New Design of Miniature C-Band Sub- strate Integrated Waveguide Bandpass Filters Using Ceramic Material

This article presents new structures and methods of design of miniature third-order substrate integrated waveguide (SIW) bandpass filters on a high-permittivity ceramic substrate for the C-band. The aim was to appraise the feasibility of such filters by using a 3D electromagnetic (EM) simulator. The substrate integrated waveguide (SIW) offers good quality factors and electrical performances compared with other planar techniques. Its integration capabilities and fabrication cost are other benefits that make it attractive. Ceramic material offer electrical properties suitable in designing of passive devices. High relative permittivity with low dielectric losses makes it possible to miniaturize passive components while exhibiting high temperature stability, which is an important selection criterion for a filter designed to equip the payload of a satellite. Three SIW filters were designed on a Trans-Tech ceramic substrate (thickness = 254 μm, εr = 90, and tanδ = 0.0009) with drastic specifications for space application. The first filter is composed of three SIW resonators with direct coupling, the second is composed of three SIW resonators with a cross-coupling to create a transmission zero, and the third is composed of three SIW resonators with circular holes etched on the top of the metal layer to achieve a super-wide band. The obtained results for the proposed filters are presented, discussed, and compared with relevant published literature. The proposed filter can be used to enhance the performance of microwave devices used for C-band, especially Satellite communications.


INTRODUCTION
Ceramic materials offer relevant dielectric characteristics for the conception of passive devices [1,2]. Some of them reach high relative permittivity while presenting low dielectric losses (tanδ < 0.001) [3][4][5]. They show themselves also very stable against temperature changes, an essential criterion for a filter used in spatial applications [6]. However, the realization of miniature filters is confronted by more restrictive technological constraints (a narrower microstrip line and finer drillings).
A substrate integrated waveguide (SIW) allows integration of the rectangular waveguide into a substrate through two arrays of via holes [7,8]. These vias must all have the same diameter and must have sufficiently small spacing to appear as perfect electric walls [9][10][11]. A recent work on the state-of-the-art of the SIW technology makes an inventory of the main published papers on SIW filters [12][13][14][15][16][17][18][19][20][21][22][23][24]. Most of the SIW filters were designed on a standard alumina substrate with excellent performances of low insert loss and high Q factor compared with the other planar techniques. However, the dimensions of these SIW filters are so large that they are difficult to integrate in satellite payload equipment.
In this paper, we propose to design SIW filters on a high-permittivity ceramic substrate for the C-band in order to achieve drastic specifications for space application with the best compromise between size and electrical performances. We begin with the design of a third-order direct-coupled SIW filter on a standard alumina substrate (thickness = 254 μm, ε r = 9.9, and tanδ = 0.0003) and then conceive its equivalent (the same order, the same frequencies) on a Trans-Tech ceramic substrate (thickness = 254 μm, ε r = 90, and tanδ = 0.0009).
The results obtained are compared in order to evaluate the performance of the high-permittivity ceramic. Then, two other third-order SIW filters are designed on a substrate with a relative permittivity of 90, the first one with a cross-coupling between resonators to create a transmission zero and the second with circular holes etched on the top of the metal layer to achieve a super-wide bandpass. Gold metal walls (σ = 41×10 6 S/m) with a thickness of 4 μm will be used for the metallization. The structures will be simulated by using the available Ansoft software High Frequency Structure Simulator (HFSS).

DESIGN OF THE C-BAND THIRD-ORDER DIRECT-COUPLED SIW BANDPASS FILTER
The filter must exhibit electrical specifications of a central frequency of 5.24 GHz with an 8% fractional bandwidth. The return loss must be better than 20 dB in the whole passband and the attenuation must be higher than 20 dB for frequencies ≥ 5.7 GHz. The coupling structure of this filter is shown in Fig. 1. where Q ein and Q eout are the external quality factors of the resonators at the input and at the output, and M 12 and M 23 are the coupling coefficients between the resonators. The external quality factors (Q ein , Q eout ) and the coupling matrix [m] of this filter are given by (1) and (2), respectively. .
where m ij denotes the so-called normalized coupling coefficient [25].
where n is the order of the filter and FBW is the designed fractional bandwidth.

