Me hod o measu ing noise pa ame e s o
mic owa e wo-po
A.
Lhza o,
L.
P adell and
J.M.
O'Callaghan
A
new une -based me hod o measu ing
he
ou noise-
pa ame e s
o
a wo-po
is
p oposed. I makes
use
o
a
no el
measu emen
a io
ha includes noise powe s and misma ch
ac o s simul aneously. In con as o p e ious wo ks,
no
es ic ions
on
he
noise sou ce,
une
s a e
empe a u es
and
cold
empe a u es a e assumed.
In oduc ion;
The measu emen o he ou noise pa ame e s
("s)
NPs
o
a
wo-po in he mic owa e equency ange is usually
pe o med by measu ing he wo-po de ice noise igu e
F
o a
minimum o ou sou ce e lec ion-coe icien s
,,
p oduced wi h a
une connec ed a he wo-po inpu ( e lec ion- ype une ) [I ~
61. The equa ion ela ing
F
and
s,
(i
=
1,
...,
N)
is exp essed in lin-
ea o m, and he esul ing o e de e mined linea equa ion sys em
is sol ed o he
NPs
[I, 2, 51.
A
numbe o measu emen me hods ha e been p oposed. In
131,
F( s )
is de e mined om he measu ed
,,
and he co esponding
noise powe s deli e ed by he wo-po o he ecei e , a oom
empe a u e. The sys em gain is compu ed om he ho and cold
noise powe s deli e ed by
a
wo-s a e noise-sou ce
13,
71.
Equal
ho and cold sou ce e lec ion-coe icien s
sH
=
s,)
mus be
assumed. Typically, his assump ion does no a ec he measu e-
men accu acy o he
NPs,
because he di e ences be ween
,,
and
s,
a e e y small, bu some applica ions ( o example, c yo-
genic measu emen s o adiome e calib a ion) may equi e di e -
en ho and cold loads. In
141,
a me hod is gi en ha a oids he
o me es ic ion by using an al e na i e measu emen magni ude,
i.e. he a io be ween he deli e ed noise powe s and
a
misma ch
coe cien . Only he ho -sou ce measu emen
is
equi ed o de e -
mine he sys em gain, bu i is implici ly assumed ha he cold
( oom) empe a u e,
T,,
equals he e e ence empe a u e,
To
(=
290K)
[4].
This assump ion is a limi a ion in a eal labo a o y
en i onmen , o whene e he une includes semiconduc o
(PIN
diode) swi ches, because he diodes add a non- he mal (sho ) con-
ibu ion o he empe a u es o he une s a es,
T,,
(i
=
1,
...,
N).
Al e na i e echniques o measu e he ou
Nps
o he pa icula
case o
a
ansis o
181,
make use o he ansis o equi alen ci -
cui as addi ional in o ma ion. Howe e , a une mus be used o
calib a e he ecei e noise.
10,
,
120,
0.4
I
I
200,
I
0
10
20
30
,GHz
(34611j
Fig.
1
Recei e noise pa ame e s measu ed using new me hod, me hod
p oposed
by
Adamian
[3]
and me hod
p oposed
by Da idson
[4]
~ new me hod
0
Da idson
V
Adamian
While
a
une is equi ed o measu e he
NPs
o a gene al wo-
po ando o calib a e he ecei e , a gene al case
csH
#
Tsc,
T,
#
To,
T,,
#
To,
and di e en
T,,
o e e y s a e
i)
is o en encoun-
e ed.
No
accu acy deg ada ion should be expec ed in hese cases
i a measu emen me hod wi h no es ic i e assump ions we e
used. The pu pose o his Le e is o p opose a new me hod o
measu ing he ou
NPs
o a wo-po , based
on
a e lec ion- ype
une . I is a mo e gene al me hod han hose in
[3,
41 because: (i)
i does no equi e measu emen o he cold-sou ce;
(ii)
T,
need
no be
To;
(iii)
c,
(i
=
1,
...,
N)
need no
be
ei he he same as o
equal o
To.
