Compact Four-Port Waveguide Circulator Using Discrete Ferrites for Injection-Locking Magnetron System

: A compact high-power four-port circulator aiming to simplify the conventional, complex, and bulky injection-locking magnetron system is proposed. To reduce the performance deterioration and the risk of ferrite rupture under long-term high-microwave-power condition, the method of breaking a monolithic ferrite into three discrete ferrites in a conventional three-port circulator is proposed. To miniaturize the size and cost of the four-port circulator, a butterfly-shaped waveguide structure is proposed, with a stub inserted into the cavity at the central point and with no connecting waveguide. Multiphysics simulation results show that the temperature coefficient of variation (COV) at the surface of the discrete ferrites is 12.4% lower than that of a monolithic ferrite circulator, with input microwave power of 10 kW. The size of the proposed four-port waveguide circulator is 27% less than the assembly of two three-port circulators, and way smaller than a conventional differential phase shift circulator (DPSC). The simulated and measured S-parameters match well, and the measured power capacity of the fabricated circulator is higher than 3 kW (limited by the experimental condition). A magnetron is successfully locked using only one designed compact circulator. The research in this paper promotes the development of injection-locking magnetron and provides a design example for the compact, high-power circulator.


Introduction
Magnetrons have been widely used in microwave energy transmission, microwave heating, and materials processing because of their advantages such as high energy conversion efficiency, low cost, and high output power [1,2].However, the microwave source using a free-running magnetron exhibits issues such as frequency instability, wide-band spectrum, coupling between output power and frequency, etc. [3].The injection-locking technology can significantly improve the output characteristics and control the output frequency of a magnetron, thus widening the applications of magnetrons [4][5][6].Yang et al. improved the uniformity of microwave heating using the injection-locked magnetron for sweep frequency output [7].Zhao et al. used an injection-locked magnetron to generate a high-flow microwave atmospheric plasma jet to achieve fast degradation of p-nitrophenol [8].
However, a conventional injection-locking magnetron system, as shown in Figure 1a, usually requires two three-port waveguide circulators.The circulator is a non-reciprocal device which can transmit the power unidirectionally among its ports; the input port is coupled to a single unique output port and is isolated from other ports [9,10].For the injection-locking magnetron, the circulators are essential to separate the magnetron's output power, the injected signal and the reflected power, which usually exists in a certain period in the applications of microwave heating or microwave plasma due to the variation of the load condition.The separation function is detailed using arrows in Figure 1a.The red, blue, and yellow arrows represent the power flow of the magnetron's output power, the injected signal, and the reflected power, respectively.The system is bulky and high-cost, which greatly limited its commercialization and further development.If a four-port circulator can be designed, it can make the injection-locking magnetron system compact, low cost, and lightweight by replacing the two circulators, as shown in Figure 1b.Furthermore, in the microwave power combining technique, which uses multiple injection-locked magnetrons, the cost and size of the system would be considerably reduced if the four-port circulators were applied [11,12].
However, a conventional injection-locking magnetron system, as shown in Figure 1a, usually requires two three-port waveguide circulators.The circulator is a non-reciprocal device which can transmit the power unidirectionally among its ports; the input port is coupled to a single unique output port and is isolated from other ports [9,10].For the injection-locking magnetron, the circulators are essential to separate the magnetron's output power, the injected signal and the reflected power, which usually exists in a certain period in the applications of microwave heating or microwave plasma due to the variation of the load condition.The separation function is detailed using arrows in Figure 1a.The red, blue, and yellow arrows represent the power flow of the magnetron's output power, the injected signal, and the reflected power, respectively.The system is bulky and highcost, which greatly limited its commercialization and further development.If a four-port circulator can be designed, it can make the injection-locking magnetron system compact, low cost, and lightweight by replacing the two circulators, as shown in Figure 1b.Furthermore, in the microwave power combining technique, which uses multiple injection-locked magnetrons, the cost and size of the system would be considerably reduced if the fourport circulators were applied [11,12].Conventionally, a four-port waveguide circulator with high power capacity is usually designed with a cascade of a quadrature hybrid coupler, nonreciprocal phase shifters, and a magic tee, which is referred as the DPSC [13].A DPSC is bulky and costly [14].Dixit et al. designed a DPSC operating at the S-band with a power capacity of 500 kW; however, the length of the DPSC is 3 m [15].Deng et al. proposed a compact four-port waveguide circulator operating at the X-band [16].In their design, two three-port junction circulators are stacked, and a composite post resonator is applied in a parallel topology to achieve coupling.Thus, the size of the four-port circulator is considerably reduced; however, the multilayered structure is difficult to assemble.Moreover, as the frequency decreases, the distance between the upper and lower sides