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I
I
o The "Arl" of
Phase Noise
f,lleasurement
DieterScherer
March1985
o
Rf & Mlcrowave
Measurement
Symposlum
ancl
txhlbltlon
ftE'HF$|IfJJ
o
O
o
o
DUCTION
INTRO
Measuring and specifying phase noise has become inereasingly important as phase
noise is the limiting facior in many RF and microwave systems,like Doppler radar and
space telemetry sy.te-. or communicationlinks. The complexity and subtleties of the
1nuurur.-unt have earned it the reputation of being more art than science.
This paper gives an introduction to phase noise measurementfocusing on the two most
and useful techniques,the "Two Source Phase Detector" and the "Delay Line
Frequenc;- Discriminator" methods. System limitations are pointed 9ut a-swell as the
"o--o1
potential ,our"". of erroneousdata when phase noise is measuredin a bench set up.
The lt72gc Carrier Noise Test Set is HP's latest contribution in this field, designed to
simplify and automate the complex task. A table of comparisons will show where the
ttTigC and the various other HP solutions are optimally employed.
O 1. Phase
Why Measure Noise?
Phasenoisecauses . .
.
environment
sensitivity multi-signal
o Lowerreceiver in
Transmiller
H
q-
DopplerSignal
DecorrelatedClutler Noise
J_
o Glutter RadarSystems
noisein Doppler
r Phase systems
errorsin digitalcommunication
phasenoiseimposes fundamentallimitations wherevera weak signal is processed the presence a
in of
.tiorrg interferini rij""r. In the aboveexample, phasenoisesidebands the receiverlocal oscillatorare
of
ti"".i"*"a to thI Ifpioduct of the strong interfering sjsnll and cover up the weak wanted signal.
signal in this caseis
A similar situatio;exists with cohereit Dopplerradar. The strong interferring
p;;;;J ty reflectionsfrom large stationarl' f5;".ts. Phasenoise side bands of this unwanted return
weak Dopplersignal'
lien"i"r. ,iecorrelateJbvdelav ind potentially coveras clutter noisethe
Phasenoise adds to
b,,r"n in the world of d-igitaliata tiansmission phasenoise is a limiting faetor.
the carrier or data clock
o*,"r^il system rroir. in.rJ"sing Bit Error Rate and may causea cycle slip in
recovery.
5
2. Noise
BasicRepresentation Phase
of o
2.1 In the Time Domain:
v(t): Signat
withrandom phasefluctuation ,0(t)
A
v(t): Vscos f?rtsl+ J O (t)l
DisPlaY
OscilloscoPe
V(t) = Vs cos 2rlsl
ar <> ao(t)
bY
Frequency Phase related
and are
f(r):##
In the time domain phase noise can be observedas phase jitter of the signal on an oscilloscopedisplal' or
a time interval counter may detect the instantaneous time fluctuations of the zero crossings.
phase or frequencyfluctuations are the same physical phenomena.One can be derivedfrom the other as
angular frequency is the first derivative of phase with respect to time.
6
O,, Domain:
In the Frequency
FJd(t):Jd(f)
S4
Fluctuations
Density Phase
Spectral of
SO(f)-Jd2rms(f)
f'3 F l i cke r FM
I d2rms
f' 2 Random W alk Phase
t-t FlickerPhase
fo White Phase
FourierFrequencY -
|
s3
Fluctuations
Density Frequency
spectral of
: :
Sr t(f) = Jf2rms(f) l2J @2rms(l) fzSO(f)
Spectraldensity distributions describe frequencyor phasenoisein the frequencydomain.Terms like
.,White,,' and ..Random
,,Flicker,' Walk" refei to the slopeof f , f-t, and f-2 of thd densitydistribution.
time domain -
rrluiiipri."tion by the Fourier frequency- conespond.rlsto differentiation in the
noise.
converti the spectraldensity of phasl noiie to the spectraldensity offrequency
7
2.3 Relation Phase
of Noise
Noiseto CarrierSideband
offset
o
The modulari6n pf the signal phase manifests itself in modulation sidebandsto the carrier at
frequencies u.hich ar" muliiples of the modulation The sideband levels are
rate rFourier frequencyr.
relatedto the magnirucle the phasedeviationby Bessel
of terms.For small'anglemodulation,onl5'thefirst
Besselterm is signrficanr and the relation betu'eenphasedeviation and sidebandlevel is approximated b1'
anglemodulalion
Forsmall
( I ar. < l radian)
J d2rms
=
?P {-t d2rms(f)
A common,though indirect.representation phasenoiseis,7{fr,the ratio of the single sidebandnoise
of
po$.er in a I Hz band*'ldth to the total carrier power specified at a given offset, f of the carrier'
produce
This representation is applicable only for very small phase deviations, sufficiently small to
negligible higher order sidebands.
Definition Y (t)
ol
y(tt=ry
+- -+
-fott fogl= |
-
\
2,5 5, Sl f:
between
Refation st
8i
b
$r
lor -\6<< lradian
E!
E:
Y (t)= iS o(t)=i -t, srf (t)
1_ 11 i
E.b
.E'E
69
*l Hz
1
L
o Techniques
3 PhaseNoiseMeasurement
o DirectSpectrumAnalysis
) o Two Sources
and PhaseDetector
o Frequency
Discriminator
) o DelayLine Frequency
Discriminator
o Carrier (OndriaBridge)
Suppression
o Heterodyne
PeriodGounter
From the multitude of techniquesto measurephaseorfrequency noisetwobasicmethods are singled out
and explained in somedetail onthe following pages:the "Two Sourcesand Phase Detector" technique and
the "Dela5' Line Frequency Discriminator" technique'
Both methods are ielatively simple to implement and are broadband solutions.They also compliment
each other well. The first method rnl.rur"s phase noise;high sensitivity is obtainable and two sourcesare
needed. The second method measures frequency noise, has inherently lower sensitivity close in but no
secondsourceis required.
3.1Two Sourcesand PhaseDetectorTechnique o
Source
Test
Under
AmPl.
lsolation
lv' Low Noise
Low PassFiller Amplifier
PhaseDetector
t_
tl ^Al
(Double Mixer)
Balanced
AmPl.
lsolation Calibration
i+
I
L--
, 1! F = F
v
Allenuator
NarrowBand
PhaseLock LooP
sd (t)
y (t)
Hz)
JV273ns(1 (forJd<
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