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f
t
I
Principles Test ethods
Design and M
jll Sources
LowPhase *t
Noise *icrowave
Scherer
Dieter
RF&Mlcrowave
Measurement
Symposlum
and
Exhlt ltlon
ftE SFTiif;T
-1-
Introduct'ion
In an increasing number microv',ave
of applications suchas satellite
cormunications toa.tn radar, the -The
dnO syitemdesignlegyires signal sources
w'iththe lowestpottiUie pnase noile. intenl of th'is papefis to.give
an overview of.bniia.ritions toi ttre designandtest of low phase noise
sources. First, .o*on definitions and specifications frequencyof
iiiUiiity are sf'own iefated io-eacnother. Then
ana designprinciplesof
iiw-pr,ai! noiseitnpriiiers, osciiiuiors andphase noisecharacteristics
o f d i v i d e r s . " . i o u e . e d s - w e l la s t h e i r i n t e g r a t i o n n t o c r u c i a l b l o c k s
a i
of iynthesized signa] sources, phuse lock loops, and reference multiplica-
lion. Finaily, mEthods measuring of phase noiseare compared'
-2-
Termi og.y
nol
r:l
v ( t ) = V rco s l e n to t + A O(tlJ r epr esentsa signal with a linear ly gr owi ng
p h a s eco mp o n e n t rfo t a n d a r andomly
Z fluctuating ter m A0( t) , phasenois e.
dq{ t)
R e c a l l th a t r(t) = J Ther efor e,we can talk in ter ms of
2n dt
p h a s efl u ctu a ti o n s o r i n ter m s of fr equencyfiuctuations to descr ibe one
andthe same ignal.
s
S o m e o n ve n ti o n a te rms fo r char acter izingfr equencystability in the ti m e
c l
domain re: (seeFig. 1a)
a
- L o n gt e r m s t a b i l i t y , d e s c r i b i n gs l o w c h a n g e o f f r e q u e n c yi k e a g i n g .
s l
- S h o rt te rm sta b i l i ty, cover ingfr equencynoise and fluctuations wit fp
r a nd o m e ri o d s sh o rte r than som e
p minutes.
al Time Domain
laf(z)l
lr I
1 sec I min I hour
Short Term Long Term
Stability stability
deviation plotted
F i g . l a sh o w s e fr actional fr equency
th
o ve r sa mpletime t.
-3-
L i k e w i se , i n th e fre q u e n cy dom ain,ter m s like Random hlalk, Flicker and W hi te
p h a s eN o i sed e scri b e th e sl ope of spectr al density. Fig. 1b plots the s pec tr al
d e n s i ty d i stri b u ti o n o f p h asefluctr .r ation. The Four jer Fr equencyher e l abel ed
(
f r ) m a ya l so b e ca l l e d si d eband equency,
Fr 0ffset Fr equencyn odulati onF r equenc y
M
or Baseband Frequency.
Domain
bl Frequency
f 4Random WalkFM
-2 (WhiteFMI
f RandomWdk Phase
aoz(fm)
*
FourierFrequencY fm
(Sideband Frequency)
(Offset Frequencyl
tModulationFrequency)
Fig.'lb
- 4-
Definition of J (f*)
The most common characterization of phasenoise of sources in the frequency
d o m a i n s th e R F p o w e rsp e ctr um , obablybecause
i pr this is what one obse r v es
o n a s p e c t r u m n a l y z e rw h e n Mn o i s e i s i n s i g n i f i c a n t ( F i g . 2 ) -
a A
T h e d i s p l a y i s s y m m e t r i c a l .T a k i n gj u s t o n e s i d e a n d l o o k i n g a t s i d e b a n d o i s e
n
i n a l Hz b a n d w i d the a d s to the definition of scr ipt4 ( fr ) :
l
Sc r i p t 4 (f*) i s d e fi n e d a s the r atio of the single sideband powerof phas e
noise in a lHz bandwidth Hertz awayfrom the carrier frequencyto the total
fm
s i g n a l p o w e r.
Fig. ?
r
grl
sl
'6 1
g
o&t
Fig.3
!sc
cL
EE
.crF
E.E
o!
?E
8s +.ll<-1 fm
62
-5-
HowDoesPhaseMod@
T h e p r evi o u sd e fi n i ti o n o f & is pr imar ily applied to r andomnoise. To r el ate
fr e quenc y
& t o r an d o m r si n u so i d a l p hasemodulation,a signal with sinusoidal
o
m o d u l ati o n s co n si d e re d rst and conver tedto phasemodulation.
i fi
f =fo+ A fpeaksestafrt
f
0 = J 2 z f ( t )d t
Q= 2ttfo t + 2n t^t
*r,"
O= Znlot+Ad peaksin 2z f,,.'t
fPgtk
v (t| = V, cos (22 fot *o sin 2rf.t)
'm
Be s s e la 'l g e b ra e l d s th e si ngle sideband car r ier r atio. For a smal l
yi to
m o d u l a t i o nn d e x , A q p e a k < 1 , t h e f o l l o w ' i n ga p p r o x i m a t i oh o l d s :
i < n
afpeak
fm
+ =,,
fS-+Y=!oop".r
(b\r= peak
+ asz
4
\u'1 Fig.4
o r i n l o g a ri th mi c fo rm:
t., \z
's-sb
1
\tt
| = -6dB+20log AS peak
\sl
-6-
For randomp h a sefl u c tuations, A$peak r eplacedwith an equivalent
is
JZ Aorms r a l H z bandwidth.
fo
4 (fr) =
ftg;,, = +({z ro"rJ'=, Ao2rms
0 r i n ve rse l y, th e S p e ctra l Densityof PhaseNoiseexpr essed 4 :
by
=
SAO(f*) = A02rms 2 J. (fr)
s^o(tr)fo,= 3dB A(fr)l
+
aa.