of the waveguide wall increases.Owing to this increased distance, realization of the required DC bias magnetic-field strength is difficult because the bias magnets are placed outside the entire cavity.Reddy et al. designed a four-port circulator by cascading two three-port junction circulators with microstrip lines [17].Their study shows that the length of the coupling line between the two ferrites strongly affects the performance of the four-port circulator.The other four-port circulators are also designed using ferrite-coupled-lines to achieve high operation band [18,19].However, these circulators built on PCB substrates cannot achieve high power capacity in kilowa s.In addition, previous research showed that the ferrite temperature in the circulator would rise under the high-microwave-power condition.The temperature rise in the ferrite would result in the risk of rupture, since the temperature gradient leads to an increase in strain and stress in the material [20].Therefore, reducing the ferrite temperature difference is quite important for a high-power microwave circulator.Conventionally, a four-port waveguide circulator with high power capacity is usually designed with a cascade of a quadrature hybrid coupler, nonreciprocal phase shifters, and a magic tee, which is referred as the DPSC [13].A DPSC is bulky and costly [14].Dixit et al. designed a DPSC operating at the S-band with a power capacity of 500 kW; however, the length of the DPSC is 3 m [15].Deng et al. proposed a compact four-port waveguide circulator operating at the X-band [16].In their design, two three-port junction circulators are stacked, and a composite post resonator is applied in a parallel topology to achieve coupling.Thus, the size of the four-port circulator is considerably reduced; however, the multilayered structure is difficult to assemble.Moreover, as the frequency decreases, the distance between the upper and lower sides of the waveguide wall increases.Owing to this increased distance, realization of the required DC bias magnetic-field strength is difficult because the bias magnets are placed outside the entire cavity.Reddy et al. designed a fourport circulator by cascading two three-port junction circulators with microstrip lines [17].
Their study shows that the length of the coupling line between the two ferrites strongly affects the performance of the four-port circulator.The other four-port circulators are also designed using ferrite-coupled-lines to achieve high operation band [18,19].However, these circulators built on PCB substrates cannot achieve high power capacity in kilowatts.In addition, previous research showed that the ferrite temperature in the circulator would rise under the high-microwave-power condition.The temperature rise in the ferrite would result in the risk of rupture, since the temperature gradient leads to an increase in strain and stress in the material [20].Therefore, reducing the ferrite temperature difference is quite important for a high-power microwave circulator.
In this study, a butterfly-shaped S-band high-power four-port circulator is proposed for the injection-locking magnetron system.To reduce the performance deterioration and the risk of ferrite rupture under long-term high microwave power condition, a three-port waveguide circulator with discrete ferrites is proposed.The temperature distribution in each ferrite is calculated through multiphysics simulation.The results indicate that breaking a monolithic ferrite disk into discrete ferrites can reduce the COV of each ferrite, thus reducing the risk of rupture.To miniaturize the size of the four-port circulator, a butterflyshaped waveguide structure is proposed.By inserting a stub between the two groups of ferrites, the connecting waveguide is removed and the whole size of the four-port circulator is reduced.The proposed four-port circulator is also fabricated and measured.Injection locking of a magnetron using the proposed compact four-port circulator is achieved.In Section 2, the three-port waveguide circulator with discrete ferrites is discussed.The butterfly-shaped four-port circulator is demonstrated in Section 3, where the fabricated four-port circulator is also measured.Section 4 shows the magnetron's injection locking using this four-port circulator.

Three-Port Circulator Using Discrete Ferrites
The material properties of the ferrites play a vital role in the circulator design.Herein, the ferrite material applied in the design is 12 V obtained from Westmag Technology Co., Ltd.(Mianyang, China), with the parameters and the M-H hysteresis curve demonstrated in Table 1 and Figure 2, respectively, where 4πMs, ∆H, ε r , tan δ and ∆H k are the saturation magnetization, the ferromagnetic resonance line width, the relative permittivity, the dielectric losses tangent, and the spin-wave line width, respectively.the risk of ferrite rupture under long-term high microwave power condition, a three-port waveguide circulator with discrete ferrites is proposed.The temperature distribution in each ferrite is calculated through multiphysics simulation.The results indicate that breaking a monolithic ferrite disk into discrete ferrites can reduce the COV of each ferrite, thus reducing the risk of rupture.To miniaturize the size of the four-port circulator, a bu erflyshaped waveguide structure is proposed.By inserting a stub between the two groups of ferrites, the connecting waveguide is removed and the whole size of the four-port circulator is reduced.The proposed four-port circulator is also fabricated and measured.Injection locking of a magnetron using the proposed compact four-port circulator is achieved.In Section 2, the three-port waveguide circulator with discrete ferrites is discussed.The bu erfly-shaped four-port circulator is demonstrated in Section 3, where the fabricated four-port circulator is also measured.Section 4 shows the magnetron's injection locking using this four-port circulator.

