Phase Noise and AM Noise Measurements in the Frequency Domain


1 Reprinted, with permission, from Infrared and Copyright 0 Press. 1984 Academic Vol. 11, 239-289, 1984. Millimeter Waves, pp. WAVES. II MILLIMETER INFRARED AND VOL. 7 CHAPTER AM Noise Measurements Noise Phase and Frequency Domain in the Lance, Seal. D. L. and Frederik Labaar Algie Wendell and Group Operations TRW Support One Space Park California Redondo Beach. INTRODKTI~N I. CONCEPT II. FUNDAMENTAL .Voise Sidebands A. B. Spectral Denstty Spectral Denstries of Phase Fluctuations in the C. Domain Freguency Theory and Spectral Density Relationships D. Modulation Processes Noise E. Integrated Phase Noise F. Noise tn G. Frequency Domain AU the PHASE-NOISE MEASUREMENTS USING THE III. 355 TECHNIQUE TWO-OWLLATOR 157 Oscrllators A. NOISY TWO Measurements the Phase-Noise Using B. Automated 358 Two-Oscillator Technique Using the C. Calibration and Measurements 259 S,vstem Two-Oscillator PHASE-NOISE MEASUREMENT SINGLE-OSCILLATOR IV. 267 TECHNIQUES SYSTEMS AND 168 an FM Discriminator The Delay Line as A. Delay Line B. Calibration and Measurements Using rhe 273 an as FM Discriminator 381 Discriminator Delay- Dual C. Line 283 Phase-Noise Wace Millimeter- D. Measurements 287 REFERENCE I. Introduction sources contain noise that appears Frequency be a superposition of to causally generated signals and random, nondeterministic noises. The random noises include thermal noise, shot noise, and noises of undetermined origin amplitude (such noise). The end result is timedependent phase and flicker as fluctuations. Measurements of these fluctuations characterize the frequency source in terms of amplitude modulation (AM) and phase modulation (PM) (frequency stability). noise 239 Cop)nght @ 1984 by Academsc Press. Inc any ~0 of reproducuon m nghtr form reserved. lSBN 0-12.117711-8 TN-190

2 240 A. LANCE, W. D. SEAL, AND F. LABAAR L. term frequency encompasses the concepts of random noise, The srabiliry incidental intended any other fluctuations of the output modulation, and and device. the general, frequency stability is a degree to which frequency In of produces the same frequency value throughout a source an oscillating of time. It is implicit in specified general definition of frequency period this that stability of a given frequency decreases if anything except stability the sine signal is the perfect wave shape. a function to is term most widely used noise describe the characteristic Phase the of frequency stability. The term spectral purity refers to the randomness ratio of power to phase-noise sideband power. Measurements of phase signal and AM are performed in thefrequency domain using a spectrum noise noise provides following frequency window that the detector (double- analyzer a measured mixer). can also be stability in the balanced Frequency time with a gated counter that provides a rime window following the domain detector. Long-term is usually expressed in terms of parts per million per stability day, month, or year. This stability represents phenomena hour, week, by the aging process of circuit caused and of the material used in elements the frequency-determining element. Short-term stability relates to frequency changes of less than a few seconds duration about the nominal frequency. Automated measurement have been developed for measuring the systems phase noise two signal sources (the two-oscillator technique) combined of single reported source (the single-oscillator technique), as a by and signal (1981). al. and Seal and Lance et When two source signals Lance (1977) applied in quadrature to a phase-sensitive detector (double-balanced are mixer), the fluctuations analogous to voltage are measured phasejuctuations detector output. The at measurement system is usually the single-oscillator using a frequency cavity or a designed line as an FM discriminator. delay Voltage analogous to frequency j?ucruations fluctuations measured at are the detector output. The integrated phase noise can be calculated for any selected range of Fourier frequencies. representation fluctuations in the frequency A of is called spectral density graph. This graph is the distribution of domain variance power frequency. versus Fundamental II. Concepts this presentation we shall In to conform to the definitions. attempt symbols, and terminology set forth by Barnes et al. (1970). The Greek letter 1’ frequency for carrier-related measures. Modulation- represents carrier frequencies related f. If the are is considered as dc, the designated frequencies measured with respect to the carrier are referred to as baseband, offset from the carrier, modulation, noise, or Fourier frequencies. TN-191

3 7. PHASE AM NOISE .MEASUREMENTS 241 NOISE AND M; ,*[email protected];: I- 270° I I FREQUENCY ANGULAR PERIOD To I_----. ------A (bl lab Sine wave characteristics: (a) voltage Y changes with time ? FIG. (b) amplitude I as with angle 4. changes phase in wave produces a sine that changes generator time t as the A voltage V changes with the phase angle 4. shown in Fig. 1. Phase is mea- amplitude from sured crossing, as illustrated by plotting the phase angle as the a zero determined rotates a constant angular rate at by the frequency. radius vector ideal (perfect) sine-wave-related parameters are as follows: vO, average The of frequency the signal; v(c), instantaneous frequency of a signal (nominal) l d4(,); (1) & v(t) = Ts;; Vo, nominal of a signal source output; r, period of an oscilla- peak amplitude of Cl, (carrier) angular frequency (rate of change (l/v,,); phase :ion signal time) in radians with = 2nv,; (2) R instantaneous frequency; V(t), instantaneous output voltage angular Rt, a signal. For the ideal sine wave signal of Fig. 1, in volts, of V, sin(2nv, f). = V(t) (3) The basic between phase c$, frequency v,,, and time interval relationship given of ideal sine wave is r in radians by the following: the f$ = 2nv,s, (4) for where is the instantaneous phase of the signal voltage, V(r), defined b(t) as the sine wave in radians ideal f#J(t) = 2w,t. (5) TN-192

4 A. LANCE. W. D. SEAL, AND F. LABAAR L. 242 instantaneous phase of V(t) for the noisy signal is The 4(t) Znv,r + &t) = w, (6) the instantaneous 4(r) fluctuation about the ideal phase where is phase of Eq. (4). 27rv, 5 illustration Fig. simplified 1 shows the sine-wave signal perturbed The in area, short a noise. In the perturbed instant the Au and At relation- for by correspond to other frequencies, as shown by ships dashed-line wave- the forms. this sense, frequency variations (phase noise) occur for a given In within the instant cycle. generator output V(r) of instantaneous signal voltage or oscillator The a now is = [V, + c(t)] sin[2nv,t + &t)], V(t) (7) where and vO are the nominal amplitude and frequency, respectively, and V, and s(r) are the instantaneous amplitude &(r) phase fluctuations of the and signal. It is assumed in Eq. (7) that $),I e(t),& and 6 for all (t), r&t) = dt$/dt. 1 (8) Equation also be expressed as (7) can f& [V, h(t)] sin[2nv,r + = + [email protected](f)], V(T) + (9) &, is a constant, 6 is the fluctuations operator, and &s(t) and where W(t) represent fluctuations of signal amplitude and phase, respectively. the by fluctuations are related to Frequency fluctuations br#~, in hertz, bv phase 1 464) z-s bv bR (10) 2ndt’ 2n i.e., radian frequency deviation is equal to the rate of change of phase devia- tion (the derivative of the instantaneous phase deviation). first-time phase fluctuations time interval br The related to fluctuations of of are 84, in radians, by &#J = (2nv,)ck (11) In the following, y is defined as thefractionalfrequencyPuctuation or fraction- to al deviation. It is the dimensionless value of 6v normalized frequency the average (nominal) signal frequency vo, (12) y = 6v/vo, TN-193

5 7. PHASE AND AM NOISE MEASUREMENTS 243 NOISE J(C) is instantaneous fractional frequency deviation from the where the vO. nominal frequency NOISE SIDEBANDS A. from thought of Noise arising sidebands a composite of low- can be as Each of these signals modulate the frequency signals. carrier-producing in sidebands separated by the modulation frequency, as components both by Fig. The signal is represented in a pair of symmetrical illustrated 2. (pure AM) and a pair of antisymmetrical sidebands (pure FM). sidebands The basis measurement is that when noise modulation indices are of correlation noise be neglected. small, can are if signals uncorrelated Two and amplitudes have their time distributions so that they do phase different cancel in a phase detector. The separation not AM and FM components ofthe are as a modulation phenomenon in Fig. 3. Amplitude fluctuations illustrated as be with a simple detector such can a crystal. Phase or frequency measured fluctuations can be detected with a discriminator. Frequency modulation (FM) noise rms frequency deviation can also be measured with an am- or variations (AM) after the FM system are converted to plitude detection variations, as shown in Fig. 3a. The FM-AM conversion is obtained AM applying quadrature signals in phase by (90”) at the inputs to a balanced two 90” (detector). mixer illustrated in Fig. 3 by the This phase advances of is the carrier. B. SPECTRAL DENSITY Stability in the frequency domain is commonly specified in terms of spectral densities. There several different, but closely related, spectral densities are are measurement to the specification and that of stability of the relevant phase, period, amplitude, and power of signals. Concise, tutorial frequency, CARRIER CARRIER V V V V” I, RADIAN FREQUENCY FREQUENCY RADIAN RADIAN FREQUENCY , (b) Id (al FIG. 2 (a) Carrier and single upper sideband signals; (b) symmetrical sidebands (pure AM); (c) an antisymmetrical patr of sldebands (pure FM). TN-194

6 244 A. LANCE, W. D. SEAL, AND F. LABAAR L. VARIATION FM I UPPER SIDEBAND AM MEASURED a- --I WITH AM DETECTOR t LOWER SIDEBAND SIDEBAND UPPER SIDEBAND LOWER 900 -I ADVANCE , VD IADVANCED) ADVANCE VI) I ; (ADVANCED) I I I (d) (cl FIG. (a) Relationships of the FM signal to the carrier: (b) relationship of the AM signal 3 converslon. the (c) to advanced 90” to obtain FM-AM conversion; (d) AM-FM carrier; carrier descriptions twelve defined spectral of and the relationships among densities them were given by Shoaf et al. (1973) and Halford et al. (1973). Recall that the perturbed area of the sine wave in Fig. 1 the frequencies in time. are for a given instant of produced This amounr of time the signal being spends in producing another frequency is referred to as the probabilitj, to den&y generated frequencies relative the vo. The frequency domain of plot is illustrated in Fig. 4. A graph of these probability densities over a period is of produces a continuous line and time called the Power spectral dens&y. TN-195

