Q!m3 DIRECT
MEASUREMENT
CHARACTERISTICS
OF
USING
THE
NONLINEAR
INJECTION
M. I.C.
LOCKING
OSCILLATOR
POLAR
DIAGRAM.
-
A.P.S. KHANNA GIGA INSTRUMENTATION Immeuble Z.A.
ATLAS Courtaboeuf
91941 (now with Frequency
–
Av. Baltique Les Ulis
FRANCE
Sources,
Inc.,
MD 20706)
Lanham,
J.OBREGON Laboratoire Electronique Microondes Universit6 de LIMOGES
123,
Abstract
rue
A.
Thomas FRANCE
97060
LIMOGES
:
(1)
Direct measurement of principal characteristics of a negative resistance nonlinear M.I.C. Oscil– later using a network analyser is presented. Theoretical considerations and experimental results are shown for the injection locking polar diagram obtained by placing the oscillator direc– tly at the unknown port without the use of a circulator.
For the known corresponding and susceptaace Ag=
Ab
2
.
The measurement of the ;have always been either The use of a little known. ments proposed
network till
microwave cumbersome analyser
The now
has
only using
The bys:
oscillators or incomplete so
oscillator a network
far
a single is based
setup. on
The injection
principle locking
of
are
presented. for
the
rapid quality
The
importance
characterisation oscillators
1 –2G
-2G
sin
is
+
change
in
AU
Ka
=
Using Au=
$01.000
2K
when
g
(2)
1) @g
(3)
2G
cosQg
frequency
AW is
given
Ag–Ab are
{a
( L)
the
in
nonlinear
(4)
(G
constants
+
.
0
of
:
cos9-l)+Gsin!3q
G2
9g Auo=
when
1 –
2G
}
COS
(!5)
Qg
(6)
2Ka G-1
A u .
0 G
the relation sin ‘d.
(5)
gives
:
~.
(7) 1 -G
Cos
0
0
Again
from (5) the injection phases Qgl and Au maximum and A ~ corresponding to %2 minimum can be calculated by putting d Au . dQ
the
This
and realisa– explained.
of an injection locked figure 1. The reflection which injection gain G constant (2) are given 1983 IEEE
A
Now
gives i3g1
Qg2
0149-645X/83/0000-0187
G the
Og
1 -
(3)
us
= 2
= 2
0
:
tan
Theory The equivalent circuit oscillator is shown in coefficient “a” and the can be assumed to be
-
COS
oscillator
a
(2)ard
the measu– the oscil–
of
~g
G2+
where K and the oscillator.
later under test, with the signal available at the unknown port of the network analyser (Fig.3) without using a circulator, and -~resentin.g the reflection or transmission injection locking polar diagram on the polar display. Use is made of the capability of the network analyser tomea– sure the magnitude and phase of the injection gain under locked condition. The visualization of the injection gain on the polar display is thus made similar to passive impedance measurement. The theoretical considerations and experimental approach tion of
COS
injection gain load conductance given by :
been
measureanaly–
ser have used the injection locked oscillator through a circulator (l). A new measurement is proposed without circulator. We present here simple ways for visualization and measurement of principal characteristics of an oscillator : for example, injection locked gain and bandwidth external quality factor, oscillator nonlinear cons– tants, output matching circuit characteristics, frequency jumps etc... in addition to output power
results
(G
G2
Introduction
using rement
value of perturbed A b are
tan
-1
-1
G–1 ~
{-a–a
G–1 ~
{
m’
“)
F’
“)
–a+a
and tan by:
Q!34-Qg2 2
501
.
G2-I --d2G
‘2+1 1983 IEEE
(10) MTT-S
DIGEST
Using quency
(8) and deviations 2K
Au=
(9)
in can
{ a(G
1
2K
{
a (G
the
be
cos
+
G2
(5)
corresponding
calculated
Qgl-l)
+
l-zcos
cos
fre–
to G
sin
be
gl
9
}
0g2-1)
All the typical
–
G2+1 above polar
Measurement
quantities injection setup
(11)
The from
Ogl
sin
+G
2G Cos
are gain
9g2}
output up to be used for
(12)
Qg2
clearly diagram.
shown (Fig.2)
in
while
a
the setupof Fig.3 b with power output up attenuators of 30 db
Injection
the to 30 dBm. In Fig.3 a in the test channel and 3 db in the reference channel are added to increase the gain measure– and to safeguard the sen– ment dynamic range 4 sitive harmonic frequency converter. The limits for the R.F. power at the reference channel input of the Harmonic frequency converter being - 16 to –44 dBm (5) a signal generator having a power output of -lo to 17 dBm covers the comPlete range of possible power variation for the setup. for an oscillator with O dBm output For example, this setup can be used to measure the power, injection
gain
range
of
3
to
30
and bandwidth without needing
quality
factor
can
from the ILPD a spectrum
now
be
calculated
,.. Zr o. — Af
‘
+ the power bandwidth.