Three-Port Circulator Using Discrete Ferrites
The material properties of the ferrites play a vital role in the circulator design.Herein, the ferrite material applied in the design is 12 V obtained from Westmag Technology Co., Ltd.(Mianyang, China), with the parameters and the M-H hysteresis curve demonstrated in Table 1 and Figure 2, respectively, where 4Ms, ΔH,  , tan  and ΔH are the saturation magnetization, the ferromagnetic resonance line width, the relative permi ivity, the dielectric losses tangent, and the spin-wave line width, respectively.For a three-port H-plane waveguide junction circulator which has a single impedance transformer, the initial radius and thickness of the ferrite disks can be calculated by Equation (1) [14].The round ferrite shape is chosen since it is a widely used option.For a three-port H-plane waveguide junction circulator which has a single impedance transformer, the initial radius and thickness of the ferrite disks can be calculated by Equation ( 1) [14].The round ferrite shape is chosen since it is a widely used option.
where k 0 = 2π/λ 0 , λ 0 is the free space wavelength.R and d are the radius and thickness of the ferrite disk, respectively.Notably, there are many possible values of d and R that satisfy (1).Herein, we can first choose R and d to be 18.7 mm and 10 mm, respectively.Where an image plane (an imaginary plane between the two coupled ferrites) or a waveguide wall is in close proximity to a ferrite resonator, a correction factor for d is required, which can be calculated by the following equation [14]: where β = π/2d, kR = 1.84.b is the spacing between resonators, as demonstrated in Figure 3. From Equation ( 2), one can easily find that ∆d is negative since the upper limit of an arctan function is π/2, and ∆d decreases with the decrease in b.Therefore, decreasing b can reduce the thickness of ferrite.
Where an image plane (an imaginary plane between the two coupled ferrites) or a waveguide wall is in close proximity to a ferrite resonator, a correction factor for d is required, which can be calculated by the following equation [14]: where Generally, a small d/S ratio, where S is the surface area of the ferrite, is beneficial for the increase in the power capacity of a circulator [21].Herein, to reduce the thickness of the ferrite (d), a second impedance converter is introduced between the first impedance converter and the ferrite since it can decrease b.After simulation and optimization, the value of d is determined to be 2.8 mm.Then, the monolithic ferrite disk is replaced by three ferrite disks to increase S. The radius of each discrete ferrite disk is reduced to 1/√3 of the radius of the monolithic ferrite disk.In this way, the collective volume of the three ferrite disks is the same as that of the monolithic ferrite.
The structure and S-parameter of the three-port circulator using the monolithic ferrite disk and three discrete ferrite disks are compared in Figure 4. Notably, the resonant frequency of the circulator with the monolithic ferrite disk is 2.43 GHz.At the resonant frequency, |S11| |S21|, and |S31| are 24.59dB, 0.13 dB, and 26.29 dB, respectively.Upon changing the monolithic ferrite to three discrete pieces, the resonant frequency of the circulator shifts to 2.41 GHz.Correspondingly, |S11| |S21|, and |S31| are 24.04dB, 0.13 dB, and 26.2 dB, respectively.Therefore, replacing the monolithic ferrite with three discrete ferrites would result in a li le downshift of the resonant frequency, and the good performance of the circulator would be preserved.Generally, a small d/S ratio, where S is the surface area of the ferrite, is beneficial for the increase in the power capacity of a circulator [21].Herein, to reduce the thickness of the ferrite (d), a second impedance converter is introduced between the first impedance converter and the ferrite since it can decrease b.After simulation and optimization, the value of d is determined to be 2.8 mm.Then, the monolithic ferrite disk is replaced by three ferrite disks to increase S. The radius of each discrete ferrite disk is reduced to 1/ √ 3 of the radius of the monolithic ferrite disk.In this way, the collective volume of the three ferrite disks is the same as that of the monolithic ferrite.
The structure and S-parameter of the three-port circulator using the monolithic ferrite disk and three discrete ferrite disks are compared in  For a high-power waveguide circulator, the temperature difference in the fer when a high-power microwave passes through is quite important, since the temperat gradient leads to an increase in strain and stress in the material, which results in rupt as the strain or stress meet critical value.Herein, the COV of the ferrite with high-inp microwave power is simulated using COMSOL multiphysics.COV stands for the u formity of the temperature distribution, which is calculated by Equation (3) [22,23]: where  is the temperature value of the sampling node,  represents the average te perature of the object being heated, n represents the number of sampling nodes, and For a high-power waveguide circulator, the temperature difference in the ferrite when a high-power microwave passes through is quite important, since the temperature gradient leads to an increase in strain and stress in the material, which results in rupture as the strain or stress meet critical value.Herein, the COV of the ferrite with high-input microwave power is simulated using COMSOL multiphysics.COV stands for the uniformity of the temperature distribution, which is calculated by Equation (3) [22,23]: where T i is the temperature value of the sampling node, T a represents the average temperature of the object being heated, n represents the number of sampling nodes, and T 0 represents the initial temperature of heating.The lower the COV value, the better the temperature uniformity.The measured thermal parameters of ferrite in the simulation are listed in Table 2.In high-power waveguide circulators, water routes usually exist in the metal walls.The flowing water takes away heat generated in the ferrite.Therefore, the side of the ferrite in contact with the metal wall is set to a Dirichlet boundary condition of 25  The COV of each ferrite surface are compared in Table 3, for different input microwave power values of 1 kW, 5 kW and 10 kW.Notably, the COV of each ferrite increases with the input microwave power.Importantly, the maximum COV of the three discrete ferrites is always smaller than that of a monolithic ferrite; for example, at 10 kW, COV d1 (0.5484) is 12.4% lower than COV m (0.6264).Lower COV could significantly reduce the risk of rupture under long-term high-microwave-power condition.In general, replacing the monolithic ferrite with three discrete ferrites would help to improve the power capacity of a circulator.The method may also be applied to break a monolithic triangle ferrite into discrete pieces, if necessary.Besides the risk of ferrite rupture, size miniaturization and cost reduction are two other important factors for the circulators in an injection-locking magnetron system.As mentioned in the introduction, replacing the two circulators with a four-port circulator would help to achieve this goal.A compact four-port waveguide circulator design is presented in the next section.

