Broadband Differential-Line-to-Waveguide Transition in Multi-Layer Dielectric Substrates With an X-Shaped Patch Element in 280 GHz Band

A broadband differential-line-to-waveguide transition covering the 260–300 GHz band was developed in this study. This transition consists of a differential line inserted from the narrow wall of the waveguide that excites an X-shaped patch located at the waveguide center. As the two corners of the patch are excited electromagnetically via differential signal lines in the opposite phase, orthogonal current components that radiate the TE10 mode into the waveguide are generated. Broadband operation is achieved via the double resonance of the X-shaped patch and a cavity formed by the via-hole arrangement with apertures patterned in a multi-layer substrate. The transition geometries are optimized via electromagnetic simulation using a finite element method. Transition performance is evaluated through measurements and simulations.


I. INTRODUCTION
M ILLIMETER-and terahertz-wave technologies have attracted attention in recent years due to the large communication capacity that these high-frequency bands are anticipated to provide. The 252-296 GHz band is focused on high-speed communication systems, particularly for highdefinition video transmission and beyond 5G/6G mobile communication systems [1], [2], [3], [4]. Furthermore, the terahertz band can cater to compact antennas and radio frequency (RF) circuits since its wavelength is shorter than 1 mm. However, the transmission loss of transmission lines and insertion loss of RF components are quite high owing to the dielectric loss tangent of the substrates and significant conductor loss generated even by small surface roughness on the metal planes.
Rectangular metal waveguides are one of the most popular transmission lines used in millimeter-and terahertz-wave bands as they have relatively low loss even in high-frequency bands. Waveguide interfaces are useful for connecting RF circuits and antennas because they can be developed independently and are connected by waveguides without interference [5], [6]. Moreover, the interfaces of measurement instruments, such as millimeter-wave modules for vector network analyzers, often serve as waveguides because the characteristics of the test devices can be easily measured from the waveguide interface. In contrast, interfacing measuring instruments with an RF integrated circuit (IC) is challenging because the RF IC is mounted on the top plane of a multi-layer dielectric substrate and signal lines need to be patterned there. Additionally, the control and bias lines are accommodated on the metal patterns between all dielectric layers and the signal lines. A planarline-to-waveguide transition is used to connect the signal line and the waveguide with low loss. High-bit-rate communication systems require all the components to have wide operation bandwidths. Microstrip lines and coplanar waveguides with the ground are popular IC connectors fabricated on the top metal planes of multi-layer substrates. Both differential and singleended lines are used for IC connections, depending on the circuit configuration. Therefore, waveguide transitions that connect from both differential and single-ended lines have been developed to prevent the use of lossy baluns. Waveguide transitions from both differential and singleended lines need to be developed for use in various applications.
Various studies have previously developed microstrip-towaveguide transitions. The back-short transition is one of the most popular transitions [7], [8] due to its broad operation bandwidth. However, a top metal cap is required and must be accurately assembled on the substrate. Transitions with back-short structures formed by via-hole arrangements in a multi-layer substrate have been fabricated via highly accurate manufacturing processes [9], [10].
Various planar microstrip-to-waveguide transitions without back-short structures have been developed using different techniques [11], [12], [13]. A radiation patch in the waveguide, electromagnetically excited from the coplanar waveguide, can be used. Although the bandwidth was narrow, the structure was simple due to the use of only one substrate. These types of transitions have recently become popular. Thus, a slot coupling technique in multi-layer substrates [14], broadband techniques [15], [16], [17], via-less transitions [18], [19], and top-side waveguide transitions [20] have been developed to meet specific requirements. Generally, both differential and single-ended lines are used at IC terminals. To avoid the use of lossy and area-consuming baluns, differential-line-to-waveguide transitions are effective for directly connecting an RF IC with a differential line to a waveguide. The signal line of a single-ended transition is inserted into a waveguide from the broad wall because the signal line becomes parallel to the electric field of the TE 10 waveguide mode. However, if both the signal lines of the differential line are inserted from a broad wall, radiation weakens due to the cancellation of radiations from the two signal lines excited in opposite phases into the waveguide. This is because the signal lines are excited 180 • out of phase. Therefore, a patch in the waveguide is excited by directly connecting the signal lines of the differential line to the narrow wall of the waveguide [21], [22]. Additionally, aperture excitation techniques have been applied to the waveguide [23], [24]. Broadband techniques have been developed using a waveguide taper [25], back-short structure [26], fin-line taper [27], or a collinear connection between the differential line and waveguide [28].
