The tuning of Microwave Circulators utilizing gyromagnetic materials requires the calibration of the biasing magneto-static field, which is mostly supplied by permanent magnets. The permanent magnets have to be tuned down from saturation to an appropriate magnetization stage by means of specialized magnetizing and tuning equipment. A tuning procedure suited for automated adjustment of the saturation level of permanent magnets is described, based on S-parameter measurements. Eigenvalues of the measured 3x3 S-matrices are used to determine a required setting on a computer controllable magnetizer. This will enable a quick and accurate automated tuning process.

1. Auto-Tuning Algorithm for
Circulators based on Eigenvalue
Adjustments
Thomas Lingel
lingel@IEEE.org

2. 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

3. 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
adjustedHi
r









 −
=
100
0
0
µκ
κµ
µ j
j
P
t
sm Mπγω 4=
22
0
0
1
ωω
ωω
µ
−
+= m
22
0 ωω
ωω
κ
−
= m
iHγω =0
E-Field Pattern

4. Th. Lingel Slide 4
Circulator Magnetic Components

5. 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
+ =

6. Th. Lingel Slide 6
Demagnetization Curves
B/µ0M
H
HcHci/HcJ
Br
BHmax
intrinsic
normal
Bm
Hm
CP
Load Line and Permeance
Coefficient for Structure with
Ferrite
The permeance coefficient is in real devices a distributed property!

7. 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.

8. Th. Lingel Slide 8
Comparison of Magnetic Materials
NdFeB
SmCo
Ceramic
AlNiCo

9. 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

10. Th. Lingel Slide 10
Capacitive Discharge Magnetizer
+
DC source, typically
100V … 3000V DC
Capacitor 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

11. Th. Lingel Slide 11
Common (Manual) Tuning Approach
Un-magnetized

12. Th. Lingel Slide 12
Common (Manual) Tuning Approach
Saturated

13. Th. Lingel Slide 13
Common (Manual) Tuning Approach
1000V

14. Th. Lingel Slide 14
Common (Manual) Tuning Approach
1300V

15. Th. Lingel Slide 15
Common (Manual) Tuning Approach
1600V

16. Th. Lingel Slide 16
Common (Manual) Tuning Approach
1700V

17. Th. Lingel Slide 17
Common (Manual) Tuning Approach
1750V

18. Th. Lingel Slide 18
Common (Manual) Tuning Approach
1760V

19. Th. Lingel Slide 19
Common (Manual) Tuning Approach
1780V
Part tuned to frequency,
magnetic calibration
finished, typically RTV will
be used now to adjust
capacitive loading on ports

20. Th. Lingel Slide 20
Common (Manual) Tuning Approach
1800V
Part de-magnetized too far
Start over (Saturation and
Calibration)

21. Th. Lingel Slide 21
Auto-Tune Setup
Computer-Controlled
Magnetizer
Magnetizing Coil
Magnetizing Coil VNAIntegrated
RF Test Jig

22. Th. Lingel Slide 22
Eigenvalues and Eigenvectors
ߣଵ ߣଶ ߣଷ
• Eigenvectors represent three simultaneous excitations
(in phase, ccw, cw)
• Eigenvalues are the respective reflection coefficients

23. Th. Lingel Slide 23
Eigenvalues and Eigenvectors
ܵ̿ =
ܵଵଵ ܵଵଶ ܵଵଷ
ܵଶଵ ܵଶଶ ܵଵଷ
ܵଷଵ ܵଷଶ ܵଷଷ
Characteristic Equation:
det ܵ̿ − ߣ‫ܧ‬ധ = 0
ߣଷ
+ ‫ߣݎ‬ଶ
+ ‫ߣݏ‬ + ‫ݐ‬ = 0
Solution using Cardano’s formula to solve for complex roots of cubic polynomial
‫ݎ‬ = − ܵଵଵ + ܵଶଶ + ܵଷଷ
‫ݏ‬ = ܵଵଵܵଶଶ + ܵଵଵܵଷଷ + ܵଶଶܵଷଷ
‫ݐ‬ = −ܵଵଶܵଶଵ − ܵଵଷܵଷଵ − ܵଶଷܵଷଶ + …
ߦଷ
+ ‫ߦ݌‬ + ‫ݍ‬ = 0
ߦଵ = ‫ݑ‬ + ‫ݒ‬
ߦଶ = −
‫ݑ‬ + ‫ݒ‬
2
+
‫ݑ‬ − ‫ݒ‬
2
݅ 3
ߦଷ = −
‫ݑ‬ + ‫ݒ‬
2
−
‫ݑ‬ − ‫ݒ‬
2
݅ 3
‫ݔ‬ଶ
+px+q=0
‫ݔ‬ଵ,ଶ = −
‫݌‬
2
±
‫݌‬ଶ
4
− ‫ݍ‬
Analogy – quadratic equation
‫݌‬ = ‫ݏ‬ −
‫ݎ‬
3
‫ݍ‬ =
2‫ݎ‬ଷ
27
−
‫ݏݎ‬
3
+ ‫ݐ‬
‫ݑ‬ =
−‫ݍ‬
2
− ‫ܦ‬
య
‫ݒ‬ = −
‫݌‬
3‫ݑ‬
‫ܦ‬ =
‫݌‬
3
ଷ
+
‫ݍ‬
2
ଶ

24. Th. Lingel Slide 24
Eigenvalue Calculation Symmetric Case
ܵ̿ =
ܵଵଵ ܵଵଶ ܵଵଷ
ܵଵଷ ܵଵଵ ܵଵଶ
ܵଵଶ ܵଵଷ ܵଵଵ
ߣଵ
ߣଶ
ߣଵ
=
1 1 1
1 exp (݆
4
3
ߨ) exp (݆
2
3
ߨ)
1 exp (݆
2
3
ߨ) exp (݆
4
3
ߨ)
ܵଵଵ
ܵଵଶ
ܵଵଷ
ܵଵଵ
ܵଵଶ
ܵଵଷ
=
1
3
1 1 1
1 exp (݆
2
3
ߨ) exp (݆
4
3
ߨ)
1 exp (݆
4
3
ߨ) exp (݆
2
3
ߨ)
ߣଵ
ߣଶ
ߣଵ
߶ଵ = ∠ߣଶ − ∠ߣଵ
߶ଶ = ∠ߣଷ − ∠ߣଵ
• 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 !

25. Th. Lingel Slide 25
Difference of Eigenvalue angles vs.
demagnetization voltage

26. 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
AngleEigenvalue[°]
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

27. 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

28. 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