Design of a 94 GHz Millimeter-Wave Four-Way Power Combiner Based on Circular Waveguide Structure

: This paper introduces a four-way power combiner operating in the 94 GHz millimeter-wave based on spatial power combining technology. The four millimeter-waves with Gaussian beams are combined in the waveguide, increasing the output power. The combiner is composed of ﬁve circular waveguides connected by four long and narrow coupling slots. Four sub-waveguides are separately connected to four input ports and one main waveguide is connected to a common output port. The TE 11 -mode is used as the input mode, which has two vertical and horizontal polarization directions. Four sub-waveguides are respectively input corresponding to polarization directions TE 11 -wave with Gaussian beams. The power of TE 11 -wave is transmitted to the main waveguide by the coupling slots, combined in the main waveguide, and output with the common port. We analyze the combiner and verify the availability of the design structure by numerical stimulation with CST MWS (Microwave Studio) software. The power-combining efﬁciency can be over 97%, and the output beams remain Gaussian beams with nearly fourfold increased power. The proposed model provides technological approaches for power combiner application in millimeter-wave. along the x direction and the y direction, respectively. X from − 12.8 mm to − 5.6 mm is the region of sub-waveguide 1, x from − 3.6 mm to 3.6 mm is the region of the main waveguide, x from 5.6 mm to 12.8 mm is the region of sub-waveguide 2. X from − 5.6 mm to − 3.6 mm and from 3.6 to 5.6 mm are the regions of coupling slot 1 and 2, respectively. Y from 5.6 mm to 12.8 mm is the region of sub-waveguide 3, y from − 3.6 to 3.6 mm is the region of the main waveguide, and y from − 12.8 mm to − 5.6 mm is the region of sub-waveguide 4. Y from 3.6 mm to 5.6 mm and from − 5.6 mm to − 3.6 mm are the regions of coupling slot 3 and 4, respectively. The two blue lines are the variation of normalization central power of the combiner at the beginning of the coupling slots. It can be observed that the power of the four sub-waveguides is high and the power of the main waveguide is very small. The two orange lines are the variation of normalization central power of the combiner at the end of the coupling slot. The power of the main waveguide becomes extremely large, and the power of the sub-waveguides becomes very small. In addition, the normalization center power of the main waveguide at the bottom of the coupling slot is approximately four times the power of one sub-waveguide at the beginning of the coupling slots. The power of the common output port is 3.8963 MW. The power-combining efﬁciency of the power combiner is 97.41% in 94 GHz millimeter-wave. The polarization TE 11 -waves with Gaussian beams of the four sub-waveguides are all coupled into the main waveguide by the coupling slots connected to the main waveguide. Only less than 4% of the power remains in the sub-waveguides or is lost in transmission, realizing the highest power-combining efﬁciency and promoting the output power.


Introduction
In general, the output power from a single power source is limited. However, higher power is required in order to have a larger action radius, stronger anti-jamming capability, and better transmission quality. Higher power generation is not possible from a single source. Therefore, the power combiner is a key component to increase output power in the microwave and millimeter-wave system. Many scholars have developed power combiners with spatial power-combining technology based on waveguide structures. Xin Cao proposed a two-way power combiner, operated on 30 GHz with 800 mw of power and 78.9% of combining efficiency [1]. Xiao et al. proposed a two-curved channel compact power combiner operating in X band that significantly reduces the impact of reflected waves in interactive areas [2]. Recently, most research for power combiner has been focused on microwave [3,4] and low-frequency millimeter-wave [5]. These have problems of too large size and low power, respectively.
