Design method of waveguide filtering phase shifter

Abstract

The invention provides a design method of a waveguide filtering phase shifter. The design method specifically comprises the following steps: (1) designing a rectangular waveguide filter; (2) calculating the voltage standing wave ratio of each stage of the filter, providing normalized reactance for calculating the length of each part in the step (1) due to the fact that adjacent resonant cavities in the designed band-pass filter have similar physical sizes, and (3) designing a phase shifter of the rectangular waveguide filter; (4) a corrugated structure is designed, and the height and the width of the corrugated structure are set; step (5), simulation optimization is carried out to reach required design indexes; and (6) calculating the phase difference, and verifying the phase shifting size and precision of the rectangular waveguide filtering phase shifter. According to the invention, the actual simulation phases of the designed rectangular waveguide filter and the rectangular waveguide filter phase shifter are compared to obtain the corresponding phase difference and accuracy.

Description

Technical Field

[0001] The invention relates to the field of microwave communication devices, and in particular to a design method for a waveguide filter phase shifter. Background Art

[0002] With the rapid development of next generation wireless communication technology, more spectrum resources are being utilized, and phased array technology is gradually being introduced into civilian base station antennas. Filters and phase shifters, as key components of communication systems, are becoming more important, and their electrical performance directly affects the quality of the entire communication system.

[0003] The filter can effectively suppress interference signals and improve the signal-to-noise ratio, while the phase shifter adjusts the phase of the signal by changing the transmission phase velocity of the electromagnetic wave. With the development and utilization of millimeter wave and terahertz frequency bands, the traditional planar transmission lines and devices have too much loss, while air waveguide transmission lines and various waveguide types of devices have received more attention from the industry due to their low loss. Waveguide filters are mainly designed based on the principle of cavity filters, and cavity filters use multiple resonant cavities and coupling cavities in cascade to form a resonant circuit (LC) equivalent circuit. Rectangular waveguide bandpass filters usually use a symmetrically coupled half-wavelength resonant cavity structure, and the length of the resonant cavity will affect the frequency response within the waveguide passband.

[0004] There are also many implementation schemes for phase shifters. According to the different transmission line structures, they can be divided into rectangular waveguide phase shifters, coplanar waveguide phase shifters, and stripline phase shifters. According to the difference in working principles, phase shifters can be divided into ferroelectric phase shifters, liquid crystal phase shifters, PIN diode phase shifters, field effect transistor phase shifters, etc., each of which has a unique structure, material and physical mechanism. For example, the substrate integrated waveguide (SIW) phase shifter combines the characteristics of rectangular waveguides and microstrip lines, and can produce phase shifts through slow wave effects or microstrip structures; the corrugated waveguide phase shifter adopts a symmetrical corrugated structure, which reflects discontinuous inductance or capacitance characteristics during the propagation of electromagnetic fields, thereby achieving an increase or decrease in phase. The patent with application number CN200820124241.7 discloses a circular polarizer with a preset phase shift curve, which proposes to add metal diaphragms at equal intervals in circular waveguides or square waveguides to achieve the purpose of phase shifting and circular polarization. This design can effectively control the phase shift of orthogonal modes during transmission. The literature [Ning Yunwei, Chen Maozheng, Wang Hui. Design of ultra-wideband corrugated waveguide orthogonal mode phase shifter [J]. Radio Engineering, 2016, 46(9):5. DO I:10.3969 / ji ssn.1003-3106.2016.09.16.] further introduced the principle and optimization process of phase shifting of this structure in detail. However, they did not test the applicability of the corrugated waveguide phase shifter in a rectangular waveguide.

[0005] In communication systems, filters and phase shifters often need to be used in combination, usually in a cascaded manner, that is, the electromagnetic wave signal is filtered by the filter, and then the phase shifter produces the corresponding phase shift. At present, multifunctional fusion microwave devices are gradually becoming a research hotspot in the microwave engineering community. Considering that the millimeter wave and terahertz frequency bands have been included in 6G wireless communications, in order to minimize transmission losses and reduce system size, it is necessary to design waveguide filter phase shifters in the millimeter wave and terahertz frequency bands.

[0006] At present, microwave devices that integrate filtering and phase shifting functions are mainly implemented using microstrip or stripline structures. Although this effectively solves the size and low-frequency loss problems, it will produce significant dielectric loss and radiation in the millimeter wave and terahertz frequency bands and cannot be effectively utilized.

