DESIGN CONSIDERATIONS IN STATE-OF-THE-ART SIGNAL PROCESSING AND PHASE NOISE MEASURENENTSYSTEMS
bY F. L.Walls, S. R. Stein, James E. Gray and David J. Glaze Frequency and Time StandardsSection National Bureau of Standards Boulder,Colorado 80302
where S isthe spectraldensity of the noise powerand Introduction P, is tRe power availableto a matched load.For Johnson noise,the most common situation, The recentrapid improvement of oscillator phase noise has resultedin significantly more stringent re- quirements forsignal hand1 ing equipment . However, in- So = kT = 4 x J formationconcerninq the phase noiseperformance of the twomost importantiypes of circuits L amplifiers and and theachie able phase noiseperformance is -184 dB mixers - isoften difficult to find. Some generalprinci- below a rad h for a 1 V,,,s,gnal from a 500 source. plesare presented which allow one to estimatethe phase noiseperformance of anamp1 ifier. Also,techniques.are In contrast to the white phase noisewhich is added describedwhich permit one to obtainthe best possible to the carrier by the amplifier, the flicker phase noise results from thetraditional double balanced mixer. A is produced by direct phase modulation in the active measurement set-upwhich has15 to 25dB improvement in its element. It has beenfound empiricallythat a transistor noise floor is shown in detail to illustrate proper mixer stagewhich does not use emitterdegeneration typically drive and termination.Although traditional circuits can hasphase noisegiven by S+(f) = rad2/f. However with extremecare achicie % = -175 dB or slightly better, the use of local RF negativefeedback can reduce this thisis not sufficient for all present requirements. One noise power by as much as a factorof lo4. [l1 Passive techniqueto obtain an additional improvement of 10 to elementscan also contribute to the flicker phase noise. 40 dB in measurementsystem noise is to reducethe mixer [Electrolytic,ceramic, and silver micacapacitors and carbon2 and amplifier contributions to the noise floor by the use compositionresistors can give excessive flicker noise of correlationtechniques. A circuitto accomplish this and shouldonly be used innon-critical locations. is discussedalong with some preliminary results. Threedesign requirements for low phase noiseampli- One of the most frequently needed systems in the fierdesign follow from the above discussion.Firstly, study and use of oscillators is thephase-lock loop. each stage of an amplifier must incorporate emitter de- However, sincethe performance of this system is often generationto minimize the flicker phase modulation. incidentalto the ultimate goal of the experimenter, e.g. Secondly, criticalpassive components should beexamined the measurement of phase noise,the design of such a forexcessive phase noise.Finally, the signal level system is sometimes giventoo littleconsideration, re- mustbe always maintained at a high enough level to sulting in unanticipated difficulties andwasted time. achievethe desired white phase noiselevel. The design of an extremelysimple phase-lock loop which is suitable for almost all high stability oscillator ap- In order to illustrate the influence of this philos- plications is discussedwith particular attention to the ophyon the design of an amplifier, a new isolation ampli- advantaqesover more traditional circuits. fier is described.This amplifier was developed to pro- I. PHILOSOPHYOF LOW NOISE AMPLIFIER DESIGN vide a high degree of isolation between verylow phase noise RF signalswhich are used to compare atomic ana If an amplifier were drivenfrom a noiseless oscil- otherfrequency standards. lator,then the output phasespectrum would typically have a flicker noise region at low frequencies and a 11. WIDE-BAND LOW-NOISEISOLATION AMPLIFIER whitenoise region at higher frequencies. The break be- tween the two is usually between one andone hundred Hz The amplifier shown in Figure 1 is designed to op- and the white noise extends out to the bandwidth of the erate from one toseveral hundred megahertz. Inorder amplifier. The source ofthe white noise modulation can to minimize current drain a method of achieving high be identified and themagnitude estimated, but similar isolationwhich used a small number of stages was generalizations can not be made for the flicker noise. needed. Thisrequirement was satisfied by a cascaded Nevertheless,empirical guide1 ines can be established pair of comnon base transistor stages, Q1 and Q2 A whichshould ensure against unnecessarily poor flicker signalapplied to theoutput port propagates towards noiseperformance. theinput through the collector-base capacitance of Q]. The2N3904 was selected because of its smalloutput Providedthat the integrated noise of the capacitance, 4 pF. Sincethe base of Q1 is grounded amplifier over its entire bandwidth is small compared to through a capacitor and theemitter looks into the high thesignal power, halfthe thermal noise power contrib- output impedance ofthe preceding stage, the signal is utesto the phase modulationof the signal. Thus the low pass filtered. A second stage of filteringis per- spectraldensity of phase fluctuations due to formedby the transistor Q2 inthe same way. It noise of the amplifier is is also possible for a signalto propagate from the outputto input through the bias chain. Transmission throughthis path is reduced to the same level as trans- SJf) = S0/2PS (1 1 missionthrough the transistor chain by the cascadedlow