7 7. PHASE AND AM NOISE MEASUREMENTS NOISE 245 FIG. power density plot. 4 A over density distribution of total variance the frequency. The spectral is The power spectral density are power units hertz; therefore, a plot of power of per density obtained from amplitude (voltage) measurements requires spectral the voltage measurements that squared. be The density of power versus frequency, shown in Fig. 4, is a rwo- spectral spectral Fourier because the range of sided frequencies f is from density infinity to plus infinity. minus notation S,(f) The the two-sided spectral density of fluctations represents of any specified timedependent quantity g(r). Because the frequency band is defined the two limit frequencies of minus infinity and plus infinity, by total fluctuation of that quantity is defined by the mean-square = (13) + m S,(f) df-. Glideband I -aD pure spectral are useful mainly Two-sided densities mathematical analysis in involving Fourier transformations. Similarly, for the one-sided spectral density, (14) Gsidebmd +=$,(f) 4 = J 0 as one-sided spectral densities The related two-sided follows: and are df = 2 S,, (1% where g1 indicates one-sided and gz two-sided spectral densities. It is noted as that one-sided density is twice the large as the corresponding two-sided TN-l%

8 A. LANCE, W. D. SEAL, AND F. LABAAR L. 246 density. The for single-sideband versus double-sideband spectral terminology totally signals the one-sided spectral density versus two- distinct is from They are totally different concepts. The defini- spectral sided terminology. concepts of spectral density tions set forth in NBS Technical Note and are (Shoaf al., 1973). 632 et C. THE SPECTRAL FLUCTUATIONS IN OF DENSITIES PHASE * FREQUENCY DOMAIN spectral density S,(f) of the instantaneous fractional frequency The J(C) as defined fluctuations a measure of frequency stability, as set forth is Barnes ef (1970). S,(f) is the one-sided spectral density offrequency by al. dimensionality basis,.i.e., the is Hz-‘. The a hertz” “per Jluctuarions on of Fourier frequency f is from zero range infinity. S,,(f), in hertz squared to per is the spectral density offrequencyfluctuations 6v. It is calculated hertz. as @hn,)2 .wf) = (16) used in bandwidth measurement of 6v,,’ the The range of the Fourier frequency f is from zero to infinity. The spectral of phasejucruations is a normalized frequency domain density of measure sidebands. S,,(f), in radians squared per phase fluctuation on the spectral is of the phase fluctuations one-sided a “per hertz. density basis : hertz” wnns (17) = s&l- > in the measurement of 84,; bandwidth used power are densities of phase and frequency fluctuation The related by spectral = (18) S,,(f) (afP,(f). is range the Fourier The f of from zero ro injnity. frequency S,,(j). in radians squared Hertz squared per hertz is the spectral density of angular fluctuations bR: frequency (1% = %%a-) (2742&vu-). spectral densities have the following relationships: The defined (20) v;s,(f) S,,,(f) (vn)2s,,(f) = f2S,,(f>; = = (21) L&f) = (l/~)2&df) = wf)2s,u) = &“u-)/f21~ Note that Eq. (20) is hertz squared per hertz, whereas Eq. (21) is in radians squared hertz. per The term S,~r(v), in watts per hertz, is the spectral density of the (square 8 See Appendix Note # 30 TN-197

9 7. PHASE AND AM NOISE MEASUREMENTS NOISE 247 root frequency power P. The power of a signal is dispersed over the of) radio owing to instability, and modulation. This con- frequency spectrum noise, to of concept of spectral density similar voltage fluctuations cept is the is more convenient for characterizing a baseband Typically. S,,(f). S,,(j) voltage, rather than power, is relevant. SJ;~-(v) is typically signal where for the convenient dispersion of the signal power in more characterizing relate of carrier frequency v,,. To nominal the two spectral vicinity the the is necessary to specify the densities, associated with the signal. it impedance definition frequency stability that relates of actual sideband power A the phase fluctuations with of to the carrier power level, discussed by respect Glaze is called U(j). For a signal with PM and with no AM, U(j) (1970). the is of S,l;?-,(v), with its frequency parameter f refer- normalized version origin the average frequency v,, as the to such that f equals enced signal’s v-v If the signal also has AM, U(f) is the normalized version of those 0. portions S,T~(V) that are phase-modulation sidebands. of vo), f Fourier frequency difference (v - the the range off is Because is minus v. to plus from Since U(f) is a normalized density (phase infinity. noise power), sideband +m = 1. L?(f)df (22) * i - w 2’(f) is as the ratio of the power in one sideband, referred to the defined carrier frequency a per hertz of bandwidth spectral density basis, input on total f power, at Fourier frequency difference the from the carrier, to signal domain one is a normalized frequency It measure of phase fluctua- per device. sidebands, expressed in decibels relative to the carrier per hertz: tion density (one phase modulation sideband) power (23) = P(f) power carrier types of signals under consideration, the definition the two phase- For by sidebands (lower sideband and upper noise at -f and f from vo, sideband, respectively) a signal are approximately of with each other, and coherent they are of approximately equal intensity. It was show that the measurement of phase fluctuations (phase previously two required double-balanced mixer with a signals in phase noise) driving so the FM-AM conversion resulted quadrature voltage fluctuations at in the output that were analogous mixer the phase fluctuations. The opera- to tion of the mixer when it is driven at quadrature is such that the amplitudes in of phase sidebands are added linearly two the output of the mixer, the resulting in four times as much power in the output as would be present if to only of the phase sidebands were allowed to contribute one the output 8 See Appendix Note # 31 TN-198

10 A. LANCE, W. D. SEAL, AND F. LABAAR L. 248 the mixer. for ) S ) < vo, and considering only the phase modulation of Hence, power, the of the (square root of) density we obtain portion spectral of (24) fMP,,,> = 4PJP(v, + LY f %4 I)/( the definition of Y(f), and, using (25) Cqm4”o fM~,oc) = = %uI)* Y(f) + fluctuations the that the phase for occurring at rates Therefore, condition and faster are small compared to one radian, a good (f) in approximation radians per hertz for one unit is squared (26) = U(f) +s*,(f). be small condition is not met, Bessel-function the must angle used If algebra relate Y(f) to S,(f). to NBS-defined spectral density is usually expressed in decibels relative The the to per hertz and is calculated for one unit as carrier (27) 1 10 Wf h3cG.df)3. = the is important Ir note that very theory, definitions, and equations previously to set forth relate to a single device. D. MODULATION AND SPECTIUL DENSITY THEORY RELATIONSHIPS Applying frequency modulation fm to a sinusoidal carrier a sinusoidal sinusoidally v. wave that is a advanced and retarded frequency produces phase as a function of times. The instantaneous voltage is expressed in as, V(f) = sin(2rrv,t Ac$ sin 2nfmt), V, + (28) A4 is the peak phase deviation caused where the modulation signal. by The term inside the first represents the linearly progressing parentheses phase of the carrier. The second term is the phase variation (advancing and modulation retarded) progressing wave. The effects of linearly can the from expressed as be f, noise or as single-sideband phase noise. For residual deviation by single sinusoidal signal, the peak-frequency a of modulation carrier (vO) is the (29) =, Avo (30) A4 = Avoifm, ratio is modulation where,/;, This the of peak frequency deviation frequency. to modulation frequency is called modulation index m so that A# = m and m = Avojf,, (31) TN-199

11 7. PHASE AM NOISE WZASUREMENTS NOISE AND 249 frequency the modulated carrier contains frequency spectrum The of values other carrier. F%r small the of modula- (sidebands) components than (m << I), tion is the case with random phase noise, only the carrier index as first and lower sidebands are upper high in energy. The and significantly of the amplitude of either single sideband to the amplitude of the ratio is carrier m/2. = V,,jV, (32) is expressed in decibels below the carrier and is This to as dBc ratio referred the given bandwidth B: for VJV, = &c(m/2) = 20 log(Av,,‘2f,) 20 10 = 10 log(Av,l’2f,)‘. (33) log(m/2)’ = the frequency deviation is given in terms of its rms value, then If = Av,;J’?. (34) Av rms Equation now becomes (33) = 2Olog(Av,,j,%5 = WV0 Y(f) (35) = 10 log(Av,,,!&)‘. of single sideband to carrier power in decibels (carrier) per hertz is The ratio (36) 20 bi$Av,m/fm) g(f) 3 = - and, decibels relative to one squared radian per hertz, in (37) = S,,(f) 20 hWr,s/fm)- interrelationships The modulation index, peak frequency deviation, of rms frequency, and spectral density of phase fluctuations can be found from the following: (38) = Av,,,/J~. Av0/2f, irn = = $Sdg(f); (39) = lOexp(Y(f)/lO) or = Av,,/,j/zfm = ,/lo exp(Y(f )/lo) = ,/‘ss,,TTT, (40) irn and = 2 Av,,J& m blf, = (41) 10 exp(U( 2J = )/lo) = 2Jm. f basic relationships are plotted in Fig. 5. The TN-200

12 3.16 I lo-‘- - to-4 x lO-5 - 3.16 to-6 - t: o lO-6 - 3.16x -z z to-6 - F 4 2 0 3.16x - lo-’ 5 to-’ - 3.16 x 10-6 - to-6 - 3.16x lO-s, LOG fff FM;. S Spectral density relationships.

13 7. PHASE AND AM NOlSE.MEASUREMENTS 251 NOISE NOISE PROCESSES E. density spectral a typical oscillator’s output is usually a com- plot The of and noise It is very useful processes. meaningful to of bination different processes categorize the first job in evaluating a spectral these because plot to determine which type of noise exists is the particular density for of Fourier frequencies. range two basic categories are the discrete-frequency The and the power-law noise noise Discrete-frequency noise is a type of noise in which there is process. that ddminant i.e., deterministic in probability, they can usually a observable related to the mean frequency, power-line frequency, vibration frequencies, be ac magnetic fields, or to Fourier components of the nominal frequency. or domain Discrete-frequency illustrated in the frequency is plot of Fig. 6. noise These frequencies can have their own spectral density plots, which can be defined as on noise. noise noise processes types of noise that produce a certain slope Power-law are are one-sided density plot. They spectral characterized by their on the on frequency. The spectral density dependence of a typical oscillator plot output usually a combination of the various power-law processes. is noise In can classify the power-law we processes into five categor- general, ies. These five processes are illustrated in Fig. 5, which can be referred to with respect to following description of each process. the frequency). Random (1) (random walk of walk The plot goes down as FM l,‘f*. This noise is usually very close to the carrier and is difficult to measure. It usually related to the oscillator’s physical environment (mechanical is shock, vibration, temperature, or other environmental effects). “0 i! h FIG. 6 A basic discrete-frequency signal display. TN-202

