Analysis of Intermodulation Distortion in Ferrite Circulators

Anuj Srivastava

Karen Kocharyan

Presented at MTT-2003

Renaissance Electronics Corporation

Harvard, MA

OVERVIEW

Introduction Linearized Equation of Motion for Magnetization Nonlinear Oscillations of Magnetization Nonlinear Model IMD Data on a PCS Circulator Summary

Basic Construction of a Stripline Ferrite Junction Circulator

Ferrite Disc

Central Junction

Top Ground plane

Top Magnet

H

OBSERVATION: As H was increased, 3rd order IMD reduced considerably.

Equation of Motion of Magnetization Vector

Ho

mt

Ms

Mz

Z

Y

X

h

hMHmm

zott

dt

d

oHh zMmt

HMM

ss

dt

d

hHH otzs mMM

Linear Theory

Assuming rf products (hmt) ~ 0

Solution of Linearized Equation of Motion

Assuming harmonic (exp(it)) time dependence of h and mt:

yzyox hMmHmi

xzxoy hMmHmi

0zmi

Solution:

yaxx hihm xayy hihm 0zm

22

o

ozM22

o

za

M

oo H Ferromagnetic resonance:

a

Below resonance

Above resonance

Ho( )

a Ho( )

Ho

500 550 600 650 700 750 800 850 900 950 1000

0.4

0.2

0

0.2

0.4

Internal Field

Sus

cept

ibil

ity

Internal field (Oe)

Suscep-tibility

, a

Tensor Susceptibility vs. Internal Field

Difference between and a is more in the below resonance than above resonance region

Nonlinear Oscillations of Magnetization

Y

X

T3

T2

h

MsZ

T1

T4

Magnetization vector does not precess in a circular path.As the rf power is increased, higher order terms become significant and can no longer be neglected. Time derivative of mz is not zero.Instability in the non-linear motion at high power levels depends on the anisotropy (shape, magneto-crystalline) present in the sample.

Harmonic Generation

mz @ 2

my0 mx0

3

Xmx0

Z 1

Y X Y

4

my0

2

1

2

34

Note: Magnetization Ms is held constant

Nonlinear Model

•Small signal approximation:

•High signal levels (for linearly polarized rf fields):

yaxx hihm xayy hihm 0zm

0zmdtd

xx hm xay him

2222222

2

)2cos(1aaxyxt

thmmm

222tzzs mmMM

)2exp( ~ 12

tiMM

mMm z

ssz

t

•Harmonics due to mt’s 2 dependence.

•When two frequencies co-exists, combined frequencies, 21,2 ± 2,1, develop.

Final Expression

Experimental Setup

MATCHED LOAD

SPECTRUMANALYZER

FILTER

D .U. T.

3 dB POWER COMBINER

40 W

40 W

ISOLATORS

ISOLATORS

GENERATOR (1930 MHz)

GENERATOR (1990 MHz)

30 dB coupler

IMD as a function of field offset

10 log Mztotal h Ho( ) Mztotal h

3000

2 n

10 n

5 n

0 n

5 n

10 n

15 n

20 n

Ho 735 750 765 780 795 810 825 850740 760 780 800 820 840

105

100

95

90

85

80

75

70

65

60

55

3rd order Intermodulation

Distortion(dBc)

Internal Magnetic Field (Oe)

Bandwidth f/f, %3 4 5 6 7 8 9 10

IMD

, dB

c

-95

-90

-85

-80

-75

-70

-65

-60

IMD vs. Bandwidth

Bandwidth is Inversely Proportional to the Internal Magnetic Field

Summary

Intermodulation distortion decreases rapidly as operating field is moved away from resonance - valid for both above resonance and below resonance devices.

Above resonance devices should have better IMD performance than below resonance.

Planar anisotropy shall result in higher intermod values with respect to Isotropic conditions.