General properties of ferrites and comparison between an ideal and a real magnetization

General properties of ferrites

The ferrite material generates “naturally” a circular polarization when it is biased by a DC magnetic field H ₀. In [Reference Roy, Vaudon, Reineix, Jecko and Jecko5], the authors presented how to take advantage of the non-reciprocity properties of ferrites by obtaining a circular polarized patch antenna. This non-reciprocity phenomenon of a ferrite material is described by its permeability tensor. For a biasing DC magnetic field applied along the z axis and sufficient to saturate the ferrite, this permeability tensor is given by equation (1) [Reference Polder11].

(1)$$\mu = \mu _0\overline{\overline {\mu _r}} = \mu _0\left[ {\matrix{ {\mu_1} & {-j\mu_2} & 0 \cr {\,j\mu_2} & {\mu_1} & 0 \cr 0 & 0 & 1 \cr}} \right]$$

where

$$\eqalign{& \mu _1 = 1 + \displaystyle{{\omega _m\omega _0} \over {\omega _0^2 -\omega ^2}},\;\mu _2 = \displaystyle{{\omega _m\omega} \over {\omega _0^2 -\omega ^2}},\;\omega _0 = \gamma \mu _0H_i + j\omega \alpha, \cr & \omega _m = \gamma. \mu _0.4\,\pi M_s}$$

γ is the gyromagnetic ratio and α is the damping factor

$$\gamma = 1.4\; \;G_{eff}$$

where G _eff is the effective Landé factor, H _i internal magnetic field

$$\alpha = \displaystyle{{\gamma. \Delta {\rm H}} \over {2.\omega}} $$

where ΔH is the resonance line width (close to the resonant frequency)

Therefore, both μ ₁ and μ ₂ are depending on the internal DC magnetic field in the ferrite material H _i, the saturation magnetization M _s, and the frequency f. When both the real and the imaginary parts of μ ₁, i.e. μ′ and μ″ respectively, are drawn, a resonance called gyromagnetic resonance (f _r) appears: f _r = γ H _i = 1.4 G _effH _i with G _eff in (MHz/Oe).

Around this resonance frequency, the magnetic losses (proportional to μ′) are too high and for frequencies just above the gyromagnetic resonance, the effective permeability of ferrite which is defined as $\mu _{eff} = {\rm \; (}\mu _1^2 -\mu _2^2 )/\mu _1$ becomes negative. Thus, Pozar has shown that the ferrite material was not usable on these frequency bands. These areas are illustrated in Fig. 1 and explained in [Reference Arnaud, Huitema, Chantalat, Bellion and Monédière12].

Fig. 1. Evolution of the real and imaginary parts of μ ₁ according to frequency and the Polder tensor.

For this study, the antenna works above the gyromagnetic resonance (weak field). The ferrite used is therefore Y36 ferrite (Table 2) with a low-saturation magnetization (4 πM _s = 290 Gauss) which allows the use of a less powerful and bulky permanent magnet to obtain the material saturation. Furthermore far from resonance, the Y36 ferrite has a small effective resonance line width ΔH _eff (Oe), minimizing magnetic losses. With the Y36 ferrite characteristics, the real and the imaginary parts of μ ₁, i.e. μ′ and μ′′ are plotted in Fig. 1 for a uniform H _i in the ferrite material equal to 300 Oe. This graph shows the operating and forbidden areas.

Table 2. Y36 ferrite characteristics (http://www.exxelia.com/fr/groupe/a-propros/temex)

Study of principle

Before designing an antenna that best meets the requirements, a first magnetostatic and electromagnetic co-simulation has been carried out on a simple case using CST Microwave Studio to show the importance of the H _i uniformity in the ferrite. A patch antenna presented in Fig. 2 has been therefore simulated to compare the ideal and real magnetization. Initially, the ferrite is submitted to an ideal and uniform H _i field of 300 Oe. This case is called “ideal case”. Then, a well-chosen 4 mm thickness permanent magnet is placed over the antenna top hat in order to create an internal static magnetic field close to 300 Oe in the material. This case is called “real case”. The simulation is made using the magnetostatic and electromagnetic modules of CST Microwave Studio. Figure 3 shows that it is possible to obtain the same boresight AR between the ideal and real case by taking a remanent flux density (Br) of 0.7 T for the magnet.

Fig. 2. Test patch antenna.

Fig. 3. Comparison of the boresight AR (ideal and real cases).

For this configuration, magnetic and dielectric losses are high (Fig. 4). This can be explained by looking at H _i in Fig. 5(a). It appears that for Br = 0.7 T, the DC magnetic field is sometimes close to 700 Oe. Thus, for a working frequency of 2 GHz we are close to the high-loss gyroresonance area (f _r = 700 Oe. 2.8 MHz/Oe = 1.96 GHz). It is necessary to change the magnet (reduce the Br to 0.4 T) to have reasonable losses. In this case, we can see that the AR is increased and the bandwidth is reduced which is due to the presence of a non-uniform H _i in the ferrite (Fig. 5(b)). There is a trade-off between circular polarization performances, impedance bandwidth, and the antenna losses. In our study, the minimization of these last ones was the most important.

Fig. 4. Comparison of the magnetic and dielectric losses (ideal and real cases).

Fig. 5. DC internal magnetic bias field within the ferrite (H _i).