SIW filter designed on a substrate (ε r =9.9)
The substrate used is alumina with a permittivity of 9.9, a thickness of 254 μm, and tanδ = 0.0003. A 50-Ω microstrip line designed on this substrate at a frequency of 5.24 GHz corresponds to a width of W M = 0.24 mm and therefore this access line can be realized. The impedance matching between the SIW filter and the 50-Ω lines is made by intermediate transitions between them [26][27][28]. The physical dimensions of these transitions control the external quality factors of the filter. The external quality factor Q e can be extracted from the structure shown in Fig. 2, an SIW square cavity (P, D, and W SIW1 = L SIW1 ) coupled to a 50-Ω access line (W M and L M ) via a microstrip transition (W T and L T ). This structure must be well sized to have a resonance frequency of 5.24 GHz (TE 101 mode). The dimensions are obtained by applying the equations and rules adopted in [29][30][31][32][33], namely D = 0.2 mm, P = 0.5 mm, W SIW1 = L SIW1 = 11.8 mm, W T = 4.72 mm, W M = 0.24 mm, and L M = 1.2 mm. The parameter involved in the study of this coupling is the length L T of the taperedmicrostrip transition. The value of Q e is obtained from the simulation and the use of the following equation [34,35]: where f 0 is the resonant frequency of the SIW cavity and Δf ± 90° is the ±90° bandwidth of the SIW cavity. Fig. 3 shows the variation of Q e as a function of L T .  We can see that the external quality factor Q e decreases when the length L T of the tapered-microstrip transition becomes larger and larger. Thus, as required for filter specifications, Q ein = Q eout = 10.6682 is obtained when L T = 15.1 mm. The coupling coefficient M 12 can be extracted from the structure shown in Fig. 4. An SIW square cavity with a resonance at 5.75 GHz coupled to another SIW cavity with a resonance at 5.47 GHz via an iris opening d 12 where f 01 and f 02 are the self-resonant frequencies of the first and second resonators, respectively, and f 1 and f 2 represent the lower and higher resonant frequencies, respectively, obtained from the EM-simulated results. Fig. 5 shows the evolution of the coupling coefficient M 12 as a function of the iris opening d 12 . We can see that the increase of the iris opening produces an increase of the coupling coefficient. Thus, as required for the filter specifications, M 12 = M 23 = 0.08242 is obtained for an iris opening equal to 7.4 mm. The geometrical structure of the third-order directcoupled SIW band pass filter on an alumina substrate (ε r = 9.9) is shown in Fig. 6. The dimensions of this filter are optimized by the HFSS software in order to obtain the desired frequency response (Table 1).
From the simulation results ( Fig. 7 (a)), the filter has a 3-dB bandwidth of 0.41 GHz (a fractional bandwidth of 7.8%) and an insertion loss of 2.43 dB at a centre frequency of 5.24 GHz. It also has a return loss better than 18.5 dB from 5.02 to 5.28 GHz and a rejection level higher than 20 dB from 6.05 to 6.67 GHz. We also note that the group delay of S 21 , shown in Fig. 7

SIW filter designed on a high-permittivity substrate (ε r =90)
The third-order direct-coupled SIW bandpass filter on a high-permittivity ceramic substrate is designed by following the same process of design as for a third-order direct-coupled SIW bandpass filter on a standard alumina substrate (ε r = 9.9). The selected substrate was provided by Trans-Tech. Its relative permittivity is 90, thickness is 254 μm, and the loss tangent is less than 0.0009. The access line that we used on this substrate has a width of W M =0.17mm, which corresponds to a characteristic impedance of 20 Ω at 5.24 GHz. As a result, the 50-Ω lines are eliminated due to the fineness of the corresponding line width (of the order of 5.8μm). Then, using equation (4)  mm, we are able to present the variation of Q e as a function of L T (Fig. 8). We can thus see that the external quality factor Q e obtained by the synthesis, whose value is 10.6682, implies the use of a length of L T = 1.15 mm.
In the same way, for the coupling between the adjacent cavities (M 12 = M 23 ), using equation (5) and the structure of Fig. 4 under the conditions of D = 0.2 mm, P = 0.5 mm, W SIW1 = L SIW1 = 4 mm, W SIW2 = 3.305 mm, L SIW2 = 6 mm, W M = 0.17 mm, and L M = 1 mm, we obtain the variation of the coupling coefficient M 12 as a function of the iris opening d 12 (Fig. 9). We can thus observe that M 12 = M 23 = 0.08242 is obtained for an iris opening equal to 2.68 mm.
The configuration and optimal physical dimensions of the third-order direct-coupled SIW bandpass filter on a high-permittivity ceramic substrate (ε r = 90) are shown in Fig. 10 and Table 2, respectively. We note that the surface area is 12.4 mm × 7.675 mm = 95.17 mm 2 , which represents a considerable miniaturization with a nearly 92% reduction in the surface area compared to the filter on an alumina substrate (Fig. 6). The results obtained with HFSS (Fig. 11) proved that the fractional bandwidth is 8% and the insertion loss is 2.66 dB at the centre frequency of 5.24 GHz. Thus, the return loss is better than 20 dB from 5.09 to 5.35 GHz, the rejection level is higher than 20 dB from 5.7 to 6.6 GHz, and the variation of group delay is less than 0.61 ns in the passband.
These results confirm that the proposed filter on a substrate with a relative permittivity of 90 (Fig. 10) satisfies the required specifications with a very significant size reduction.

