD3) was greatly reduced, com- time-varying components are becoming design power, are not conjugately pared with a sine-wave LO. When I much more important in modern elec- matched. They are, and this is a very substituted a square-wave LO (with the tronics. We now run into switching useful concept (my physics back- same current into the mixer), I got an power supplies, switched-capacitor fil- ground). In summary, Mr. Fisher is intermediate result for IMD3: much ters, DSP sample-and-holds, various writing about a resistance, Rs, that has better than with the sine wave, but not “pumped” components at microwave and nothing to do with the output impe- nearly as good as in the dc case. What many other linear, time-varying net- dance of an HF tuned power amplifier, was going on? The results should have works and components. So maybe it’s is not used for design and cannot be been independent of LO frequency, since time for more discussion of these measured. Discussing it only confuses the diode-ring mixer is designed to have interesting devices and I would suggest the issue. What is the sense of further no energy storage (although there is that QEX including Communications discussion when two sides are some in the diode capacitance and Quarterly is the right forum.—73, addressing a different parameter using transformers.) So the dc and square- John Gibbs, KC7YXD,17623 15 Pl W, words that do not mean the same wave LO cases should have given Lynnwood, WA 98037 thing?—73, Jack Belrose, VE2CV roughly the same distortion levels if we were seeing nonlinear distortion with A Class-B Audio Amplifier Notes on “Ideal” Commutating the diodes biased fully on by the LO, but Mixers (Nov/Dec ’99) this assumes that the LO square wave (Mar/Apr ’00) Hi Doug, has zero transition time. Gentlemen, I enjoyed your article on mixers. I’m The finite transition time of real I find the March/April issue of QEX/ glad you’re trying to clear the air about waveforms causes two problems. First, Communications Quarterly contains them. Much misinformation and many the nonideal switching element (the many interesting opinions on a wide oversimplifications have only confused diode) is in its nonlinear region for a variety of subjects. It was particularly the situation. I’ve had the opportunity significant period of time. It is starved of disturbing, though, to look at Figs 2 to learn this in the “school of hard LO current for a fraction of its operating and 3 on p 46 and find positive feed- knocks” while designing a commercial cycle and so generates severe distortion back in one schematic and negative in HF spectrum analyzer. during the transitions. The second the other. Perhaps Figure 2 should As you pointed out, commutating problem is that during the transition have been labeled “high-power mixers are linear. I don’t think this time, the exact time when the switch Schmitt-trigger circuit!” Kindest simple fact can be overstressed. While turns on or off is modulated by the RF regards—Bruce Meyer, W0HZR, 9410 microwave mixers generally exploit signal. This is equivalent to phase Blaisdell Ave S, Bloomington, MN nonlinear behavior to generate the modulating the LO; these sidebands 55420; [email protected] product of two signals, HF-mixer appear on the IF as IMD. Reducing the Thanks, Bruce, for pointing out the designers do their best to design the transition time can reduce both of these error in Fig 2. The inverting and non- most-linear circuit possible. Other- sources of distortion. However, this inverting inputs of the op amp are wise, IMD would make the rig nearly requires lots of current in the LO drive swapped—Ed. useless on our crowded bands. circuit and makes the LO rich in A Synthesized Down-Converter One of my first “brain-locks” on harmonics. These harmonics can com- for 1691-MHz WEFAX mixers was this linear/nonlinear con- bine with the harmonics of other LOs in flict. We know that linear, time-invar- the receiver: This is the source of (Mar/Apr ’00) iant circuits do not produce distortion birdies. Engineering is always the art of There are several errors in the or mixing products. When we predict compromise. down-converter article: The EMWIN the output of a circuit using convo- Transition distortion is why square- Web site is at iwin.nws.noaa.gov/ lution (or Fourier analysis), we may be wave drive is better than sine-wave emwin/wintip.htm. using simplified formulas that assume drive. It has been incorrectly stated In Fig 2, the PLL IC (U3) is a the circuit is time-invariant. So, the that because the diodes clip the LO, Motorola MC12179D. The crystal key to understanding the ideal commu- sine-wave drive is as good as square- should be 6.068359 MHz (Interna- tating mixer is to realize it is a linear, wave drive. Obviously, there is very tional Crystal F.O. 8030953, GP-26C, time-varying circuit. The best HF little difference at peak drive, but there catalog #004331612). The connections front-end mixers are linear switches is a considerable difference in these two at C12 are wrong. Pin 2 of the VCO that route the RF input based on the cases during the transition period. connects directly to pin 8 of the mixer, phase of the LO. These switches can be Generally, passive Schottky-diode U2; C12 connects that track to R8. diodes or transistors, but the principle mixers have very fast transitions (little (The connection dot and the U2 pin 8 remains the same. I have found that in charge storage) but require high LO lead between C12 and R8 belong at a well-designed commutating mixer, power. This can cause EMC problems C12’s right-hand end.) the nonlinear distortion products are and birdies, as mentioned above. Active In Fig 5 the component layout, C12 generally much lower than the distor- mixers have inherent decoupling of the (1500 pF at center, below the 250 Ω tion caused by switching. signal and the LO, so are better at resistor) needs to be moved to the left 3 Using an off-the-shelf diode-ring reducing zero-crossing distortion; how- /16-inch, so it connects the VCO output, mixer, I ran the LO into the IF port and ever, active mixers simply can not pin 2 (a backward L-shaped pad) to R8 a two-tone signal into the RF port; for an switch as quickly as Schottky, hot- (250 Ω).—Jim Kocsis, WA9PYH, 53180 IF, I used a spectrum analyzer on the LO carrier devices, so transition nonlin- Flicker Ln, South Bend, IN 46637; port. Then I reduced the LO frequency to earities are a bigger problem. [email protected]

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