High-frequency millimeter-wave has the advantage of narrow beams, strong penetrability, high resolution, and better anti-interference, displaying well-applied prospects in communications [6][7][8][9], imaging [10,11], and radar [12,13]. Simultaneously, high-frequency millimeter-waves have a shorter wavelength, which could effectively reduce the size of components and provide more benefits in terms of system miniaturization. The power of a single source in high-frequency millimeter-wave is limited by material properties. The power combiners in low frequency millimeter-wave with high-power output have a large system size. The high-frequency millimeter-wave power combiners are preferable to low frequency ones in anti-jamming, transmission quality, imaging resolution, and precision The following is the principle of the four-way power combiner. According to coupled wave theory, the waves will couple with each other during the transmission process when mutually parallel waveguides are adjacent to each other. While there is a coupling structure between two adjacent waveguides, power exchange occurs during wave transmission between waveguides. The coupling equation is as follows: For a single mode, effective coupling can occur when the propagation constants are equal: Assuming that waveguide-b has a single mode wave propagation and waveguide-a has no wave propagation at z = 0 (port 4), E b (0) = E b0 , E a (0) = 0. The power of the Electronics 2021, 10, 1795 3 of 12 two waveguides is |E a (z)| 2 and |E b (z)| 2 , respectively. The schematic is shown in Figure 1. According to power conservation conditions, d dz |E a (z)| 2 + |E b (z)| 2 = 0 (5) When ( ) P z reaches the maximum with realizing the maximum power conversion between the two waveguides. The excitation power input to port 4 is transmitted to waveguide-a by favorable coupling structures and output from port 2. Port 1 and port 3 have basically no power output. The power of waveguideb is almost completely transmitted into waveguide-a, and the maximum power conversion efficiency is as follows: When 0 k Δ = , complete power conversion is realized. Among the transmission modes of a circular waveguide, the TE11-mode is the fundamental mode of circular waveguide and suitable mode for antenna. The TE11-mode has vertical and horizontal polarization directions, and the coupling coefficients in the two polarization directions are very different. Furthermore, the TE11-mode could cause direct radiation into the atmosphere. According to the orthogonal polarization mode theory, the polarization direction of the TE11-mode is associated with the structural direction of the designed coupling slot when coupling the TE11-wave from one waveguide to another. When the designed coupling slot structure is appropriate for coupling the vertical polarization TE11-wave, the vertical polarization TE11-wave input to one waveguide can be completely coupled to another waveguide by the coupling slot, but the horizontal polarization TE11-waves input to one waveguide can be rarely coupled to another waveguide. When The powers of the waveguide-a and the waveguide-b are as follows: When K 2 + (∆k) 2 1/2 z = π/2, the P a (z) reaches the maximum with realizing the maximum power conversion between the two waveguides. The excitation power input to port 4 is transmitted to waveguide-a by favorable coupling structures and output from port 2. Port 1 and port 3 have basically no power output. The power of waveguide-b is almost completely transmitted into waveguide-a, and the maximum power conversion efficiency is as follows: When ∆k = 0, complete power conversion is realized. Among the transmission modes of a circular waveguide, the TE 11 -mode is the fundamental mode of circular waveguide and suitable mode for antenna. The TE 11 -mode has vertical and horizontal polarization directions, and the coupling coefficients in the two polarization directions are very different. Furthermore, the TE 11 -mode could cause direct radiation into the atmosphere. According to the orthogonal polarization mode theory, the polarization direction of the TE 11 -mode is associated with the structural direction of the designed coupling slot when coupling the TE 11 -wave from one waveguide to another. When the designed coupling slot structure is appropriate for coupling the vertical polarization TE 11 -wave, the vertical polarization TE 11 -wave input to one waveguide can be completely coupled to another waveguide by the coupling slot, but the horizontal polarization TE 11 -waves input to one waveguide can be rarely coupled to another waveguide. When the designed coupling slot structure is appropriate for coupling the vertical polarization TE 11 -wave, the horizontal polarization TE 11 -wave input to one waveguide can be completely coupled to another waveguide by the coupling slot, but the vertical polarization TE 11 -waves input to one waveguide can rarely be coupled to another waveguide. These principles are shown in Figures 2 and 3 by numerical stimulation software CST. the designed coupling slot structure is appropriate for coupling the vertical polarization TE11-wave, the horizontal polarization TE11-wave input to one waveguide can be completely coupled to another waveguide by the coupling slot, but the vertical polarization TE11-waves input to one waveguide can rarely be coupled to another waveguide. These principles are shown in Figures 2 and 3 by numerical stimulation software CST.  