Fluctuations, Relatedto Sr t.,landr C
Sp e c tra l D e n si t.v f F re q u enc.v
o
S t a b i l i ty me a su re me n tsth fr equency
wi discr im inator s give the Spectr al
D e n s i t yo f F r e q u e n cF l u c t u a t i o n s .
y
Saf (fm) = Af2r*,
T o r e l a te th e sp e ctra 'ld e n sity of fr equency fluctuations to the spec tr al
d e n s i ty o f p h a sen o 'i sew e recall that
r .|Ao(t)
=oa
Af(t)= 6
into the frequencydomain:
Transformed
Af(fr) = f, A0 (fm)
s^f(fm) = Af2.*r(fr) = f*2 s4(r*) = 2 f Z .{ (fr)
m
-7-
NBSproposesto standardizethe spectral density of fractional frequency
f l u c t ua ti o n s. T h e i n sta n taneous equencydeviation is nor m alized the
fr to
carrier frequencyfo.
v(t)= +(!.t
to
= rZ '#.,(r,n)
s^f(fm) =TJ 1*,rr,
I m
sy(fm) =6
$o
'c
C h a r acte ri zi n gfra cti o n a l fr equencyfluctuations allows better com pa r i s on
b e t w ee n u rce sw i th d i ffe rent car r ier fr equencies'
so
Residual FMRelated to .C[fr)
Residual FMis another conmon way to specify the frequencystability of
s i g n al g e n e ra to rs. R e si d ualFMis the total r ms fr equencydeviation wi thi n
used bandwidths are 50Hzto 3kHz, 300H2 to
a specified bandwidth. conmonly
3 k H z ,2 0 H zt o l 5 k H z .
-
rrres=
6I-l r.o2drt
r(rm)
a-
( f* ) anA
T h e t ab l e b e l o wco rre l a te s Af"., and { ( fr ) for specific sloPesof I
JOtkHz=-100d8c.
Slope of J (fm) Residual efr", [Hzl
FM
50 Hz to 3 kHz 300 Hz to 3 kHz 2OHzto 15 kHz
- 10 0 0dB 1.y 1.9 r5.0
-100 -3 dB .95 .94 4.74
-100 -6 dB .77 .73 1.73
- 10 0 -9 dB .90 .68 1.15
- 8-
*For any J @ t kxz differentto -100 dBc multiply
100-ll@lkHz/dBcl
afr", of the tableby antilog
sidebands.
any microphonic spurious
The tabledoesnot takeinto account or
Example:
.C@ 1 kHz = -88 dBc,Slope dB
-9
For bandwidth Hz to 15 kHz:
20
100 -88 = 4.6 Hz
Afres= 1.15Hz x antilog
A l l a n V a r i a n c e e l a t e dt o 4 ( f * )
R
F o r m a n y p p l i c a t i o n sl,i k e h i g h s t a b i ' l i t y c r y s t a l o s c i l l a t o r s o r d o p p l e rr a d a r
a
s y s t e m s,i t i s mo rere l e va n t to descr ibefr equencystability in the tim e dom ai n.
T h e c h ara cte ri za ti o ni s b a sedon the sam ple ianceof fr actional fr equenc y
var
f l u c t u a ti o n s. A ve ra g i n g i ffer ences of consecutive
d sam ple pair s with n o dead-
t i m e i n b e t w e e y i e l d s t h e A l l a n V a r i a n c e , o r z t r ) , w h i c hi s t h e p r o p o s e d
n
s t a n d a rdme a su re f fre q u e n cystability.
o
M-1
of,rr)-#1) \
L F1.'1-V1)2
K=1
Tn ts the averagefractiona'l frequencydifference of the k-th samplemeasured
o v e r s amp l e me t.
ti
C o n v e rsi o n fro m fre q u e n cyto time domain
s data and vice ver sa ar e possi bl e
but tedious. The powerspectrum l-(fr) needsto be approximated integer by
s l o p e so f 0 , - 1 , - 2 , - 3 , - 4 . T h e nc o n v e r s i o no r m u l a s( s e e T a b l e b e l o w )c a n
f
b e a p p l i e d . A g o o dd e s c r i p t i o no f t h i s p r o c e d u r es g i v e n i n [ Z ] a n a [ S ] .
i
- 9-
ConvercionTable
oto! lrl
Stope orlrl = J(f)= Slopeof "C(f)
,-
WHITEPHASE
./rJfr4,-r (3rt,t'rotz.sost)2
2.565{o f6
*
r ttt t (z.teo /n1rn
't) (o, trt rofz.sosl)2
FLICKERPHASE - r.9 " f-l
2.565fo Z.1u+ ln $6r I
ffi 1t2 to)2 12 -2
WHITEFREO. - I t-1t2 (o, trt"
fo
-
1.665\,/x (fl fr -3
o.:or(o, trt to)2t-3
FLICKER REO.