[0007] The transmission lines and devices commonly used in the millimeter wave and terahertz frequency bands often adopt waveguide form, while the waveguide filters and waveguide phase shifters currently available are all discrete devices, which need to be cascaded when building communication systems, which not only increases the overall size and weight of the system, but also introduces more transmission losses due to the connection between devices. Summary of the invention

[0008] To solve the above problems, the present invention discloses a design method for a waveguide filter phase shifter, which combines a symmetrically coupled half-wavelength resonant cavity structure and a corrugated waveguide phase shift structure, thereby effectively integrating the phase shifting function without increasing the size of the original waveguide filter.

[0009] A design method for a waveguide filter phase shifter specifically comprises the following steps:

[0010] Step (1) rectangular waveguide filter design, as a reference path for the actual rectangular waveguide filter phase shifter, technically adopts a symmetrically coupled half-wavelength resonant cavity structure; according to the design index, the order of the filter is determined by the Chebyshev filter design model, and the normalized step impedance and voltage standing wave ratio of each stage are calculated according to the low-pass to band-pass conversion formula, thereby obtaining the normalized reactance; the length θ, θ of each part is determined by using formula (1). i The i in the column represents the i-th stage;

[0011]

[0012] Step (2) calculates the voltage standing wave ratio of each stage of the filter, providing the normalized reactance for calculating the length of each section in step 1. Since adjacent resonant cavities in the designed bandpass filter have similar physical dimensions, their impedance ratio is approximately 1; the normalized reactance μ, μ i The i in the equation represents the i-th stage; it is calculated by formula (2), where ρ represents the voltage standing wave ratio, ρ iThe i in it indicates the i-th stage, which indicates the voltage standing wave ratio;

[0013]

[0014] Step (3) Design of a rectangular waveguide filter phase shifter, adding ripples to achieve a phase difference with a reference path. A ripple phase shift structure of equal height and width is symmetrically placed in the middle part of the resonant cavity of the rectangular waveguide filter in step (1); added to the long side or short side of the rectangular waveguide filter according to the actual required phase shift direction;

[0015] Step (4) corrugation structure design, designing the corrugation to achieve the purpose of changing the phase shift size and accuracy. According to the sensitivity and size of the actual required phase shift, the height and width of the corrugation structure are set;

[0016] Step (5) simulation optimization to achieve the required design indicators; establish a corresponding structural model in the three-dimensional electromagnetic field simulation software HFSS, simulate the corresponding results, and optimize the design and adjust the parameters under the premise of meeting the corresponding parameters:

[0017] Step (6) Calculate the phase difference to verify the phase shift size and accuracy of the rectangular waveguide filter phase shifter. Compare the actual simulated phases of the designed rectangular waveguide filter and the rectangular waveguide filter phase shifter to obtain the corresponding phase difference value and accuracy.

[0018] Furthermore, under the premise of fully satisfying the performance index, the optimization design result of step (5) is as follows:

[0019] In the Ka-band and the frequency range of 26.5 to 40 GHz, standard rectangular waveguides and WR-28 are used.

[0020] The parameters are

[0021] W1=4.97mm, W2=4.06mm, W3=3.81mm, W4=3.75mm, L1=3.61mm, L2=4.31mm, L3=4.55mm, L4=4.58mm, L w =7.12mm,L c =1.49mm, h=0.33mm, s=0.25mm, B=3.556mm, A=7.12mm

[0022] In the frequency range of 90 to 120, standard rectangular waveguide and WR-4 are used. The specific parameters are W1 = 1.425mm, W2 = 1.16mm, W3 = 1.085mm, W4 = 1.07mm, L1 = 1.17mm, L2 = 1.443mm, L3 = 1.507mm, L4 = 1.517mm, L w =2.032mm,Lc =0.625mm, h=0.046mm, s=0.098mm, B=1.016mm, A=2.032mm.

[0023] Furthermore, in step (3), adding ripples to the short side of the rectangular waveguide can achieve phase shift in the positive direction, and adding ripples to the long side of the rectangular waveguide can achieve phase shift in the negative direction.