In Figures 2 and 3, the two identical waveguides are connected by a coupling slot. Significantly, the connected direction of the two waveguides by the coupling slot is different, and the transverse and longitudinal electric-field distributions are shown. In Figure  2a, the horizontal polarization TE11-wave with Gaussian beams is input to a single waveguide, and the connected direction of two waveguides by the coupling slot is the y-direction. In Figure 2b, it can be clearly seen that the great majority of power of the horizontal polarization TE11-wave input to one waveguide is transmitted to another waveguide by the coupling slot. Similarly, the vertical polarization TE11-wave with Gaussian beams is input to one waveguide, and the direction of the coupling slot connected with two waveguides is the x-direction, as shown in Figure 3. The great majority of power of the vertical polarization TE11-wave input to one waveguide is transmitted to another waveguide. In the designed coupling slot structure is appropriate for coupling the vertical polarization TE11-wave, the horizontal polarization TE11-wave input to one waveguide can be completely coupled to another waveguide by the coupling slot, but the vertical polarization TE11-waves input to one waveguide can rarely be coupled to another waveguide. These principles are shown in   In Figures 2 and 3, the two identical waveguides are connected by a coupling slot. Significantly, the connected direction of the two waveguides by the coupling slot is different, and the transverse and longitudinal electric-field distributions are shown. In Figure  2a, the horizontal polarization TE11-wave with Gaussian beams is input to a single waveguide, and the connected direction of two waveguides by the coupling slot is the y-direction. In Figure 2b, it can be clearly seen that the great majority of power of the horizontal polarization TE11-wave input to one waveguide is transmitted to another waveguide by the coupling slot. Similarly, the vertical polarization TE11-wave with Gaussian beams is input to one waveguide, and the direction of the coupling slot connected with two waveguides is the x-direction, as shown in Figure 3. The great majority of power of the vertical polarization TE11-wave input to one waveguide is transmitted to another waveguide. In In Figures 2 and 3, the two identical waveguides are connected by a coupling slot. Significantly, the connected direction of the two waveguides by the coupling slot is different, and the transverse and longitudinal electric-field distributions are shown. In Figure 2a, the horizontal polarization TE 11 -wave with Gaussian beams is input to a single waveguide, and the connected direction of two waveguides by the coupling slot is the y-direction. In Figure 2b, it can be clearly seen that the great majority of power of the horizontal polarization TE 11 -wave input to one waveguide is transmitted to another waveguide by the coupling slot. Similarly, the vertical polarization TE 11 -wave with Gaussian beams is input to one waveguide, and the direction of the coupling slot connected with two waveguides is the x-direction, as shown in Figure 3. The great majority of power of the vertical polarization TE 11 -wave input to one waveguide is transmitted to another waveguide. In Figure 4, the connected direction of the coupling slot between two waveguides is the x-direction, and the two waveguides are input horizontal and vertical polarization TE 11 -wave with Gaussian beams simultaneously, respectively. It can clearly be seen that the vertical polarization Electronics 2021, 10, 1795 5 of 12 TE 11 -waves are mostly coupled to another waveguide by the coupling slot. Nevertheless, the structure of the coupling slot is not appropriate for coupling the horizontal polarization TE 11 -wave. Hence, the horizontal polarization TE 11 -wave is absolutely transmitted in its own waveguide and is isolated from another waveguide. Fang et al. [27] proposed a two-way power combiner using circular waveguides based on spatial power combining technology with this theory in 9-10 GHz. The input mode of the microwave is the vertical polarization TE 11 -wave, which realized the transmission and combination of 3 GW power in engineering.
Electronics 2021, 10, x FOR PEER REVIEW 5 of 13 Figure 4, the connected direction of the coupling slot between two waveguides is the xdirection, and the two waveguides are input horizontal and vertical polarization TE11wave with Gaussian beams simultaneously, respectively. It can clearly be seen that the vertical polarization TE11-waves are mostly coupled to another waveguide by the coupling slot. Nevertheless, the structure of the coupling slot is not appropriate for coupling the horizontal polarization TE11-wave. Hence, the horizontal polarization TE11-wave is absolutely transmitted in its own waveguide and is isolated from another waveguide. Fang et. al [27] proposed a two-way power combiner using circular waveguides based on spatial power combining technology with this theory in 9-10 GHz. The input mode of the microwave is the vertical polarization TE11-wave, which realized the transmission and combination of 3 GW power in engineering.

