Receiver Dynamic Range: Part 1

The Communications Edgeª Tech-note Author: Robert E. Watson

The task of the radio receiver has always only by linear amplification, frequency trans- measures of receiver linearity, dominate the been to “get the signal.” However, with the lation, and bandwidth. Because noise figure signal overload end of receiver dynamic- proliferation of high-powered transmitters degrades with each successive stage of the range specifications. It is tempting to define and the burgeoning growth of electronic receiver, the most desirable measurement receiver dynamic range in terms of noise noise pollution, often weak-signal reception port is the audio output. Measurement at floor and overload level alone. However, is difficult, if not impossible. Receiver this port can be accomplished in either the measurement of second- and third-order dynamic range is the measure of a receiver’s cw or ssb mode because both of these are intercept is somewhat more problematic ability to handle a range of signal strengths, pre-detection modes. Note, however, that than measurement of noise figure. from the weakest to the strongest. Because of some receivers may not use a true product Nonetheless, these measurements can be the severe dynamic range requirements detector for cw detection, and the apparent used to predict a wide range of receiver per- placed on modern receivers, it is imperative noise figure will be degraded. In the case of formance. to define rational criteria for evaluating receivers that do not have pre-detected audio The second-order input intercept point receiver performance. This two-part article outputs, the IF output may be used for (IIP2) is the receiver input level at which the provides a tutorial review of receiver dynam- noise-figure measurements. The most rigor- curves of linear output and second-order dis- ic-range specifications and measurements. It ous measurement will require the selection tortion intersect. The third-order input discusses the limits and applicability of the of the narrowest available IF bandwidth intercept point (IIP3) is, similarly, the receiv- various measurements, highlighting potential because it is under this condition that the er input level at which the curves of linear errors and misleading specifications. largest number of receiver stages are in the output and third-order distortion intersect Procedures for estimating and measuring signal path. (see Figure 1). true receiver performance are recommended. In general, the noise figure of most radios In the most common measurement of these will vary both with receiver temperature and PRIMARY MEASUREMENTS parameters, two equal-amplitude sinusoids tuned frequency. Because of this, it is useful are linearly combined and applied to the Primary measurements that affect receiver to note the frequency and temperatures over receiver input. The distortion products dynamic range include: noise figure, second- which the receiver data is valid. appear at the output as new frequency com- order intercept, third-order intercept, 1-dB ponents whose relative magnitudes are mea- compression, phase noise, internal spurs and SECOND- AND THIRD-ORDER sured and compared to the original inputs. A bandwidth. This group of receiver measure- INTERCEPT single set of data is then used to extrapolate ments is considered primary because most Second- and third-order intercept, which are the curves of receiver distortion. For conve- other receiver dynamic-range measurements can be predicted from them.

NOISE FIGURE SECOND-ORDER The most common expression of noise fig- THIRD-ORDER INTERCEPT INTERCEPT POINT ure is the ratio (in dB) of the effective receiv- POINT er input noise power with respect to -174 dBm/Hz. This single number dominates those receiver characteristics which are generally described as sensitivity. It also describes OUTPUT dB THIRD-ORDER DISTORTION the “noise floor” of most dynamic-range SLOPE = 3 LINEAR OUTPUT measurements. SECOND-ORDER DISTORTION SLOPE = 2 To determine noise figure accurately, it should be measured at a pre-detected output INPUT dB of the receiver: that is, at any output which is a version of the received input modified Figure 1. Receiver distortion vs. input power intercept point extrapolation (theoretical).

WJ Communications, Inc. ¥ 401 River Oaks Parkway ¥ San Jose, CA 95134-1918 ¥ Phone: 1-800-WJ1-4401 ¥ Fax: 408-577-6620 ¥ e-mail: [email protected] ¥ Web site: www.wj.com The Communications Edgeª Tech-note Author: Robert E. Watson

