Wideband Directional Coupler for Millimeter Wave Application based on Substrate Integrated Waveguide

Recently, Substrate Integrated Waveguide (SIW) techniques have been noticed for millimeter wave devices in microwave applications. In this paper, we are developing a wide band directional 3 dB coupler with a phase of 90̊ phase delay in the range of 30-40 GHz based on periodic vias and multi hole structure. For achieving this wide bandwidth multi-section coupler is designed based on the theoretical modeling and the simulation result is compared with HFSS and CST with two different numerical methods show good performance with low insertion and return loss, broad operational bandwidth and high isolation. A fractional bandwidth is about 28.5 %.

In the other hand, the substrate integrated waveguide is suggested at high frequency applications and exactly it is working as same as rectangular waveguide that the sidewalls are replaced by two rows of metallic posts [8].Therefore, The Substrate Integrated Waveguide technology usually has been used in mm-wave systems and has advantages such as high Q-factor, compact profile, low cost platform and easy fabrication [9].Directional 3dB coupler or 90º degree hybrids have been implemented in various applications in communication circuits such as modulators, mixers, feed networks and other microwave devices.Branch line, Lange, Bethe hole, short slot and cruciform coupler are well-known conventional types of 90-degree hybrids [10].
In the last decade, various form of the SIW coupler are suggested for radar or mm-wave application for 90º phase delay such as sum-difference comparator [11], HMSIW with double-slot coupler [12], cruciform directional coupler [13] crossed-SIW directional couplers with different angles [14] and Waveguide-Hybrid Branch Line Coupler [15].They are also noticed for 180º phase delay such as Narrow wall directional coupler [16] Half Mode Substrate Integrated Waveguide (HMSIW) for 180º phase delay [17], non-uniform width [18].Furthermore, multi-layer SIW structures are attractive for directional coupler based on coupling from Bethe hole [19][20].Apparently, in single layer SIW the Bethe hole made between two waveguide by the elimination of some vias.challenging specifications in terms of both operating frequency and bandwidth, new multi-branch SIW H-plane couplers on a single-layer substrate are proposed.The bandwidth around 28.5% is achieved and at last, the results are compared with previous research.

2-Design Theory
The TE10 is known as dominate mode in the waveguide and cut off frequency define as shows in Equation 1; where  and  are selected for width and height of the conventional waveguide. is the light speed and   is the substrate permittivity [21].The distance between the via (S) is affected on the radiation losses will create because of the leakage field in SIW structure and S≤2d and d≤λg/5 are given ideal situation where the d is the diameter of the via.The guided wavelength for the dominant mode in SIW is obtained by Equation 2 [22]: Multi-hole coupling structures are noticeably for enhancement of the bandwidth and coupling characteristic in directional coupler with various techniques such binomial, Chebyshev, and superimposed to calculate the coupling of each hole.In addition, many researches have been done around the effect of the number of holes on directivity and them shows that distances between the holes and hole dimensions will effect on the coupler characteristic [23].The multihole waveguide coupler is employed in this design, and as shows in Figure 1 they are a few holes with uniform arrangement are modified here for the conventional directional coupler.This method is a useful technique for improving the bandwidth of the coupler.
However, the best dimension of the hole is obtained for diameter of λg/4 and for wideband structure the λg is obtained by Equation 3where λg1 and λg2 are for upper and lower frequency: The even and odd modes or mode matching method can be used for modeling the SIW coupler [24][25].However, for common design, the length of each branch is assumed λg/2 and the width of the aperture is λg [16].

3-The Coupler Design
Figure 2 (a) shows the basic model of the 3 dB SIW coupler with Symmetrical dimensions [26].Here, TE10 is the dominate mode so each branch of the coupler is working as a conventional rectangular waveguide and widest aperture is modified for coupling between top and bottom waveguide and the step shape of the waveguide at center part is used for matching.The frequency band of the waveguide determines the size of the waveguide by Equation 1.The diameter of the via is chosen to be equal or smaller than a tenth of the wavelength of the maximum operating frequency for less linkage loss.The taper microstrip line is used for matching connecting of the SIW part to50Ω feed with bent line.It is a common method for wideband SIW line [27][28].Thus, the width and length are chosen so that the input impedance of the microstrip feed line matched to the SIW input impedance.Figure 2 (c) shows the geometry of the prototype feed line with taper formation.
A prototype 3dB SIW symmetrical coupler is designed by replacing the single hole by the multi section structures.Figure 2 (b) shows the designed 3dB coupler geometrical dimension for 30-40 GHz.The coupler is designed on a Rogers RT/Duroid 5880 substrate.The height of the substrate is 0.508 mm with (loss tangent 0.0009) with total dimension of 38.973×93.33 mm 2 .In addition, all dimensions have been presented in Table 1.
As described in pervious part, we have two essential parts in our design.At first based on the dominate mode, the dimensions of the waveguide are calculated and assumed the initial value of the λg of the center frequency.In the second part, we should modify the structure and connect it to SMA connector with matching taper line.
In the E-plane branch-line coupler, the branch parts are between the broad walls of the main waveguides so there is a plane of symmetry through the centers of the broad walls of all the waveguides.It reduces the aperture sizes and thus increases the distance between apertures that are later to be manufactured by via holes.Finally, fine optimizations for the 3 dB coupler are required to ensure that all dimensions fall into the possible range of via holes.Combining the E-plane, multi-branch line coupler and the main directional coupler that is introduced above, lead to wideband directional coupler.