Model
Figure 5a is the designed 3D (three-dimensional) structure of the four-way millimeter-wave power combiner in this paper. The center is the main-waveguide, and the four sub-waveguides are symmetrically located above, below, left, and right of the main-waveguide. The combiner is a centrally symmetrical structure at the XY cross section. The mainwaveguides are closely connected with each sub-waveguide by four coupling slots. Figure  5b,c show the detailed structure parameters of the combiner. Figure 5b is the XZ cross section of the combiner. The radius R and length of the five waveguides are equal, while the length of the four coupling slots is also equal. The distance W between the main-waveguide and sub-waveguides is equal. The position of the main waveguide along the z-direction relative to the sub-waveguides is 15 mm apart. In the z-direction, the starting position of the coupling slot is 5 mm away from the starting position of the main waveguide, the bottom of the coupling slot is 5 mm from the bottom of the sub-waveguide and 20 mm from the bottom of the main waveguide. Figure

Model
Figure 5a is the designed 3D (three-dimensional) structure of the four-way millimeterwave power combiner in this paper. The center is the main-waveguide, and the four sub-waveguides are symmetrically located above, below, left, and right of the mainwaveguide. The combiner is a centrally symmetrical structure at the XY cross section. The main-waveguides are closely connected with each sub-waveguide by four coupling slots. Figure 5b,c show the detailed structure parameters of the combiner. Figure 5b is the XZ cross section of the combiner. The radius R and length of the five waveguides are equal, while the length of the four coupling slots is also equal. The distance W between the mainwaveguide and sub-waveguides is equal. The position of the main waveguide along the z-direction relative to the sub-waveguides is 15 mm apart. In the z-direction, the starting position of the coupling slot is 5 mm away from the starting position of the main waveguide, the bottom of the coupling slot is 5 mm from the bottom of the sub-waveguide and 20 mm from the bottom of the main waveguide. Figure 5c is the XY cross-section structure of the combiner. The width of the four coupling slots is L w . The starting position of the sub-waveguides is z = 0 mm along the z-direction. The center of the main-waveguide is x = 0 mm and y = 0 mm in XY coordinates. The main waveguide is the powercombining and common output channel, and the four surrounding sub-waveguides are the input channels. Port 1 and port 2 are input vertical polarization TE 11 -waves with Gaussian beams. Port 3 and port 4 are input horizontal polarization TE 11 -waves with Gaussian beams. c L is the designed coupling length of the four coupling slots. When c L reaches a certain value, the entire power can theoretically be transmitted from the sub-waveguides to the main-waveguide. Four TE11-waves are coupled to the main-waveguide by four coupling slots, and combined in the main channel. This combiner was input identical power, so the variation of theoretical power in the main waveguide is as follows: Theoretical variation of the power of one sub-waveguide and main-waveguide is shown in Figure 5d, and the final output power is 4P0 at the common output port. This structure could theoretically increase the output power by four times, which is a solution to the limited application of a single power millimeter-wave source.

Results
To verify the availability of the model proposed in Section 2, we use 3D CST MWS with the finite integral method to numerically design and investigate the four-way power combiner in 94 GHz millimeter-wave. The numerical simulation frequency band is 93-95 GHz, and the center frequency is 94 GHz. Port 1 and port 2 are input 1 MW power of vertical polarization TE11-waves with Gaussian beams, respectively. Port 3 and port 4 are input 1 MW power of horizontal polarization TE11-waves with Gaussian beams, respectively. For the operating frequency, the circular waveguide's radius R is optimized to 3.6 mm. The distance W between the main-waveguide and sub-waveguides is 2 mm. According to the coupled wave theory, the power transmission degree is closely related to the width w L and length c L of the coupling slot. The narrower the w L , the longer the c L L c is the designed coupling length of the four coupling slots. When L c reaches a certain value, the entire power can theoretically be transmitted from the sub-waveguides to the main-waveguide. Four TE 11 -waves are coupled to the main-waveguide by four coupling slots, and combined in the main channel. This combiner was input identical power, so the variation of theoretical power in the main waveguide is as follows: Theoretical variation of the power of one sub-waveguide and main-waveguide is shown in Figure 5d, and the final output power is 4P 0 at the common output port. This structure could theoretically increase the output power by four times, which is a solution to the limited application of a single power millimeter-wave source.