14 252 A. LANCE, W. D. SEAL, AND F. LAMAR L. Flicker FM of frequency). The plot goes down as l/f3. This (2) (flicker typically related the physical resonance mechanism of the active noise is to design used choice of parts the for the electronic or power or oscillator or environmental properties. The time domain frequency even or supply, extended stability over constant. high-quality is oscillators, this periods In flicker be white FM (l/f’) or by phase modulation may marked noise It may be masked by @4 in low-quality oscillators. (Id). drift White (white frequency, random walk FM phase). The plot goes (3) of as l/f’. A common down of noise found in passive-resonator frequency type standards. and rubidium frequency standards have white FM noise Cesium because the (usually quartz) is locked to the reso- characteristic oscillator time of devices. This noise feature better as a function of these nance gets it (usually) becomes flicker FM (l/f’) noise. until Flicker $M (flicker modulation of phase). (4) plot goes down as The l/c noise may relate to the physical resonance mechanism in an oscil- This be It common lator. the highest-quality oscillators. This noise can is in introduced by noisy electronics-amplifiers necessary to bring the signal amplitude up to a usable level-and frequency multipliers. This noise can be reduced careful design by hand-selecting all components. by and 4M f”. phase). White phase noise plot is flat White Broadband (5) (white as noise produced in the same way generally flicker 4M (l/f). Late phase is of amplification are usually responsible. This noise can be kept low stages careful by of components and by narrow-band filtering at the output. selection power-law processes illustrated in Fig. 5. are The PHASE NOISE INTEGRATED F. integrated phase noise is a The of the phase-noise contribution measure (rms rms degrees) over a radians, range of Fourier frequencies. designated The integration is a process of summation that must be performed on the measured spectral within the actual IF bandwidth (B) used in the density of be . Therefore, the spectral density S,(f) must measurement un- S$,,, to bandwidth particular normalized used in the measurement. Define the in radians squared, as the unnormalized spectral density: S,(f), S,(f) = 2[10 exp(.Y(f) + 10 log B)/lO]. (42) Then, integrated phase noise over the the of Fourier frequencies (f, tof.) band where measurements are performed using a constant IF bandwidth, in radians squared, is (43) to fn> = j-I” &(f 1 dJ &LA II TN-203

15 7. PHASE AND AM NOISE MEASURELMENTS 253 NOISE in rms or, radians, calculated integrated in rms degrees is noise as and the phase 360/2x). S,( (45) the phase in decibels relative to noise carrier is calculated as The integrated = 10 log()s:). SB (46) The calculations correspond to the illustration in Fig. 7, which previous two over (Bl and B2) includes two ranges of Fourier frequencies. bandwidths bandwidths the program, different IF measurement are used as set In forth by Lance er al. (1977). The total integrated phase noise over the differ- ent ranges Fourier frequencies, which are measured at constant band- of radians widths is calculated in rms illustrated, as follows: as I S (47) BlOl . (s,,)’ + . + . + (s,)Z, = dSB# where it is recalled that the summation is performed in terms of radians squared. f FIG. 7 Integrated phase noise over Fourier frequency ranges at which measurements were performed using constant bandwidth. TN-204

16 254 A. LANCE, W. D. SEAL, AND F. LABAAR L. AM NOISE THE FREQUENCY DOMAIN G. IN density The fluctuations of a signal follows the same of spectral AM of given the spectral density for phase flucta- derivation general previously fluctuations & of the signal under tions. produces voltage Amplitude test 6A the output of the mixer. Interpretating the mean-square fluctuations at we & in spectal density fashion, 6 obtain S,,(f), the spectral fluctuations and of amplitude fluctuations be of a signal in volts squared per hertz: density = v,)2C&“LfwLns)21. S,,(f) cf term m(f) is the normalized version of the amplitude modulation (AM) The of S,;?-,(Y), its frequency parameter f referenced to the signal’s portion with such frequency taken as the origin , that the difference frequency average Y,, v - v,,. The range of Fourier frequency difference fequals is from minus f rO plus infinity. to amplicude- term is defined as the ratio of the spectral The ofone m(f) density inodulated to the total signal sideband at Fourier frequency difference power, f from the signal’s average frequency v,, , for a single specified signal or device. The dimensionality per hertz. U(f) and m(f) are similar functions; the is cor- is of phase-modulated (PM) sidebands, the later is a measure former a measure of amplitude-modulated (AM) sidebands. We introduce responding symbol m(f) to have useful terminology for the important concept of the AM power. normalized sideband the types of signals under consideration, by definition the two ampli- For sidebands and sideband tude-fluctuation upper sideband, at -f (lower coherent from f of a signal are vo, with each other. Also, they respectively) are of equal intensity. The operation of the mixer when it is driven at colinear phase is that the amplitudes of the two AM sidebands are added linearly such times the of the mixer, resulting in four in as much power in the output output as would be present if only one of the AM sidebands were allowed to contri- Hence, bute output of the mixer. the for ) to f) < vo, W~m9 f + = 4CS3v(vo lYC%,,)2 S,(l f and, using the definition we find, in decibels (carrier) per hertz, (51) 4f) = (1/2~3UIf I). TN-205

17 7. PHASE AND AM NOISE MEASUREMENTS NOISE 255 III. Using the Two-Oscillator Phase-Noise Measurements * Technique system of the two-oscillator block for measuring A diagram functional is shown in Fig. 8. NBS has performed phase noise measurements phase noise 1967 using basic system. The signal level and sideband levels can since this The measured of voltage or power. terms low-pass filter prevents local be in leakage power from overloading the oscillator analyzer when spectrum baseband are performed at the Fourier (offset) frequencies measurements the interest. will interfere with autoranging and with signals of Leakage range of the spectrum analyzer. dynamic low-noise, high-gain preamplifier provides additional system sensi- The tivity by the noise signals to be measured. Also, because spectrum amplyfying figure, analyzers high values of noise have this amplifier is very de- usually sirable. As an example, if the high-gain preamplifier had a noise figure of 3 dB spectrum analyzer had a noise figure of 18 dB, the system sensi- and the dB. this has been improved by 15 point The overall system sensitivity tivity at not necessarily be improved 15 dB in all cases, because the limiting would mixer. could been imposed by a noisy have sensitivity SIGNAL NOISY QUANTITY THE IS fTHlS BE TO MEASURED) OSCILLATOR PHASE SHIFTER TEST UNDER 11_1 NOISE ONLY SMALL FLUCTUATIONS f SPECTRUM - LOW-PASS ANALYZER FILTER l b LOW-NOISE AMPLIFIER REFERENCE NO NOISE OSCILLATOR 8 The two-oscillator technique FIG. measuring phase noise. Small fluctuations from for nominal voltage are equivalent to phase variations. The phase shifter adjusts the two signals noise to in the mixer, which cancels carriers and converts phase quadrature to fluctuating dc voltage. 8 See Appendix Note # 6 TN-206

18 A. LANCE, W. D. SEAL, AND F. LABAAR L. 256 that the oscillator is perfect (no phase noise), and that it Assume reference adjusted can Also, assume that both oscillators are extremely in be frequency. the that can be maintained without quadrature use of an so stable, phase loop or reference. The double-balanced external acts phase-locked mixer a detector so that when two input signals are identical in frequency as phase a in quadrature, the output is phase small fluctuating voltage. This and are the phase-modulated (PM) sideband component of the signal represents due quadrature the because, of the signals at the mixer input, the mixer to the amplitude-modulated sideband components to FM, and converts (AM) sideband same the converts the PM time components to AM. These at it components can be detected with an amplitude detector, as shown in AM 3. Fig. the two oscillator signals applied to the double-balanced mixer of Fig. 8 If slightly a of zero beat, are slow sinusoidal voltage with a peak-to-peak out mixer voltage be measured at the can output. If these same signals I/ptp are returned to zero beat and adjusted for phase quadrature, the output of the mixer a small fluctuating voltage (au) centered at zero volts. If the is voltage is compared to 4 I$,,,, the phase quadrature con- fluctuating small angle” is maintained and the “small closely condition is being dition being Phase fluctuations in radians between the test and reference signals met. are (phases) = 6(4, - 4,). w (52) These produce voltage fluctuations at fluctuations output of the phase the mixer, (53) i = w, &I vp,p sin phase are in radian where and angles S# = S# for small 84 measure (64 Q 1 rad). Solving for 64, squaring both sides, and taking a time average gives (54) = 4((W2 >/( I$,)‘, (@4)2 > the brackets represent the time average. where angle the sinusoidal beat signal, For (53 J&J2 ( = W’nd2~ voltage mean-square of The S4 and fluctuations 60 interpreted in a phase spectral density fashion gives the following in radians squared per hertz: (56) S,(f) &u-)/wrm,)2. = Here, S,,(f), in volts squared per hertz, is the spectral density of the voltage Because fluctuations the mixer output. at the spectrum analyzer measures TN-207

19 7. PHASE AND AM NOISE MEASURE.MENTS NOISE 257 rms noise voltage is in units of volts per square root hertz, which voltage, the per means bandwidth. Therefore, square volts root = C~%J~l (&d2/& = uf) (57) the noise where bandwidth used in the measurement. B is power was assumed that the reference oscillator Because not contribute any it did the fluctuations ulms represent the oscillator under test, and noise, voltage terms spectral the phase fluctuations in of of the voltage measure- the density performed with the spectrum analyzer, in radians squared per hertz, ments is (58) i c(~~rIns>2:~( Kns>21. S,,(f) = (46) is expressed as Equation sometimes (59) s,“ml~2~ = Sk&-> is the calibration factor in volts per radian. For sinusoidal beat where K slope peak of the signal equals the voltage of the zero crossing the signals, volts per in Therefore, (VP)’ = 2(V,,,)‘, which is the same as the radian. denominator Eq. (56). in term one can be expressed in decibels relative to The square radian S,,(f) S,,(f) hertz calculating 10 log by of the previous equation: per S,,(f) = 20 log(&,,,) - 20 log(&) - 10 log(B) - 3 (60) A of 2.5 is required for the tracking spectrum analyzer used in correction expressed measurement differs by 3 dB and is U(f) in decibels these systems. per hertz as (carrier) = 20 log(bu,,,) - 20 log( I$.,,,) - 10 log(B) - 6. 9(f) (61) A. NO~SY~SC~LLATORS Two measurement system of Fig. 6 yields the output noise from both The If is reference oscillator oscillators. superior in performance as assumed the a the discussions, then one obtains in direct measure of the noise previous characteristics of the oscillator under test. If the and test oscillators are the same type, a useful approxima- reference is noise assume that the measured tion power is twice that associated to in with oscillator. This approximation is noisy error by no more than one 3 dB for the noisier oscillator, even if one oscillator is the major source of density noise. for the spectral equation of measured phase Huctuations The in radians squared per hertz is + s,,(f~)l#, sdf)l#2 = Isdf)l.wode”i..,, + wLJL t /zs,d/)~(o”ede”ice, (62) TN-208