4-Simulation Results
The design parameters tuned finely by using three-dimensional (3-D) electromagnetic (EM) simulation software high frequency structure simulator (HFSS) to achieve wide band performance.In the first step, we designed conventional branch line coupler without multi hole and then the result is compared with final directional coupler when the multi hole techniques are implemented.Figure 3 shows a comparison between the suggested model of coupler in the presence and absence of the vias.As shows here, for S11 (reflection factor) are around -16 dB in the range of 31-37 GHz for simple model and when the vias are implemented, the result is improved and S11 is reduced to -40 dB and bandwidth enhanced and increased.In this case, the coupler is covered range of 30-40 GHz as shows in Figure 3 (a).Figure 3 (d) shows that we have similar condition for S14 (Isolation factor) and the return loss value and bandwidth is increased drastically.
For S12 (through factor) is around -3 to -4 dB in the range of 30-37GHz for simple model and when the vias are implemented, the result is improved and the bandwidth enhanced and increased.In this case, the coupler is covered range of 30-40 GHz as shows in Figure 3 (c) with -3 to -4 dB loss.Figure 3 (d) shows that we have similar condition for S13 (coupling factor) and the return loss value is around -3.8 to -4.8 dB for 30-40 GHz.  Figure 5 shows the current distribution at 35 GHz on the surface of the prototype coupler.It is found that the input signal from port 1 interacts with metallic posts in the hole region, and is coupled equally to port 2 and port 3. We show the current distribution for single hole and multi-hole method at Figure 5

5-Comparison
This structure is noticed in many researches of the symmetrical form and reciprocal response [13] however asymmetric forms are studied in pervious researches [25].In the other multi-hole are noticed for improving the resulting bandwidth [24,29].In this section, we presented a comparison between current work and pervious models of the SIW coupler and the comparison is given at Table 2.
We have noticed bandwidth and S12 as important values and on the other hand, compared phase and length of them in wavelength.In addition, we are noticing the structure as a symmetric or asymmetric structure and denoted them by (S) and (A) in Table 2.

6-Conclusion
Broadband directional coupler in SIW technology is presented for MM wave-band applications.The specifications towards tight coupling and broadband performance require several stages in the design process.In order to overcome higher-order mode excitation commonly observed in the upper frequency range of components with tight coupling, the design process is done to place them out of operational range.The performance of the proposed coupler for 3 dB demonstrates good agreement between HFSS and CST simulations.However, the results for the through and coupled ports show additional losses between 2.5 dB and 1.3 dB.Although these are good results in the 30 GHz frequency range, the main contributions to loss appear to because by the microstrip-to-SIW transition and the dielectric substrate.

Figure 2 (
Figure 2 (b) shows the geometry of the prototype directional coupler for MM wave application.

Figure 2 .
Figure 2. Geometry of the coupler (a) primary SIW coupler (b) the prototype SIW coupler (c) the final prototype coupler.

Figure 3 .
Figure 3.Comparison between suggested model of coupler in presence and absence of the vias (a)S11 or reflection factor (b) S12 or through factor (c) S13 or coupling factor (d) S14 or Isolation factor.

Figure 4 Figure 4 .
Figure 4 shows the phase difference between two output ports with single-hole and with multi-hole techniques.It can be seen the outputs at ports 2 and 3 are -3.8 dB to -4.5 dB, respectively, the phase difference is distributed in the range of 88.3 ~ 92.5 o within the frequency band of 30 to 40 GHz.
Figure5shows the current distribution at 35 GHz on the surface of the prototype coupler.It is found that the input signal from port 1 interacts with metallic posts in the hole region, and is coupled equally to port 2 and port 3. We show the current distribution for single hole and multi-hole method at Figure5(a) and (b) respectively.

Figure 5 .
Figure 5. Simulated current distribution at 35 GHz for (a) single hole model (b) multi hole model.