http://www.hfoscillators.com/apskhanna/articles/IMS1983Direct

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