269 pass filters.Typical isolation which is achieved is The bestperformance has been obtained with units which greaterthan 120 dB at 5 MHz degradingto 100 dB at 50 usehot carrier diodes in the ring. Some differences may MHz. alsoresult from the type of transformers in the coupling circuits. The noiseobserved at the output of the mixer, The common emitterinput stage determines the col- consistingof mixer and amplifiercontributions, is nearly lectorcurrent of the transistors. The27n dc emitter constantover a range ofinput power level. However, the resistanceproduces an average collector current of outputsignal, proportional to the phase fluctuations, 40 mA. Noiseperformance isgenerally best when the increaseswith the drive power. The bestsignal-to-noise amplifieroperates well within the class A region.With ratiofor Fourier frequencies in the white noise region a 50n loadthis amplifier can produce an output of nearly isobtained at very high drive levels. For one type of 1 V (13 dBm) with minimum distortion. The gainof the mixer,using a singlediode in each arm, thebest noise amprlfieris determined by theload resistance and the floor was obtainedwith approximately 30 mA rms current unbypassedportion, 27n, ofthe emitter resistance. With at each input.This drive level exceeded themanufac- thevalues shown, thefull. output swing occurs for an turer's maximum drivecurrent specification. The optimum inputof approximately 1.5 Vptp. driveis not necessarily the same forall Fourier fre- quencies. The same mixerperformed best. below 40 Hz at The white noise floor which onewould estimate for lowerdrive level. Since such a doublebalanced thisamplifier is S+ = -184 dB. Themeasured noise mixer is a dynamicimpedance theaverage drive current floor is shownas curve A ofFigure 2. The noisefloor does notsufficiently describe the operating conditions. appears to beonly -174 dB, butsince this level cor- Theoptimum method of coupling to the mixer also depends responds to the measurementsystem noise it canonly be upon theoutput impedanceof the signal source. Although saidthat the amplifier is not worse than this. The theuse of 50n pads toattenuate the drive level is tradi- measured flickgr phase noise of the amplifier is tional, a seriesresistor whose valueis chosen to set S = rad /f. Thisperformanre level reachedis thedesired current often gives superior performance. btcauseeach transistor has a reasonable amount of local The improvementswhich are observed may bedue to reduced RF negativefeedback. The emittersof Q1 and Q2 both ringing of the drive currents. lookinto the high dynamic impedance ofthe preceding stage while the emitter of Q3 hasthe unbypassed 270 The signal-to-noise ratio at the mixer output is also resistor.For a givenapplication, this unbypassed re- affectedby the type of termination used. Since the mixer sistorshould be made as largeas possible, limited has a lowoutput impedance, near 500, thedc termination onlyby the necessity of having full output voltage mustbe high impedance compared to 50R. Failureto ob- swing. servethis may result in 6 dB or more lossin signal level. However, it hasbeen determined empirically that the mixer In additionto achieving low noise levels it is mustbe terminated differently at F!F. In thecircuit shown .!n necessaryto minimize microphonics and pickup of power- Figure 4 theimpedance to ground at the output of the mixer linefrequencies and othersignals. For this reason, no is 1 kR at dcand approximately 50R at 10 MHz. The net usehas been made of filter inductors or coupling trans- result of the high drive level and theoutput termination formers. It isalso possible that temperature changes is illustrated in Figure 5, which shows thebeat frequency could cause sufficient collector current variation to betweenthe two oscillators in Figure 4 atlow drive degradethe flicker performance. As a result,the level(sinewave) and high drive level (clipped waveform). diodehas been included inthe bias chain to further The slopeof the clipped waveform at the zero crossings is stabilizethe collector current. It shouldbe placed in morethan twice the slope of the sinewave. It follows physicalcontact with transistor Q3. The amplifierhas from Eq. (2) thatthe noise floor is improved morethan been constructedon a doublesided printed circuit board 6 dB bythis technique. The increasein slope is not real- measuring 3.25 cm x 9 cm. The art work for this circuit izedwithout appropriate termination, but the optimum cir- board isavailable from the authors. cuit has notbeen determined. The noisefloor achieved with the circuit of Figure 4 is shown in curve C of 111. DOUBLEBALANCED MIXERS AND PHASE Figure 2. The spectraldensity of phase is -150 dB at NOISE MEASUREMENTSYSTEMS 1 Hz anddrops to a floor of -176 dB.