This study proposes a wideband differential-line-towaveguide transition in multi-layer substrates. The signal lines are located on the top layer of the multi-layer substrate, where IC chips can be mounted. An X-shaped patch is formed on the second layer, which is excited by electromagnetic coupling from the differential line. The electromagnetic wave radiates into the waveguide through apertures on the lower layers of the substrate. Broadband operation is obtained by the multiresonance of the X-shaped patch and the cavity formed by the apertures and via-hole arrangement.
The rest of this article is organized as follows. The structure and operating principle of the proposed transition are described in Section II. Section III presents the simulation performance and characteristics of the optimized transition numerically investigated by electromagnetic field analysis using high frequency structure simulator (HFSS), a finite element method [29]. The feasibility of the proposed design approach, experimentally verified by measurements, is discussed in Section IV. Finally, the conclusion is presented in Section V.

II. STRUCTURE AND PRINCIPLE
The geometries and principles of the proposed transition are explained in this section. The transition connects a waveguide to a differential line patterned on the top layer of the multi-layer dielectric substrate, as shown in Fig. 1. The differential line comprises of two parallel coplanar waveguides with the ground. These coplanar waveguides are surrounded by via-hole arrangements. Thus, the lines are isolated to prevent the increasing loss and change of characteristic impedance dependent on the line layout caused by the mutual coupling of signal lines. The via-hole arrangement allows the design of the characteristic impedance of the differential line to be dependent only on the structure of the single coplanar waveguide. The coplanar waveguides are Differential line-to-waveguide transition configuration with an X-shaped patch element in a multi-layer dielectric substrate. excited 180 • out of phase, resulting in differential line mode operations.
The signal lines are inserted into the waveguide region from the waveguide narrow wall. Thus, the direction of the electric field generated between the two signal lines is identical to that of the electric field of the TE 10 mode in the waveguide. A patch is located on the second layer near the signal lines and is electromagnetically excited without a via-hole connection. The apertures are opened in all lower metal plates from the second layer. The radiated field passes through the lower dielectric layers along the apertures into the waveguide. When a square patch is used similar to that in conventional transitions [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], the coupled currents flow parallel to the signal lines that are orthogonal to the electric field of the TE 10 mode of the waveguide. To overcome the strong coupling from the signal lines to the patch and for effective TE 10 mode polarization from perpendicularly connected differential signal lines, a symmetrical X-shaped patch is proposed in this article.
The configuration of the developed transition is shown in Fig. 1. The multi-layer substrate comprises of eight copper plates separated by seven dielectric plates. Three prepreg layers are stacked on both sides of the core layer. A multilayer substrate is manufactured by heating under high pressure. Micropatterns with fine pitches are manufactured via the modified semi-additive process (MSAP). The metal patterns are plated with 0.05-μm gold after applying 4-μm nickel on the interface of the copper plate. MSAP forms a rounded corner at the edge of the metal pattern, and the radius of the corner is 10 μm. The accuracies of the metal patterns on the same layer and different layers are 10 and 25 μm, respectively. The accuracy of the pattern width of the signal lines is ±10 μm. The multi-layer substrate is placed on the aperture of the metal waveguide (WR3, 0.864 × 0.432 mm). The top metal plane is defined as layer 1, and the lower layers are sequentially defined as layers 2-8 (see Fig. 1). An X-shaped patch is located on layer 2 as the patch center is identical to the waveguide center shown in Fig. 2. As the patch corner diagonally overlaps the signal line, the diagonal component of the current on the signal line excites the current on the patch corner [30]. The same phenomenon occurs at both patch corners. The induced currents on both corners of the patch are in opposite directions, generating a strong current component in the y-direction. Consequently, the patch radiates the TE 10 mode into the waveguide.