[0024] Furthermore, in step (4), increasing the length of the ripple can achieve a larger phase shift, while reducing the width of the ripple can make the phase shift more stable. The specific parameters are determined according to actual needs.

[0025] Further, W1 is the width of the first coupling cavity, W2 is the width of the second coupling cavity, W3 is the width of the third coupling cavity, W4 is the width of the fourth coupling cavity, L1 is the length of the first resonant cavity, L2 is the length of the second resonant cavity, L3 is the length of the third resonant cavity, L4 is the length of the fourth resonant cavity, Lw is the length of the transmission transition section, Lc is the length of the coupling cavity, h is the corrugation height, s is the corrugation width, B is the length of the short side of the rectangular waveguide, and A is the length of the long side of the rectangular waveguide.

[0026] Beneficial effects of the present invention:

[0027] 1. Reduce the volume of the system. In the present invention, only ripples need to be added to the original cavity structure of the waveguide filter to achieve the combination of filtering and phase shifting, and the original external structure of the waveguide filter is almost unchanged.

[0028] 2. Reduce system weight and electromagnetic wave transmission loss. Compared with the current industry's need to cascade waveguide filters and waveguide phase shifters, the present invention only needs to add a corrugated structure inside the existing waveguide filter, which reduces the total weight of the system and the transmission loss caused by the cascade of devices.

[0029] 3. Reduce costs. The present invention improves the mature waveguide filter structure without adding additional materials, which can effectively reduce system costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a top view of the bandpass filter cavity structure;

[0031] Figure 2 This is a model diagram of the bandpass filter cavity structure;

[0032] Figure 3 It is a top view of the bandpass filter cavity structure;

[0033] Figure 4 It is a side view of the bandpass filter cavity structure;

[0034] Figure 5Model diagram of rectangular waveguide cavity with filtering and phase shifting combined by adding ripples to the long sides;

[0035] Figure 6 Model diagram of rectangular waveguide cavity with filtering and phase shifting combined by adding ripples to the short side;

[0036] Table 1 shows the specific values ​​of the relevant parameters in the simulation experiment of adding corrugations to the short side of the present invention;

[0037] Figure 7 A top view and a side view of the invention with corrugations added to the short side;

[0038] Figure 8 is the transmission characteristic curve of the reference waveguide filter;

[0039] Fig. 9 Comparison of the return loss of the waveguide filter with the reference waveguide filter after adding a corrugated structure in the middle of the short side of the resonant cavity;

[0040] Fig.10 The insertion loss of the waveguide filter after adding a corrugated structure in the middle of the short side of the resonant cavity is compared with that of the reference waveguide filter;

[0041] Fig.11 is the phase difference between the rectangular waveguide filter phase shifter and the waveguide filter shifter;

[0042] Table 2 shows the specific values ​​of the relevant parameters in the simulation experiment of adding corrugations to the long side of the present invention;

[0043] Fig.12 A top view and a side view of the invention with corrugations added to the long side;

[0044] Fig.13 is the transmission characteristic curve of the reference waveguide filter;

[0045] Fig.14 Comparison of S(1,1) between the rectangular waveguide with corrugations on the long sides and the reference path;

[0046] Fig.15 Comparison of S(2,1) between the rectangular waveguide with corrugations on the long sides and the reference path;

[0047] Fig.16 Phase difference between a rectangular waveguide with corrugations on its long sides and the reference path. DETAILED DESCRIPTION

[0048] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to directions in the accompanying drawings, and the words "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0049] A design method of a waveguide filter phase shifter in this embodiment has the following design ideas: 1. Symmetrically coupled half-wavelength resonant cavity structure:

[0050] In order to measure the phase change produced by the phase shifter, a reference transmission waveguide is designed, whose structure adopts a symmetrically coupled half-wavelength resonant cavity. The specific design adopts the method of alternating cascade of resonant cavity and coupling cavity (such as Figure 1 The wavelength of the electromagnetic wave in the waveguide is λ g It can be calculated by formula (1), where λ is the wavelength of the electromagnetic wave in free space, λ c is the cut-off wavelength, which depends on the transmission method and the size of the waveguide.

[0051]

[0052] The adjacent resonant cavities in the designed bandpass filter have similar physical dimensions, so their impedance ratio can be approximated to 1. Normalized reactance μ, μ i The i in the equation represents the i-th stage, which can be calculated by formula (2), where ρ represents the voltage standing wave ratio (ρ i The i in the figure represents the i-th stage).