Antenna description

After a reminder of ferrite properties and an explanation of the importance of H _i, this section describes the final design taking into account the previous conclusion and the dimensional constraints to achieve the desired antenna characteristics. The design presented in Fig. 2 is not suitable for the requirements due to its narrow impedance matching bandwidth. To improve this characteristic, the antenna is modified. The radiating part of the new structure consists of two stacked patches (ϕ _patch1 = 12.4 mm and ϕ _patch2 = 24 mm) glued on a 4.98 mm thickness polyetheretherketone plastic (PEEK, ε _r = 3.1 and tanδ = 0.004). This new choice for the radiating part and the dimensions of the antenna (12 mm height and 80 mm diameter) requires changing the position and shape of the permanent magnet. Finally, Fig. 6 shows the new design. To our knowledge, no one has made a patch antenna using a ferrite material without a permanent magnet behind the ground plane. The magnetization around the ferrite is therefore innovative. The feeding part of this patch antenna is obtained using a microstrip-slot transition. A slot (L _slot = 25 mm) and a microstrip line is machined respectively on a 0.5 mm E24 steel disc and etched on the bottom of a 0.508 mm thickness laminate Duroid RT5870. The top the aforementioned substrate is completely etched. E24 disc corresponds to the patch antenna ground plane (GND). As it is made of steel, it also improves the H _i distribution inside the 6 mm thickness ferrite disc (40 mm of diameter) placed above and in the middle of the GND. A SMP-M type coaxial connector is soldered to the input of the microstrip line. A 6 mm thick ring-shaped neodymium permanent magnet with a negative axial direction of magnetization surrounds the Y36 ferrite. With this orientation, the antenna produces a LHCP. The inner and outer diameters are respectively 60 and 70 mm and the remanent field Br of the permanent magnet is 1.22 T. These parameters have been optimized to avoid the H _i inside the ferrite close to 700 Oe. A 0.5 mm E24 washer is located on the top of the magnet to improve H _i. The support is also made of steel for the same reasons. This last one also creates a cylindrical cavity below the patch feed and reduces the antenna back radiation due to the slot.

Fig. 6. Cut-plane view and the exploded antenna photograph.

Measurement and simulation

A new magnetostatic and electromagnetic co-simulation was done. Figure 7 presents the “real” internal magnetic field H _i within the realized antenna. It is, as desired, well below 700 Oe with a 150 Oe average value. Figure 8 shows a photograph of the antenna positioned on our antenna test range support (ATRS). The first measurement shows measured S ₁₁ parameter which is quite different from the simulation (Fig. 9). In simulation, the impedance bandwidth is greater than 8%. A frequency shift appears, the antenna operates at higher frequencies and the level is also higher. Simulations have been done to explain these differences and the best explanation remains the decrease of the ferrite relative permittivity (ε _r = 11.0 instead 13.7). With this value, to meet the desired characteristics, notably the amplitude of the S ₁₁ parameter, the slot length also had to be increased in simulation and in realization. Taking into account these two changes, a new simulation called “retro-simulation” has been realized. Figure 9 shows the retro-simulation and the new measurement after this change (second measurement). Even if the measurement result is not identical to the theory, the antenna now has a good impedance matching. Figure 10 compares the boresight AR in different cases. Initially, it is lower than 6 dB in the frequency bandwidth (12%). With the kind of antenna, the AR bandwidth is generally greater than the impedance bandwidth. Unfortunately, the mistake of the ferrite relative permittivity value increases the AR level and decrease the bandwidth.

Fig. 7. DC internal magnetic bias field within the ferrite (H _i).

Fig. 8. Photograph of the antenna positioned on our ATRS.

Fig. 9. Simulated and measured S ₁₁ parameter.

Fig. 10. Simulated and measured AR.

The directivity and realized gain (RG) are plotted in Fig. 11. Initially, the simulated directivity and RG were similar, so total losses were close to 0.5 dB in bandwidth. The measured directivity is like the simulated one even if the radiation patterns are disturbed by the ATRS. After all the changes, the simulated total losses are increased (2 dB). This is due to metal losses induced by the steel on the ground plane. The electromagnetic field distribution is different for each case. For the last case, this field is higher and so causes more losses. The measured total losses are also increased (<3 dB). The three-dimensional (3D) LHCP radiation pattern theory-measurement comparison (Fig. 12) is presented at 2.1 GHz in directivity after the modifications. Figure 13(a)–(d) compare the simulated and measured LHCP RG and AR at 2.1 GHz. The result is almost identical to the other frequencies. The minimum gain in LOC is greater than – 6 dB in simulation and measurement even if the radiation patterns of the latter are less symmetrical. It is not possible at this time to have an AR in LOC lower than 6 dB even in the simulation. It would take a boresight AR close to 3 dB to have a good AR in the LOC. This condition is perhaps possible but it would be necessary to perfectly know all the parameters of the antenna, notably the ferrite permittivity at the working frequency. Then, it would be necessary to redesign the antenna, in particular ferrite and permanent magnet dimensions taking into account these new parameters.

Fig. 11. Simulations and measurements of the boresight directivity and RG.

Fig. 12. 3D radiation patterns.

Fig. 13. Radiation patterns (2.1 GHz). (a) LHCP simulated RG. (b) LHCP measured RG. (c) Simulated AR. (d) Measured AR.