Results
To verify the availability of the model proposed in Section 2, we use 3D CST MWS with the finite integral method to numerically design and investigate the four-way power combiner in 94 GHz millimeter-wave. The numerical simulation frequency band is 93-95 GHz, and the center frequency is 94 GHz. Port 1 and port 2 are input 1 MW power of vertical polarization TE 11 -waves with Gaussian beams, respectively. Port 3 and port 4 are input 1 MW power of horizontal polarization TE 11 -waves with Gaussian beams, respectively. For the operating frequency, the circular waveguide's radius R is optimized to 3.6 mm. The distance W between the main-waveguide and sub-waveguides is 2 mm. According to the coupled wave theory, the power transmission degree is closely related to the width L w and length L c of the coupling slot. The narrower the L w , the longer the L c required for the entire power transmission when the size of radius R is constant. Consequently, we have indicated the influence of L w and L c on power-combining efficiency under decidedly circular waveguide radius. Finally, we present the numerical simulation results of the four-way power combiner in 94 GHz millimeter-wave.

The Influence of the Coupling Length L c
The coupling slot length L c is critical when the combiner employs long and narrow coupling slots for power transmission. Suppose that L c is shorter, only part of the power could be transmitted into the main waveguide, while part of the power remains in the sub-waveguide. Nevertheless, the too long coupling slot length L c is not beneficial for device miniaturization. Therefore, we have investigated an appropriate length of L c . In accordance with the radius R of circular waveguides, we first choose an integer value 3 mm from R as the coupling width L w . Figure 6 shows the power-combining efficiency at different L c . In Figure 6a, the L c ranges from 40 mm to 90 mm, and the interval is 5 mm. In Figure 6b, the L c ranges from 65 mm to 75 mm, and the interval is 1 mm. When L c is 70 mm, the highest power-combining efficiency is 97.05%. The power-combining efficiency decreases when L c is more than 70 mm. As a result of operating on the high frequency millimeter-wave condition, some higher order modes are generated in waveguides. The power carried by higher order modes is transmitted back to the sub-waveguides because of the too long coupling slots, so the power-combining efficiency is reduced. In the subsequent studies of the combiner, the coupling slot length L c is 70 mm in all cases. required for the entire power transmission when the size of radius R is constant. Consequently, we have indicated the influence of w L and c L on power-combining efficiency under decidedly circular waveguide radius. Finally, we present the numerical simulation results of the four-way power combiner in 94 GHz millimeter-wave.

The Influence of the Coupling Length c L
The coupling slot length c L is critical when the combiner employs long and narrow coupling slots for power transmission. Suppose that c L is shorter, only part of the power could be transmitted into the main waveguide, while part of the power remains in the sub-waveguide. Nevertheless, the too long coupling slot length c L is not beneficial for device miniaturization. Therefore, we have investigated an appropriate length of c L . In accordance with the radius R of circular waveguides, we first choose an integer value 3 mm from R as the coupling width w L . Figure 6 shows the power-combining efficiency at different c L . In Figure 6a, the c L ranges from 40 mm to 90 mm, and the interval is 5 mm. In Figure 6b, the c L ranges from 65 mm to 75 mm, and the interval is 1 mm. When c L is 70 mm, the highest power-combining efficiency is 97.05%. The power-combining efficiency decreases when c L is more than 70 mm. As a result of operating on the high frequency millimeter-wave condition, some higher order modes are generated in waveguides. The power carried by higher order modes is transmitted back to the sub-waveguides because of the too long coupling slots, so the power-combining efficiency is reduced. In the subsequent studies of the combiner, the coupling slot length c L is 70 mm in all cases.

The Influence of the Coupling Length L c
For invariant waveguide radius R and coupling slot length L c , numerical simulation research demonstrates that there is an upper limit of the coupling slot width L w to achieve higher transmission efficiency. Excessive coupling slot L w width could cause serious damage to the boundary conditions of circular waveguides. If the L w is greater than this value, the transmission power would decrease. The coupling slots' length L c is 70 mm in all cases. The coupling slot width L w ranges from 2 mm to 4 mm, and the interval is 0.2 mm. Figure 7 shows the power-combining efficiency at different L w . As L w ranges from 2.6 mm to 3.2 mm, the power-combining efficiency can reach about 97%. The highest powercombining efficiency is 97.41% when L w is 2.8 mm. For L w is 4 mm, the power-combining efficiency drops to only 52.30%. L w has the greatest influence on the power-combining efficiency compared with the coupling slot length L c , and a slight difference could lead to great variation of power-combining efficiency.
