1. Analysis of Intermodulation Distortion in Ferrite Circulators Anuj Srivastava Karen Kocharyan Presented at MTT-2003 Renaissance Electronics Corporation Harvard, MA

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

3. Basic Construction of a Stripline Ferrite Junction Circulator Ferrite Disc Central Junction Top Ground plane Top Magnet H OBSERVATION: As H was increased, 3 rd order IMD reduced considerably.

4. Equation of Motion of Magnetization Vector HoHo mtmt MsMs MzMz Z Y X h Linear Theory Assuming rf products (hm t ) ~ 0

5. Solution of Linearized Equation of Motion Assuming harmonic (exp(i  t)) time dependence of h and m t : Solution: Ferromagnetic resonance:

6.  aa Below resonance Above resonance 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

7. Nonlinear Oscillations of Magnetization Y X T3 T2 h MsMs Z 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 m z is not zero.  Instability in the non-linear motion at high power levels depends on the anisotropy (shape, magneto-crystalline) present in the sample.

8. Harmonic Generation m z @ 2  m y0 m x0 3 X Z 1 YXY 4 m y0 2 1 2 3 4 Note: Magnetization M s is held constant

9. Nonlinear Model Small signal approximation: High signal levels (for linearly polarized rf fields):

10. Harmonics due to m t ’s 2  dependence. When two frequencies co-exists, combined frequencies, 2  1,2 ±  2,1, develop. Final Expression

11. Experimental Setup MATCHED LOAD SPECTRUM ANALYZER FILTER D.U. T. 3 dB POWER COMBINER 40 W ISOLATORS GENERATOR (1930 MHz) GENERATOR (1990 MHz) 30 dB coupler

12. IMD as a function of field offset 3 rd order Intermodulation Distortion (dBc) Internal Magnetic Field (Oe)

13. IMD vs. Bandwidth Bandwidth is Inversely Proportional to the Internal Magnetic Field

14. Summary l Intermodulation distortion decreases rapidly as operating field is moved away from resonance - valid for both above resonance and below resonance devices. l Above resonance devices should have better IMD performance than below resonance. l Planar anisotropy shall result in higher intermod values with respect to Isotropic conditions.