Design and Measurement of the Compact Four-Port Circulator
A four-port circulator can be easily achieved by connecting two three-port circulators through a waveguide.However, the length of the connecting waveguide (L in Figure 5) has a great impact on the performance of the circulator.As demonstrated in Figure 5, when L is around or larger than 40 mm (approximately λ g /4, where λ g is the waveguide wavelength), the circulator functions well.But the size of the whole structure is quite large.As the length of the connecting waveguide decreases from 40 mm to 10 mm, the isolation (|S 41 |and |S 42 |) and insertion loss decrease by around 15 dB,18 dB and 1 dB at the resonance frequency, respectively.The isolation between Ports 1 and 2 (|S 12 |) shows a resonance characteristic, and the resonant frequency increases dramatically with the decrease in L.
The return loss at Port 2 does not show significant variation, with only a small resonant frequency shift of 40 MHz.But if a stub is inserted at the symmetrical center of the structure with optimized length in the cavity, the performance of the circulator is improved even with a short connecting waveguide length.When L is 10 mm, an improvement of the insertion loss (around 0.5 dB) and isolation between Ports 1 and 2 (the resonant frequency decreases) is observed after the stub is inserted, as the black dashed lines in Figure 5 indicate.The results suggest that a compact circulator might be designed even with no connecting waveguide (L = 0 mm).through a waveguide.However, the length of the connecting waveguide (L in Figure 5) has a great impact on the performance of the circulator.As demonstrated in Figure 5, when L is around or larger than 40 mm (approximately λ /4, where λ is the waveguide wavelength), the circulator functions well.But the size of the whole structure is quite large.As the length of the connecting waveguide decreases from 40 mm to 10 mm, the isolation (|S41|and |S42|) and insertion loss decrease by around 15 dB,18 dB and 1 dB at the resonance frequency, respectively.The isolation between Ports 1 and 2 (|S12|) shows a resonance characteristic, and the resonant frequency increases dramatically with the decrease in L. The return loss at Port 2 does not show significant variation, with only a small resonant frequency shift of 40 MHz.But if a stub is inserted at the symmetrical center of the structure with optimized length in the cavity, the performance of the circulator is improved even with a short connecting waveguide length.When L is 10 mm, an improvement of the insertion loss (around 0.5 dB) and isolation between Ports 1 and 2 (the resonant frequency decreases) is observed after the stub is inserted, as the black dashed lines in Figure 5 indicate.The results suggest that a compact circulator might be designed even with no connecting waveguide (L = 0 mm).The compact four-port circulator with no connecting waveguide is designed, with a butterfly-shaped structure presented in Figure 6a.It comprises two pairs of discrete ferrites in two half-circular radial-and one rectangular-linked air cavities while being connected to four rectangular WR340 waveguides.The ferrite disks are placed on the inside walls of the cavity, with a bias magnetic field applied along the z-axis direction.The angle between the normal directions of Port 1 and 2 is (2/3)π.The structure is symmetrical with respect to the ZOX plane as the origin of coordinates is located in the middle of the two pairs of ferrite disks.A metal stub is inserted in the cavity at the origin of the coordinates, with optimized length (12 mm) and radius (2 mm) in the cavity.Step structures with Chebyshev characteristics are applied between the central cavity and the WR340 waveguide ports for impedance matching.
between the normal directions of Port 1 and 2 is (2/3).The structure is symmetrical with respect to the ZOX plane as the origin of coordinates is located in the middle of the two pairs of ferrite disks.A metal stub is inserted in the cavity at the origin of the coordinates, with optimized length (12 mm) and radius (2 mm) in the cavity.
Step structures with Chebyshev characteristics are applied between the central cavity and the WR340 waveguide ports for impedance matching.The microwave field distribution with the excitation of Port 1 or 2 is also demonstrated in Figure 6.When the microwave is fed from Port 1, as shown in Figure 6b, most of the energy is coupled to Port 2 because of the birefringence of the left two ferrites, which is very similar to a conventional three-port waveguide circulator.The insertion of the stub hardly affects the performance of the device because there is almost no electromagnetic field at that location.When the microwave is fed from Port 2, the energy is mainly coupled to Port 3 after a stub is inserted into the cavity, as demonstrated in Figure 6c.The inserted stub adjusts the phase of the microwave between the two pairs of ferrites, which replaces the function of the connecting waveguide and reduces the size of the circulator.Due to the symmetry of the bu erfly-shaped structure, nonreciprocal transmission of microwaves in the four ports (Port 1 → Port 2 → Port 3 → Port 4 → Port 1) can be achieved.Importantly, the proposed four-port circulator offers a remarkable reduction in size, which is 27% smaller than the conventional combination of two three-port circulators, and way smaller than a DPSC.
The simulated and measured S-parameters of the circulator are compared in Figure 7.The measured S-parameter matches with the simulation results.As indicated in Figure 7a, the measured resonance frequency is at 2.39 GHz, with a slight shift of 0.01 GHz compared with the simulated results.The measured −10 dB bandwidth reaches over 16%.
Notably, Figure 7b shows that |S21| overlaps with |S43|, as |S32| and |S14|, owing to the symmetry of the structure.The insertion loss from Port 1 to Port 2 is a li le bit lower The microwave field distribution with the excitation of Port 1 or 2 is also demonstrated in Figure 6.When the microwave is fed from Port 1, as shown in Figure 6b, most of the energy is coupled to Port 2 because of the birefringence of the left two ferrites, which is very similar to a conventional three-port waveguide circulator.The insertion of the stub hardly affects the performance of the device because there is almost no electromagnetic field at that location.When the microwave is fed from Port 2, the energy is mainly coupled to Port 3 after a stub is inserted into the cavity, as demonstrated in Figure 6c.The inserted stub adjusts the phase of the microwave between the two pairs of ferrites, which replaces the function of the connecting waveguide and reduces the size of the circulator.Due to the symmetry of the butterfly-shaped structure, nonreciprocal transmission of microwaves in the four ports (Port 1 → Port 2 → Port 3 → Port 4 → Port 1) can be achieved.Importantly, the proposed four-port circulator offers a remarkable reduction in size, which is 27% smaller than the conventional combination of two three-port circulators, and way smaller than a DPSC.
The simulated and measured S-parameters of the circulator are compared in Figure 7.The measured S-parameter matches with the simulation results.As indicated in Figure 7a, the measured resonance frequency is at 2.39 GHz, with a slight shift of 0.01 GHz compared with the simulated results.The measured −10 dB bandwidth reaches over 16%.
Notably, Figure 7b 7d.All lines have similar frequency verification owing to the rotational symmetry of the device structure.The measured isolation results all match the simulation prediction.At 2.45 GHz, the isolations are all higher than 16 dB.The measured S-parameters of the device indicate that it is suitable for the injection-locking magnetron application.The small deviation between the simulations and experimental results may result from the uneven bias magnetic field provided by the magnets outside the cavity and the manual placement of the ferrites during fabrication.