Mo eo e , i demons a es an imp o ed accu acy in
c i ical measu emen si ua ions (i.e.
l opTl
in he wo-po close o
1).
Expe imen al e i ica ion is gi en up o 26GHz.
,GHz
~
Fig.
2
HEMT
noise pa ame e s measu ed using new me hod, me hod
p oposed
by
Adamian
131,
me hod p oposed by Da idson
[4]
and
F50
me hod
[8]
~
new
me hod
0
Da idson
Adamian
0
F50
Measu emen me hod:
To calib a e he ecei e , he une is con-
nec ed o i s inpu and he noise powe deli e ed o he ecei e
de ec o is measu ed o e e y une s a e
,
(i
=
1,
...,
N).
This
powe can be exp essed as:
whe e
k
is he Bol zmann cons an ,
,
is he ecei e inpu e lec-
ion coe icien ,
Ts
is he noise empe a u e o he sou ce imped-
ance
,,,
TJ ,)
is
i s co esponding ecei e noise empe a u e,
(Cop)
is he ecei e ansduce powe gain,
Go
is he ecei e
ansduce powe gain o
a
ma ched sou ce
( ,
=
0),
and
p( R,
,)
=
(l-~~s~z)~l-~s~R~z is a misma ch ac o .
Go
is a cons an
h oughou he measu emen , because i only depends on ecei e
pa ame e s.
To
elimina e he gain cons an
Go
he noise powe PH
deli e ed by a ho sou ce (whose ho empe a u e
TH
is known), is
used as a e e ence o de ine a no el measu emen a io
R,:
The ecei e noise empe a u e
T,
is exp essed in a linea o m by
using he Lane's pa ame e s
A,
B,
C,
D
[I],
whch a e unc ions o
he ecei e
NPs,
T,,,,,,
G,,,
Bop, and
R,,:
whe e
Y,
=
Gs
+
jBs is he sou ce admi ance. Subs i u ing eqn.
3
in o eqn. 2, he ollowing o e de e mined linea equa ion sys em
is
ob ained o
A,
B, C,
D:
[Sz]
=
[VI
.
[A
B
C
D]'
(i
=
1,
...,
N)
(4)
S,
E
R,TH
-
Ts,
(5)
The sys em in eqn.
4
is sol ed o
A,
B,
C,
D,
by weigh ed leas -
squa es using he concep o he pseudo-in e se ma ix, and he
ecei e
NPs
a e eadily compu ed. This calcula ion comple es he
ecei e calib a ion. Then he wo-po is inse ed, and by using
he F iis's o mula, he ollowing equa ion is eadily de i ed:
s;
=
TDUT( Sz)
-
R:T~~~(~~~)
(i
=
1,
...,
N)
(8)
1332
ELECTRONICS
LETTERS
25 h
June
1998
Vol.
34
No.
13
whe e
R,‘
is de ined as in eqn. 2, bu wi h he e lec ion coe icien
,
e e ed o he wo-po inpu . In eqn.
9,
he e lec ion coe i-
cien s
,,’,
s/
co espond o
s,
and
,,,
espec i ely, bu a e
e e ed o he wo-po ou pu .
TDUT
and
Ga DuT
a e he wo-po
noise empe a u e and a ailable gain, espec i ely, and
72
is he
ecei e noise empe a u e, compu ed om he ecei e
NPs
p e i-
ously measu ed. The wo-po noise empe a u e in eqn.
8
is
exp essed in linea o m, and a linea sys em simila o eqns. 4
-
7
is ob ained o
[A
B
C
DITDuT,
wi h
R,
and S, eplaced by
R,‘
and
SE’,
espec i ely.
Expe imen al esul s:
The me hod has been es ed on on-wa e
ansis o s. The es se up includes a b oadband (2-26GHz), com-
me cial une [6] wi h nine a ailable sou ce s a es. The une and
ho sou ce e lec ion-coe icien s a e measu ed oge he wi h hei
co esponding noise powe s and used in [2
-
91. Fig.
1
shows ha
he measu ed ecei e
NPs
up o 26GHz o he me hod p oposed
he e and o hose p oposed in [3, 41 a e almos iden ical, which is
o be expec ed since he es condi ions needed in he o me me h-
ods [3, 41 a e me
(TsX
=
,,
o [3] and
T,,
=
To
o [4]). Fig. 2
compa es he measu ed
NPs
o an on-wa e HEMT up o 26GHz.