20 A. LANCE, W. D. SEAL. AND F. LABAAR L. 258 measured value therefore divided by two to obtain the value for the The is oscillator A the noise of each of can be made oscillator. single determination has three oscillators that can be measured in all pair combinations. if one noise source each phase 1, 2, and 3 is calculated as follows: The of 10 + = 1()4913tf)/lo _ 1()923(Jwo)], U,(f) ~og[+(lo”“‘/“lo (63) = p(f) log[+(l(-J’“‘/“10 + 1()Y23m/lo _ 10913m’10)], 10 (64) = 10 log[L#)‘L”/“‘O + p(f) _ 1(-JYl2UV10)]~ ]()Y23U)/lO (65) AUTOMATED PHASE-NOISE USING THE MEASUREMENTS B. TECHNIQUE TWO-OSCILLATOR phase-noise measurement system is shown in Fig. 9. It is The automated of a calculator. Each step programmable the calibration and by controlled sequence is included in the measurement The software program program. controls slection, bandwidth settings, settling time, amplitude frequency measurements, graphics, and data plotting. Normally, ranging, calculations, system is used the obtain a direct plot of Y(f). The integrated phase noise to can be calculated for any selected range Fourier frequencies. of quasi-continuous plot phase noise performance U(f) is obtained A of measurements by Fourier frequencies separated performing the IF by at the of analyzer used during spectrum measurement. Plots of bandwidth the defined parameters can be obtained other plotted as desired. and The bandwidth settings for the Fourier (offset) frequency-range IF are in the following tabulation: selections shown Fourier IF Fourier IF bandwidth frequency frequency bandwidth (kHz) (Hz) (kHz) W-M 0.001-0.4 I 40-100 3 100-400 3 0.4-I IO 14 400-1300 10 30 100 4-10 200 10-40 particular range of Fourier frequencies is limited by The particular the spectrum used in the system. A analyzer Fourier analyzer (FFT) is also fast incorporated in the system to measure phase noise from submiIlihertz to 25 kHz. sources can be High-quality without multiplication to enhance measured the phase noise prior to downconverting and measuring at baseband fre- the because measurements are not completely automated quencies. The calibration sequence requires several manual operations. TN-209

21 7. PHASE AND AM NOISE MEASUREMENTS NOISE 259 OSCILLATOR UNDER TEST I I I I :KLYZER 11 /-j pREAMpL,F,Eij osc~LLoSCoPEj .&’ - - - L - - - - * - - - - l \ I------ PHASE-LOCKED LOOP .I 9 automated phase-noise measurement system. FIG. An AND USING THE CALIBRATION C. MEASUREMENTS TWO-OSCILLATOR SYSTEM a is frequency domain measure of phase-fluctuation side- L?(f) normalized power. The band power is measured relative to the carrier power noise level. must be applied because of the type of measurement and Correction characteristics the measurement equipment. The general procedure the of the calibration and measurement sequence includes the following: for the the power bandwidth for each IF bandwidth setting on measuring noise Tracking Spectrum Analyzer (Section III.C.l); establishing a carrier refer- ence power level referenced to the output of the mixer (Section 1II.C.Z); obtaining phase of the two signals applied to the mixer (Section quadrature measuring noise power at the selected Fourier frequencies III.C.3); the III.C.4); performing the calculations and plotting the data (Section (Section and noise the system III.C.5); floor characteristics, usually re- measuring to sensitivity. the system ferred as 1. ,Voise-Power Bandwidth of analyzer-noise bandwidths Approximations not adequate for phase are noise measurements and calculations. The IF noise-power bandwidth of the tracking spectrum must be known and used in the calculations of analyzer the noise Figure 10 shows parameters. results of measurements per- phase formed using automated techniques. For example, with a l-MHz signal input the tracking spectrum analyzer, the desired incremental frequency to changes covering the IF bandwidth are set by calculator control. TN-210

22 260 A. LANCE, W. D. SEAL, AND F. LABAAR L. BANDWIDTH ~-HZ d8 -20 - 3.251 NOISE Hz BANDWIDTH: FREQUENCY Plot automated noise-power bandwidth. of 10 FIG. power The is recorded for each frequency setting spectrum analyzer output range, over illustrated in Fig. 10. The 40-dB level and the 100 incre- the as in are not the minimum frequency values. The recorded ments permissible be plotted for each IF bandwidth, as illustrated, and can noise-power the bandwidth calculated in hertz as is + (Pt + P, + P, + ... PI”) Af power = noise bandwidth (66) ’ power reading peak Afis the frequency increment in hertz and the where power is the maxi- peak mum point obtained during the measurements. All power values measured are in watts. A. Setting 7 Carrier Power Reference Level the Recall from Section III.6 that for sinusoidal signals the peak voltage of the signal the slope of the zero crossing, in volts per radian. A frequency equals the is the peak power of and difference frequency is mea- offset established, as the carrier-power reference level; this establishes the sured calibration factor the mixer in volts per radian. of in the IF attenuator is used Because the calibration process, one precision must be aware that the impedance looking back into the mixer should be 50 R. the mixer output signal should be sinusoidal. Fischer (1978) Also, element” the as the “critical mixer in the measurement system. discussed It is advisable to drive the mixer so that the sinusoidal signal is obtained TRW at output. In most of the mixer systems, the mixer drive levels are the 10 dBm for the reference signal and about zero dBm for the unit under test. TN-211

23 7. PHASE AND AM NOISE MEASUREMENTS NOISE 261 System be increased by driving the mixer with high-level sensitivity can lower the output impedance to a few ohms. This presents signals that mixer establishing the calibration factor of in mixer, because it a problem the different to the mixer for calibrate Fourier frequency be might necessary ranges. sensitivity = slope equation beat-note amplitude does not hold The = output 3047 the mixer is not a sine wave. The Hewlett-Packard the if of noise system phase allows accurate calibration automated measurement inputs phase-detector even with high-level the by using the of sensitivity of the Fourier representation of the signal (the fundamental and derivative its harmonics). slope at 4 z 0 radians is given by The 34 sin B sin 34 + C sin 54 = A cos 4 - 3E cos - + 5C cos 54 A 4 = + SC + 3B *. . ’ A- (67) to Fig. 9, the carrier-power reference level is obtained as follows. Referring The precision IF step attenuator is set to a high value to prevent (1) the analyzer (assume 50 dB as our example). overloading spectrum The reference and test signals at (2) mixer inputs are set to approxi- the mately 10 dBm and 0 dBm, as previously discussed. (3) If the frequency of one of the oscillators can be adjusted, adjust its frequency for IF output frequency in the range of 10 to 20 kHz. If neither an is adjustable, the oscillator under test with one that can oscillator replace identical as and adjusted can be set to the required power level of the be that under test. oscillator The resulting IF power level is measured by the (4) analyzer, spectrum and measured value is corrected for the attentuator setting, which was the to is 50 dB. The correction assumed necessary because this attenuator be indication will to its zero decibel set during the measurements of noise be power. Assuming a spectrum analyzer reading of -40 dBm, the carrier- power reference. is calculated as level dBm power = 50 dB - 40 level = 10 dBm. carrier reference (68) Phase Quadrature of the Mixer Input Signals 3. After the reference has been established, the oscillator under carrier-power to and reference oscillator are tuned test the same frequency, and the the original reference levels that were used during calibration are reestablished. Three The depends on the type of system used. adjustment quadrature possibilities, illustrated in Fig. 9, are described here. (I) If the oscillators are very stable, have high-resolution tuning, and are zero dc oscillator frequency of one phase-locked, is adjusted for not the TN-212

24 A. LANCE, W. D. SEAL, AND F. LABAAB L. 262 output of mixer as indicated by the sensitive oscilloscope. voltage the has shown the quadrature setting is not critical if the Note: Experience that AM an characteristics. As low example, experiments sources have noise degradation two synthesizers showed that 3335 of the using performed HP became noticeable with a phase-quadrature phase-noise measurement 16 of offset degrees. the common reference frequency is used, as illustrated in Fig. 9. then (2) If oscil- necessary include a is shifter in the line between one of the to it phase and mixer (preferably between the the and mixer). The lators attenuator shifter is adjusted to obtain and phase zero volts dc at the mixer maintain output. correction for a nonzero dc value can be applied as exemplified by A HP 3047 phase-noise measurement system. the automated phase-locked one If phase-locked using a oscillator loop, as shown (3) is in on Fig. 9, the frequency of the unit under test is adjusted for zero dotted output indicated the mixer as dc on the oscilloscope. of function phase-locked a feedback system whose is is to force a A loop oscillator (VCO) to be coherent voltage-controlled a certain frequency, with i.e.. is highly correlated in both it and phase. The phase detector frequency is a mixer circuit that mixes the input signal with the VCO signal. The mixer locked. input the loop is when the VCO duplicates the output + rO. is vi so that difference frequency is zero, and the output is a dc frequency the to The phase difference. proportional low-pass filter removes voltage the component frequency but passes the dc sum to control the the component The time constant of the loop can VCO. adjusted as needed by varying be amplifier and RC filtering within the loop. gain loose loop is characterized by the following. A phase-locked 1) The correction voltage varies ( phase (in the short term) and phase as variations are therefore observed directly. (2) The bandwidth of the servo response is small compared with the Fourier frequency be measured. to The response is very slow. (3) time A phase-locked tight is characterized by the following. loop The correction (1) of the servo loop varies as frequency. voltage (2) bandwidth of the The response is relatively large. servo (3) The response time is much smaller than the smallest time interval T at which are performed. measurements of 11 the Figure characteristics shows the H.P. 86408 synthe- phase-noise sizer measured at 512 MHz. The phase-locked-loop attenuation character- istics to 10 kHz. The internal-oscillator-source characteristics are extend plotted at Fourier frequencies beyond the loop-bandwidth cutoff at 10 kHz. TN-213

25 7. PHASE AND AM NOISE MEASUREMENTS NOISE 263 I ; -PHASE-LOCKED I LOOP 512-MHz OSCILLATOR -160 I I I I I -160 10 104 103 106 102 105 FOURIER FREQUENCY (Hz) I Phase-locked-loop characteristics of the H.P. 86408 signal generator. showing FIG. I phase-noise the power spectral density. normalized sldeband Calculations. Data Plots Measurements, and 4. sequence is The except for the case where manual measurement automated are required to maintain adjustments quadrature of the signals. After phase phase of the signals into the mixer is established, the IF atten- quadrature setting. is the zerodecibel reference to This attenuator is uator returned to a high value [assumed to be 50 dB in Eq. set to prevent saturation (65)] of spectrum analyzer during the calibration process. the The measurements are executed, and the direct measurement automated and data plot of U(f) is obtained in decibels (carrier) per hertz using the equation 2.5 [carrier power level - - power level - 6 + (noise af-> = 10 B - 3)]. - log (69) noise power (dBm) is measured relative to the carrier-power level The and the remaining terms of (dBm), equation represent corrections that the the be because must the type of measurement and applied characteristics of of the measurement equipment, as follows. (1) The measurement of noise sidebands with the signals in phase quadrature requires -6dB correction that is noted in Eq. (69). the The spectrum of the (2) analyzer’s logarithmic IF amplifier nonlinearity results compression of the noise peaks which, when average-detected, in require the 2.5dB correction. (3) bandwidth correction is required because the spectrum analyzer The measurements of random or white noise are a function of the particular bandwidth used in the measurement. TN-2 14