case.
Figure 7c exhibits the isolation between the adjacent ports in the counterclockwise direction.Interestingly, |S12| and |S34| indicate a resonance characteristic, which is very similar to the isolation performance of a three-port waveguide circulator, whereas |S41| and |S23| demonstrate relatively wide band isolation.The reason for this phenomenon is the same as that of the insertion loss.The two pairs of ferrites contribute to isolation for |S41| and |S23|.Simultaneously, the isolation of the ports at meta positions is demonstrated in Figure 7d.All lines have similar frequency verification owing to the rotational symmetry of the device structure.The measured isolation results all match the simulation prediction.At 2.45 GHz, the isolations are all higher than 16 dB.The measured S-parameters of the device indicate that it is suitable for the injection-locking magnetron application.The small deviation between the simulations and experimental results may result from the uneven bias magnetic field provided by the magnets outside the cavity and the manual placement of the ferrites during fabrication.The photographs of the whole assembled proposed four-port circulator (with bias magnets) and a DPSC, both working at 2.45 GHz, are compared in Figure 8.The dimensions of the proposed circulator are 36 × 26 × 13 cm, while the dimensions of the DPSC are 90 × 36 × 17 cm.When compared with the assembly of two conventional three-port circulators, the size of the proposed circulator is 27% smaller than that.The cost of the injectionlocking system can also be reduced since the cost of a four-port circulator is lower than The photographs of the whole assembled proposed four-port circulator (with bias magnets) and a DPSC, both working at 2.45 GHz, are compared in Figure 8.The dimensions of the proposed circulator are 36 × 26 × 13 cm, while the dimensions of the DPSC are 90 × 36 × 17 cm.When compared with the assembly of two conventional three-port circulators, the size of the proposed circulator is 27% smaller than that.The cost of the injection-locking system can also be reduced since the cost of a four-port circulator is lower than that of two convention circulators, and is way lower than that of a DPSC.The comparison of the proposed four-port circulator with some published works is demonstrated in Table 4.
The power capacity of the device is measured with the experimental setup illustrated in Figure 9.A continuous wave magnetron (2M259G from Panasonic, Osaka, Japan) is connected to a dual directive coupler, which then connects to Port 1 of the circulator.The remaining three ports are connected to water loads to absorb both the output and the reflected power.Another dual directive coupler is inserted between Port 2 and the water load to couple the small power for measuring the power flows through the circulator.The incident and reflected power, as well as the power transmitted through the circulator, are measured with microwave power meters (2438CB from Ceyear Technologies Co., Ltd., Qingdao, China) and demonstrated in Table 5, as the output power from the magnetron source increases from 1 kW to 3 kW.Notably, the return loss and insertion loss are approximately 16 dB and 0.5 dB, respectively, and have almost no variation under different microwave powers.The experimental results indicate that this four-port circulator has a power capacity of at least 3 kW, which is the highest output microwave power for most S-band magnetrons with permanent magnets [25,26].The power capacity is obviously higher than 3 kW, but we do not have the very high microwave power source to detect the upper limit.
Electronics 2024, 13, x FOR PEER REVIEW 9 of 13 that of two convention circulators, and is way lower than that of a DPSC.The comparison of the proposed four-port circulator with some published works is demonstrated in Table 4.The power capacity of the device is measured with the experimental setup illustrated in Figure 9.A continuous wave magnetron (2M259G from Panasonic, Osaka, Japan) is connected to a dual directive coupler, which then connects to Port 1 of the circulator.The remaining three ports are connected to water loads to absorb both the output and the reflected power.Another dual directive coupler is inserted between Port 2 and the water load to couple the small power for measuring the power flows through the circulator.The incident and reflected power, as well as the power transmi ed through the circulator, are measured with microwave power meters (2438CB from Ceyear Technologies Co., Ltd., Qingdao, China) and demonstrated in Table 5, as the output power from the magnetron source increases from 1 kW to 3 kW.Notably, the return loss and insertion loss are approximately 16 dB and 0.5 dB, respectively, and have almost no variation under different microwave powers.The experimental results indicate that this four-port circulator has a power capacity of at least 3 kW, which is the highest output microwave power for most S-  band magnetrons with permanent magnets [25,26].The power capacity is obviously higher than 3 kW, but we do not have the very high microwave power source to detect the upper limit.power of the magnetron is absorbed by the water load, with a dual directive coupler inserted between the circulator and the load for measurement.The reflected microwave power is absorbed by the water load connected to Port 3. The injection signal is provided by a solid-state source connected to Port 4, with a coaxial dual directive coupler inserted for power measurement.The spectrum is monitored by the spectrum analyzer (RSA5126B from Tektronix Inc., Shanghai, China).The spectra of the solid-state source and the free-running magnetron (without injection signal) are compared in Figure 11a, as their output powers are set to be 50 W and 1.4 kW, respectively.The central frequency of the free-running magnetron is 2.459 GHz, and the bandwidth (the frequency range is greater than the base noise) is 2.63 MHz.When the signal from the solid-state source is injected into the magnetron, the bandwidth of the magnetron is narrowed down and the output frequency of the magnetron is locked to that of the injection signal, as Figure 11b shows.The output frequency of the magnetron can also be adjusted by changing the frequency of the injection signal.Herein, the measured injection-locking bandwidth is 5 MHz (from 2.458 to 2.462 GHz), which corresponds to the predicted value obtained using Equation ( 5), with a  of 50.