nience, these curves can be completely speci- not agree, the validity of the intercept speci- the input filter can also produce distortion fied by the intercept points. fication is in doubt. products (see Figure 2). The filtering in a typical receiver is produced by the cascade of Several problems exist with intercept specifi- Another problem of intercept measurements several different parts of the receiver. For cations. The first problem is that the inter- is their frequency dependence. Second-order example, the filtering is provided by the cept points are not directly measurable. distortion produces distortion components input (rf) filter, followed by a narrower first Because the intercept points are mathemati- at twice the frequency of a single input sig- IF filter, and finally, a still narrower final IF cally extrapolated, their accuracy depends on nal (second harmonic distortion) and at the filter. Because as signals pass through the the assumption that the curves of second- sum and difference frequencies of two input receiver they are increasingly distorted, it is and third-order distortion are described by signals. It can be shown that a band-pass fil- necessary to specify at what frequencies the ter at the receiver input can suppress the straight lines with slope values of two and unwanted signals occur with respect to the undesired signal that would otherwise pro- three, respectively. To be useful, this assump- tuned frequency. Typically, third-order dis- duce second-order distortion products at the tion must be valid over the usable dynamic tortion, due to signals at frequencies within receiver’s tuned frequency. Because realizable range of the receiver. Unfortunately, there the final IF passband, is worse than that due filters are not ideal, rejection of second-order are two potential errors associated with this to signals in the first IF passband, but out- distortion will typically vary with the fre- assumption. First, as the receiver approaches side the final IF. Distortion from signals in quency of the undesired signals as well as overload compression, the actual distortion the input filter passband, but outside the with the receiver’s tuned frequency. curves are no longer straight lines. This first IF, is even less, and distortion from sig- effect can be avoided by measuring the dis- Third-order distortion effects are even more nals with frequencies outside the input filter tortion products at relatively low input lev- frequency dependent than second-order dis- is the least. For this reason, measurements of els. Typically, the intercept measurements tortion. This is because third-order distor- receiver third-order intercept can vary radi- will be most accurate if measured at input tion can produce distortion components cally depending on the frequencies of the levels where the distortion products are 60 from unwanted signals that a receiver input test signals with respect to the receiver’s dB less than the input signals. Second, cer- filter cannot remove. In this case, the distor- tuned frequency (see Figure 3). It is typical tain nonlinear radio components do not tion components from two input sinusoids for receiver manufacturers to specify the seem to produce distortion curves of the occur at frequencies of twice the first fre- third-order intercept point for test tones at appropriate slope. Examples of this are fer- quency minus the second. While a receiver frequencies in the first IF. Another common rite and GaAs FET components. This effect input filter can remove most of the unde- specification is for test-tone frequencies out- can be detected by measuring the intercept sired signals that can produce third-order side the first IF, but inside the input filter. In point at two different input levels and com- distortion products at the tuned frequency, this case, the manufacturer should specify paring the results for agreement. If they do the signals which are within the passband of the frequencies of the test signals with

OUTSIDE SIGNALS PRESELECTOR FINAL IF FILTER IN PRE-

AMPLITUDE SELECTOR IN FIRST IF IN FINAL IF DISTORTION DISTORTION PRODUCT PRODUCT THIRD-ORDER INTERCEPT

(2f1-f2)f1 f2 (2f2-f1)

TUNED f ∆f ∆f ∆f FREQUENCY

Figure 2. Third-order distortion products from two signals inside the Figure 3. Third-order intercept as a function of test-tone frequency relative to receiver input filter. receiver-tuned frequency.