Electronics 2021, 10, 1795 8 of 12 w L ranges from 2.6 mm to 3.2 mm, the power-combining efficiency can reach about 97%.
The highest power-combining efficiency is 97.41% when w L is 2.8 mm. For w L is 4 mm, the power-combining efficiency drops to only 52.30%. w L has the greatest influence on the power-combining efficiency compared with the coupling slot length c L , and a slight difference could lead to great variation of power-combining efficiency.

Stimulation Field
The dimensions of the combiner with the highest power-combining efficiency are as follows: As shown in Figure 8, this is the electric and power field distribution of the combiner. In Figure 8a,c, they are the electric and power field distribution in the main waveguide and the subwaveguides 1 and 2 (XZ cross section). In Figure 8b,d, they are the electric and power field distribution in the main waveguide and the sub-waveguides 3 and 4 (YZ cross section). It could be clearly observed that the polarization TE11-waves input in the four sub-waveguides are largely coupled into the main-waveguide by the coupling slots, and only a small part of the power remains in the sub-waveguides. Figure 9 shows the electric field distribution of the XY cross section of the combiner. Figure 9a is the electric field distribution of the vertical polarization TE11-waves with Gaussian beams of the sub-waveguides 1 and 2 and the horizontal polarization TE11-waves with Gaussian beams of the sub-waveguides 3 and 4 of the initial position ( 0 z mm = ) of the combiner. Figure 9b shows that the majority of the power is still in the sub-waveguides and a very small part of the power begins to be coupled into the main waveguide at the beginning of the coupling slots. Figure 9c shows that the power of sub-waveguides coupled to the main-waveguide happens by the coupling slots, and a portion of the power remains in the sub-waveguides at the middle of the coupling slot ( 6 0 z mm = ). Additionally, we can see the combination phenomenon of the four waves in the main waveguide. Figure 9d shows that most of the powers are coupled to the main waveguide near the bottom of the coupling slots ( ). Only very small amount of power is retained in the four sub-waveguides.

Stimulation Field
The dimensions of the combiner with the highest power-combining efficiency are as follows: R = 3.6 mm, W = 2 mm, L w = 2.8 mm, and L c = 70 mm. As shown in Figure 8, this is the electric and power field distribution of the combiner. In Figure 8a,c, they are the electric and power field distribution in the main waveguide and the sub-waveguides 1 and 2 (XZ cross section). In Figure 8b,d, they are the electric and power field distribution in the main waveguide and the sub-waveguides 3 and 4 (YZ cross section). It could be clearly observed that the polarization TE 11 -waves input in the four sub-waveguides are largely coupled into the main-waveguide by the coupling slots, and only a small part of the power remains in the sub-waveguides. Figure 9 shows the electric field distribution of the XY cross section of the combiner. Figure 9a is the electric field distribution of the vertical polarization TE 11 -waves with Gaussian beams of the sub-waveguides 1 and 2 and the horizontal polarization TE 11 -waves with Gaussian beams of the sub-waveguides 3 and 4 of the initial position (z = 0 mm) of the combiner. Figure 9b shows that the majority of the power is still in the sub-waveguides and a very small part of the power begins to be coupled into the main waveguide at the beginning of the coupling slots. Figure 9c shows that the power of sub-waveguides coupled to the main-waveguide happens by the coupling slots, and a portion of the power remains in the sub-waveguides at the middle of the coupling slot (z = 60 mm). Additionally, we can see the combination phenomenon of the four waves in the main waveguide. Figure 9d shows that most of the powers are coupled to the main waveguide near the bottom of the coupling slots (z = 89 mm). Only very small amount of power is retained in the four sub-waveguides. Two horizontal and two vertical TE 11 -waves are basically completely combined in the main waveguide. Figure 9e shows the electric field distribution at the common output port of the main waveguide. Two horizontal and two vertical polarization Gaussian beams are basically completely combined in the main waveguide, and the output beams are still Gaussian beams with higher power. The maximum electric field and power of the combiner are 1.355 × 10 7 V/m and 3.996 × 10 11 V × A/m 2 , respectively.