F
'o
RANDOMWALK 3.63 o,l'l ''1t2 'o)t 'o
+l 1112 (to.zzet
FREO. lo
= bandwidth
time, v = A folfo, fo ='carrier, I = sideband frequency' fh rmeasurementsystem
t - measurement
lrlehave coveredthe most frequently used measures Phasenoise and hav e
of
inter-related them. Next we take a look at the gener ationo f p h a s e o i s e i n
n
a m pilf i e r s a n d o s c i l l a t o r s .
- 10-
Ph a s e 'i se a u se d y A d d 'i ti veNoise
No C b
L e t u s exa mi n e o wp h a sen o i se is added
h
t o a s i g n a l p a s s i n gt h r o u g ha n a m p ' l i f i e r
w i t h n o i s ef i g u r e F .
P,,,
a) -F
The powerspectrum wh'ite noise added
of
t o t h e si g n a l ca n b e th o u g ht of as the Vnrmsl=
s u mo f l H z b a n d se a ch o f w h ich has the
a v a i l a b l e p o w e r f F k T . E a c hb a n di s
o
n o wr e p l a ce db y a d i scre te signal l Hz fo+f-
V n. r , o f e q u iva 'l e n ta va il a ble power :
bl
vn = tF
'*'
T h e p h a s o rd ' i a g r a in F i 9 . 5c reveals
n
t h e p h a seP e rtu rb a ti o nA 0 caused
Peak' fo-f'n
bY Vnrr, .
For smallA0, -
v n r m s l ,FkT
-''peak 'l -
AC\
v, uu
=\lGu
c)
"*,
A0- = I
I rms fi
A t f o - fm a n o th e r n o i se si g nal of equal a @- ,
magni tude b.u wi th random
t phasere'lati on
Vou r-anE
t o t h e n o i se si g n a l a t fo +fm causesthe
same hase luctuation of the signa1.
p f
v
a)o
Both A0"r, add powervtise and result in
a total
A0rmstotal = Fig.5
- 11-
T h e s p ectra l d e n si ty o f p h a senoise is ther efor e:
=ao'"rr=
S0,., $*u
4,=i FKT
E- a v
's
U s i n g ava i l a b l e si g n a l a n d n oise powerassum ed m atched
a input. But the s am e
s i g n a l - to -n o i se ra ti o a n d th er efor e the sam ephasenoise r esults with m i s m atc hed
i n p u t , assu mi n g re ma i n su nchanged.
F
E x a m p l e :A s i g n a l o f O d B ma s s i n gt h r o u g ha n a m p l i f i e r w i t h S d Bn o i s e f i g u r e
p
s h o u l d h a vea sp e ctra l d e n sity of phasenoise of
SaO = -174dBm 5dB - 0dBm -169dB
+ =
T h i s t h e o re ti ca l fl o o r ca n be obser ved ly at some on' offset. lr { ith a pr ac ti c al
t r a n s i s t o r a m p l i f i e r , S O , s h o w s f l i c k e r c h a r a c t e r i s t i cw h i c h i s e m p i r i c a l l y
a
described by the corner frequencyfc. For Fourier frequencies below f., SAO
i n c r e a s e sw i th fr-1 .
f . i s ve ry d e vi ce -d e p e n d e nt can r ange fr om lkHz to lM Hz. It is cau s edby
and
l o w f r e q u e n cyd e vi ce n o i se m odulatingthe phaseof the passingsignal by
modu'lating the transconductance the inp.ut and output impedances the
and of
a m p l i f ie r. U p co n ve rsi oo f the low fr equency
n device noise has the sam e aus e'
c
t h e n o n-l i n e a r p a ra me te rs f the device. The effect of this m ultip' lica ti v e
o
processcan be reducedby:
1. N e g a ti vefe e d b a ck t l o w fr equency.
a
?. So m e e g a ti ve fe e d b a ck RF fr equencyto stabilize the tr ansconduc tanc e.
n at
3. D e si g n i n gth e R F a mp l i fi er for low noise figur e also at low fr equenc y .
-12-
Actual Phase
Noise
so=ff (.*)
+1,,'
Fis.6 fc
S I O i n c l u d i n g t h e e m p i r i c a lm o d j f i c a t i o nd u e t o l o w f r e q u e n c y e v i c en o i s e
d
i s m o d e l e dn F i g . 6 a n d w i l l b e u s e da s t h e p h a s e o j s e s t i m u l u s i n t h e
i n
f o l ' l o w i n g o d e lo f a f e e d b a c k s c i l l a t o r .
m o
L e e s o n ' s o d e lo f P h a s e o i s ei n 0 s c i l l a t o r s
M N
L e e s o n , s o d e lo f a f e e d b a c k s c i l l a t o r d e s c r i b e s h a s e o i s e i n f r e e r u n n ' i n g
m o p n
o s c i l l a t o r s [ e ] . I t c o n s i s t so f a n a m p l i f i e r w i t h n o i s e f i g u r e F a n d a
f i l t e r , e .g . a re so n a to ri n the feedback loop. Ref. [el Aescr ibesa mor e
g e n e r a lmo d e l .