respect to the tuned frequency. Like second- receiver gain setting. The receiver-gain effect undesired signals near the tuned frequency order distortion, third-order distortion can occurs because many receivers, as part of will interact with the receiver phase noise also vary with tuned frequency, so a proper their gain-control scheme, attenuate signals and degrade the SNR of the desired signal. specification should list a worst-case value or early in the receiver signal path. If a receiver Receiver second- and third-order intercept specify the frequency range of validity. were to control its gain by rf attenuation points are typically much greater than the alone, its 1-dB compression point could the- 1-dB compression points, but there is no 1-DB COMPRESSION oretically be unlimited. For this reason, the reliable method for predicting one value 1-dB compression point is best used to The 1-dB compression point is the measure from the others. Two receivers with identical describe the upper limit of dynamic range of receiver performance that indicates the 1-dB compression points may have third- for desired signals only. input level at which the receiver begins to order intercept points which differ from deviate radically from linear amplitude Measuring the 1-dB compression point due each other by as much as 20 dB, and vice response. In a linear device, for each dB of to blocking can be accomplished by combin- versa. For this reason, the 1-dB compression input-level increase, there is a corresponding ing a small, desired sinusoid with a large, point is a useful specification to supplement dB increase in output level. In the case of undesired sinusoid, and applying them to the other measurements as an indicator of input overload, the output does not contin- the receiver input. The desired sinusoid is at receiver performance at high signal levels. ue to increase with each input increase, but the receiver’s tuned frequency and is adjusted instead, the output tends to limit. The input for a 10-dB signal-to-noise ratio (SNR) in PHASE NOISE level at which the output deviates from lin- the narrowest receiver bandwidth at maxi- Receiver phase noise is a measurement of ear response by 1 dB is known as the 1-dB mum receiver gain. The amplitude of the phase and frequency perturbations added to compression point. undesired, out-of-band sinusoid is then the input signals by the receiver frequency- increased until the output of the desired There are two general forms of 1-dB com- conversion oscillators. For signals inside the sinusoid is reduced by 1 dB. pression which are useful as receiver specifi- final IF bandwidth, the effect of this phase cations. The first is the 1-dB compression of One-dB compression due to blocking mea- noise is to degrade angle-modulated signals. the desired signal due to its own signal surements is strongly affected by the relative A second effect of phase noise is due to power causing receiver overload. The second frequency of the interfering signal with undesired out-of-band signals which mix form is the 1-dB reduction of the output respect to the receiver’s tuned frequency. with oscillator phase noise to produce in- level of the desired signal due to a strong Like third-order intercept, the blocking per- band noise that degrades receiver sensitivity. undesired signal causing receiver overload. formance of most receivers will improve as This second effect is usually called reciprocal This second form is usually called blocking the undesired signal is moved away from the mixing. Receiver phase noise can be or desensitization. receiver’s tuned frequency. Blocking is usual- expressed as the amplitude of the phase ly specified for undesired signals outside the noise sidebands added by the receiver to a Measuring the 1-dB compression point of first IF bandwidth. In part, this is because spectrally pure input sinusoid. This is most the receiver due to overload by the desired signal can be performed by noting the input level, in manual gain mode, at which an input-level decrease of 10 dB causes an out- OUTPUT put-level decrease of 9 dB (see Figure 4). A dB 1-dB delta of 10 dB is a convenient value because COMPRESSION smaller deltas may make the 1-dB compres- POINT sion point difficult to measure due to the 9 dB gradual compression characteristics of some devices. Conversely, larger deltas may indicate 1-dB compression points at levels far from the onset of input overload. This 1-dB compression point value is usually 10 dB INPUT dBm somewhat affected by the receiver tuned frequency, and is often strongly affected by the Figure 4. 1-dB compression point.

