When applying a static magnetic field to a ferrite material, this material shows anisotropic and dispersive characteristics. In more detail, if a high frequency magnetic field is applied perpendicularly to the direction of the static magnetic field Hin , the magnetic dipoles of the ferrite are rotating around the axis of the static magnetic field. The material is therefore called gyrotropic material and can be tuned by the static magnetic field.
This behavior is strongly non-reciprocal and very often used in microwave components such as circulators or one way transmission devices. The dispersive and non-isotropic behavior can be described by a permeability tensor, the so-called Polder tensor . This tensor is directly implemented in one of the material descriptions of CST MICROWAVE STUDIO® (CST MWS)....
The structure of interest is a ferrite-loaded waveguide antenna (courtesy and permissions of KAIST Korea) as shown in Figure 1. The ferrite material is used as a tunable medium to achieve a beam-scanable slot antenna in this case.
Figure 1: Ferrite-loaded waveguide antenna.
Three different approaches to investigate this problem are shown. First, the antenna can be described by the model shown in Figure 2. Second, the antenna can easily be simulated with CST MWS. In Figure 3 the corresponding model is shown. Last but not least, the results are compared with measurements. The measurements are all performed with the fabricated model shown in Figure 4.
Figure 2: 2D model for analytical solution .
Under the follwing assumptions a 2D model for structure to be investigated can be found :
- There is no field variation in y-direction
- The electric field shows only a y-component. That means the TE01 mode is propagating.
- The ferrite is magnetised in y-direction.
The directions refer to Figure 1.
Figure 3: CST MWS Model of the structure.
Figure 4: Image of the real fabricated structure
The simulated results show nice agreement to the results measured for the real fabricated structure as shown in Figure 5, where the measured and simulated reflection coefficients are displayed. Furthermore, the simulation agrees very well with analytical solution. This can be seen from the analytically derived and simulated radiation intensity diagrams in Figure 6. At the same time, validation for the analytical solution can be found by comparing radiation patterns of the measurements with the radiation pattern resulting from the analytical solution (Figure 7).
Figure 5: Comparison between measurements and simulation.
Figure 6: Comparison between analytical theory and simulation.
Figure 7: Comparison between analytical theory and measurements.
To conclude, ferrite-loaded antennas can be easily simulated with CST MWS with good agreement to real results. Where, under assumptions, an analytical solution is found, the results also agree well.
 D. Polder, "On the Theory of Ferromagnetic Resonance", Philosophical Magazine, Vol. 40, pp. 99-115, 1949.
 K. C. Hwang and H. J. Eom, "Radiation from a ferrite-filled rectangular waveguide with multiple slits", IEEE MIcrowave Wireless Component Letters, Vol. 15, No. 5, pp. 345-347, May 2005.