26 264 A. LANCE, W. D. SEAL, AND F. LABAAR L. The - correction is required because this is a direct measure of (4) 3-dB rwo are assuming that the oscillators of of a similar type Y(f) oscillators, each that contribution is the same for noise oscillator. If one oscil- and the is sufficiently superior to the other, this correction is not required. lator defined can densities Other be calculated and plotted as desired. spectral density plotted value of the spectral stored of phase fluctuations The or decibels relative to one square radian (dBc rad’/Hz) is calculated as in (70) S,,(f) + 3. = an hertz, spectral of phase fluctuations, in The squared per density is radians calculated as (71) Wf) = 10 ev&&fWO), The spectral density of frequency fluctuations, in hertz squared per hertz, is (72) Wf) = f%m radian. S,,(F) decibels with respect to 1 in where is System Noise Floor Verification 5. plot of the system noise floor (sensitivity) is obtained A repeating the by automated procedures with the system modified as shown in measurement 12. Accurate measurements can be obtained using the configuration Fig. shown in Fig. 12a. The reference source supplies 10 dBm to one side of the mixer and dBm to the other mixer input through equal path lengths; 0 phase quadrature maintained with the is shifter. phase @------50-R TERMINATION (a) lb) (a) FIG. System configurations for measurmg the system noise floor (sensitivity): I2 (b) contiguration for accurate measurements: used alternate configuration sometimes used. TN-215

27 7. PHASE AND AM NOISE MEASUREMENTS 265 NOISE configuration shown Fig. 12b is sometimes used and does not The in the greatly because the reference signal of 10 dBm is noise degrade floor IV.C.4 signal See Sections 1V.B and frequency. for additional than larger the to system sensitivity and discussions system evaluation. related recommended selection drive and output termination of the double-balanced Proper of dB result can by 15 to 25 in in the performance of phase- mixer improvement measurements, as discussed by Wails et al. (1976). The noise frequency beat between two oscillators can be a sine wave, as previously mentioned, the proper low levels. This requires a proper terminating impedance with drive mixer mixer. high drive levels, the the output waveform will be for With The slope of the clipped waveform at the clipped. crossings, illustrated zero by et al. (1976), is twice the slope of the sine wave and therefore Walls im- proves noise floor sensitivity by 6 the i.e., the output signal, proportional dB, to the phase fluctuations, increases with drive level. This condition of clipping requires characterization the Fourier frequency range, as previously over for the 3047 phase noise measurement system. mentioned Hewlett-Packard can amplifier An to increase the mixer be levels for devices that used drive insufficient output power to drive the double-balanced mixers. have noise can Lower be achieved using high-level mixers when available floors levels be sufficient. A step-up transformer can drive used to increase are and the voltage because the signal drive noise power increase in the mixer same ratio, and the spectral density of phase of the device under test is un- changed, but noise floor of the measurement system is reduced. the et technique (1976) used a correlation Walls that consisted primarily al. the of measurement systems. At TRW phase-noise technique is used as two shown in Fig. 13. The cross spectrum is obtained with the fast Fourier product transform that performs the analyzer of the Fourier trans-- (FFT) form of one signal and the complex conjugate of the Fourier transform of DUAL- CHANNEL FFT i FIG. 13 Cross-spectrum measurement using the two-oscillator technique. TN-216

28 266 A. LANCE, W. D. SEAL, AND F. LABAAR L. is second cross spectrum, which This a phase-sensitive character- the signal. gives a phase and amplitude sensitivity measure directly. A signal- istic, enhancement 20 than to-noise dB can be achieved. greater the system phase noise measurement If does not provide double-balanced a floor sufficient for measuring a high-quality source. frequency noise multiplier chains can be used if their inherent noise is lo-20 dB below the measurement system In frequency multiplication the noise increases noise. to according log(fina1 frequency/original frequency). 10 * (73) r B - 102 103 104 106 10 106 FOURIER FREQUENCY IHI) (al -160 FIG. 14 Data plots of the automated phase-noise measurement system: (a) a high quality 3 S-MHz oscillator; (b) combined noise of two H.P. 8662A synthesizers (subtract quartz dB for single unit). a 8 See Appendix Note X 32 TN-217

29 7. 267 AND AM NOISE MEASUREMENTS PHASE NOISE following equation used to correct for noise-floor contribution The is dBc!Hz, Pnr, or necessary: if in desired [P,,;;--;nf] + log -U(f) 10 = Y(f)(corrected) noise-floor contribution The also be obtained by using correction for can of S,,(f) of Eq. (57). the of S&J’) of the oscillator measurement Measurement floor obtained, then S,,(f) is obtained for the noise floor only. is plus Then, (75) (ror = S,“(f) /lo,c+nfl - S,“u-) l”f S,“(f) 14a shows a phase noise plot of a very high-quality (~-MHZ) Figure oscillator, by quartz the two-oscillator technique. The sharp measured below 1000 represent the 60-Hz line frequency of the power supply peaks Hz oscillator its are not part of the and phase noise. Figure 14b and harmonics measurements to 0.02 Hz of the carrier at a frequency of 20 shows MHz. IV. Phase-Noise LMeasurement Systems and Single-Oscillator * Techniques measurements of a single-oscillator phase-noise based on the The are of measurement jhctuations using discriminator techniques. The jkequency with discriminator practical a filter acts finite bandwidth that suppresses as the carrier and the sidebands on both sides of the carrier. The ideal carrier- suppression filter provide infinite attentuation of the carrier and would attenutation of other frequencies. The effective Q of the practical zero all how signals the determines are attenuated. discriminator much at discrimination high frequencies (VHF) has been ob- Frequency very using slope detectors and ratio detectors, by tained of lumped circuit use elements inductance and capacitance. At ultrahigh frequencies (UHF) of the can and microwave regions, measurements between be performed VHF with beating, heterodyning, the UHF signal by a local oscillator to obtain or a VHF signal that is analyzed with a discriminator in the VHF frequency range. Those provide a means for rejecting residual amplitude- techniques (AM) discriminators on the signal under test. The VHF modulated noise employ or limiter usually ratio detector. a et Ashley (1968) and Ondria al. have discussed the microwave (1968) cavity discriminator that rejects AM noise, suppresses the carrier so that the a input be increased, and provides can high discriminated output to level improve the signal-to-noise floor ratio. The delay line used as an FM dis- (1975), criminator been discussed by Tykulsky (1966), Halford has and * See Appendix Note # 6 TN-218

30 268 A. LANCE, W. D. SEAL, AND F. LABAAR L. fb) ial . DIGITAL SIGNAL LINE DELAV - ANALYZER / \ IFFTI 4 LOW-NOISE OSCILLATOR : AMPLIFIER UNDER TEST g 2 5 ICI Single-oscillator phase-noise measurement techniques: FIG. cavity discriminator; 15 (a) reflective-type dlscrlmmator; (c) one-way delay hne. (b) delay-hne proposed al. Ashley et al. (1968) et the reflective-type delay- Ashley (1968). discriminator shown in Fig. 15b. line cavity can also be used to replace The delay The one-way delay line shown in Fig. 1% is implemented in the line. measurement this The theory and applications set forth in TRW systems. are this on a system of section particular type. based A. DISCRIMINATOR LINE AS AN FM THE DELAY 1. The Single-Oscillator Measurement System The single-oscillator signal is split into two channels in the system shown in Fig. One channel is called the nondelay or reference channel. It is also 15. the to local-oscillator (LO) channel because the signal in this referred as drives the mixer at the prescribed impedance channel (the usual LO level drive). signal in the second channel The at the mixer through a delay arrives line. The two signals are adjusted for phase quadrature with the phase the shifter, output of the mixer is a fluctuating voltage, analogous to the and frequency of the source, centered fluctuations approximately zero dc on volts. The delay line yields a phase shift by the time the signal arrives at the on balanced The phase shift depends mixer. the instantaneous frequency of TN-219

31 7. 269 AND AM NOISE MEASUREMENTS PHASE NOISE signal. The of frequency modulation (FM) on the signal gives the presence differential the modulation (PM) at to output of the differential rise phase This its (nondelay) reference line. associated relationship is linear delay and the delay ~~ is nondispersive. This is the property that allows the delay line if to be as an FM discriminator. In general, the conversion factors are a used of of delay (sd) and the Fourier frequency f but not function the carrier the frequency. by phase The of the nominal frequency vO caused differential the delay shift line is AC$I = 2nv, Td, (76) where ?d is the time delay. The phase at the mixer are related to the frequency fluctuations fluctuations the f) by (at rate &$ = 2nT,6V(f). (77) spectral density relationships are The (78) 1 (2’&)2 s,,(f) MS = OSE mixer and S,,(f) = f2 S,,(f). (79) Then, (80) = mki)2 S,,(f) %b(f) OS.2 dlm where the subscript dlm indicates delay-line method. From Eq. (56), the spectral density phase for the two-oscillator technique, in radians squared of hertz, is per S&&f 1 (81) 1 m,,>2 [ = 4 S,“(f) = = 7 -L(f) Km> 3 I/,,,)B 8 cv,,,>’ because 8h,,,)2 [email protected]~,,,)~1 = ’ = WJ2 = and (82) -wf) = W,,(f)/(&J2) = b%&vLJ2~ per hertz. TN-220