Themost common andalso most sensitive method of measuringphase noise is to use a doublebalanced mixer. Severalother special circumstances may occur. One If theinput ports are driven by quadrature signals, may wishto measure the signal from a devicewhich has thenthe output voltage isproportional to the phase insufficient output power to drive a doublebalanced deviationof the input signals from the quadrature con- mixer.Figure 6 shows a simplebuffer amplifier which dition. The spectraldensity of the phase noise can be may beused under the circumstances. In keepingwith the calculatedfrom the very simple expression stated philosophy of amplifier design, this circuit can drive a mixerwith a nominal50n input impedance with a V,, 1 V,, signalin class A operation. The mixerinput im- S$(f) pedanceappears as an unbypassed 200n in the emitter =[F] circuit which results in excellent flicker noise perform- 2 2 ance. As shown incurve B ofFigure 2, thespectral den- where V, (f) is the noise density in units V /Hz atthe sity of phase is -149 dB at 1 Hz and falls off to the output of the mixer and Vs is the sensitivity of the noisefloor of the measurementsystem. The 10 dB improve- mixerin V/rad. ment in flickernoise over the previously described isolationamplifier is probably due tothe greater emit- A variety of circuits for the measurement of phase terdegeneration or lower intrinsic flicker noise in the noisehave been discussed extensively in the literature. 2N5943 transistor compared to the 2N3904 orboth. The Here we will look closely at specific problem areas 2N5943 was suggestedfor use in this circuit by Charles common toall circuits using double balanced mixers: Stone ofAustron Inc. components, inputdrive levels and output termination. Dataare presented which show thatproper treatment If the device being tested is capable of moreoutput of these details results in a 15 to 25 dB improvement in powerthan a standarddouble balanced mixer can accept, theperformance of phase noise measurement systems. then it ispossible to achieve even lower noise floors. Providedthe driving voltage exceedsabout 1 Vrms, it is Figurp 3 shows a typicaldouble balanced mixer. possibleto use a highlevel mixer. Such a device has morethan one diode in each leg of the ring and is there- fore able to achieve higher output voltage without a
270 appear coherently on bothchannels and can’t be distin- correspondingincrease inthe noise. The circuitdia- guishedfrom real phase noise between the two oscillators. gram of the mixer in Figure 3 shows twodiodes in each One half of the noise power appears in amp1 itude and ’ leg.Using a mixerwith three diodes per leg a noise one half in phase modulation. floor of -184 dBwas achieved with a drive level of 1.6 Vrms. If theoscillator’s output impedance is low but the voltage is insufficient to drive a high level Curve A of Figure 8 shows S+(f) for the mixer and mixer a step-uptransformer can beused to obtain the ap- dc amplifiers in Channel 1 and 2 when used separateiy. The mixers in this casehave threediodes in each leg propriatedrive voltage. Since the signal and noise instead of the two shown in Figure 3 and are driven power increase by the same ratio,the spectral density withapproximately 5 V tp at 5 MHz from10n source im- of phase of the device under test is unchanged butthe pedance using 33n serigsresistors. Curve B Figure 8 noise floor of the measurement system is reduced. indicates the correlated component of this noise between IV. CORRELATION TECHNIQUE the two channels. Inorder to predict performance in a specific measurement using this scheme, thenoise level With all of the improvements describedthe tradi- of the isolation amplifiers usedwould have to be added tionaldouble balanced mixer phase noise measurement to Curve A and proportionately to Curve B. system is unable to resolve the noise floor of the best oscillators ‘and amplifiers. The above data clearly indicate that significant im- provementsover any presently existing phase noise meas- Iftimes 20 or more frequency multiplier chains with urementsystem can be obtained using correlation tech- noise levels 20 dB below that of the measurementsystem niques. Such improvements arevitally necessary in order shown in Figure 2 were available,thenthat would solve the to measure presentstate-of-the-art signal processing presentproblem. So far we are unaware of such multi- equipment and to test future components and circuits. p1 ier chains, a1 though some prototype mu1 tip1 ier chains The simplesingle frequency correlator used in this ex- show whitenoise