-13-
L(<'rt) =
Output Ad(on,) t* i.r n2 or oad
sao (fm) J (fm)
AO(o*)
quivalent
Lowpassfor
Resonator
Fig.7
F i g . 7 sh o w s o wth i s mo d e l.tr ansfer sinto a phasefeedback
h loop. Tr ans m i s s i on
theory states that the transfer function of a phasem odulated signal Pas s i ng RF
t h r o u g ha b a n d p a ss q u a l s the tr ansfer function of t h e m o d u l a t i n g i g n a l
e s
p a s s i n gt h r o u g ha n e q u i v a l e n tl o w p a s s .
A t a n k ci rcu i t a s a b a n d p a ssesults in the following lowpass ansfer
r tr
f u n c t i on :
L(r,rr) = t'r*zQload
t * t
,o
u)^
w'ith -fi representing the half bandwidth the resonator.
of
zel oad
p h y s i ca l l y i n te rp re te d , th e phasemodulationis tr ansfer r ed unattenuated
through the resonator up to rates equal to half of its bandwidth. As the
m o d u l a ti o n te i n cre a se sfur ther , the r esonatorattenuatesthe passin gphas e
ra
m o d u l ati o n i th 6 d BP e r o ctave.
w
-14-
T h e c l ose d l o o p re sp o n se f the phasefeedback
o loop due to a stim ulus
a o ( o m)i s
=(1
ao(.^,m)+ ao(c^,,n)
l;;fu)
Its powertransfe r fu n cti o n equal
s
=
sr(f,r.,) h . q (.g )'l xs6s
t^2' 2oroad'
-" (rm)
L J
\
Transfer
Phase Function Phase
Perturbation
=*
.crt,"r
[.,.# (+-,.,)'],o"
t",
o - F k r _ ( 1+
Dao=;-
's av +m
' .
T h i s e q u a t i o n d e s c r i b e s p h a s en o i s e a t t h e o u t p u t o f t h e a m p ' l i f i e r . I t
i l l u s t r a t e s h o w S o r , t h e p h a s ep e r t u r b a t i o n a t t h e i n p u t o f t h e a m p l i f i e r ' i s
e n h a n c e d y t h e p o s i t i v e p h a s e f e e d b a c k w i t h i n t h e h a l f b a n d w i d t ho f t h e
b
4
resonator, ;g
a vl oad
D e p e nd i no n th e re l a ti o n o f the cor ner fr equency flicker noise, f., i n
g of
S O , t o th e h a l f b a n d w i d th f the r esonator , two char acter istic phaseno i s e
o
d i s t r i b u ti o n s re su l t fro m m ultiplying the tr ansfer function with the pe r tur ba-
t i o n . T h e ya r e d e p i c t e di n F i g . 8 .
- 15-
High O Oscillator Low O Oscillator
to e
j'9 -. r
ar^
b 20
' 'c
20
Noise ResultingPhaseNoise
ResultingPhase
.C(fm) (fml
"C
5- 5
20 2()
Fig.8
-16-
O p t i m i z a t i o n f P h a s e o i s ei n O s c i l l a t o r s
o N
L e t u s e xp a n d e e so n 's q u a tionto expose
L e the var ious Par ameter of an ac tual
s
focus on J , ( tt)
o s c i l l a t o r w h i c ha r e r e l e v a n t t o p h a s e o i s e optim ization. t,{ e
n
w i t h i n th e h a l f b a n d w i d th f the r esonator :
o
fo
for f. (
2otoad
/\2
1 l-o \ FkT
& ( f m )- 1 2
n P,"u. * )
(
;'\zo*t
Typical Oscillator
FKT
o@2=
/
G
\
( 1+
ftr P,,,
AO
/
Rr",
Fig. 9
Q l o a dc a n b e e xP re sse d s:
a
-oWe -oW"- -
- ReactivePower
otoad= = power
ffi, F;;. p;F%is Totil dissipated
where is the reactive energygo'ing
W. between and C
L
w"=trru' Pr.,=*
-L7-
J{-r}=}
tr"
to2
*m 2
.3*lt
. owe/
(.*)
Input Powerover
ReactivePower
T h i s e q u a ti o n i s p a rti cu l a rl y significant because encom passes of the
it most
c a u s e s f p h a s en o i s e i n o s c i l l a t o r s . M j n i m i z a t i o n f p h a s e o i s e d i c t a t e s
o o n
t h e f o l l o w i n g d e s i g nr u l e s :
. M a x i mi ze e u n l o a d e d
th Q
. l,laximize the reactive energy by means a high RF voltage V across the
of
C. The limits ar e set by br eakdown
r e s o n a to ra n d a h i g h ca p acitance
bythefor war d bias condi ti on
v o l t ag e s o f th e a cti ve d e vice and var actor and
of the varactor.
. L i m iti n g sh o u l d o ccu r w i thout degr adation Q. A two- stageam p' lifier '
of
. 9 . , i so l a te s th e l i mi ti n g por t fr om the r esonator . For war dbias of
t h e va ra cto r d u e to h i g h RF vo' ltageshould be avoided.
. C h o o s e n a c t i v e d e v i c ew i t h l o w n o i s e f i g u r e F . F i s t h e n o i s e f i g u r e i n
a
the actual impedance environment the device sees.