commonly specified as a single sideband to assure that the test signal does not exceed For some receivers, this may be a daunting noise spectral density expressed as dBc/Hz; the receiver blocking 1-dB compression task. A broadband receiver may require mea- that is, noise power in a 1-Hertz bandwidth point and that the output noise is dominat- surements at over 10,000,000 discrete fre- compared to the signal (“carrier”) power. ed by phase noise. quencies. Tuning manually at one frequency Discrete spectral lines, usually called “spurs,” per second, a single test of all frequencies Receiver phase-noise performance is the are specified in dBc with no reference to would take nearly four months of continu- product of both the oscillator phase noise bandwidth (see Figure 5). These spurs are ous testing. Unfortunately, it is generally and the receiver filtering. Consequently, the troublesome because they can cause frequen- necessary to test all possible frequencies phase-noise performance is strongly affected cy translation of out-of-band signals into the because modern frequency-synthesized local by the frequency offset from the tuned fre- receiver-tuned frequency band. oscillators generate a myriad of interacting quency. A typical receiver’s phase noise might spurs, each of which may appear only at a Receiver phase noise can be measured by be specified at offsets of 100 Hz, 1 kHz, single tuned frequency. This type of spur is connecting a spectrally pure sinusoid to the 10 kHz, 100 kHz, 1 MHz, and 10 MHz. often colloquially called a “pop-up” spur receiver input and measuring its phase-noise because it pops up in a single frequency degradation. Phase noise close to the “carri- INTERNAL SPURIOUS SIGNALS increment. Automation of testing can speed er” can be measured by examining the IF Spurious signals internal to the receiver up the process, but practical testing must output spectrum with a spectrum analyzer. effectively degrade the receiver noise floor. also be based on a deeper understanding of However, the analyzer, like the test signal, The severity of this problem is a function of the spur mechanism so that fewer frequen- must have better phase-noise specifications both the magnitude and number of the cies need to be tested. than the receiver under test. Phase noise out internal spurs. Unless otherwise indicated, it of the receiver passband; that is, farther must be assumed that a spur specification BANDWIDTH removed from the “carrier,” can be measured (which lists only a spur level) indicates that Bandwidth plays a dominant role in receiver by observing reciprocal-mix effects. The the receiver has many spurs of that level. A dynamic range because it generally describes receiver is set in manual-gain mode and the more complete specification might, for a receiver’s ability to reject unwanted signals, IF output is observed with a spectrum ana- example, indicate a maximum number of which can reduce its ability to detect weak, lyzer as the test sinusoid is moved in fre- spurs per MHz with a certain power limit desired signals. Undesired signal rejection quency with respect to the receiver’s tuned and a lower limit for all others. includes: rejection of undesired signals by frequency. The signal amplitude is adjusted the final IF filter so that they do not reach until the reciprocal-mix phase noise can be Internal spur measurement requires that the the detector stages (adjacent channel rejec- measured at the IF output. The receiver receiver be set in maximum gain mode and tion); rejection by the input and first IF fil- phase noise (dBc) is equal to the output level scanned in its narrowest bandwidth over its ters to protect the receiver from overload entire range of tuned frequencies, while minus the receiver gain, and then compared and phase noise effects; and rejection by the to the test-signal level. Care must be taken using the finest tuning resolution available. input and first IF filters of undesired input signals at image and IF frequencies.