Conclusions
In this work, a compact bu erfly-shaped high-power four-port circulator using discrete ferrites is proposed for the injection-locking magnetron system.First, in a three-port The spectra of the solid-state source and the free-running magnetron (without injection signal) are compared in Figure 11a, as their output powers are set to be 50 W and 1.4 kW, respectively.The central frequency of the free-running magnetron is 2.459 GHz, and the bandwidth (the frequency range is greater than the base noise) is 2.63 MHz.When the signal from the solid-state source is injected into the magnetron, the bandwidth of the magnetron is narrowed down and the output frequency of the magnetron is locked to that of the injection signal, as Figure 11b shows.The output frequency of the magnetron can also be adjusted by changing the frequency of the injection signal.Herein, the measured injection-locking bandwidth is 5 MHz (from 2.458 to 2.462 GHz), which corresponds to the predicted value obtained using Equation ( 5), with a Q ext of 50.
power of the magnetron is absorbed by the water load, with a dual directive coupler inserted between the circulator and the load for measurement.The reflected microwave power is absorbed by the water load connected to Port 3. The injection signal is provided by a solid-state source connected to Port 4, with a coaxial dual directive coupler inserted for power measurement.The spectrum is monitored by the spectrum analyzer (RSA5126B from Tektronix Inc., Shanghai, China).The spectra of the solid-state source and the free-running magnetron (without injection signal) are compared in Figure 11a, as their output powers are set to be 50 W and 1.4 kW, respectively.The central frequency of the free-running magnetron is 2.459 GHz, and the bandwidth (the frequency range is greater than the base noise) is 2.63 MHz.When the signal from the solid-state source is injected into the magnetron, the bandwidth of the magnetron is narrowed down and the output frequency of the magnetron is locked to that of the injection signal, as Figure 11b shows.The output frequency of the magnetron can also be adjusted by changing the frequency of the injection signal.Herein, the measured injection-locking bandwidth is 5 MHz (from 2.458 to 2.462 GHz), which corresponds to the predicted value obtained using Equation ( 5), with a  of 50.

