4. Applications of ferrite materials

The ferrites are crystals having small electric conductivity compared to ferromagnetic materials. Thus they are useful in high-frequency situations because of the absence of significant eddy current losses. Three commonly used ferrite devices are discussed below. These are phase shifters, circulators, and isolators [13–16].

#### 4.1 Phase shifter

The phase shifters are important applications of ferrite materials, which are two-port components that provide variable phase shift by changing the bias magnetic field. Phase shifters find application in test and measurement systems, but the most significant use is in phase array antenna where the antenna beam can be steered in space by electronically controlled phase shifters. Because of the demand, many different types of phase shifters have been provided. One of the most useful designs is the latching nonreciprocal phase shifter using a ferrite toroid in the rectangular waveguide. We can analyze this geometry with a reasonable degree of approximation using the double ferrite slab geometry.

displayed in Figure 6(a) for an empty waveguide and a waveguide with two ferrite slabs. The phase difference Δϕ, shown in Figure 6(b), is calculated under two conditions: with and without ferrites. The simulation parameters are the same as example 9.4 of Pozar's textbook. The saturation magnetization (4πMs) is 1786 G, the dielectric constantε<sup>0</sup> is 13.0, and the resonance linewidth ΔH is 20 Oe. The

Schematic diagrams of the operation of a stripline circulator. (a) The incident wave is injected from Port 1 and the transmitted wave ideally goes to Port 2. (b) The incident wave from Port 2 will go to Port 3. The color spectrum is the electric field pattern inside the ferrite disks. It is a three-port, nonreciprocal device. A full-wave

Simulation results. (a) The field pattern to the left is for the empty waveguide. The right figure shows field

strength with ferrites. (b) The phase difference Δϕ as a function of the internal bias field H0.

Circulator, a nonreciprocal device, has been widely used in various microwave systems. Figure 7 schematically shows the function of a stripline circulator. The circulator is, in general, a three-port device. If the incident wave is injected from Port 1, then the wave will ideally go to Port 2, while Port 3 will be isolated as shown in Figure 7(a). On the other hand, if the wave is injected from Port 2, it will go to Port 3 and isolate from Port 1 as shown in Figure 7(b). There are three figures of merit for a circulator: transmission, reflection, and isolation. The transmission from Port 1 to Port 2 should be as high as possible, i.e., the insertion loss should be as small as possible. The reflection received at Port 1 due to the incident wave of Port 1 (S11) and the isolation from Port 1 to Port 3 (S13) should be as small as possible. The nonreciprocity of the circulator can be used to protect the oscillators from the damage of the reflected power in plasma or material processing systems. It can also be used to separate the transmitted and the received waves in radar or

length and thickness of the ferrite are L = 37.50 mm and t = 2.74 mm.

solver, high-frequency structure simulator (HFSS), is used [18].

4.2 Circulator

145

Figure 6.

Ferrite Materials and Applications

DOI: http://dx.doi.org/10.5772/intechopen.84623

Figure 7.

communication systems [13–17].

Figure 6 shows the full-wave simulation for a two-port phase shifter using highfrequency structure simulator (HFSS, ANSYS). A standard waveguide WR-90 is employed with a width of 22.86 mm and height of 10.16 mm. The field patterns are

#### Figure 5.

The idea is to place the sample at the maximum of the H-field. It exhibits resonant absorption when the internal bias field is changed to Hr. By changing the magnetic field, we will obtain the absorption. H<sup>1</sup> and H<sup>2</sup> are associated with the 3-dB absorption. The difference between these two values is the resonance linewidth ΔH.

Ferrite Materials and Applications DOI: http://dx.doi.org/10.5772/intechopen.84623

#### Figure 6.

The idea is normally implemented using a TE10n (n even) cavity in the X-band region [9, 12]. The test sample is placed at the H-field maximum. The sample is spherical with a diameter of approximately 0.040 inches, which is much easier to estimate than the internal bias field H0. A cross-guide coupler is used with the coupling iris. The loaded Q (QL) of the empty cavity should be 2000 or greater. The sample, mounted on a fused silica or equivalent rod, is positioned away from the cavity wall at a point of minimum microwave electric field and maximum microwave magnetic field. A power meter can be used to read off the half-power points by adjusting the DC magnetic field and measuring the difference in H0-field directly

The three key parameters are obtained in three experimental setups under different sizes and geometries of the samples. If the samples' properties are slightly different or the machining error is not negligible, the error will be large or even unacceptable. The ultimate goal is to integrate the measurements and to extract the parameters using one experimental setup. The three key parameters will be used in

The ferrites are crystals having small electric conductivity compared to ferromagnetic materials. Thus they are useful in high-frequency situations because of the absence of significant eddy current losses. Three commonly used ferrite devices are