injection
gain
and
The nonlinearity constants a and K can be determined , from the measured values of G, A ~ and 0 (Fig.2), with the help of equations (6)0 and (7f’, The approach provides a rapid means of determining a and K and visualizing the effects of the parameters like biasing voltage variation on their values. The assymetry of the locking range which is a function of a as shown in equations (8) to (12) as well as the elliptical power variation in the injection locked fquency range can be easily verified from the directly displayed
:
10 dBm oscillators
external :
where G represents f the injection
For the oscillator measurements described in this paper HP network analyser 8410 was used. Fig.3a represents the setup for the oscillators having an RF can
gain Fig.2
Qext
Au= 2
The injection as shown in analyser .
:
Locking
Polar
Diagram.
Directly displayed ILPD also gives a quick information about the oscillator output circuit. The frequency jumps due to improper tuning of the output circuit can be easily visualized as shown Fig.5 thus a rapid means of testing and aligning the output load circuit.
In the case of two or more (6) output ports oscil– lators, the transmission injection locking polar diagram can be obtained Fig.4 (b) in the same way and can be compared to the reflection ILPD at each port rapidly.
db.
CONCLUSION Calibration A direct presented
The set up can be calibrated for transmission and reflection coefficient modulus using a through the phase can line and a short circuit , while be calibrated under injection locked condition with a very high injection gain ( 30 dB). With this it can be easily assumed that the phase difference between the locked and the locking source at the at the parallel tuned center frequency is zero circuit oscillator plane or 180° at the series tuned circuit oscillator plane. The reference adjustable transmission line is adjusted to bring the polar plane
injection (Fig.4a)
locking
diagram
in
its
This MIC can
desired
1-
Osc .
allows rapid oscillators. be measured
=
‘sig.
gen.
–
20
dB
+
Injection at f i
has been diagram.
testing and alignment of All the principal characteristics from the directly displayed
J.C.T.
YOUNG
and of
the trans–
STEPHENSON
Large
Signal
state Devices Technique” pp. 1320-1323,
characteristics using
an
Dec.
1974
2.-
J.P. QUINE teristics of Proc. IEEE April 1969
3.–J.
OBREGON and APS KHANNA “Exact ion of the nonlinear negativeresistance oscillator pulling figure” lEEETyans. lWTTpp 1109-1111 , july
4.-HP
Application
5.-Instruction Convester
setup
I.M.
the
of Microwave Solid Injection Locking IEEE Trans. MTT,
controls without using a powermeter, power for the case of measurements Fig.3 a, at any frequency fi being
technique polar
reflection characteristics of the oscil– form of injection locking polar diapolar display of the network analyser.
“Measurement
“Injection Phase Locking Charac– LSA–mode transferred oscillators” (Lett.) vol. 57 pp.715-717
note Manual 8411 A.
deriva–
1982.
117 HP
Harmonic
Frequency
6.-APS KHANNA et Al “Efficient Low–Noise Port X–Band FET oscillator using Two Resonateurs” - 1982 IEEE-MIT-S ’Digest page 277-279.
by P
measurement Injection locking
~~FERENcEs
Once the calibration is complete the injection locking polar diagram (1. L. P. D.) can be obtai– ned on the polar display for different values of injection again using the Test channel gain control, signal generator sweep bandwidth and out– put power Fig.4a . Using the test channel gain control the point on the ILPD corresponding to Og = O is brought to the outer edge of the polar display. The oscillator power output can now be determined to the accuracy of the signal
given
oscillator using
mission and later in the gram on the
Measurements
generator oscillator shown in
in
Gain
502
Three Dielectric
/
I
-znm3z0 i—
0
bl
Fig.
1
Injection
locked
0
oscillator
,./ @ D 1
I
I
Au!
S
parameter
:;s~Bset
-——
Fig.2
Typical
injection
locking
polar
Diagram
Net-work Anal yser
Sweep generator
v m
-------- 4
Oscillator
under
!
Transmission
;
‘etUrn
,
test
‘haseshifterwm i I
J
4 (a)
Reflection G=
Sweep generator
Dual couple
Fig.
3
Measurement
set
Typical
frequency
Am:.
1.2
MHz
up
4
Fig.5
26dB
Oscillator under test
directional r
(b)
Fig.4
jumping
Trarsmi G=26dB Injection dielectric
503
ssion A locking resonator
u=
2.3
polar
MHz diagrams
oscillator
of at
9.5
a GHz