The geometrical parameters of the proposed transition are defined in Fig. 3. The transition is symmetrical in the zx-plane across the waveguide center. The X-shaped patch is located at the center of the waveguide in layer 2. The geometry of the X-shaped patch is based on the ordinary rectangular patch with width W and length L. Triangles with base angle θ at the narrow-wall sides and trapezoids with length W c and angle θ at the broad-wall sides are subtracted from the initial rectangular patch, resulting in the X-shaped patch. The overlap length ρ of the signal line on the corner of the X-shaped patch is an important parameter for controlling the coupling from the signal line to the patch. Furthermore, for wideband matching, inductive and capacitive irises are provided in the apertures of all the metal patterns [31]. All the vertical and horizontal widths of the apertures are optimized via electromagnetic simulations. The via-holes with 0.07 mm diameters are arranged around the waveguides with 0.18-mm center separations to prevent the leakage of parallel-plate modes between all metal planes. When manufacturing the substrate, the position variation of a via-hole is ±25 μm and the diameter variation is ±20 μm. The materials of both the core and prepreg layers are HL972LF-LD [32] (Mitsubishi Gas Chemical Company, Inc.) with a thickness of 0.1 mm for the core layer and 0.03 mm for the prepreg layers in the multi-layer configuration. The thickness variations of the core and prepreg layers are ±15 and ±10 μm, respectively. The 0.03-mm prepreg thickness is chosen to obtain strong proximity coupling between the signal line and patch. To take advantage of the proximity of layers 1 and 2, the signal lines are chosen to be coplanar waveguides with the ground. The thickness of the copper plate is 0.015 mm. The variation in thickness of the copper plate is ±7 μm. The substrate was manufactured by CONNECTEC JAPAN Corporation.
All the geometrical parameters were optimized to achieve wideband matching. The dimensions of the X-shaped patch were designed to control the coupling between the signal line and resonant frequency. When designing the X-shaped patch, the cutting angle θ is a crucial parameter. If θ increases, the direction of the X-patch corner becomes closer to the signal line. Consequently, the coupling from the signal lines to the patch becomes stronger; however, the radiation polarized in the TE 10 mode decreases. Furthermore, when θ changes, the path length of the current flowing on the X-shaped patch changes, resulting in a change in the resonant frequency. Therefore, deciding of θ is a priority to balance the coupling between the signal line and resonant frequency. The other parameters can be fine-tuned subsequently. The design of the aperture sizes of all the metal layers is shown in Fig. 4. As the iris extensions increase from layers 2 to 5 and form a cavity around the patch, low-Q resonance due to the extension of the area distributing the electromagnetic field for wide bandwidth can be obtained by the large cavity volume. The extensions of layers 5-8 gradually become smaller and taper, like a horn antenna. The cavity structure is expected to generate one more resonance for the multiple resonances. The equivalent horn structure is expected to achieve smooth radiation into the waveguide. Based on these principles, the transition was designed for a wideband covering 252-296 GHz. First, the  patch length L in the y-direction was designed to obtain the center operating frequency. Then, the width W and angle θ of the figure of the X-shaped patch were designed to balance the y-polarized radiation and coupling from the x-directed signal line. Well coupling contributes low reflection due to superior transmission performance. The apertures of layers 4 and 5 above and below the core material were adjusted. Finally, the apertures of the remaining layers were fine-tuned from layers 3 and 6 for cavity formation. All these parameters indicated in Fig. 3 were optimized for reflection to be lower in wide bandwidth without increasing transmission loss in fabrication conditions. Figs. 5 and 6 show the electric field amplitude and current vector distributions on the X-shaped patch, respectively, which help understand its behavior. The X-shaped patch is highly excited by the coupling from the signal lines (see Fig. 5). As shown in Fig. 6, the y-component current strongly flows from both corners of the patch. This indicates that the coupling from the two differential signal lines to the X-shaped patch with the opposite phase excites TE 10 mode radiation into the waveguide. That is, the mode conversion from the signal line to the waveguide is performed by the resonance of the X-shaped patch. The quasi-TEM mode of the signal line is converted to the TE 10 mode propagating in the waveguide. Fig. 7 shows the electric field amplitude distribution on the zx-plane. As shown in Fig. 7, the cavity is formed by extending the wide-wall width of substrate layer 5, and the electromagnetic wave  is smoothly radiated into the waveguide by the quasi-horn structure.