floors 5 to 10 dB belowFigure 2. It perimentcould be replaced by a fast digital system wouldalso be convenient if the measurementsystem were whichwould simultaneously compute the correlated phase broadband so as toaccept carrier frequencies from ap- noisefor a large band ofFourier frequencies. Ultimate proximately 1 to 100 MHz. Figure 7 shows theblock noisefloors could probably be reduced 40 dB belowthe diagram of a phase noise measurementsystem which is in- noiselevel of a singlechannel. herentlyvery broadband and also has the capability of improvingthe measurement systemnoise by at least 20 dB. ‘V. PHASE-LOCKTECHNIQUES It consists primarily of two equivalenttraditional phase noise measurement systems. One ofthe most ubiquitous elements of phase noise measurementsystems isthe phase-lockloop.[2,3] When At theoutput of each doublebalanced mixer there the phase noise of a pair of oscillators is measured a is a signalwhich is proportional to the phase differ- phase-lockloop is normally used tomaintain a condition ence, A$, between the two oscillators and a noiseterm, of approximatephase quadrature. For accurate measure- VN, due tocontributions from the mixer and amplifier. ments it is necessary to keep the phase errorless than The voltagesat the input of eachbandpass filter are about1/6 rad despite any initial frequency offset be- tween the two oscillators or anyfrequency drift during Vl(BP filterinput) = Al A$(t) + ClVNl(t) thecourse of the measurement. The phase-lockloop is (3) usually the most neglected element of the measurement VZ(BP filterinput) = A2 n$(t) t C2VN2(t) systembecause its purpose isonly tangential to the measurement requirements. As a consequence it often performsmarginally. In this section the requirements where VNl(t) and VNn(t)are substantially uncorrelated. for a phase-locksystem are discussed andan extremely Each bandpass filter produces a narrow band noisefunc- simple yet elegant circuit is presentedwhich more than tion around itscenter frequency f: meets theserequirements.
A specific example illustratesthe problem:Design a feedbackloop to lock a 5 MHzVC0 to a reference os- cillator with a unitygain frequency of .l6 Hz and cal- culate the open loopfrequency difference for phase error of1/6 rad. The VC0 has a tuningrate of 5 x Hz/V and the phase deviationfrom quadrature. One solution, the first order phase-lockloop, is shown in Figure 9. whereand B2 arethe equivalent noise bandwidths Of The 50e resistor and 0.1 UF capacitor are for proper ter- filters 1 and 2 respectfully.Both channels are band- mination of the mixer and do not contribute appreciably pass filtered in order to help eliminate aliasing and to thefrequency response of the phase-lock loop. The dynamicrange problems. The phases w(t),nl(t) and n2(t) open loop gain of this servo is take on a1 1 valuesbetween 0 and 2; with equal 1 ikel i- hood. They varyslowly compared to l/f and are substan- tiallyuncorrelated. When these two voltagesare multi- 2 (5x10-,Hz/”) (0.17 Wad) Gam (U) plied together and low pass filtered only one term has Gservo(U) = jU finite averagevalue. The outputvoltage is (b)
+ O,
271 ISOLATION AMPLIFIER To produce a unitygain frequency Of 0.16 HZ, Or an *24V@4hA attack time of one second, requiresamplifier gain Of 185. The loopproduces negligible correction for Fourier fre- quenciesgreater than 1 Hz and may therefore be used to make phase noise measurements in this frequencyrange. The open-loopfrequency offset whichcorresponds to a 1/6 rad phase error is I AV = (1/6rad) (0.17 V/rad)(5 x 10'3Hz/V)(185) = 2.5 x lo-, Hz (7) oronly 5 partsin lo9 at 5 MHz. It is often difficult toachieve and maintain such a smallfrequency offset. However, thefollowing circuit increases the dc gain of thefeedback loop by lo5 and decreasesthe phase error proportionally, The improvedperformance is achieved by adding a stage of quasi-integration which makes a second orderloop asshown inFigure 11. The first stage of amplification is the same as in the first order loop. The second stage has gainequal to R,/R, forFourier frequencieslarger than l/(2nRICl). If R,C,exceeds the attack time of the first order loop the new phase- lockloop is stable. It is critically dampedwhen R,Clis approximately four times the attack time and has good stepresponse for R,C,between 1 and one and fivetimes the attack time. The solidcurve in Fig- ure10 is the magnitude of the open loop gain of the second orderloop assuming R, = R,. Figure 12 compares the step response of a first order loop to that of a second orderloop with RIClequal to the attack time.