0 Measuring receiver filter bandwidths, unfortunately, can be a difficult or impossible task to accomplish without invading the “guts” of the receiver. Measuring the -3-dB bandwidth of the final IF filter is usually easy; however, DISCRETE SPURS measuring the preselector filter band width is much more difficult, and measuring the

PHASE NOISE dBc/Hz ultimate attenuation of the IF filters may be impossible. The overall receiver bandwidth can be mea- OFFSET FROM TUNED TUNED FREQUENCY sured by setting the receiver to manual gain FREQUENCY and frequency sweeping the input with a

Figure 5. Receiver phase noise. constant amplitude sinusoidal test signal.

The IF output, measured relative to its out- ingful comparisons between receivers a diffi- can be predicted by knowing the signal type, put when the test tone is at the tuned fre- cult task at best. signal strength, receiver bandwidth and noise quency, determines the receiver’s frequency figure. Because signal type and strength vary response. A narrowband spectrum analyzer SENSITIVITY with the receiver application, the advantages can be used to increase the sensitivity of the Sensitivity is probably one of the most con- of comparing receiver sensitivities on the measurement because it can be used to look fusing, misquoted and often most complete- basis of noise figure are apparent. for the signal output “below” the IF noise. ly misunderstood of all receiver specifica- Signal strength is properly defined in terms Because of possible receiver nonlinearity tions. It attempts to indicate how well a of available signal power, which effects, this test should be performed with receiver will capture weak signals, but unlike is commonly given in dBm. Unfortunately, more than one input level, and the results noise figure, it can be specified in many dif- for historical reasons, signal strength is often compared. True filter response should be ferent ways. independent of input level. specified in terms of signal voltage, com- Most sensitivity specifications list a required monly given in microvolts, millivolts, dB(V Specification of receiver bandwidth should signal strength for a certain received signal and dBmV. The first problem with voltage include the -3-dB and -60-dB bandwidths. quality with a specified bandwidth, modula- specifications is that it is not clear where the These two numbers give a good indication tion type and percentage of modulation. voltage should be measured. Some specifiers of the signal bandwidth that the receiver will With so many variables, the possible number prefer to use source emf; that is, the unter- pass and the separation required between of different specifications is virtually unlimit- minated (open circuit) output of the signal signals so that the receiver can reject them. ed. In order to minimize the confusion, it is generator. Other specifiers measure the volt- The -3-dB bandwidth should be a guaran- useful to examine each of the variables inde- age across the receiver input terminals. In an teed minimum bandwidth and the -60-dB pendently. impedance-matched system, this difference bandwidth should be a guaranteed maxi- amounts to a 6-dB advantage to receivers Signal quality for sensitivity specifications is mum. The choice of the -3-dB and -60-dB whose sensitivities are specified with voltages given most frequently in terms of signal-to- bandwidths is somewhat arbitrary, but not at the input terminals. For this reason, most noise ratio (SNR); that is, the ratio of out- without reason. The -3-dB bandwidth is a manufacturers who specify voltage sensitivity put signal power to the output noise power. more realistic estimator of usable signal use the latter method. bandwidth than the often-quoted -6-dB A convenient - if somewhat arbitrary - com- A second problem with the voltage specifica- bandwidth. In addition, for most modern monly quoted value is an SNR of 10 dB. tions is that the source and load impedances multipole filters, the -3-dB bandwidth is Because it is not always convenient to mea- must be known. At one time in the United approximately equal to the filter noise equiv- sure SNR directly, the related measurement, States, it was common practice to specify alent bandwidth. The -60-dB bandwidth signal plus noise-to-noise ratio ([S+N]/N) is FM broadcast receiver sensitivities in terms represents a level of undesired signal attenua- used. Mathematically, (S+N)/N = S/N+1. of microvolts without direct reference to tion which is easily achieved with good While the relationship is simple when input impedance. Since all of these receivers bandpass filters; however, for receivers with expressed as simple ratios, expressed in dB, used 300-ohm inputs, direct comparisons of good intercept and phase-noise specifica- the difference between the two measure- sensitivity could be made. However, many tions, a useful specification might include ments depends on their value. For example, manufacturers added 75-ohm inputs to the -70-dB or -80-dB bandwidth. a ([S+N]/N) ratio of 3 dB equates to an SNR of 0 dB. At the more usual level of 10 match a common coaxial cable impedance. Soon after, some of the less scrupulous man- SECONDARY MEASUREMENTS dB ([S+N]/N), the SNR is 9.54 dB. Another related measure that is increasingly popular ufacturers began to specify their sensitivities Common secondary measurements of in microvolts at the 75-ohm input instead of is signal-plus-noise-plus-distortion to noise- receiver dynamic range include: sensitivity, the 300-ohm input. To the unwary con- plus-distortion ratio (SINAD). This mea- cross modulation, intermodulation distor- sumer, these receivers appeared to be twice as surement is essentially the same as tion, and reciprocal mix. This group of mea- sensitive as their competition because the ([S+N]/N) with distortion included in the surements is considered secondary because, required voltage had been halved. In order noise term. This is useful because, for most while they are useful, they can generally be to counter this sort of deception, the Federal users, the distortion is no more usable than predicted from the results of the primary Trade Commission required the use of sensi- the noise. measurements. In some cases, the wide vari- tivity specifications in dBf (dB from a fem- ety of ways they are presented makes mean- In general, signal quality expressed as SNR towatt). If, for typical communications