III. SIMULATION RESULTS
Simulated parameter dependencies of the reflection characteristics for the proposed transition are discussed in this section. The electromagnetic simulator HFSS was used in the simulation [29]. A wide bandwidth is required, and the bandwidth can be controlled by the resonant frequencies of the multiple resonances. The goal was to increase the bandwidth of reflections to less than −10 dB for a center frequency of 275 GHz. The basic principle of the transition was explained from the geometries in Section II. The principal details for the wideband design of the transition were investigated via the parameter simulation discussed in this section.
The dimensions W l and G of the single coplanar waveguide with ground were designed for a characteristic impedance of 50 . When W l and G are 0.04 and 0.035 mm, respectively, the characteristic impedance becomes 55.2 and the differential line becomes 110.4 . The important parameters for controlling the resonant frequencies are the patch length L and patch cut width W c . The patch cut width W c and overlap length ρ strongly affect coupling from the signal lines to the patch. As shown in Figs. 8 and 9, the higher resonant frequency lowers when L or W c increases because the path length of the current on the patch becomes longer than the half-wavelength of the design frequency. The overlap length ρ   was optimized with 0.05 mm as the appropriate coupling; thus, the S 11 level was reduced (see Fig. 10). When ρ is shorter, the coupling becomes weak. Consequently, the S 11 level increases. Although the bandwidth of reflections less than −10 dB increases owing to double resonance, the resonant frequency also slightly shifts when ρ changes. Accurate control of the resonant frequencies is important to achieve wide bandwidth.
As explained in Section II via Fig. 7, the effect of the cavity in the substrate generates another resonance in double resonance for wideband characteristics. The aperture width Fig. 11.
Simulated reflection characteristics of the proposed transition depending on the width W s5 of the aperture on layer 5. Simulated reflection characteristics of the proposed transition depending on the width W s6 of the aperture on layer 6 and simulated transmission for the optimum parameters. W s5 of layer 5 is the parameter for controlling the effect of the cavity. The extended metal pattern forming the aperture works as an inductive iris, affecting the resonant frequency of the cavity. As shown in Fig. 11, when W s5 becomes larger, the lower resonant frequency lowers further because the leakage of the electromagnetic field increases the cavity length. The aperture width W s6 of the next lower layer 6 controls the quasi-horn antenna toward the waveguide. When W s6 increases (see Fig. 12), both resonant frequencies decrease because the additional inductive iris affects the resonant frequencies.
Based on the electromagnetic simulation, the optimal design parameters are listed in Table I. The patch length L was set to approximately 1/2 λ, and the cut angle θ was 30 • for both TE 10 mode radiation and strong coupling with the signal line. The transmission characteristic S 21 and the reflection characteristic S 11 for the optimum parameters are shown in Fig. 12. Accordingly, broadband characteristics were obtained by double resonance. The bandwidth of the reflections less than −10 dB was 66.3 GHz. At the design frequency of 275 GHz, the transmission loss was 1.2 dB.