The ag eemen be ween he ou me hods (Fs0 me hod
[SI
is also
compa ed) is good excep a low equencies, o which
l oPTl
is
e y high (close o 1). The new me hod is mo e obus o his c i -
ical measu emen si ua ion han hose in [3, 41, which ha e non-
physical pa ame e s.
Conclusions;
A
no el une -based me hod o measu ing he ou
NPs o a gene al wo-po wi h no es ic ions in he noise sou ce
o une , has been p oposed and success ully applied o he
ecei e calib a ion and o an HEMT. I has been compa ed o
o he une -based me hods in he li e a u e, demons a ing accu-
acy imp o emen s in he de e mina ion o he NPs o c i ical
measu emen si ua ions, such as a de ice
I &
close o
1.
Acknowledgmen :
This wo k has been suppo ed by he esea ch
p ojec s TIC93-672-C04-03 and TIC97-1129-C04-04 manced by
he Spanish CICYT.
0
IEE 1998
Elec onics Le e s Online
No:
19980942
A. Laza o, L. P adell and J.M. O’Callaghan
(Poly echnic Uni e si y
o
Ca alunya
(UPC),
Dep . TSC, Campus No d UPC,
08034
Ba celona,
Spain)
7
May
I998
Re e ences
LANE, R.Q.:
‘The de e mina ion o de ice noise pa ame e s’,
P oc.
CARUSO, G.,
and
SANNINO,
M.:
‘Compu e -aided de e mina ion o
mic owa e wo-po noise pa ame e s’,
ZEEE T ans. Mic ow.
Theo y Tech.,
1978,
26,
(9), pp. 639-642
ADAMIAN,
A.,
and
UHLIR,
A
:
‘A no el p ocedu e o ecei e noise
cha ac e isa ion’,
IEEE T ans. Zns um. Meas.,
1973,
22,
(6), pp.
181-182
DA iDsoN, A.c.,
LEAKE,
B.w.,
and
STRID,
E.:
‘Accu acy imp o emen s
in mic owa e noise pa ame e measu emen s’,
IEEE T ans.
Mic ow. Theo y Tech.,
1989, 37, (12), pp. 1973-1978
OCALLAGHAN,
J.M., and
MONDAL,
J.P.:
‘A ec o app oach o noise
pa ame e i ing and selec ion
o
sou ce admi ances’,
ZEEE T ans.
Mic ow. Theo y Tech.,
1991,
37,
(12),
pp.
1376-1382
NPTS-26 Sys em, Cascade-Mic o ech, Inc., 14255 SW B igadoon,
Bea e on,
OR
97005
CROZAT,
P.]
DOUTLX,
c.,
CTI*””ET,
M
,
DANELON,
V.)
SYLVESTRE)
a.,
and
VERNET,
G.:
‘SO
0
noise measu emen s wi h ull ecei e
calib a ion wi hou une ’,
Elec on. Le .,
1996,
3,
pp. 261-262
LAZARO,
A.,
PRADELL, L., BELTRAN, A.,
and
O’CALLAGHAN,
J.M.:
‘Di ec ex ac ion
o
all ou ansis o noise pa ame e s om
Son
noise igu e measu emen s’,
Elec on. Le .,
1998,
32,
(3),
pp.
289-
291
ZEEE,
1969,
57,
pp.
1461-1462
Nonlinea s abili y anallysis
o
mic owa e
ci cui s using comme cial so wa e
A.
Sua ez,
V.
Iglesias,
J.-M.
Collan es, J. Jug0 and
J.L.