32 270 A. W. D. SEAL, AND F. LABAAR L. LANCE, (noise floor) the two-oscillator measurement system The sensitivity of and of noise of the mixer and the noise thermal the base- includes shot the is to input). This noise floor its measured with (referred band preamplifier under test inoperative. The measurement system sensitivity of the oscillator system, on a per hertz density basis (dBc/Hz) is the two-oscillator (83 10 = Wf)nr logc2(~~“)2/(1/,,,)21. is the rms noise voltage measured in a one-hertz bandwidth. where SC, system yields two-oscillator the output noise from both The therefore in If oscillator is superior reference performance, as assumed oscillators. the the previous discussions, then one obtains a direct measure of the noise in of characteristics under test. If the reference and test oscillators the oscillator same to a useful approximation is the assume that the measured are type, noisy is that associated with one twice oscillator. This approxi- noise power is in error by no more than 3 dB for the noisier oscillator. Substituting mation have, Eq. using the relationships in Eq. (56) we and per hertz, (80) in =wf) = 2c(~~,,,)2/(~~/p,,)21(2~f~d)2 (84) dim of this equation reveals the following. Examination two-oscillator The in the brackets represents the term response. (1) of the two-oscillator method. represents the noise jloor Note that this term Therefore, adoption the delay-line method results in a higher noise by the of (2nf?d)2 when with the two-oscillator measurement method. factor compared time (noise for delay sensitivity with different values of floor) delay The lines illustrated in Fig. 17. are Equation (84) also indicates that the measured value of (2) is U(f) in w = 2x5 This is shown in Fig. 21. The first null in the responses periodic cali- at Fourier is f = l/7,, The periodicity indicates that the the frequency bration of the discriminator is range and that valid measurements limited occur only in the indicated range. as verified by the discriminator slope shown in Fig. (See Fig. 23.) 16. than The of (2nfrd)2 can be greater value unity (it is 4 at (3) maximum = 1 ‘27,). This 6-dB f is utilized in the noise-floor measurement. advantage However, is beyond the valid it range of the delay-line system. calibration The 6-dB advantage is offset by the line attenuation at microwave frequencies, as discussed Halford (1975). by in delay-line system The been analyzed discriminator terms of a power- has limited system (a particular idealized system in which the choice of power line, oscillator the attenuator of the delay voltage, and the conversion loss TN-22 1

33 7. PHASE AND AM NOISE MEASUREMENTS NOISE 271 of are limited by the capability of the mixer) by Tykulsky (1966). the mixer particular and al. (1977). For this et case, Eq. (83) (1975), Ashley Halford an increase in the length of the delay line (to increase r,, indicates that for of frequencies closer to the carrier) results in an decorrelation Fourier causes attenuation the line, which of a corresponding decrease increase in I&. The optimum length occurs in rd is such that the decrease in where VP,, approximately compensated by the increase in (211fTd), i.e., where is W-G d o --= . (85) _. \ , condition occurs where the attenuation of the delay line is 1 Np This dB). the when (8.686 system is not power limited, the attenuation However, input the of is not limited, because the delay power to the delay line can line be adjusted to maintain VPIP at the desired value. The optimum delay-line length is at a particular selectable frequency. However, since determined attenuation varies (approximately proportional to the square root the slowly this characteristic allows near-optimum operation over a of frequency), frequency range without appreciable degradation in the considerable measurements. A view of the time delay (rd) and Fourier-frequency functional practical can the obtained by reviewing relationship basic concepts be the of dual- time-delay measurement system channel by Lance (1964). If the discussed differential delay between the two channels is zero, there is no phase differ- ence at detector output when a swept-frequency cw signal is applied the detected to Figure 16 shows the system. output interference display when the a swept-frequency cw signal (zero to 4 MHz) is applied to a system that has f=4MHz f=2MHr FIG. 16 Swept-frequency interference display at the output of a dual-channel system with a differential delay of 500 nscc. TN-222

34 272 A. W. D. SEAL, AND F. LABAAR L. LANCE, channels. delay nsec between the two 500 The signal ampli- differential of a assumed to be almost equal, thus producing the familiar tudes are voltage- pattern interference display. Because this is a two-channel standing-wave or is a null every 360”, as shown. system, there System Sensitidy (Noise Floor) When Using the 2. De+Line Dtflerenrial Technique has single- that the sensitivity (noise floor) of the Halford (1975) shown delay-line technique is reduced relative to the two- oscillator differential techniques. The sensitivity is modified by the factor oscillator = 1 - cos 2,&d). 2( 035) Sd WT~ = 2ndTd < 1 a good approximation iS For (87) = 2(1 - COS 2,tfrd) = (Wr,,)‘[l - &(w?d)*] = (2tt,kd)2 = 8’, s; where 6’ the phase delay of the differential delay line evaluated at the is 1: two- 17 shows the relative sensitivity (noise floor) of the frequency Figure technique with the single-oscillator technique oscillator different and Fourier lengths. fW2 delay-line is noted at The frequencies beyond slope -20 - -40 - -60 - ;; z - -00 u 5 - -100 - -120 3 ii -140 - P -160 - -100 - -190 1 I 1 I I I I 103 104 105 106 10’ 10 102 FOURIER FREQUENCY FIG. 17 Relative sensitivity (noise floor) of single-oscillator and two-oscillator phase- noise measurement systems. TN-223

35 7. PHASE AND AM NOISE MEASUREMENTS NOISE 273 about For Fourier frequencies closer to the carrier, the slope is f -3. I kHz. sum the the f -’ slope of Eq. (87) and the f - ’ flicker noise. i.e., of sources have characteristics that cannot be Phase-locked phase-noise close-in at frequencies using this basic system. The measured Fourier sensitivity of the system relative be improved by using a dual (two- can channel) system and performing cross-spectrum analysis, which delay-line be presented this chapter. will in developed the (1982) rf bridge configuration shown in Labaar delay-line 18. At microwave frequencies Fig. a high-gain amplifier is available, where suppression the carrier by the rf of allows amplification of the noise bridge going into the mixer. A relative sensitivity improvement of 35 dB has been obtained without The limitations of the technique depend on the difficulty. the rf the carrier suppression by and bridge. Naturally, if available power rf input to the bridge is high the must use the technique with adequate one precautions prevent mixer damage that to occur by an accidental bridge can unbalance. Labaar (1982) indicated the added advantage of using the rf bridge carrier-suppression when attempting to measure phase technique is close the noise when AM noise to present. Figure 19 shows the carrier PHASE SHIFTER DELAY-LINE rf ERIDGE 7 DELAY LINE MIXER PHASE SHIFTER FIG. 18 Carrier suppression using an rf bridge to increase relative sensitivity. (Courtesy Instrument Society of America.) TN-224

36 274 A. LANCE, W. D. SEAL, AND F. LABAAR L. z > AM LEAKAGE f co Frequancv (Hz) detector output (AM-PM FIG. 7, delay time. Phase 19 crossover); for phase (PM) and amplitude (AM) noise in the single- mixer output FM delay-line system. It is noted that the phase oscillator discriminator will AM intersect and that the AM and therefore limit the mea- noise noise accuracy near the carrier. Even though AM noise is much surement lower than noise in most sources, and even though the AM is normally phase the about there is still AM at dB, mixer output. This output suppressed 20 AM leakage and is caused by the finite isolation between the is ports. mixer The technique does not experience this problem to this two-oscillator noise extent phase noise and AM the maintain their relative rela- because tionships at the mixer output independent of the offset frequency from the carrier. B. AND MEASUREMENTS IXE DELAY CALIBRATION USING AN DISCRIMINATOR AS FM LINE diagram of The practical single-oscillator phase noise measure- block a system is shown in Fig. 20. The signals in ment delay-line channel of the the system the one-way delay of the line. With adequate source experience optimum the is not limited to the power, 1 Np (8.686 dB) previously system discussed for a power-limited system. Measurements are performed using the following procedures. operational Measure forth tracking spectrum analyzer IF bandwidths as set (1) the in Section III.C.1. Establish the (2) power levels (Section 1V.B.I). system (3) Establish the discriminator calibration factor (Section IV.B.2). (4) and plot the oscillator characteristics in the automatic Measure system used (Section IV.B.3). (5) Measure the system noise floor (sensitivity) (Section IV.B.4). TN-225

37 7. PHASE AND AM NOISE MEASUREMENTS NOISE 275 A ATTEN. ATTEN AMP SPECTRUM : 1 A pNtLJyfE_R DELAY LINE J A MIXER HIGH GAIN MEASUREMENT 1. TO AUTOMATIC SYSTEM 5420A DIGITAL SIGNAL ANALYZER HP 2. 25 kHz) 6UEMlLLlHERTZ TO 539OA 3. STABILITY HP FREQUENCY Hz 10 kHzI (0.01 TO ANALYZER Single-oscillator phase noise FIG. system using the delay line as an 20 measurement discrimmator. (From Lance ef al., 1977a.) FM System Levels 1. Power system power are set using attenuators, as shown in Fig. 20. The levels is characteristic of attenuator No. 4 impedance 50 R, mismatch Because the will occur if the mixer output errors is not 50 R. As previously impedance discussed, mixer drive levels are set so that the mixer output the as signal, observed calibration, is sinusoidal. during has been accomplished in This TRW systems with a reference (LO) signal level of 10 dBm and a mixer input level about 0 dBm from the delay line. of source power be used to increase the can signal to the measure- A amplifier system. This amplifier must not contribute appreciable additional ment to signal. noise the Discriminator 2. Calibration discriminator characteristics are measured as a function of The frequency and The hertz-per-volt sensitivity voltage. the discriminator is defined of as the calibrarion factor (CF). The calibration process involves measuring the effects intentional modulation of the source (carrier) frequency. A of modulation index must be obtained to calculate the calibration known factors of the discriminator. The modulation index is obtained by using amplitude to establish the carrier-to-sideband ratio when there modulation is considerable instability of the source or when the source cannot be fre- quency modulated. TN-226

38 A. LANCE, W. D. SEAL, AND F. LAMAR L. 276 is convenient consider the system equations and calibration techniques It to of in of stable sources. If the source to be frequency terms modulation frequency must it be be replaced, during the measured cannot modulated, a modulatable source. The calibration process process, calibration with described using a modulatable source and will 20-kHz modulation be a However, modulation frequencies can be used. The cali- frequency. other of found type discriminator has been factor to be constant over bration this resolution Fourier range, within the frequency of the measuring the usable The calibration factor of the discriminator is established technique. the after system levels have been set with the unit under test as the source. power discriminator calibration are as follows. The procedures attenuator dB. 4 (Fig. 20) to 50 Set (1) No. signal the under test with a Replace generator or oscillator (2) oscillator can be frequency modulated. that power and operutingfrequenc) The outpur the generator must be set to the same precise frequency and amplitude of that will oscillator under test values present to the system during the mea- the ‘surement process. kHz Select modulation frequency of (3) a and increase the modulation 20 until the carrier is reduced to the first Bessel null, as indicated on the spectrum analyzer connected coupler No. 1. This establishes a modulation index to = 2.405). (m the mixer, shifter for zero volts dc at the output of the (4) Adjust phase in on oscilloscope connected as shown the Fig. 20. This estab- as indicated the quadrature condition for the two inputs lishes the mixer. This quadrature to condition continuously monitored and is adjusted if necessary. is Tune modulation tracking spectrum analyzer to the (5) frequency the frequency 20 of power reading at this kHz. is recorded in the program The and is corrected for the 50-dB setting of attenuator No. 4, which will be set to zero during the automated measurements. decibel indication + ( dBm power reading) = 50 dB P(dBm) - (88) power level is converted to the equivalent rms voltage that the spectrum This been would read if the total signal had have applied: analyzer V J1oP’lO/lOOO + R. (89) rms = (6) discriminator calibration factor can now be calculated because The this power in dBm can be converted to the corresponding rms voltage using the equation: following = j(lOp”o/lOOO) x R, (90) V,,, = 50 R in this system. where R TN-227