[0053]

[0054] The order of the filter can be determined by the Chebyshev filter design model. According to the low-pass to bandpass conversion formula, the normalized step impedance and voltage standing wave ratio of each stage can be calculated to obtain the normalized reactance. The length of each part θ, θ can be determined using formula (3). i The i in represents the i-th stage.

[0055]

[0056] The bandpass filter designed directly by the above method generally exhibits poor electrical performance during the implementation process and cannot meet the design index requirements. Therefore, in the actual design process, it is necessary to continuously adjust and optimize the parameters to achieve the ideal effect. Figure 2 The bandpass filter cavity model designed by the present invention as a reference transmission waveguide is demonstrated. Figure 3 For this top view of the model, Figure 4 This is a side view of the model.

[0057] 2. Corrugated waveguide orthogonal mode phase shifter:

[0058] Corrugated waveguide phase shifter is widely used in circular waveguide and square waveguide. It achieves stable phase shifting function by adding corrugated structure evenly on the symmetric surface of the waveguide.

[0059] In square waveguides and circular waveguides, the main transmission mode is TE 10 and TE 01 Therefore, the corrugated waveguide phase shifter is often used to transmit orthogonal modes, so it is also called corrugated waveguide orthogonal mode phase shifter.

[0060] Because of its unique corrugated transmission structure, the corrugated waveguide orthogonal mode phase shifter can be analyzed through a network cascade model to analyze the periodic transmission structure in the waveguide, that is, the transmission matrix can be used to describe each discontinuous loading part, and finally they are cascaded to form an overall transmission matrix. In this way, its scattering (S) parameters and phase shift can be calculated. TE 10 and TE 01 The transmission matrices of the modes are expressed by formula (4) and formula (5) respectively.

[0061]

[0062] TE 10 and TE 01 The transmission matrix of the mode at the nth pair of discontinuous ripples can be expressed as formulas (6) and (7), where: and is the normalized induction and accommodation of the nth pair of ripples, θ=2πS / λ g , θ is the electrical length of the waveguide section between the corrugations.

[0063]

[0064] Through the above calculation, TE 10 and TE 01 The S parameters of the mode can be expressed as formulas (8) to (11), TE 10 and TE 01 The phase difference between the modes is expressed as equation (12).

[0065]

[0066] 3. Rectangular waveguide with integrated filtering and phase shifting functions:

[0067] The present invention applies the corrugated structure from square waveguide to rectangular waveguide, and realizes the integration of filtering and phase shifting functions by adding corrugated structures of equal height and width in the middle part of the symmetrically coupled half-wavelength resonant cavity structure of the rectangular waveguide. When we add corrugated structures in order on the long side of the rectangular waveguide, the corrugated structure has a great influence on the main propagation mode TE. 10 The mode shows discontinuous capacitive properties, which leads to a decrease in the phase velocity of the main mode, thereby reducing the propagation phase of the electromagnetic wave relative to the reference waveguide. Figure 5 A model diagram showing the rectangular waveguide filter phase shifter after adding ripples to the short sides.

[0068] On the contrary, when we add a corrugated structure to the short side of the rectangular waveguide, the corrugated structure has an important influence on the propagation of the main mode TE. 10 The mode exhibits discontinuous inductive characteristics, which leads to an increase in the phase velocity of the main mode, so that the phase of the magnetic wave during propagation increases relative to the reference waveguide. Figure 6 A model diagram showing the rectangular waveguide filter phase shifter after adding ripples to the short sides.

[0069] Different lengths and widths of the corrugated structure will result in different angles of phase shift during filtering and phase shifting. Increasing the length of the corrugation can achieve a larger phase shift, while reducing the width of the corrugation can make the phase shift more stable. However, since there is an electromagnetic coupling relationship between the filtering frequency response and the phase shift of the symmetrically coupled half-wavelength resonant cavity structure, the introduction of the phase shift will also affect the original filtering frequency response, causing the operating frequency of the bandpass filter to shift. The experimental results show that there are significant differences in the phase shift size outside the passband range of the filter. Therefore, within the passband range of the filter, the waveguide filter phase shifter can produce a relatively stable phase shift effect.