Conclusions
In this work, a compact bu erfly-shaped high-power four-port circulator using discrete ferrites is proposed for the injection-locking magnetron system.First, in a three-port

Conclusions
In this work, a compact butterfly-shaped high-power four-port circulator using discrete ferrites is proposed for the injection-locking magnetron system.First, in a three-port waveguide circulator, the maximum COV in discrete ferrites is 12.4% lower than that of a monolithic ferrite circulator, with the input microwave power of 10 kW.With the increase in the input power, COV difference between the discrete ferrites and a monolithic ferrite is enlarged.The lower COV can significantly reduce the risk of rupture under the long-term high-microwave-power condition.The compact butterfly-shaped four-port circulator is designed using discrete ferrites.The connecting waveguide is removed by inserting a stub into the cavity at the central point.The size of the proposed circulator is 27% smaller than the assembly of two three-port circulators, and way smaller than a conventional DPSC.The cost of an injection-locking magnetron system can also be reduced by using the proposed circulator.The measured results match well with the simulation prediction, with return loss, insertion loss, and isolation of 20 dB, 0.3 dB (port 1 to port 2), and 16 dB at 2.45 GHz.The measured power capacity is higher than 3 kW (limited by the experimental condition).Injection-locking of a magnetron is achieved using the proposed four-port circulator.

Figure 2 .
Figure 2. M-H hysteresis curve of the ferrite material.

Figure 2 .
Figure 2. M-H hysteresis curve of the ferrite material.

Figure 3 .
Figure 3. Waveguide junction circulator geometries (a) with a single impedance transformer, (b) with two impedance converters.

Figure 3 .
Figure 3. Waveguide junction circulator geometries (a) with a single impedance transformer, (b) with two impedance converters.