The phase shifters are important applications of ferrite materials, which are two-port components that provide variable phase shift by changing the bias

magnetic field. Phase shifters find application in test and measurement systems, but the most significant use is in phase array antenna where the antenna beam can be steered in space by electronically controlled phase shifters. Because of the demand, many different types of phase shifters have been provided. One of the most useful designs is the latching nonreciprocal phase shifter using a ferrite toroid in the rectangular waveguide. We can analyze this geometry with a reasonable degree of

Figure 6 shows the full-wave simulation for a two-port phase shifter using highfrequency structure simulator (HFSS, ANSYS). A standard waveguide WR-90 is employed with a width of 22.86 mm and height of 10.16 mm. The field patterns are

The idea is to place the sample at the maximum of the H-field. It exhibits resonant absorption when the internal bias field is changed to Hr. By changing the magnetic field, we will obtain the absorption. H<sup>1</sup> and H<sup>2</sup> are associated with the 3-dB absorption. The difference between these two values is the resonance linewidth ΔH.

discussed below. These are phase shifters, circulators, and isolators [13–16].

[12]. Figure 5 shows how the resonant linewidth is determined.

the design of the microwave ferrite devices in the next session.

approximation using the double ferrite slab geometry.

4. Applications of ferrite materials

Electromagnetic Materials and Devices

4.1 Phase shifter

Figure 5.

144

Simulation results. (a) The field pattern to the left is for the empty waveguide. The right figure shows field strength with ferrites. (b) The phase difference Δϕ as a function of the internal bias field H0.

#### Figure 7.

Schematic diagrams of the operation of a stripline circulator. (a) The incident wave is injected from Port 1 and the transmitted wave ideally goes to Port 2. (b) The incident wave from Port 2 will go to Port 3. The color spectrum is the electric field pattern inside the ferrite disks. It is a three-port, nonreciprocal device. A full-wave solver, high-frequency structure simulator (HFSS), is used [18].

displayed in Figure 6(a) for an empty waveguide and a waveguide with two ferrite slabs. The phase difference Δϕ, shown in Figure 6(b), is calculated under two conditions: with and without ferrites. The simulation parameters are the same as example 9.4 of Pozar's textbook. The saturation magnetization (4πMs) is 1786 G, the dielectric constantε<sup>0</sup> is 13.0, and the resonance linewidth ΔH is 20 Oe. The length and thickness of the ferrite are L = 37.50 mm and t = 2.74 mm.

#### 4.2 Circulator

Circulator, a nonreciprocal device, has been widely used in various microwave systems. Figure 7 schematically shows the function of a stripline circulator. The circulator is, in general, a three-port device. If the incident wave is injected from Port 1, then the wave will ideally go to Port 2, while Port 3 will be isolated as shown in Figure 7(a). On the other hand, if the wave is injected from Port 2, it will go to Port 3 and isolate from Port 1 as shown in Figure 7(b). There are three figures of merit for a circulator: transmission, reflection, and isolation. The transmission from Port 1 to Port 2 should be as high as possible, i.e., the insertion loss should be as small as possible. The reflection received at Port 1 due to the incident wave of Port 1 (S11) and the isolation from Port 1 to Port 3 (S13) should be as small as possible. The nonreciprocity of the circulator can be used to protect the oscillators from the damage of the reflected power in plasma or material processing systems. It can also be used to separate the transmitted and the received waves in radar or communication systems [13–17].

An isolator is commonly used to prevent the high reflected power from damaging the precious and expansive microwave source. For example, the impedance of a plasma system changes a lot when the plasma is ignited. The radical change of the impedance will result in impedance mismatch and cause serious reflection which might kill the source instantly. An isolator can be used in place of a matching or tuning network. However, it should be realized that the reflected power will be absorbed by the ferrite of the isolator, as shown in Figure 9(b). When the ferrite absorbs the reflected energy, the temperature will rise and the performance will be

compromised. Therefore, a simple isolator can be implemented by using a

experimental study is needed.

Ferrite Materials and Applications

DOI: http://dx.doi.org/10.5772/intechopen.84623

5. Conclusions

Acknowledgements

147

circulator with one port well terminated [19]. For example, if Port 3 in Figure 8(a) is matched with water load, the power injected from Port 2 will go to Port 3 and will be isolated from Port 1. The power handling capability can be improved.