[0070] Figure 7 The figure shows a waveguide filter phase shifter formed by adding corrugations to the short sides of a rectangular waveguide filter. Table 1 further gives the detailed structural parameters of this embodiment.

[0071]

[0072]

[0073] Without adding ripples, the waveguide filter designed as a reference waveguide has bandpass filtering characteristics in the Ka-band. Figure 8 The return loss and transmission coefficient of the waveguide filter are given. As can be seen from the figure, the waveguide filter can achieve excellent bandpass filtering performance at 29.625-34.26 GHz. Then, the short sides of the middle part of the rectangular waveguide filter resonant cavity are symmetrically engraved with equal height and width corrugated structures (such as Figure 8 As shown), this corrugated structure is suitable for the main mode of rectangular waveguide transmission - TE 10The mode exhibits inductive characteristics, which leads to an increase in the phase velocity of the electromagnetic field during propagation, so that the rectangular waveguide with integrated filtering and phase shifting exhibits a 45° phase shift characteristic compared with the reference waveguide filter. Fig. 9 and Fig.10 The return loss and insertion loss curves of the waveguide filter after adding a corrugated structure in the middle of the short side of the resonant cavity are compared with those of the reference waveguide filter. It can be seen from the figure that the passband range of the filter is slightly shifted, but the passband range has not changed significantly. Fig.11 The phase difference between the rectangular waveguide filter phase shifter and the waveguide filter phase shifter is further given. It can be seen from the figure that the phase shift characteristic of 45°±5° can be stably achieved within a large range of the waveguide filter passband. The frequency range of this stable phase shift accounts for 69.4% of the passband, indicating that the design can effectively realize the functions of filtering and phase shifting.

[0074] Fig.12 The figure shows a waveguide filter phase shifter formed by adding corrugations to the long sides of a rectangular waveguide filter. Table 2 further gives the detailed structural parameters of this embodiment.

[0075] Parameter meaning parameter Initial value [MM] Width of the first coupling cavity W1 1.425 Width of the second coupling cavity W2 1.16 Width of the third coupling cavity W3 1.085 Width of the fourth coupling cavity W4 1.07 The length of the first resonant cavity l1 1.17 The length of the second resonant cavity l2 1.443 The length of the third resonant cavity l3 1.507 The length of the fourth resonant cavity l4 1.517 Transmission transition length lw 2.032 Length of coupling cavity lc 0.625 Corrugation height h 0.046 Corrugation Width s 0.098 Rectangular waveguide short side length b 1.016 Rectangular waveguide long side length a 2.032

[0076] Without adding ripples, the waveguide filter designed as a reference waveguide has bandpass filtering characteristics in the terahertz band. Fig.13 The return loss and transmission coefficient of the waveguide filter are given. As can be seen from the figure, the waveguide filter can achieve excellent bandpass filtering performance at 101.18-109.31 GHz. Then, the same height and width corrugated structures (such as Figure 8 As shown), this corrugated structure is suitable for the main mode of rectangular waveguide transmission - TE 10 The mode exhibits capacitive characteristics, which leads to a decrease in the phase velocity of the electromagnetic field during propagation, so that the rectangular waveguide with filtering and phase shifting combined exhibits a -45° phase shift characteristic compared with the reference waveguide filter. Fig.14 and Fig.15 The return loss and insertion loss curves of the waveguide filter after adding a corrugated structure in the middle of the long side of the resonant cavity are compared with those of the reference waveguide filter. It can be seen from the figure that the passband range of the filter is slightly shifted, but the passband range has not changed significantly. Fig.16 The phase difference between the rectangular waveguide filter phase shifter and the waveguide filter phase shifter is further given. It can be seen from the figure that the phase shift characteristic of -45°±5.5° can be stably achieved within a large range of the waveguide filter passband. The frequency range of this stable phase shift accounts for 71.2% of the passband, indicating that the design can effectively realize the functions of filtering and phase shifting.