Two horizontal and two vertical TE11-waves are basically completely combined in the main waveguide. Figure 9e shows the electric field distribution at the common output port of the main waveguide. Two horizontal and two vertical polarization Gaussian beams are basically completely combined in the main waveguide, and the output beams are still Gaussian beams with higher power. The maximum electric field and power of the combiner are 1.355 × 10 7 V/m and 3.996 × 10 11 V × A/m 2 , respectively.  The transmission coefficient from input port 1 to output port S51 is −0.11 dB, and the transmission coefficient from other input ports to the output ports are identical because the four sub-waveguides are symmetrical with the main waveguide. The reflection coefficient from input port S11 is −39.95 dB, and other input ports have identical reflection coefficient owing to symmetry. The transmission coefficient between two input ports S12 is −37.95 dB when the two input ports are in the same direction. The transmission coefficient between two input ports S13 and S14 is 57.67 dB when the two input ports are in different directions. Owing to the symmetry of the structure of the power combiner, the transmission coefficients between other two input ports are identical with port 1.
In the combiner, z from 20 mm to 90 mm is the coupling area. The blue line in Figure  10a is the variation of normalization center power of the sub-waveguide 1 ( 0, 0 x y mm = = ) along the z direction. The normalization center power of the subwaveguides gradually decreases to a small value of the coupling region. The orange line Two horizontal and two vertical TE11-waves are basically completely combined in the main waveguide. Figure 9e shows the electric field distribution at the common output port of the main waveguide. Two horizontal and two vertical polarization Gaussian beams are basically completely combined in the main waveguide, and the output beams are still Gaussian beams with higher power. The maximum electric field and power of the combiner are 1.355 × 10 7 V/m and 3.996 × 10 11 V × A/m 2 , respectively.  The transmission coefficient from input port 1 to output port S51 is −0.11 dB, and the transmission coefficient from other input ports to the output ports are identical because the four sub-waveguides are symmetrical with the main waveguide. The reflection coefficient from input port S11 is −39.95 dB, and other input ports have identical reflection coefficient owing to symmetry. The transmission coefficient between two input ports S12 is −37.95 dB when the two input ports are in the same direction. The transmission coefficient between two input ports S13 and S14 is 57.67 dB when the two input ports are in different directions. Owing to the symmetry of the structure of the power combiner, the transmission coefficients between other two input ports are identical with port 1.
In the combiner, z from 20 mm to 90 mm is the coupling area. The blue line in Figure  10a is the variation of normalization center power of the sub-waveguide 1 ( 0, 0 x y mm = = ) along the z direction. The normalization center power of the subwaveguides gradually decreases to a small value of the coupling region. The orange line The transmission coefficient from input port 1 to output port S 51 is −0.11 dB, and the transmission coefficient from other input ports to the output ports are identical because the four sub-waveguides are symmetrical with the main waveguide. The reflection coefficient from input port S 11 is −39.95 dB, and other input ports have identical reflection coefficient owing to symmetry. The transmission coefficient between two input ports S 12 is −37.95 dB when the two input ports are in the same direction. The transmission coefficient between two input ports S 13 and S 14 is 57.67 dB when the two input ports are in different directions. Owing to the symmetry of the structure of the power combiner, the transmission coefficients between other two input ports are identical with port 1.