I n ma n ya p p l i ca ti o n s i t i s pr efer able to deal with equivalent noise v ol tage
a n d n o i se cu me n t si n ce they ar e independent the sour ceim pedance.In
of
t h e exa mp l e f F i g u re 9 , the amplifier input is coupledinto the r es onator .
o
T h e r e fo reth e so u rce i mp edance changes astlcally as a function of t he
dr
offset frequency.
. M i n i mi zep h a sep e rtu rb a ti on given by the r atio of additive noise to t he l ow es t
s i g n a l l e v e l . I n t h e s w i t c h e d e a c t a n c e s c i l l a t o r , F i g u r el 5 ' t h e h i g h i n p u t
r o
impedance the two-stage FETamplifier allows the input powerto be
of
n e g le cte d . F kT ca n b e r eplacedwith the r atio of noise voltage t o
P, u,
s i g n a l vo l ta g e a t
-18-
port(FJ' .
rherimitins Obviously,he limited signal voltage,VSL'
t
s h o u l db e m a x i m a l .
. C h o o s e n a c t i v e d e v i c ew i t h l o w f l i c k e r n o i s e '
a
. M i n i mi zeth e e ffe ct o f fl icker noise whichm odulates ansconducta nc er i nput
tr
and output impedances the active device by low frequencyfeedbackand
of
p r o pe r b i a s. T h e e ffe ct of m odulated input and output im pedance fur ther can
b e m i n i m j z e d y m a x i m i z i n gh e s t a b l e t a n k c i r c u i t c a p a c i t a n c e s w a s
b t a
p r e vi o u sl y a d vo ca te d r a differ ent r eason.
fo
. M i ni mi zeth e si g n a l p o w ertaken out without going belowthe lim its s et by
additive noise.
C o up l eth e si g n a l p o w e rof the r esonatorso that ther e is a continui ng
d r o p o f p h a sen o i se b e Y ondthe half bandwidth the r esonator .
of
T h e s e e s i g np r i n c i p l e s w e r ea p p l i e d i n t h e 3 1 0 t o 6 4 0 M H zC O f F i g u r e 1 5 .
d V o
As a n e xa mp l ee t u s ca l cu l 'atethe phasenojse per for mance this VCO
l of at
5 0 0 M Ha n d a t l 0 0 K H z ffse t.
z o
T h e i n p u t p o |e r o f th e tw o -stageFET_.ampl' ifier ,can be
noi s e
n e g l e cte d . T h e p h a sep e rtur bationf,q ( f * F ) is r eplacedby the
' s av m
v o l t a ge to si g n a 'l ra ti o a t the
' i n p u t o f th e 2 n d sta g e , th e lim it' ing por t'
For a 2N5397 Vn = 6nV ( accounts for both FET' s)
vsL=I
C = 23pF
V = lOV
Qunl = 200
P = 4ml,l
slg
fo = SooMHz
= +(Tlgl'z (t#T(rh- 'z
{. o,ookHz
l, G100kHz=-l44dBc
T h e actu a l o sci l 'l a to r me asur edl42dBc.
-
-19-
F i g . ' 1 0 s h o w s e p h a sen o i se per for mance some ee- r unningoscillator s
th of fr
c annot
d e s i g n e d i th l o w p h a sen o i se as a pr imar y goal. 0f cour se, the cur ves
w
be compared directly with each other since they not only differ in RF frequencies
b u t a l s o h a veq u i te d i ffe re n t obiectives in ter ms of tunability'
310 to 640 MHz
Osc.
Switclred Reactance
@500 MHz (
C'
-90
6 |tor
2-6 GHz YIG-Oscillt
!t
a
tt
.;
-100 \I f6GHz
i
!t
g
E
o
N
- Ei40 Cavity \
-110 I ut||iu \rtr,il
.5 500MHz
o
o
E \
\\
.g -120
6
(J
o \
g lll lllb I mnad \ \
-130
o or
LC Oscillat
z lr
I
o I
I It
\
I
o.
!t
-140 1 0 M i-lz Crystal lr \\
c lstor
o
tt
o
B \
v, \
q, -150
ED
tr \
v,
\
E
\
ql -160
-\ \
\
t-
-170
1 0H z 100Hz 1 kHz 10 kHz lfi!kHz 1 MHz
Offset from Garrier(Hz)
Fis. 1O
-20-
P h a s e o i s e h a r a c t e r i s t i co f D i v i d e r s
N C s
B e f o r e a n a l yzi n gth e p h a senoise per for mance phaselocked sour ces, l et
of
u s c o n si d e r p h a sen o i se i n troducedby fr equencydivjder s. As the next
p a r a g r a p h 'i 1 l p o i n t o u t, they maybe the lim iting component a phas e
w in
l o c k 1 o o p . T h e ya l s o p l a y a k e y r o l e i n d i r e c t f r e q u e n c y y n t h e s i s .
s
P h a s e o i se a t th e i n p u t o f the divider appear sat the divider output r educ ed
n
b y N . I n t h e r e s i d u a l p h a s e o i s e m e a s u r e m eo f t F i g . l l t h i s i n p u t ( s o u r c e )
n n
n o i s e co n tri b u ti o n ca n ce l sand on' ly phasenoise gener ated the divider i s by
m e a s u r e d .P h a s e o i s e d a t a r e f e r t o t h e d i v i d e d - d o ws i g n a l . A p h a s e o i s e
n n n
f l o o r o f -1 5 0 to -l 6 0 d B ci s typical for ECLdevices. The consider ablyl ow er
f l o o r o f T T Ld i v i d e r s i s m e a s u r e a b oe l y i f c a r e i s t a k e n t o a v o i d s a m p l i n g
ln
effects.