Figure 4 .
Notably, the resonant frequency of the circulator with the monolithic ferrite disk is 2.43 GHz.At the resonant frequency, |S 11 | |S 21 |, and |S 31 | are −24.59dB, −0.13 dB, and −26.29 dB, respectively.Upon changing the monolithic ferrite to three discrete pieces, the resonant frequency of the circulator shifts to 2.41 GHz.Correspondingly, |S 11 | |S 21 |, and |S 31 | are −24.04dB, −0.13 dB, and −26.2 dB, respectively.Therefore, replacing the monolithic ferrite with three discrete ferrites would result in a little downshift of the resonant frequency, and the good performance of the circulator would be preserved.Electronics 2024, 13, x FOR PEER REVIEW 5 o

Figure 4 .
Figure 4.The structure and S-parameter of the three-port circulator: (a) single ferrite disk, (b) th ferrite disks.

Figure 4 .
Figure 4.The structure and S-parameter of the three-port circulator: (a) single ferrite disk, (b) three ferrite disks.

Figure 5 .
Figure 5. (a) A four-port circulator consisting of two three-port circulators and a section of ridge waveguides, (b) a short stub is inserted at the symmetrical point when L = 10 mm; (c-g) simulation results.

Figure 6 .
Figure 6.(a) The structure of the proposed bu erfly-shaped four-port circulator.Electromagnetic field distribution in the cavity, excitation at (b) Port 1, (c) Port 2 (color represents microwave electric field, arrows represent microwave magnetic field).

Figure 6 .
Figure 6.(a) The structure of the proposed butterfly-shaped four-port circulator.Electromagnetic field distribution in the cavity, excitation at (b) Port 1, (c) Port 2 (color represents microwave electric field, arrows represent microwave magnetic field).
shows that |S 21 | overlaps with |S 43 |, as |S 32 | and |S 14 |, owing to the symmetry of the structure.The insertion loss from Port 1 to Port 2 is a little bit lower than that from Port 2 to Port 3, because microwave propagates through two pairs of ferrites from Port 2 to Port 3, whereas it propagates through only one pair from Port 1 to Port 2. At 2.45 GHz, the simulated |S 21 | is −0.3 dB, measured |S 21 |, |S 32 | and |S 14 | are −0.4 dB, −1.3 dB and −1.4 dB, respectively.Although the measured |S 32 | (or |S 14 |) is slightly lower than the simulation result, it does not affect the injection-locking magnetron system because Port 3 is used to absorb the reflected power from Port 2 with a water load and the low power injection signal flows from Port 4 to Port 1. Simultaneously, there is water flows in the cavity wall to absorb heat and to cool down the ferrite in the extreme high-power case.
Figure 7c exhibits the isolation between the adjacent ports in the counterclockwise direction.Interestingly, |S 12 | and |S 34 | indicate a resonance characteristic, which is very similar to the isolation performance of a three-port waveguide circulator, whereas |S 41 | and |S 23 | demonstrate relatively wide band isolation.The reason for this phenomenon is the same as that of the insertion loss.The two pairs of ferrites contribute to isolation for |S 41 | and |S 23 |.Simultaneously, the isolation of the ports at meta positions is demonstrated in

Figure
Figure 7d.All lines have similar frequency verification owing to the rotational symmetry of the device structure.The measured isolation results all match the simulation prediction.At 2.45 GHz, the isolations are all higher than 16 dB.The measured S-parameters of the device indicate that it is suitable for the injection-locking magnetron application.The small deviation between the simulations and experimental results may result from the uneven bias magnetic field provided by the magnets outside the cavity and the manual placement of the ferrites during fabrication.

Figure 11 .
Figure 11.(a) The spectrum of the free running magnetron and the solid-state source, (b) the spectrum of the magnetron's output with the injection signal at different frequencies.

Figure 11 .
Figure 11.(a) The spectrum of the free running magnetron and the solid-state source, (b) the spectrum of the magnetron's output with the injection signal at different frequencies.

Figure 11 .
Figure 11.(a) The spectrum of the free running magnetron and the solid-state source, (b) the spectrum of the magnetron's output with the injection signal at different frequencies.

Table 1 .
Parameters of the ferrite material.

Table 1 .
Parameters of the ferrite material.
[24] The initial temperature is set to be 20 • C, and the convective heat transfer coefficient at the boundary between ferrite and air is set to be 10 W/ m 2 •K[24].

Table 2 .
Thermal parameters of material in the simulation.

Table 3 .
The COV difference with different input microwave power values.

Table 4 .
Comparison of the proposed four-port circulator with published works.

Table 4 .
Comparison of the proposed four-port circulator with published works.

Table 5 .
Power capacity measurement of the four-port circulator.