In the combiner, z from 20 mm to 90 mm is the coupling area. The blue line in Figure 10a is the variation of normalization center power of the sub-waveguide 1 (x = 0, y = 0 mm) along the z direction. The normalization center power of the sub-waveguides gradually decreases to a small value of the coupling region. The orange line in Figure 10a is the variation of the normalization central power of the main waveguide along the z direction, and the normalization central power of the main waveguide gradually increases in the coupling region. In Figure 10b, the blue line and the orange line are the variation of normalization power of sub-waveguide 1 and main waveguide, respectively, along the z direction. As the four sub-waveguides are centrally symmetrical with the main waveguide in the XY cross section, the variation of the power of four sub-waveguides, which are not to be described in detail, is identical. This can also be observed and demonstrated by Figures 8 and 9. Figure 10c,d are the variation of normalization center power of waveguides along the x direction and the y direction, respectively. X from −12.8 mm to −5.6 mm is the region of sub-waveguide 1, x from −3.6 mm to 3.6 mm is the region of the main waveguide, x from 5.6 mm to 12.8 mm is the region of sub-waveguide 2. X from −5.6 mm to −3.6 mm and from 3.6 to 5.6 mm are the regions of coupling slot 1 and 2, respectively. Y from 5.6 mm to 12.8 mm is the region of sub-waveguide 3, y from −3.6 to 3.6 mm is the region of the main waveguide, and y from −12.8 mm to −5.6 mm is the region of sub-waveguide 4. Y from 3.6 mm to 5.6 mm and from −5.6 mm to −3.6 mm are the regions of coupling slot 3 and 4, respectively. The two blue lines are the variation of normalization central power of the combiner at the beginning of the coupling slots. It can be observed that the power of the four sub-waveguides is high and the power of the main waveguide is very small. The two orange lines are the variation of normalization central power of the combiner at the end of the coupling slot. The power of the main waveguide becomes extremely large, and the power of the sub-waveguides becomes very small. In addition, the normalization center power of the main waveguide at the bottom of the coupling slot is approximately four times the power of one sub-waveguide at the beginning of the coupling slots. The power of the common output port is 3.8963 MW. The power-combining efficiency of the power combiner is 97.41% in 94 GHz millimeter-wave. The polarization TE 11 -waves with Gaussian beams of the four sub-waveguides are all coupled into the main waveguide by the coupling slots connected to the main waveguide. Only less than 4% of the power remains in the sub-waveguides or is lost in transmission, realizing the highest power-combining efficiency and promoting the output power. The electric field distributions in Figures 8 and 9 show that the four TE11-waves input to four input ports are largely coupled from sub-waveguides to the main waveguide. The power measured at the output port also shows that most of the power is combined and The electric field distributions in Figures 8 and 9 show that the four TE 11 -waves input to four input ports are largely coupled from sub-waveguides to the main waveguide. The power measured at the output port also shows that most of the power is combined and output in the main waveguide. It is observed that the variation of normalization power of sub-waveguides and main waveguide in Figure 10a,b is roughly consistent with the variation of theoretical power in Figure 5d. It is proved that the model is a feasible method.

Discussion
Several combiners with large size or low power in microwave and low frequency millimeter-wave are introduced in the Introduction section. Compared with these power combiners, the four-way power combiner in 94 GHz could increase output power by four times and has a structure with a small size, which is conducive to system miniaturization. The carried power capacity can reach MW level using circular waveguides based on spatial power-combining technology. A long and narrow coupling slot is employed, which facilitates the power coupled from sub-waveguides to the main waveguide. In addition, the sub-waveguides are located in the upper, lower, left, and right directions of the mainwaveguide. The TE 11 -waves of different polarization directions are input. The structure has good isolation between sub-waveguides to achieve high power-combining efficiency. Nevertheless, the size of the coupling slot is small, which needs to be more precise in the production. A slight variation of the size of the coupling slot might lead to a large variation of power-combining efficiency. When the processing procedure is imperfect or waveguides are inhomogeneous, the polarization direction of the TE 11 -mode could be rotated.
In engineering application, the 94 GHz signal source can be connected to the W 10 rectangular waveguide port through the coaxial. Because the design of the four-way power combiner is a circular waveguide port, a rectangular-to-circular converter is required. The 94 GHz signal source generally transmits millimeter-wave signal with TE 10 or TM 10 mode. It can be connected to the input ports of the four-way power combiner of the manuscript through over-mode bent waveguide, which can realize the mode conversion to generate the TE 11 mode. The mode converter can be used to ensure the propagation of a single mode.

Conclusions
This paper presents a four-way power combiner in 94 GHz high frequency millimeterwave. The power combiner is designed with a symmetrical structure by circular waveguides and coupling slots. We employ the coupled mode theory and the coupling coefficient difference of the two vertical and horizontal polarization directions TE 11 -mode. Four-way TE 11 -waves with Gaussian beams are coupled to the main waveguide by the corresponding coupling slot structure. Then, the four millimeter-waves are combined in the main channel and output with a common port, the power-combining efficiency can be over 97%, and output power is increased by nearly four times. Furthermore, the combined output beams remain Gaussian beams. The four-way power combiner is a solution to the power limitation of a single millimeter-wave source, which can realize 3.8693 MW high-power combination and output in the high-frequency millimeter-wave.