1. Measurement Techniques and Application of Combined Parallel/Orthogonal Magnetic Bias on a Ferrite Tuned Resonator in Low Frequency Range (3-10 MHz) G. Favia Impedance WG meeting 03/06/2015

2. Introduction  Hysteresis loop  Sintered ferrite consists of small crystals. Domains exist within these crystals (Weiss domains) in which the molecular magnets are already aligned (ferrimagnetism).  When a driving magnetic field (H) is applied to the material the domains progressively align with it.  A so-called hysteresis loop is the result.

3. When a magnetic field is applied to a soft magnetic material, the resulting flux density is composed of that of free space plus the contribution of the aligned domains. where M is the magnetization. The ratio of flux density and applied field is called absolute permeability. It is usual to express this absolute permeability as the product of the magnetic constant of free space and the relative permeability (μ r ). The initial permeability is measured in a closed magnetic circuit (ring core) using a very low field strength. Permeability definition

4. BIAS FIELD RF FIELD BIAS FIELD RF FIELD operating in the perpendicular bias mode would require a significantly larger bias range and would make the design of the bias power supply very difficult and expensive; ferrite materials are magnetically lossy at low magnetization and the losses become smaller at high magnetization. In order to take advantage of the low losses at high magnetization fields it is necessary to perpendicularly bias the ferrite. Bias field orientation

5. Ferrite contributes in this way: It enhances the value of B rf for a given current, allowing the cavity to be small; It provides a means of dynamically tuning the cavity. The ferrite determines the equivalent inductance and the losses of the cavity. It is possible to tune the cavity by varying its inductance: Application of ferrite

6. Bias field orientation

7. Shorted coaxial line: Ferrite inductors: Inductors formed with ferrite as a core material exhibit an increase in inductance value as well as losses The impedance of the inductor is: 4 Coaxial line approximation

8. Toroidal coil with a rectangular section RF FIELD with A e being the section crossed by the magnetic field and l m the effective length. Rectangular cross section approximation

9. Reflection coefficient measurements Data elaboration S 11 ( l h ) Re {Z(l f )} Im {Z(l f )} μ”μ” μ’μ’ Empty coaxial line impedance Permeability evaluation methods 50Ω connector Ferrite ring Short end

10. r4 r1 r3 r2 For a current flowing in the coaxial line the impedance per unit length L t is: 6 Air gap correction

11. empty before normalization after normalization Data analysis Results:

12. BIAS FIELD  Bias field parallel to the RF field.  RF choke coil necessary to filter out the RF towards the DC power supply.  Accurate VNA calibration crucial for the measurement accuracy.  Calibration with DC power supply set to 0 A and 0 V.  Voltage limitation of the power supply set to 10 V.  Setup able to withstand up to 50 A. Fig. 2: Permeability variation with bias current of 4s2 ferrite sample VNA DC POWER SUPPLY I BIAS RF FIELD Calibration plane Parallel bias field application

13.  3-10 MHz resonator made of two coaxial lines shorted on one end completely filled of ferrite.  Characterization of several ferrite samples required in order to find the ones featuring the lowest losses in the required frequency range.  Varying the orthogonal bias field, at a fixed operating point given by the parallel bias, implies a resonant frequency variation and ferrite losses reduction. An optimum combination of the amplitude and the relative orientation of the two bias fields reduces the losses by a factor of two for the ferrites under test. HH H  Fig. 4: Results of the application of combined bias technique Combined \\  bias field