39 7. PHASE AND AM NOISE MEASUREMENTS 277 NOISE The discriminator factor is calculated in hertz per volt as (7) calibration (91) modulation for the first Bessel null m used in this technique The index as The modulation frequency is is 2.405. /A. .Measurement Data Plotting and 3. signal is After the modulated discriminator source is re- the calibrated, with the frequency source to be measured. Quadrature of the signals placed into the is reestablished, attenuator No. 4 (Fig. 20) is set to 0 dB, and mixer measurement process begin. the can calculations, and measurements, plotting are completely auto- The data The calculator program selects the Fourier frequency, performs mated. autoranging, and the bandwidth, and measurements of Fourier frequency sets analyzer. are by the tracking spectrum power Each Fourier performed frequency noise-power reading P, (dBm) is converted to the corresponding rms voltage by lrml = x R. \/‘10’Pn+2~5”10/1U10 V (92) rms are calculated The as frequency fluctuations vtrm, x CF. = Sv,,, (93) spectral density of frequency fluctuations The hertz squared per hertz is in calculated as = (94) Wf> @hn,>2/~1 B is the measured where noise-power bandwidth of the spectrum analyzer. IF The spectral density of phase fluctuations in radians squared per hertz is calculated as (95) = S,,(f> L(fYf2. NBS-designated spectral density in decibels (carrier) per hertz The cal- is culated as (96) a/),, = 10 1% b%,(f 1. Spectral density is plotted in real time in our program. However, the data in can stored and the desired spectral density can be plotted be other forms. Integrated phase noise can be obtained as desired. TN-228

40 278 A. LANCE, W. D. SEAL, AND F. LABAAR L. KoisesFloor Measurements 4. sensitivity relative of the single-oscillator measurement (noise The floor) two-oscillator as Fig. 12a for the in technique. measured shown system is must be removed and equal channel The constructed, delay line lengths Fig. The same power levels used (12a). the original calibration and in as in reestablished, and measurements noise floor is measured at specific are the frequencies, the same calibration-measurement technique, Fourier using repeating automated measurement sequence. by the or for the noise floor requires a measurement of the A voltage correction rms the (cirms) and a measurement of oscillator noise floor rms voltage of the These voltages are used in the following equation (ulrrns). obtain the to corrected value: = Jhrln32 hns)2. (97) ~rnls - r,,, The value in the calculation then frequency fluctuations. used is of memory is available, each value of ulnnr If be stored and used adequate can the set of measurements are performed other the same Fourier after at frequencies. following technique was developed by Labaar The Carrier sup- (1982). pression obtained using the rf bridge illustrated in Fig. 18. One can easily is sensitivity GHz than 40 dB. At 2.0 and 3.0 improve 70-dB carrier more was the In general, suppression improvement in sensitivity will realized. amplifier depend availability of an the or adequate input power. on Figure 21 shows the different noise floors in a delay-line bridge discrimi- nator. It good measurement discipline to always determine these noise is also, the displayed in Fig. 21, give a quick under- floors; measurements, the trace process involved. The first of is obtained by term- standing physical analyzer. input the baseband spectrum of The measured output inating the power is then a direct measure of the spectrum analyzer’s noise figure noise (NF). input noise is thermal noise and is usually indicated by “KTB,” The is absolute for “the thermal noise power at which temperature of 7 short number K(elvin) degrees hertz bandwidth (B). This KTB per is, at 18°C one about - 174 dBm/Hz. Figure 2la shows that trace number 1 for frequencies above about 1 kHz is level with value of about - 150 dBm = - (174-24) dBm, which means that a up spectrum has an NF of 24 the At 20 Hz the NF has gone analyzer to dB. about dB. To improve the 48 a low-noise (NF, 2dB). low-frequency NF, (10 Hz-10 MHz) amplifier is inserted as a preamplifier. Terminating its the input in trace number 2. At results high frequency end, the measured now power goes up by about 12-13 dB, and the amplifiers gain is 34 dB. This - means the NF is improved by 34 that 12-13 = 21-22 dB, which is an TN-229

41 7. PHASE AND AM NOISE MEASUREMENTS NOISE 279 = . -I-“- - g ” 0 -160 - x c! “kTE” * T I I I I I -180 I 1.0 10 100 low 0.01 0. 10,000 fktiz) FREQUENCY GAiN = 34 dB F2~lds J NF

42 A. LANCE, W. D. SEAL, AND F. LABMR L. 280 FREOUENCY IHzI FOURIER (From Phase 600-MHz oscillator multiplied to 2.4 GHz of Lance et al.. noise FIG. 22 1977a.) was nsec long, as noted by the first null, i.e., the reciprocal of the about 500 frequency of 2 MHz Fourier the approximate differential time delay. is Note a shorter delay line (approximately 250 nsec differential) is used that measure because higher frequency to the delay-line discriminator the frequency is only to a Fourier calibration at approximately 35% of valid the Fourier frequency at which the first null occurs, if a linear transfer function is assumed. discriminator actual of a delay-line function (classic and rf The transfer types) is sinusoidal, as shown in Fig. bridge The baseband spectrum 23a. analyzer power in a finite bandwidth, measures as a consequence it is and possible to measure through a transfer-function null if the noise power does not over a spectrum-analyzer bandwidth. The following substantially change relations then hold: power c,+Ao.'2 P(w) (98) = P(w). P(w’) do’ 1 bw do’ = 1lAw P,,,,(w) s o-Au.2 TN-23 1

43 7. PHASE AND AM NOISE MEASUREMENTS NOISE 281 CORRECT (SINUSOIDAL1 -100 - TRANSFER ;; FUNCTION F P - 0 -120 = 4 -140 - CORRECTION BREAKOOWN - -160 LINEAR TRANSFER FUNCTION -180 - I I I1111 I IIII I III1 I IllI III1 1GU 10,wlY loo0 1.0 10 FREQUENCY fktid fb) 23 Transfer functions for a delay-line rf bridge FIG. (a) actual; (b) discriminator: approximate and “correct” (sinusoidal). Phase noise: H.P. 8672A at 2.4 GHz. (linear) approximation 23b results using a linear the and the “cor- Figure shows transfer function for a delay-line rect” bridge discriminator. The correct rf transfer breaks down close to function null because the signal level the drops below the system’s noise floor, as explained by Labaar (1982). Using the transfer function in the calculator software gives sinusoidal to results intervals of 5 frequency 10 spectrum analyzer’s correct barring (10 x 30 = 300 kHz) bandwidths at the transfer function nulls. centered These data were selected to particular the characteristics of the illustrate system. Recall that one can easily make the noise floor 40 dB lower using the rf shown in Fig. 18. bridge C. DELAY-LINE DISCRIMINATOR DUAL 1, Phase Noise Measurements The dual delay-line discriminator is shown in Fig. 24. This system was for suggested (1975) as a technique Halford lowering the noise floor by of the delay-line phase noise measurement system. The system consists of TN-232

44 282 A. LANCE, W. D. SEAL, AND F. LABAAR L. 1 I.“. -~ (FRED.-MOD. I H ‘&fAillLlfYlI / 1 DELAY LINE t A r--x+ ORTEC AMP. an,r 1 HEWLETT-PACKARD f 5420A DIGITAL SIGNAL ANALYZER T CcG OATEC AMP. I 9431 I 1 f DELAYl&NE 24 A dual delay-line phase noise measurement system. (Courtesy Instrument Society FIG. America.) of differential delay-line systems. The single-oscillator signal is applied two is to and cross-spectrum analysis systems performed on the signal both output from the two delay-line systems. Signal processing is performed with the Hewlett-Packard digital signal analyzer. The cross spectrum is 5420A by of the product of the Fourier transform obtained one signal and taking of the of the Fourier transform conjugate a second signal. It is complex a phase-sensitive characteristic resulting in a complex product that serves of as of the relative phase measurement two signals. Cross spectrum gives a a phase- and amplitude-sensitive measurement directly. By performing certain the SJ(~) . Sx(f‘)*, a product signal-to-noise enhancement is achieved. TN-233

45 283 7. AND AM NOISE MEASUREMENTS PHASE NOISE low-noise amplifiers the digital signal analyzer are used The preceding measurements at frequencies from 1 Hz to 25 kHz. when performing Fourier not used when performing measurements below the are The amplifiers 1 Hz. of frequency Fourier the Dual Delay-Line System 2. Calibrating line delay the system is calibrated separately following the same Each in set 1V.B. in Section procedure The Hewlett-Packard 5420 basic forth the spectral density of frequency fluctuations in hertz measures one-sided per hertz. The spectral squared of phase fluctuation in radians density squared hertz can be calculated as per (99) = S,,(f) S,“WfZ~ and = -wf’) [email protected] Mfw-2, The Hewlett-Packard 5420 per of S,,(j) in Hz’/Hz must, hertz. measurement be corrected by li2f 2. However, thef2 correction must be entered therefore, in terms radian frequency (o = 2j). This conversion is accomplished by of (101) = Wf2X4n2/4n2) W-) C27r2S,,(fM42 = S,,(fX stated hertz Eq. per can be since in the following terms: (100) c2~2ww4w. Signal-to-noise enhancement greater than 20 dB has been obtained using the dual-channel system. delay-line MILLIMETER-WAVE PHASE-NOISE D. MEASUREMENTS Density Phase Fluctuations Spectral of I. line used as an FM discriminator is based, in principle, The a delay on delay However, a waveguide can line. used as the delay nondispersive be because line Fourier frequency range of interest is a small percentage the of operating bandwidth (seldom over 100 MHz), and the dispersion can the be considered negligible. as calibration measurement are The and set forth in Section performed 1V.B. The modulation index m is usually established using the carrier-to- sideband ratio uses amplitude modulation because millimeter sources that either approaches or cannot be modulated. The two are to measure- unstable Figs. ments frequencies are shown in millimeter 25 and 26. Figure 25 at shows the direct measurement using a waveguide delay line. This system is offers if adequate input power sensitivity available. The rf bridge improved and delay-line portion of the system differs from Fig. 18 because pre- and TN-234