E xa mp l eof Phase
s Noise Intr oducedb.vDivider s
-lm
-t t0
6
I
a
: -r20
.g
a ECL l(x) MHz+ t0 l9tlH90l
C'
g -130
.!
o
z
E -rao
B
!
c
2 ECLrlEoMHr + tl (1lc05l
g
-r50
! E
g
l/,
-160
-t70
Ot{r.t
Fig. ll
-2t-
N o i s e C o n si d e ra ti o n s r P h a s e- L
fo
Phae Integrator Shaper
Detector Filter Pret-une Attenuator
Vn det
Fig. l2
F i g . 1 ? sh o w s typ i ca l p h a s e- 1ock
a loop ( PLL) - typical with the excepti onof
t h e a t t en u a to r a t th e o sci 'l l ator tuning por t. This attenuator is iustifi ed
i n t h e f o l l o w i n g d e s i g nr u l e s . T h e o b i e c t i v e i s t o m i n i m i z e Q o u d u e t o
A a
a n y n o ise i n p u t. T h e fo l l o w ing design r ules em er ge whenwe look at r es pec ti v e
t r a n s f e r fu n cti o n s:
' M i n i mi zep h a sen o i se o f the fr ee r unning VCO
Adout
adfi = r@
1
e o . , ( s ) i s t h e o p e n o o Pg a i n :
' l
= fm
*r
Go;(s) K, A(s) K.(s) ft 3
K,
Fis. 13
loop gai n'
Ph a se o ise of the free running oscillator is r educed the
n by
T h i s l e a d s to the next rul.e.
-2?-
M a x i m i z e a n d w i d t a n d o p e n - l o o p a i n . T h e b a n d w i d t hs l i m i t e d b y a
b h g j
n u m b eo f co n stra i n ts. B y com par ing
r phasenoise of the fr ee- r unning V C O
w i t h ph a sen o i se co n tri b u ti ons fr om the r efer encesour ce, the divider
o u t p ut,a n d tl e p h a se e te cto r, the bandwidth deter m ined.
d is
A l l 3 p h a sen o i se so u rce shavethe same ansfer function:
tr
aoo*-
=
a|ret r* t
Gol( s)
M a x i mi zi n g e l o o p b a n d width akes
th m senseon' ly as long as r efer ence
n o i s e ( o r d ' i v i d e r n o i s e , o r p h a s e e t e c t o r n o i s e ) m u l t i p ' l i e db y N d o e sn o t e x c e e d
d
t h e p ha sen o i se o f th e fre e- r unningVC0.
0 t h e r c o n s i d e r a t i o n ss u c ha s t h e f i l t e r i n g o f t h e r e f e r e n c es i g n a l o r
,
s p u r i o u so n t h e r e f e r e n c es i g n a l a n d l o o p s t a b i l i t y ' c a n
d e t e r mi n e e ch o i ce o f th e bandwidth.
th
A v o i d d i v i d e r s i f p o s s i b ' l e . A s n o t e da b o v e ,t h e y c a u s e u l t i p l i c a t i o n
m
b y N o f th e re fe re n ce , p h asedetector , and divider output phasenoise.
M i n i mi zei n te g ra to r, sh a p erand attenuator noise. The choice of impe danc e
l e v e l s a n d p r e t u n ef i l t e r i n g m i g h t b e c o n s t r a i n e d y s w i t c h i n gs p e e d
b
c o n s de ra tio n s.
i
M a x i m i ze h a sed e te cto r g a in K*.
p 'l
A n y n oi se i n p u t fo l l o w i n g the phasedetector is reducedby ,\ , .
t
0
ojoul_
=- 1 N
Vn int K^ rI r - - I
'
Gog(s)
Minimizehe sensitivity, Ko
t ot
fuH'rv], the V C 0 . G i v e na chosenbandw i dth,
phase oisedueto Vnr,
n V . and V i s p r o p o r t i o n a lto Ko.
na- nt
Ko
H=',;fu
-23-
. E m p l o y n a t t e n u a t o ra n d m i n i m i z eK u ( s ) . A g a i n , g i v e n a c h o s e n a n d w i d t h '
a b
n o i se i n p u ts p re ce d i n gth e attenuator ar e r educedby Ku( s) . This hol ds
a l s o f o r n o i s e o u t s i d e t h e l o o p b a n d w i d t h . F o r e x a m p l e p h a s en o i s e o u t s i d e
,
t h e l o o p b a n d w i d th u sedbY Vn, amounts
ca to:
1
A d o u t= K " (s) , K o l un,na
K
T h e a t t e n u a t o ri s u s u a l l y a l e a d - l a g n e t w o r k .