The second orderloop increases the long-term gain by the open loopgain of the second operationalampli- fierprovided that the leakage resistance, RL, ofthe capacitoris sufficiently large. The open loopfre- quency offset between the two oscillators which can be toleratedis therefore increased to a limit determined either by the maximum voltage swing of the second amp- lifier or the maximum tuningavailable in the VCO. The Fig. l Schematic of 1 MHz to 200 MHz isolation amp- second orderloop can be implemented with a single op- lifier. The isolationis -120 dB at 5 MHz. erational amplifier rather than the two which were shown Art work for this amplifier is available from forclarity. In this casethe attack time is adjusted the authors. by varyingthe input resistor, R,, of theoperational amplifier, A, and omitting amplifier Al in Figure 11.
ACKNOWLEDGMENTS
The authorswould like to thankCharles Stone of AustronInc. for many helpfulconversations and in par- ticularforhis advice concernina low noise transistors -1."".._" - I % and other components. I F: F: REFERENCES 2s -150 F Y 02 I DonaldHalford, A.E. Wainwright, and James A. Barnes, in Proc. 22nd Annual Symposium Frequencyon Control -lm- (NTIS Accession No. AD 844911), 1968, p. 340. ..,e 2% E -170- a-- l21 F. M. Gardner,Phaselock Techniques (John Wiley, m* New York,1966). -*
. .. [31 Don Kesner, EDN 5 Jan 1973, p. 54. 1 10 1 02 10' 10' FCUIIER FREWNCV f, h
Fig. 2 Spectraldensity of phase, S (f), for A) the isolation amplifier of Figurg 1 at 5 MHz, B) the buffer amplifier of Figure 6 at 5 MHz, C) noise floor of the measurementsystems of Figure 4 with a single diode mixer.
272 PHASE NOISE NEASURDlENT SYSTM
LW NOISE 'T WPLIFIER
,.3W 1M
Fig. 4 Typicalsystem formeasuring Sg(f) of a pair of equalfrequency oscillators. Noise floor for this system is shown in Figure 2, curve C.
BEAT NAVEFOW BUFFER AMPLI F I ER .5r +28V I
6.81kn FERRITE BEAD
INPUT BEAD
-.sL
Fig. 5 Fi1 tered waveform atthe output (x Port) Of doublebalanced mixer due to frequency dif- ference between signalsat R and L ports. The solid curve is obtained at high drive levels while the dashed curve is obtained at low , drive 1 eve1 S. Fig. 6buffernoiseamplifier low Verywhichcan be used todrive mixers. The noise performance is shown in Figure 2 curve B.
273 -14~r 4 %:%?K FIRST ORDER PHASE-LOCK LOOP
DOUBLE BALANCED I MIXER
Fig. 9 Schematic of typical first order phase-lock loop. Loop attacktime is adjusted by chang- -220 1 ing amplifier gain.
-230 I I I I 1 10 100 10) 10' 1 o5 f (Hz)-
Fig. 8 Curve A shows S (f)for eachchannel ofthe measurement system of Figure 7 excluding the isolationamplifiers. Curve B shows the cor- related component of S+(f) between the two channel s.
SECW ORDER PHASE-LOCKLOOP
OPEN-LOOP GAIN
6or +i a L ___-___ .#
Fig. 11 Second orderphase-lock loop. The attacktime is adjusted by changinggain as in Figure 9. The timeconstant R C,is adjustedto be 1 to 5 timeslonger than the attack time. m 12 dB/OCTAVE -U 3 v PHASE-LEK LOOP STEP RESPONSE 0 > a W v) W
20 -
.a001 .001 .01 -1 1
274