receivers, an input impedance of 50 ohms tion may be increased at low SNR, and this equal-amplitude test tones, the power of the were specified, the problem would seem to will be reflected in degraded SINAD values. intermodulation distortion product is equal be avoided. Again, this is not the case FM SNR performance is often complicated to three times the power of a single test tone because even a relatively good VSWR speci- further by the effect of de-emphasis filtering minus two times the third-order intercept fication of 2:1 allows input impedance varia- which, therefore, should be specified when point, where all powers are in dBm. That is: tions which will affect the signal input used. Pim = 3Pt - 2 Pip power by up to (3 dB. Specifying signal strength in terms of available power (prefer- CROSS MODULATION where: ably in dBm) eliminates all of the ambigui- Cross modulation specifies the amount of Pim is the power of the intermodulation ties and is, therefore, the preferred method. AM modulation which is transferred from product in dBm an undesired signal to a desired signal. This Pt is the power of a single test tone in Bandwidth specification is mandatory for dBm any sensitivity specification because the specification includes the percentage of modulation of the interfering signal, its sig- Pip is the power of third-order intercept amount of noise power relative to the signal point in dBm increases linearly with bandwidth. For exam- nal power, and frequency offset from the tuned frequency. The conditions of this ple, cw sensitivity in a 1-kHz bandwidth is RECIPROCAL MIX improved 10 dB in a 100-Hz bandwidth. specification vary from receiver to receiver, but the level of cross modulation can be pre- The reciprocal-mix specification typically An additional subtlety related to bandwidth dicted by using the receiver third-order states that the magnitude of the noise power is that post-detection “video” filtering can intercept point data. The percentage of in a specific bandwidth is caused by an out- have a significant effect on output SNR. For modulation on the desired signal due to of-band undesired signal of a specified level example, the detected SNR of an AM signal cross modulation is equal to the percentage and frequency offset mixing with receiver with 1-kHz modulation, tuned in a 10-kHz of modulation of the undesired signal multi- phase noise. This can be readily calculated IF bandwidth, can be improved 3 dB by plied by four times its power and divided by from a knowledge of receiver phase noise. reducing the post-detection bandwidth from the sum of the third-order intercept power The reciprocal mix phase-noise power is the customary one-half IF bandwidth of and twice the undesired power. In algebraic equal to the amplitude of the undesired sig- 5kHz to an audio bandwidth of 2.5 kHz. notation, this can be expressed as: nal plus ten times the log of the measure- This may explain the popularity of specify- ment bandwidth plus the receiver phase %d = %u (4 P )/(P + 2 P ) ing receiver sensitivity with low-frequency u ip u noise at the frequency offset of the undesired modulations measured at the audio output. where: signal. That is: Modulation type and percentage modulation %d is the percentage of modulation on Ppn = Pu + 10 log BW + Ppnr are probably the most confusing compo- the desired signal due to cross mod- nents of the sensitivity specification, because ulation Where: the signal quality may not be linearly related %u is the percentage of modulation on Ppn is the equivalent input phase noise in to signal strength in the case of some modu- the undesired signal dBm lations. For example, both AM and FM Pu is the power of the undesired signal Pu is the power of the undesired signal modulations exhibit “threshold” effects at Pip is the receiver third-order input in dBm low SNRs. This is especially true for FM sig- intercept point power BW is the receiver test bandwidth in Hz nals with wide deviations and low modula- Ppnr is the receiver phase noise at the tion frequencies. Above threshold, the INTERMODULATION undesired frequency offset in dBc/Hz DISTORTION detected SNR is better than the predetected Part 2 of this article introduces comprehen- SNR, but below threshold, the reverse may Intermodulation distortion is used to sive measurements, which attempt to charac- be true. In general, for most signals, SNR is describe the effects of receiver third-order terize a receiver’s dynamic range as a single improved with increases in modulation level. distortion. It usually specifies the levels and number. In the case of AM and FM above threshold, frequency offsets of two test signals and the the detected SNRs will increase as the square level of the resultant in-band distortion com- of the modulation percentage and modula- ponent. Like cross modulation, intermodulation index increase, respectively. For high- tion distortion can be predicted from the percentage modulation AM signals, distor- receiver third-order intercept point. For two

REFERENCES The following list of books and articles rep- 3. McDowell, Rodney K., “High Dynamic Meaning of Signal-To-Noise Ratio,” resents a sampling of the more readable liter- Range Receiver Parameters,” Tech-Notes, Microwaves and RE, Vol. 23 No. 2, ature relating to the subject of this paper. Vol. 7 No. 2, March/April 1980. February 1984.

1. Grebenkemper, C. John, “local Oscillator 4. Erst, Stephen J., Receiving Systems 7. Fisk, James R., “Receiver Noise Figure Phase Noise and Its Effect on Receiver Design, Artech House, 1984. Sensitivity and Dynamic Range - What Performance,” Tech-Notes, Vol. 8 No. 6, the Numbers Mean,” Ham Radio, November/December 1981. 5. Hsieh, Chi, “GaAs FET IMD Demands October 1975. Better Standard,” Microwaves, Vol. 21 2. Dexter, Charles E., “digitally Controlled 8. Schwartz, Mischa, Information No. 6, June 1982. VHF/UHF Receiver Design,” Tech- Transmission, Modulation and Noise, Notes, Vol. 7 No. 3, June 1980. 6. Hirsh, Ronald B., “Knowing the McGraw-Hill, 1980.

WJ Communications, Inc. ¥ 401 River Oaks Parkway ¥ San Jose, CA 95134-1918 ¥ Phone: 1-800-WJ1-4401 ¥ Fax: 408-577-6620 ¥ e-mail: [email protected] ¥ Web site: www.wj.com