46 284 A. LANCE, W. D. SEAL, AND F. LABAAR L. 1 1 9845A 9872A CIRCULATOR PLOTTER IL m I PHASE OSCILLOSCOPE ATTEN. DELAY LINE delay Millimeter-wave measurements using a waveguide noise line. (From 25 FIG. phase Lance. 1981.) Seal and with appropriate gain are not available, so the sensi- amplifiers post-bridge equal the amount of carrier suppression. can tivity 26 shows the use of a harmonic mixer Figure downconvert to the to convenient frequency where post-bridge amplifiers are available. lower delay- relatively to frequency drift that is characteristic of sensitivity The low discriminators becomes an advantage here. line separate calibration A used is as shown in Fig. 25, and a power meter is generator to assure required, proper power levels during the calibration process. 2. SPECTRAL DENSITY OFAM~LI'IZIDEFLUCTUATIONS AM noise require equal electrical length in the two channels measurements line supply to the mixer. The delay signals must be replaced with the that the length of transmission line to necessary the equal-length condition establish when systems shown in Figs. 25 and the are used. The AM noise measure- 26 ment system is calibrated and the noise measurements are performed directly the in power for a direct measurement of m(f) in dBc/Hz. m(f) is of units spectral of one modulation sideband density by the total signal divided power at a Fourier frequency difference f from the signal’s average frequency lno. system calibration establishes the detection characteristics in terms The of total power output at the IF port of the mixer (detector). TN-235

47 7. PHASE AND AM NOISE MEASUREMENTS NOISE 285 + 0 dBm 20 dBm A A A 9 ----------------- -------------- r SO LI O-STATE A FIG. hybrid phase noise measurement system that produces IF 26 millimeter-wave and uses a frequency discriminator at IF frequency. (From Seal and Lance, 1981.) delay-line The noise measurements are performed according to the following. AM A known AM modulation (carrier-sideband ratio) must be estab- (1) lished to calibrate this detector in terms of total power output at the IF port. The modulation be low enough so that the sidebands are at least must the dB the carrier. This is to keep 20 total added power due to the below modulation small enough to cause an insignificant change in the detector characteristics. (2) rf power levels are adjusted The levels of approximately 10 dBm for at the reference port and 0 dBm at the test port of the mixer. TN-236

48 A. LANCE, W. D. SEAL, AND F. LABAAR L. 286 Approximately 40 is set in the precision IF attenuator. The system (3) dB for our-of-phase quadrature condition. adjusted an is modulation frequency and power level are (4) by the The measured baseband spectrum analyzer. The total carrier-power reference automatic is measured power, plus the carrier-sideband modulation ratio, plus level IF attenuator setting. the set The is removed. the IF attenuator modulation to ,O dB, and (5) AM system re-checked to verify the out-of-phase quadrature (maximum dc the selected from mixer IF port). Noise (V,) is measured at the the Fourier output frequencies. A direct calculation of m(f) in dBc/Hz is ,,Q) = [(modulation power (dBm) + carrier-sideband ratio (dB) + IF (dB) - noise power (dBm) + 2.5 dB attenuation 10 - log(BW)]. (102) 27 illustrates the measurements of AM and phase noise of two Figure oscillators in were offset GUNN frequency by 1 GHz. The measurements that were performed the coaxial delay-line system. using -20 7 9 > B z -40 - g "0 - -60 a E -60 - i? m K -loo- s ,o -120 4 2 s -140 z % $ -160 I 102 103 104 106 106 10' FOURIER FREOUENCYWZI FIG. 27 Phase noise and AM noise of 40- and 41-GHz Gunn oscillators. (From Seal and Lance. 1981.) TN-237

49 7. PHASE AND AM NOISE MEASUREMENTS NOISE 287 V. Conclusion and fundamentals measurement of phase noise have techniques The for technique for systems. The two-oscillator basic provides forth two been set measuring high-performance cw sources. the system capability for The superior the single-oscillator technique to measuring phase is sensitivity for close noise the carrier. very to sources as those used in frequency standards applica- High-stability such be without using phase-locked loops. However, most can measured tions exhibit frequency instability microwave requires phase-locked sources that to maintain the necessary quadrature conditions. The characteristics loops the phase-locked loops must be evaluated to of the source phase obtain noise Also, in principle, one must have three sources at the characteristics. frequency to a given source. If three sources are not avail- same characterize is one that either one source assume superior in performance or able, must they have equal phase noise contributions. that single-oscillator employing the The technique line as an FM dis- delay has sensitivity for measuring most microwave sources. criminator adequate economic advantages of using this system include The fact that only the one is required, phase-locked loops source not required, system configur- are ation is relatively inexpensive, and the system is inherently insensitive to oscillator frequency drift. single-oscillator technique the delay-line discriminator can The using to sources the phase noise of pulsed sources. Pulsed adapted be measure at measured 94 GHz by F. Labaar been TRW, Redondo Beach, have at California. ACKNOWLEDGMENTS imtial preparations for developing a phase noise measurement capability were the result Our Our was JOrg Raue of TRW. Dr. first phase noise development effort of discussions with in and evaluation of phase noise measurement systems designed assisting developed by the of Hook TRW Bill 1973). The efforts of Don Leavitt of TRW were vital in initiating the (Hook, measurement program. We are very grateful to Dr. Donald Halford of the National Bureau of Standards in Boulder, Colorado, for interest, consultauons, and valuable suggestions during the development of his phase systems measurement the at TRW. noise C. appreciate We cross-checks performed by the Reynolds, J. Oliverio, and measurement H. Cole of the Hewlett-Packard Company. Dr. J. Robert Ashley of the University of Colorado, Missile Colorado G. Rast of the U.S. Army and Command, Redstone Arsenal. Springs, Huntsville, Alabama. REFERENCES Allen, D. W. (1966). Proc. fEEE 54.221-230. M. Ashley, R., Searles. C. B., and Palka, F. J. (1968). IEEE Trans. .tficrowaor Theory Tech. MIT-M(9). 753-760. TN-238

50 288 A. LANCE, W. D. SEAL, AND F. LABAAR L. J. R.. T. A., and Rast, Ashley. Barley, (1977). IEEE Microwave Theorv Tech. G. J. Trans. 294-3 18. M-t-T-25(4). R. N., and Nelin. B. J.. (1965). Proc. IEEE 53,704-722. Baghdady, E. Lincoln, D. (1969). “Tables of Bias Functions, Barnes, and B,. for Variances Bawd on Finite 1. A. i3, Processes Power Law Spectral Densities,” with Bureau of Standards of Samples National 375. Technical Note A., J. A. R., and Cutler, L. S. (1970). “Characterization of Frequency Stability,” Barnes, Chic, IEEE Trans. Insrrum in also published Technical of Note 394; National Bureau Standards 105-120 (1971). TM-20(2). Meas. Ann. F., Halford. Brandenberger. and Shoaf, J. H. (1971). Proc. 25th Hadorn, Symp. H., D., Conrrol, Fort Monmouth. New Jersey, pp. 226-230. Freq. 54, IEEE Proc. 136154. C. L. (1966). Searle. and L. Culter, S.. M. C. “Frequency Domain Measurement Systems.” Paper presented at the Fisher. (1978). Planning Precise Time Interval Applications and and Meeting, Goddard Annual 10th Time Center, Greenbelt, Maryland. Space Flight * D. Proc. Halford. 56(2), 251-258. IEEE (1968). Standards National Bureau of Technical (1975). Delay Line “The D. Halford, Discriminator,” IO, pp. 19-38. Note D.. Wainwright, A. E.. and Barnes, J. A. Halford. Proc. 22nd Ann. Symp. Freq. Conrrol. (1968). Fort New Jersey, 340-341. Monmouth, Symp. D.. H., and Risley. A. S. (1973). Proc. 27rh Ann. J. Freq. Conrrol, Cherry Halford. Shoaf, New Jersey, pp. 421-430. Hill. W. R. Hook. “Phase Noise Measurement Techniques for Sources Having Extremely (1973). Low Noise.” TRW Defense and Space Phase Group Internal Document, Redondo Systems Beach, California. Hewlett-Packard Company (1965). “Frequency and Time Standards,” Application Note 52. Hewlett-Packard Co., Alto, California. Palo Company (1970). Counter Applications Library,” Application Hewlett-Packard “Computing Palo 22. 29. Hewlett-Packard Co.. and Alto, California. 7, Notes 27, (1976). “Understanding and Measuring Phase Noise in the Fre- Hewlett-Packard Company Application Domain,” 207. Hewlett-Packard Co., Loveland, Colorado. quency Note Microwaues 21(3), 65-69. Testing.” Phase Noise F. (1982). Discriminator Boosts Labaar. “New A. L. (1964). ” Lance, to Microwave Theory and Measurements.” McGraw-Hill, Introduction New York. N. W. (I 977a). Microware J. 20(6). and Hudson, Seal, A. W. D., Mendoxa, F. G.. Lance. L., 87-103. A. L.. Seal. Lance, D., Mendoza, F. G.. and Hudson. N. W. (1977b). Proc. 31~1 Annu. Symp. W. Freq. Confrol. Atlantic City, New Jersey, pp. 463-483. Lance. A. L.. Seal. W. D., Halford, D.. Hudson, N.. and Mendoza. F. (1978). “Phase Noise Measurements Using Analysis.” Paper presented at the IEEE Conference on Cross-Spectrum Measurements, Ottawa, Electromagnetic Canada. (1982). L.. W. D., and A. F. Seal. Lance. Labaar, Trans. 21(4). 37-44. ISA D. G. (1970). IEEE Trans. Meyer. 215-227. IM-19(4), Ondria. (1968). IEEE Trans. Microwave Theory Tech. MTT-16(g), 767-781. J. Ondria. J. (1980). G. Inf. IEEE-MTT-S Symp. Dig.. pp. 24-25. Microware Payne, J. B., 111 (1976). Microivare Svstem News 6(2). 118-128. RF Scherer, *. Design Principles and Measurement Low Phase Noise (1979). and Microwave D. Sources.” Hewlett-Packard Co.. Palo Alto. Califorma. Seal. W. D.. and Lance, A. L. (1981). Microware Swrem News ll(7). 54-61. S. Shoaf. Halford. D.. and Risley. A. H.. (1973). “Frequency Stability Specifications and J. Measurement.” National Bureau of Standards Technical Note 632. * See Appendix Note # 33 TN-239

51 7. PHASE AND AM NOISE MEASUREMENTS 289 NOISE A. Proc. IEEE 54(2), 306. Tykulsky, (1966). Duzer, V. (1965). Van IEEE-NASA Symp. Definition Meas. Short-Term Freq. Subility. Proc. NASA SP-80.269-272. Walls, F. L., and Stein, S. R. (1977). Proc. 31~1 Ann. Symp. Freq. Conrrol, Atlantic City, New Jersey, 335-343. pp. Proc. 3Orh Ann. Stem, S. R., Gray, J. E.. Glaze. D. J., and Allen, D. W. (1976). Walls. F. L.. Symp. Freq. Cornrrol. Atlantic City, New Jersey, p. 269. TN-240

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