Ga cia
A new echnique is p esen ed o he s abili y analysis
o
s eady
nonlinea egimes in mic owa e ci cui s, using comme cial
so wa e. The Nyquis s abili y c i e ion is applied o he open-
loop
ans e unc ions o he ci cui linea isa ion a ound he
s eady s a e. Th ough a simple nonlinea op imisa ion echnique i
is also possible o de e mine he p edic ed quasi-pe iodic o
pe iod-doubled s eady solu ions. The s abili y analysis o wo
a ac o -based ci cui s has p o ided excellen esul s when
compa ed wi h ime domain simula ions and measu emen s.
In oduc ion:
Ha monic balance (HB) comme cial simula o s a e
an in aluable ool o he analysis
o
he nonlinea s eady egimes
o mic owa e ci cui s, such as powe ampli ie s, oscilla o s o e-
quency double s.
A
nonlinea s abili y analysis is also necessa y in
o de o ensu e he physical exis ence o he simula ed solulions
[l,
21.
This analysis p o ides in o ma ion abou he possible exis -
ence o uns able na u al equencies ha would gi e ise o, o en
undesi able, quasi-pe iodic o pe iod doubled egimes. Howe e ,
he s abili y analysis o hese egimes is no ye a ailable. Ins ead,
comme cial simula o s only include s abili y analysis op ions o
he DC solu ions o oscilla o ci cui s.
In his Le e , a new echnique is p esen ed o he s abili y
analysis o nonlinea s eady egimes, using comme cial so wa e. I
is based on he Nyquis s abili y c i e ion, which is applied o he
open-loop ans e unc ion o he ci cui linea isa ion a ound i s
nonlinea s eady solu ion. To calcula e his ans e unc ion, a
eal equency pe u ba ion is in oduced o e he s eady egime,
in he o m o an auxilia y gene a o (AG) o neghgible ampli ude.
This enables he e alua ion o he open-loop ans e unc ion a
he AG loca ion. The Nyquis plo s a e hen di ec ly ob ained by
sweeping he
AG
equency. Fo a igo ous analysis, a oiding
unce ain y abou possible ze o-pole cancella ions, se e al obse -
a ion po s should be conside ed sequen ially.
A new echnique is also p esen ed o he s eady-s a e analysis
o he p edic ed au onomous quasi-pe iodic and equency di ided
egimes. This is based on nonlinea op imisa ion o he auxilia y
gene a o a iables, imposing a non-pe u ba ion condi ion. The
uns able na u al equency is es ima ed om he Nyquis plo ,
which p o ides a aluable s a ing poin o he op imisa ion.
Since he new analysis echniques a e in ended o comme cial
simula o s, hey a e eadily usable by any mic owa e-ci cui
designe . Ad an age is also aken o he lexibili y o comme cial
so wa e, which enables he analysis o complex opologies, which
a e ypically di icul o in oduce in in-house so wa e.
He e, he p oposed analysis me hod has been applied o he
s abili y analysis o wo a ac o -based ci cui s: a simple ci cui
o equency di ision and a equency double ha exhibi s an
asynch onous ins abili y. The espec i e pe iod doubled and quasi-
pe iodic solu ions we e p edic ed and de e mined by means o he
new me hod, ob aining an excellen ag eemen wi h ime domain
simula ions and measu emen s. Fo bo h he s abili y and s eady
s a e analysis, HP-MDS comme cial so wa e has been used.
Fig.
1
Block diag am
o
pe u bed ci cui , linea ised a ound nonlinea
pe iodic solu ion
XpO
Analysis me hod:
A
nonlinea ci cui , exhibi ing a s eady egime o
pe u ba ion will be supe imposed o e he s eady solu ion
X,O.
This is done by in oducing in o he ci cui an auxilia y gene a o
(AG) o negligible ampli ude
E
and a iable equency ,, wi h a
il e which elimina es i s in luence a all equencies di e en om
i s own [3]. The inpu immi ance a ,, obse ed om he AG e -
minals, may be spli in o wo con ibu ions. Whene e possible,
-d-en al ;,,
will
he
conside ed
To
analyse
i s
s abili y,
a
small
ELECTRONICS LETTERS
25 h
June
7998
Vol.
34
No.
13
1333