IV. EXPERIMENTAL PERFORMANCES
To verify the simulation validity of the proposed transition, transmission loss and reflection characteristics of the fabricated transitions were measured. The measurement system is shown in Fig. 13. Two identical transitions with the same geometrical parameters were connected by a differential line to the fabricated substrate, forming a back-to-back configuration, as shown in Fig. 13(a). The substrate was mounted on a metal jig with waveguides at both terminals to connect the flanges of the standard waveguides. Choke structures were formed around the waveguide on the jig surface to reduce leakage from the gap between the substrate and jig. The substrate was fixed at the exact location with high accuracy via microscrews of 1 mm diameter. The accuracy of the measurement was confirmed by repeating the assembly and measurement processes. Millimeter-wave extension modules VDI WR3.4-VNAX were connected to the vector network analyzer ANRITSU MS4647B, as shown in Fig. 13(b). Two ports of the standard waveguides extending from the millimeterwave modules were calibrated using WR3 waveguide Anritsu Calibration Kit Model SM6567 at the planes connected to the waveguide in the metal jig. Reflection and transmission characteristics including the waveguide in the jig and transmission lines between the two transitions were measured. A gating function in the time domain equipped with the vector network analyzer was performed during the measurement of the scattering parameters to prevent the effects of multiple reflections [33]. The full frequency band of WR3 between 220 and 320 GHz was set to obtain a high time resolution.  To accurately evaluate the insertion loss of an individual transition, the losses of the differential line between the transitions and the waveguide in the jig were measured to obtain the compensation. The substrates of the transitions connected by differential lines with different lengths (see Fig. 14) were fabricated for each parameter combination. Two transitions were connected via a transmission line. Four different lengths (i.e., 1.136, 3.136, 5.136, and 7.136 mm) were used to measure the transmission loss of the transmission line. The length of a transmission line was defined as the length between the narrow waveguide walls of two transitions, as shown in Fig. 2. Fig. 15 shows the transmission when using differential lines of 1.136, 3.136, 5.136, and 7.136 mm at 262.5, 275, and 287.5 GHz, respectively. The transmission loss at 275 GHz was estimated to be 1.1 dB/mm using the slope of the curves. Next, the loss of the jig was measured by connecting two identical jigs, as shown in Fig. 16. Fig. 17 shows the individual loss of each part for estimating the insertion loss of one transition. The measured transmission of the substrate with a differential line of 5.136 mm including all the losses from Port 1 to Port 2, indicated using the blue dashed line, was obtained via S-parameter measurement. The black solid line represents the transmission with waveguide loss in the jig obtained via jig measurement, as shown in Fig. 16. The green dotted line shows the loss of the differential line of 5.136 mm, estimated from the difference in the measured transmissions of the substrates with different lengths, as shown in Fig. 14. The characteristics of the proposed transition, indicated using a thick red line, are finally derived by embedding the losses of the jig and the differential line from the measured transmission of the substrate. The losses of the two jigs were obtained as 1.8 dB at 275 GHz and that of one jig was estimated to be 0.9 dB by dividing the measured transmission of the two jigs by two. The loss errors at the band edges can be caused due to approaching the cutoff frequency around 220 GHz and higher order mode propagation around 320 GHz. Degradation of the reflection characteristics at the band edges can cause an additional error in the transmission characteristics. However, an almost-flat frequency characteristic was obtained for the transition operating frequencies from 240 to 300 GHz. Fig. 18 shows the measured transmission and reflection coefficients evaluated by the procedure described earlier and the simulated results. The solid and dashed lines represent the measured and simulated results, respectively. Wide bandwidth was obtained by generating double resonance. The two measured resonant frequencies were 250.9 and 308.7 GHz. The measured lower resonant frequency is 6 GHz lower than the simulation, and the measured higher resonant frequency is 10 GHz higher than the simulation. Due to the frequency shift, although the reflection level around the middle frequency increased by 3 dB, the bandwidth increased. However,   the measured loss at the design frequency of 275 GHz was still 2.6 dB. The surface roughness of the multi-layer substrate used in fabrication was 0.3 μm, while the depth of the copper skin effect was 0.12 μm, which is almost the same size as the surface roughness. It was therefore found that surface roughness thus significantly affects the conductor loss.

V. CONCLUSION
A differential line-to-waveguide transition in a multi-layer dielectric substrate was developed for use in the 280 GHz band. An X-shaped patch is excited by the signal lines of the differential line inserted from the narrow wall of the waveguide. Mode transformation from the differential line to the waveguide is achieved by the strong coupling of the signal line to the radiating patch. This principle can be applied to various connection circuits without signal line via connections, realizing low-loss transmission. The proposed transition was designed to be broadband owing to the multiple resonance of the X-shaped patch and the cavity in the multi-layer substrate. The simulated bandwidth of the reflections less than −10 dB was 66.3 GHz in the 280 GHz band. Two resonant frequencies of the double resonance shifted, and the difference between the two frequencies increased. Consequently, the reflection level at the middle of the two frequencies increased by 3 dB. However, the measured insertion loss was still 2.6 dB at a design frequency of 275 GHz, and wide frequency bandwidth was confirmed via measurements.