[0077] Based on the above embodiments of the present invention, relevant personnel can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A design method for a waveguide filter phase shifter, characterized in that: The specific steps include: Step (1) rectangular waveguide filter design, as a reference path for the actual rectangular waveguide filter phase shifter, technically adopts a symmetrically coupled half-wavelength resonant cavity structure; according to the design index, the order of the filter is determined through the Chebyshev filter design model, and the normalized step impedance and voltage standing wave ratio of each stage are calculated according to the low-pass to band-pass conversion formula, thereby obtaining the normalized reactance; Use formula (1) to determine the length θ of each section, where θ i The i in the column represents the i-th stage; Step (2) calculates the voltage standing wave ratio of each stage of the filter to provide the normalized reactance for calculating the length of each section in step 1. Since adjacent resonant cavities in the designed bandpass filter have similar physical dimensions, their impedance ratio is approximately 1; Normalized reactance μ, where μ i The i in the equation represents the i-th stage; it is calculated by formula (2), where ρ represents the voltage standing wave ratio, ρ i The i in the column represents the i-th stage; Step (3) Design of a rectangular waveguide filter phase shifter, adding ripples to achieve a phase difference with a reference path. A ripple phase shift structure of equal height and width is symmetrically placed in the middle part of the resonant cavity of the rectangular waveguide filter in step (1); added to the long side or short side of the rectangular waveguide filter according to the actual required phase shift direction; Step (4) corrugation structure design: the corrugation is designed to achieve the purpose of changing the phase shift size and accuracy, and the height and width of the corrugation structure are set according to the sensitivity and size of the actual required phase shift; Step (5) simulation optimization to achieve the required design indicators; establish a corresponding structural model in the three-dimensional electromagnetic field simulation software HFSS, simulate the corresponding results, and optimize the design and adjust the parameters under the premise of meeting the corresponding parameters: Step (6) calculates the phase difference to verify the phase shift size and accuracy of the rectangular waveguide filter phase shifter; and obtains the corresponding phase difference value and accuracy by comparing the actual simulated phase of the designed rectangular waveguide filter and the rectangular waveguide filter phase shifter.

2. The method for designing a waveguide filter phase shifter according to claim 1, characterized in that: Under the premise of fully meeting the performance index, the optimization design result of step (5) is as follows: In the Ka-band and 26.5-40 GHz frequency range, standard rectangular waveguide and WR-28 are used. The specific parameters are: <h2 style=";text-align:left;direction:ltr">W1 = 4.97mm, W2 = 4.06mm, W3 = 3.81mm, W4 = 3.75mm, L1 = 3.61mm, L2 = 4.31mm, L3 = 4.55mm, L4 = 4.58mm, L<h2 style=";text-align:left;direction:ltr"> w <h2 style=";text-align:left;direction:ltr"> =7.12mm,L<h2 style=";text-align:left;direction:ltr"> c <h2 style=";text-align:left;direction:ltr"> =1.49mm,H=0.33mm,S=0.25mm,B=3.556mm,A=7.12mm In the frequency range of 90 to 120, standard rectangular waveguide and WR-4 are used. The specific parameters are W1 = 1.425mm, W2 = 1.16mm, W3 = 1.085mm, W4 = 1.07mm, L1 = 1.17mm, L2 = 1.443mm, L3 = 1.507mm, L4 = 1.517mm, L w =2.032mm,L c =0.625mm, h=0.046mm, s=0.098mm, B=1.016mm, A=2.032mm.

3. The method for designing a waveguide filter phase shifter according to claim 1, characterized in that: In step (3), adding ripples to the short side of the rectangular waveguide can achieve phase shift in the positive direction, and adding ripples to the long side of the rectangular waveguide can achieve phase shift in the negative direction.

4. The method for designing a waveguide filter phase shifter according to claim 1, characterized in that: Step (4) Increasing the length of the ripple can achieve a larger phase shift, while reducing the width of the ripple can make the phase shift more stable. The specific parameters are determined according to actual needs.

5. The method for designing a waveguide filter phase shifter according to claim 2, characterized in that: Where W 1 is the width of the first coupling cavity, W2 is the width of the second coupling cavity, W3 is the width of the third coupling cavity, W4 is the width of the fourth coupling cavity, L1 is the length of the first resonant cavity, L2 is the length of the second resonant cavity, L3 is the length of the third resonant cavity, L4 is the length of the fourth resonant cavity, L w is the length of the transmission transition section, L c is the length of the coupling cavity, h is the corrugation height, s is the corrugation width, B is the length of the short side of the rectangular waveguide, and A is the length of the long side of the rectangular waveguide.

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