Circulator and isolator can be implemented using the self-bias [20–22], just like the latch phase shifter (H<sup>0</sup> ¼ 0) shown in Figure 6 using the remnant field Br or Mr only. The self-biased ferrite devices will simplify the design and fabrication, but the overall performance is still not good enough. Further theoretical and

Ferrimagnetism and ferromagnetism share many magnetic properties in common, such as hard and soft magnets, but the conductivity differentiates these two materials. Ferrites are ceramic materials and suitable for the high-frequency operation. The electromagnetic properties of ferrite materials are difficult to understand in that the magnetic susceptibility is a tensor and depends on the saturated magnetization Ms, the internal bias field H0, and the resonance linewidth ΔH. The magnetic susceptibility also depends on the frequency of the microwave ω as well as the

This chapter was supported in part by the Ministry of Science and Technology of

Taiwan and in part by China Steel Company/HIMAG Magnetic Corporation, Taiwan. The author is grateful to the Taiwan Branch of ANSYS Inc. for technical assistance and to Dr. Hsein-Wen Chao and Mr. Wei-Chien Kao for their assistance in the full-wave simulation. Dr. Hsin-Yu Yao and Mr. Shih-Chieh Su are appreciated

for the discussion of the ferrites' characterization.

polarization of the wave. The first two sessions explain the basic properties. The complex permittivity ε<sup>r</sup> þ iεi, the saturation magnetization Ms, and the resonance linewidth ΔH are the most important electromagnetic properties of ferrites. How to measure the ferrite's properties are discussed in Section 3. The fullwave simulation is conducted to demonstrate how the phase shifter, circulator, and isolator work, which are shown in Section 4. Although the examples are discussed in many textbooks, Section 4 offers in-depth simulation results for the first time. At high-power operation, the ferrite devices will be heated. The spin wave linewidth may be taken into account. Besides, the ferrites will become paramagnetism when the temperature exceeded the Curie temperature. These two factors are important for high-power operation, which are not considered in this chapter.

#### Figure 8.

(a) Schematic diagrams of the operation of a waveguide circulator. A full-wave solver, HFSS, is used with the saturation magnetization (4πMs) is 1600 G, the dielectric constantε<sup>0</sup> is 13.0, and the resonance linewidth ΔH is 10 Oe. The radius and thickness of the ferrite disks in rust red are R = 21.0 mm and t = 5 mm, respectively. The waveguide is a standard WR 340 with 86.36 � 43.18 mm<sup>2</sup> . The electric field pattern is displayed in color. (b) Simulation results of the waveguide circulator like the one in Part (a). The solid red curve is the transmission or insertion loss; the blue curve represents the reflection loss, and the black is the isolation.

#### Figure 9.

The simulated field strength for a two-port isolator using the full-wave solver. (a) The high forward transmission (S21) and (b) the low reverse transmission (S12). The saturation magnetization (4πMs) is 1700 G, the dielectric constant ε<sup>0</sup> is 13.0, and the resonance linewidth ΔH is 200 Oe. The length and thickness of the ferrite are L = 24.0 mm and t = 0.5 mm.

In addition to the stripline circulator, there are other types such as the microstrip circulator and the waveguide circulator. The microstrip circulator is similar to the stripline circulator in many ways. Here we show a waveguide circulator which is capable of high-power operation. Figure 8(a) shows the structure of the nonreciprocal device and the simulated electric field strength. The simulation parameters are described in the caption. The circulator is, in general, a three-port device. If the incident wave is injected from Port 1, then the wave will ideally go to Port 2, while Port 3 will be isolated as shown in Figure 8(b). On the other hand, if the wave is injected from Port 2, it will go to Port 3 and be isolated from Port 1 as shown in Figure 8(b).

#### 4.3 Isolator

The isolator is one of the useful microwave ferrite components. As shown in Figure 9, the isolator is generally a two-port device having unidirectional transmission characteristics (nonreciprocity). From Port 1 to Port 2 (S21), the forward transmission is high (i.e., low insertion loss in Figure 9(a)). However, from Port 2 to Port 1 (S12), the reverse transmission is low (i.e., high isolation in Figure 9(b)). Besides, the reflection (S11 and S22) should be as low as possible. The simulation parameters in Figure 9 are the same as Ex. 9.2 of Pozar's textbook [5]. The simulation parameters and the sample's geometry are described in the caption.

#### Ferrite Materials and Applications DOI: http://dx.doi.org/10.5772/intechopen.84623

An isolator is commonly used to prevent the high reflected power from damaging the precious and expansive microwave source. For example, the impedance of a plasma system changes a lot when the plasma is ignited. The radical change of the impedance will result in impedance mismatch and cause serious reflection which might kill the source instantly. An isolator can be used in place of a matching or tuning network. However, it should be realized that the reflected power will be absorbed by the ferrite of the isolator, as shown in Figure 9(b). When the ferrite absorbs the reflected energy, the temperature will rise and the performance will be compromised. Therefore, a simple isolator can be implemented by using a circulator with one port well terminated [19]. For example, if Port 3 in Figure 8(a) is matched with water load, the power injected from Port 2 will go to Port 3 and will be isolated from Port 1. The power handling capability can be improved.

Circulator and isolator can be implemented using the self-bias [20–22], just like the latch phase shifter (H<sup>0</sup> ¼ 0) shown in Figure 6 using the remnant field Br or Mr only. The self-biased ferrite devices will simplify the design and fabrication, but the overall performance is still not good enough. Further theoretical and experimental study is needed.