T h e f o l l o w i n g e q u a t i o ns u m s p a l l t h e p h a s e o i s e c o n t r i b u t i o n s .
u n
=
aolu,(s) * a2o6;,r,1
(;;r' [420,"1t,t
- ir(th * *nLr'd'
+frz v2n,{s} u,?.,,1
o",t'rV2n;n1(s)
I Iv2"
T h e g r ou p i n go f th e e q u a ti o nem phasizes effect of r efer enceand divi der
the
n o i s e , p h a s e e t e c t o rg a i n a n d o s c i ' l l a t o r n o i s e a n d s e n s i t i v i t y .
d
-24-
Loop
A c t u a l Re su l tsA ch i e ve d n a LowNoise Refer ence
i
I n t h e fo l l o w i n g e xa mp l e f a phaselock loop ( Pt- L) ,effor ts wer e made
o to
e m p l o y l l t h e l i s t e d d e s i g nr u l e s .
a
As the frequencyreference loop of the HP8662ASynthesized Signal Generator
( F i g . 1 4 ) , t h e l o o p ' s f u n c t i o n i s t o f i l t e r t h e h i g h s p u r i o u sc o n t e n to f a
3 2 0 - 6 4 0 MH zfe re n ceso u rce . The r efer encesour ceis dir ectly synthesiz ed
re
f r o m m u l tj p l e s o f l OMH z, ps in 2OtlHz
ste steps, and contains - 40dBcspuri ous
s i g n a l s . T h e l o o p r e d u c e s p u r i o u ss i g n a l s t o - l 0 0 d B ca n d , a s a n a d d i t i o n a l
s
f u n c t i o n s , p r o v i d e sl Q M H s t e p sa n d s w j t c h e si n l e s s t h a n 5 O U s e c '
z
10 or 20 MHz SwitchedRerctanceOsc.
310 to 620 MHz in 10 MHz steps
Spurious -100 dBc
10 or 20 MHz
320-640 MHz in 20 MHz stePs
Spurious -40 dBc
1OMHz X-Oscillator
Fig.l4
T h e 3 1 0-6 2 0 MH z Q f th e l o cp, also used in a second
VC o loop as a 320- 640M H z
V C o ,h a s a n o v e l s w i t c h e d e a c t a n c e e s o n a t o r( F i g . 1 5 ) . I t c o n s i s t s o f 5
r r
i n d u c t or a rra ys sw i tch e di n a binar y fashion. They pr ovide 32 fr equen c y
s t e p s . F o r a co n ti n u o u s quency
fre cover age,the var actor has to cover onl y
l O M H zn te rva l s. C o mp a reto a conventional
i d VCO ith a var actor cover ing
w'
t h e e n ti re 3 .|0 to 6 2 0 l " l H z nge, this switchedschem eesults in dr astica'l 'l y
ra r
r e d u c e d s c iI l a t o r s e n s i t i v i t y .
o
I
-25-
T h e n a tu re o f th e re so n a to ralso allows ver y high signal levels ( tt0Vp.uk ) ,
h i g h Q ( 1 5 0 - 2 5 0 ) , a s t s w i t c h i n g ,a n d p r e c i s e p r e t u n i n g '
f
310-640 MHzSwitched Oscillator
Reactance
Frsqwncy InPut
Fig. t5
-26-
T h i s l o o p a c h ' i e v ea n o i s e f l o o r o f - l 4 3 d B ca s c l o s e i n a s l 0 k H z ' W i t h i n
s
l 0 k H z , n o i s e o f t h e re fe re n cesection is dominant.
(J
6
!,
N
-120
tr
o \
o
() -130
o I
I
tl
o ResidualPhase Loop
Noisl of Reference
z
(l'
SeEtion 500 MHz
includingReference @
v, I
s
o -140
4 r--__\
E' -
c
to
ll PhaseNoiseof
o
p ReferenceLoop only
u) - 1 5 0
o
(tt
.g
v,
.o
p
va
(D -160
E 100kHz 1 MHz
1 kHz 10kHz
Offset *
Fig. l6
-27-
R e f e r e n ce l ti P li ca ti o n
Mu
- typically a 5 or ' lQMHz
Sy n t h e si ze d u rce su se a re fer enceoscillator
so
To ar r ive at
X - o s c i l la to r w i th e xce l l e n t shor t and long ter m stability'
most cr ucial
l o w p h a sen o i se si g n a l s i n th e RF and micr owaveange the
r
r ange'
f a c t o r i s h o wth e re fe re n ces ignal is m ultiplied into the RF
signal
F i g . 1 7 co mp a re 3 me th o d s f obtaining a low phasenoise 640M Hz
s o
s t a r t i n g w i th a l OMH crysta l oscillator '
z
640 MHz
Sc*remeC
640 MHz
160 MHz X'Filter
160MHz
X-Osc.
Sdpme A
640 MHz
+ OrSampler
lx6al
H
to MHzX-osc. 10 MHzX'O:c.
@
Fig.17
-28-
(, -90
6
E'
N
.E - 1 1 0
.9 \
.E
o \ L--
o A
o -1 a\
'6
U'
2 \ to MHz 'Osc.
X,
o
0 \
.!
E
c -1
\ \-e
!o 50 tc
u, r\\
U'
0'
f \-_
r.D ID
o
.8 - 1 70
1 0H z 100 Hz 1 kHz 10 kHz lfi) kHz
Offset
Fig.l8
Method results in straight multiplication of the reference hase oise.
