Circulator Autotuning

Auto-Tuning Algorithm for

Circulators based on Eigenvalue

Adjustments

Thomas Lingel

[email protected]

Th. Lingel Slide 2

• Circulator Magnetic components

• Permanent Magnet Materials and

Magnetization/Calibration Process

• Magnetizer Overview

• Common Tuning Approach

• Eigenvalues and Eigenvectors of Junction Circulators

• Auto-Tuning Algorithm

• Summary

Outline

Th. Lingel Slide 3

Circulator Operation

• Non-reciprocal behavior is based on elements of permeability

tensor,

• For above resonance devices the center frequency is adjusted

with the Magneto-Static Bias Field and requires very accurate

calibration

adjustedH i

r

−

=

100

0

0

µκ

κµ

µ j

j

P

t

sm Mπγω 4=

22

0

01ωω

ωωµ

−+= m

22

0 ωω

ωωκ

−= m

iHγω =0

E-Field Pattern

Th. Lingel Slide 4

Circulator Magnetic Components

Th. Lingel Slide 5

Permanent Magnetic Materials

H

B

HB 0µ=

B

H

)(0 MHB += µ

M

H

)(HM

Material Contribution

Soft-Magnetic

Hard-Magnetic

B

H

+ =

Th. Lingel Slide 6

Demagnetization Curves

B/µ0M

H

HcHci/HcJ

Br

BHmaxintrinsic

normal

Bm

Hm

CP

Load Line and Permeance

Coefficient for Structure with

Ferrite

The permeance coefficient is in real devices a distributed property!

Th. Lingel Slide 7

Calibration of Permanent Magnets

B/µ0M

H

Measured Demagnetization Curve

• Tuning is necessary to account for material and mechanical tolerances.

• The Operating point will in this case be on a minor hysteresis loop.

Th. Lingel Slide 8

Comparison of Magnetic Materials

NdFeBSmCo

Ceramic

AlNiCo

Th. Lingel Slide 9

• Magnetization and Demagnetization is typically

performed with capacitive discharge devices driving

water cooled solenoids or air-cooled Bitter coils

• Field strengths in the order of 2x..3x Hcj are required

to fully saturate a unit

• Eddy currents will be generated which will increase

the DUT temperature (auxiliary cooling devices and

fixtures which minimize Eddy currents can be

necessary)

Magnetizer Overview

Th. Lingel Slide 10

Capacitive Discharge Magnetizer

+

DC source, typically

100V … 3000V DCCapacitor Bank

Magnetizing Coil

High Current Switch,

typically SCR

• There are more advanced versions offering different pulse shapes

• DC voltage is controlled to adjust the magnetic field level

• Energy levels typically ranging from 100J to 20kJ depending on magnet material

Th. Lingel Slide 11

Common (Manual) Tuning Approach

Un-magnetized

Th. Lingel Slide 12


Saturated

Th. Lingel Slide 13


1000V

Th. Lingel Slide 14


1300V

Th. Lingel Slide 15


1600V

Th. Lingel Slide 16


1700V

Th. Lingel Slide 17


1750V

Th. Lingel Slide 18


1760V

Th. Lingel Slide 19


1780VPart tuned to frequency,

magnetic calibration

finished, typically RTV will

be used now to adjust

capacitive loading on ports

Th. Lingel Slide 20


1800VPart de-magnetized too far

Start over (Saturation and

Calibration)

Th. Lingel Slide 21

Auto-Tune Setup

Computer-Controlled

Magnetizer

Magnetizing Coil

Magnetizing Coil VNAIntegrated

RF Test Jig

Th. Lingel Slide 22

Eigenvalues and Eigenvectors

��

• Eigenvectors represent three simultaneous excitations

(in phase, ccw, cw)

• Eigenvalues are the respective reflection coefficients

Th. Lingel Slide 23

Eigenvalues and Eigenvectors

�̿ =

��

��

��

Characteristic Equation:

det �̿ − �� = 0

�� + �� + �� + � = 0

Solution using Cardano’s formula to solve for complex roots of cubic polynomial

� = − �� + �� + ��

� = �� + �� + ��

� = −�� − �� − �� + …

�� + �� + � = 0

�� = � + �

�� = −� + �

2+

� − �

2� 3

�� = −� + �

2−

� − �

2� 3

��+px+q=0

��,� = −�

2±

��

4− �

Analogy – quadratic equation

� = � −�

3

� =2��

27−

��

3+ �

� =−�

2− %

&

� = −�

3�

% =�

3

�

+�

2

�

Th. Lingel Slide 24

Eigenvalue Calculation Symmetric Case

�̿ =

��

��

��

��

��

��

=

1 1 1

1 exp()4

3*) exp()

2

3*)

1 exp()2

3*) exp()

4

3*)

��

��

=1

3

1 1 1

1 exp()2

3*) exp()

4

3*)

1 exp()4

3*) exp()

2

3*)

��

,� = ∠�� − ∠��

,� = ∠�� − ∠��

• In the lossless case the magnitude of the Eigenvalues is 1

• Only the difference of the Eigenvalue angle needs to be considered

3x3 complex S-parameter matrix with 18 numbers is reduced to two numbers !

Th. Lingel Slide 25

Difference of Eigenvalue angles vs.

demagnetization voltage

Th. Lingel Slide 26

Observation Angle Eigenvalues vs.

Demagnetization Voltage

100

110

120

130

140

150

160

170

180

190

0 200 400 600 800 1000

An

gle

Eig

en

valu

e [°]

Demagnetization Voltage [V]

• Use 120°target angle only

• Complex 3x3 S-parameter matrix is reduced to one number !!!

• The 120°angle can be used to extrapolate the required demagnetization voltage

• Different Hcj values impact the required tuning voltage

• Demagnetization behavior can be fitted with a square polynomial

- - Square Polynomial Fit

Threshold Point

Th. Lingel Slide 27

• Place completely assembled unit into test-jig, residing in

magnetizing fixture

• Saturate unit

• Demagnetize until threshold is reached

• Perform two additional demagnetization steps to be able to

fit square polynomial

• Extrapolate to target angle of 125°

• Use last three data points and extrapolate to target angle of

120°

• Algorithm can be applied at center frequency or a mean value

across the operating frequency band

Auto-Tuning Algorithm

Th. Lingel Slide 28

• A robust algorithm for auto-tuning of circulators is presented

for the first time

• The 3x3 complex S-Parameter matrix is reduced to a single

number

• The angle difference of two Eigenvalues vs. demagnetization

voltage can be fitted with a square polynomial and can be

used to extrapolate to the target of 120°

• The algorithm is in particular useful for high volume

applications

Summary

Engineering

Circulator Autotuning