A p n
M u l t i p ' l i c a t i o nc a n b e d o n eb y d o u b l i n gs i x t i m e s o r m u l t i p l y i n g w i t h a h i g h e r
o r d e r mu l ti p l 1 e r o r sa mp 'l er . Refer ence oscillator noise is incr easedb y 36d8.
M e t h o d i s a l so stra 'i g h t multiplication, but at appr opr iatefr equencyl ev el s
B
( 4 0 a n d l 6 0 MH z), a rro u r a ndcr ystal filter s ar e used to r educesideband s e.
n b noi
M e t h o d e mp l o ys l 6 0 MH z
C a crystal oscillator to achievea low phasenoi s e
f l o o r . I t i s l o c k e dt o t h e l o M H z r y s t a l o s c i l l a t o r . A s p r e v ' i o u s l y i s c u s s e d ,
c d
t h e b an d w i d th f th e l o o p 'i s deter m ined compar ing
o by the phasenoise of the
crysta l oscillator with noise of the r efer enceosci l l ator
f r e e - r u n n i n gl 6 0 MH z
a n dd i v i d e r n o i s em u l t i p l i e d b y 1 6 . A s p l o t C i n d i c a t e s , d i v i d e r n o i s e
d o m i n a t e i n t h i s c a s e , r e s u l t i n g i n h i g h e r c l o s e - i n n o i s e w i t h s c h e mC
s e
t h a n w i th a n y o f th e o th e r schem es.
- 29-
usesm ethod
T h e H p 8 6 6 2 A yn th e si ze d i g nal Gener ator
S S B. Potential pr ob l em s
o f t h i s a p p ro a ch re :
a
. A d d i t i v e n o i s e i n t h e f i r s t s t a g e so f m u l t i p l i c a t i o n .
. L o wf r e q u e n cyd e vi ce n o i se and powersupply noise, causingphase
m o d u l a t i o nn a m p l i f i e r s , m o s t s e n s i t i v e a g a i n i n t h e f i r s t s t a g e s
i
of multiplication.
. Doubler oise.
n
. Crystal filter noise.
. 'in crystal f i I ters.
crophoni noi se i nduci phasenoi se
l',li c ng
Signal GeneratorSlstem
overal'l PhaseNoise Performance a S.vnthesized
of
S o f a r , ci rcu i ts a n d mo d u l e s have beenoptimizedfor low phasenoise. T hey
f o r m t h e b u i l d i n g b l o cks fo r synthesizer s. The par ticular examples used
e a r l i e r a re p a rt o f th e n e wHP8662A Synthesized Signal Gener ator . The gr aph
o f F i g . l 9 b e l o ws h o w s h e d y p i c a l r e s i d u a l s i n g l e s i d e b a n d h a s e o i s e o f
t p n
t h e s y ste m. B e l o wl 0 kH z, p h asenoise of the r efer encesection dom inates .
Froml0 to 500 kHz the reference loop and sumloop determinethe phase
n o i s e p e rfo rma n ce .F a rth e r out the sumloop oscillator is the dominan t
p h a s en o i se so u rce .
T h e 8 6 62 A syste mi s co mp a red with an older synthesizerdesign of signifi c antl y
different structure, the 8660C/86602A. covers the Same It frequencyrange'
b u t w a s n o t d e si g n e d i th l o w phasenoise as a pr im ar y objective. The H P86408
w
excellent phasenoise per for -
c a v i t y -tu n e d g e n e ra to ri s a 'lso included, showing
m a n c e t 2 0 kH z ffse t a n d fa r ther out. 0f cour se, it cannotcom pete
a o clos e- i n
w i t h s y n th e si ze d e n e ra to rs.
g
310-G20 MHe/
fht#*"Elo
2?5-3.S5 GHr/ O#
l0 MHa
100 MHz Stpr
H-:3-ts
1f20 rilHr/
\tu-
I Hr SoF
396{.05 GHt/
t l|lSF l0ltlHe
X-Orc.
8660C/86602A 86624
Fig.l9
-30-
.g
.9
3
o
o
-90
o
1t
=
co
-100
I
.g
0,
.2 -110
o
z
(t,
I
E
o- -120
rEt TYPICAL
an
U' RECEIVER
E CHANNEL
.9 -130
ct SPACING
10 Hz 1 0 0H z 1 kHz l 0 k H z 1fi) kHz
Offset from Carrier
Fig.?0
T h e o v e ra l l re su l t o f th e pr eceding design consider ations a synthes i z er
is
w i t h no t o n l y e xce p ti o n a lclose- in noise per for m ance' but also ver y low phas e
n o i s e a t fa rth e r-o u t o ffse t fr equencies wher etr ad' itionally cavity osc i l l ator s
w e r e f ar su p e ri o r. w i th a switching speedof500usec RF settling) the H P8662A
(
a l s o co mb i n e s e u su a l 'l yconflicting r equir ements low phasenoise w i th
th of
h i g h f r e q u e n cya g i l i tY .
-31-
Measurement PhaseNoise
of
T h e e m ph a si s n l o w p h a sen o i se sour cesin this paperalso guides the
o
s e l e c t i on o f te st me th o d s. P hase techniques
noise measur ement will be
c o m p a r edn th e b a si s o f mi n i mum
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