DESIGN C-BAND THIRD-ORDER CROSS-COUPLED SIW BANDPASS FILTER WITH CERAMIC SUBSTRATE
This filter must be centered at 5.24 GHz with a fractional bandwidth of 8% and a rejection of 52 dB at 5.77 GHz. The substrate used is also the ceramic substrate with a relative permittivity of 90, a thickness of 254 μm, and tanδ = 0.0009. The coupling structure of this filter is shown in Fig. 12.
Then, by following the same method of design as for the third-order direct-coupled SIW bandpass filter on a high-permittivity ceramic substrate (Fig. 10), we can obtain the results presented in Figs. 8 and 9. From these results, we can extract the dimensions of the coupling elements (L T , d 12 , and d 23 ). Table 3 presents the coupling coefficients to be applied with their correspondence in the physical dimension. The cross-coupling between resonators 1 and 3 is achieved by an iris d 13 (Fig. 13). The cross-coupling coefficient M 13 is obtained from the simulation by [38]- [40]: where f 1 and f 2 also represent the lower and higher resonant frequencies, respectively, obtained from the EM-simulated results.  The geometrical structure and optimal dimensions of the third-order cross-coupled SIW bandpass filter on a high-permittivity ceramic substrate (ε r = 90) are shown in Fig. 15 and Table 4, respectively. Based to the simulated frequency response in HFSS (Fig. 16), the filter has a fractional bandwidth (FBW) of 8% and an insertion loss (IL) of 2.57 dB at a centre frequency (CF) of 5.24 GHz. It also has a return loss better than 20 dB from 5.12 to 5.4 GHz and attenuation of 51.65 dB at 5.77 GHz. In order to examine the precision of the obtained results, we compared them with published results in [41]. Table 5 illustrates the comparison between the third-order cross-coupled SIW bandpass filter on a highpermittivity ceramic substrate (ε r = 90) and the filters presented in [41]. From this comparison, we have demonstrate that the proposed filter (Fig. 15) has low insertion loss, a good upper stopband (30 dB from 5.6 to 6.6 GHz), and a very compact size compared to the SIW filters presented in [41], which are designed on the same high-K substrate (ε r = 90). We conclude that the proposed filter (Fig. 15) has the advantage of compact size that is easy to integrate with other planar circuits and good out-band suppression with simple structure.   This work (Fig. 15) High-K Ceramic (ε r =90)/SIW 3 5.24 8 2.57 30dB 5.6-6.6 GHz 12.4×7.505×0.254

DESIGN C-BAND THIRD-ORDER DIRECT-COUP-LED SUPER-WIDE BANDPASS SIW FILTER WITH A CERAMIC SUBSTRATE
This filter must exhibit performances of a centre frequency of 6.9 GHz with a ripple of 0.1 dB and a fractional bandwidth of 38%. The substrate used is also a ceramic substrate with a relative permittivity of 90, a thickness of 254 μm, and a loss tangent of 0.0009. The coupling structure (Fig. 17), the normalized coupling matrix [m], and the external quality factors (Q ein , Q eout ) of this filter are given below:  Fig. 18 (a) shows the structure of the SIW cavity with a circular hole etched on the top of the metal layer. The dimensions of the SIW cavity are fixed (P = 0.2 mm, D = 0.5 mm, and W SIW1 = L SIW1 = 4 mm) and therefore the resonant frequency depends only on the diameter R 1 of the circular hole. Fig. 18 (b) shows the variation of the resonant frequency as a function of R 1 .
We notice that an increase in the diameter R 1 of the circular hole makes it possible to shift the resonant frequency towards a higher frequency. We can therefore reach the desired frequency (6.9 GHz) by applying a diameter of R 1 = 1.624 mm. Then, using a Conductor Backed Coplanar Waveguide (CBCPW) as a transition to connect a microstrip line to an SIW square cavity with a circular hole etched on the top of the metal layer ( Fig. 19 (a)), we can extract the external quality factor Q e . The parameter involved in the study of Q e is the length L CPW of CBCPW transition. Fig. 19   For the calculation of M 12 , we simulate the structure of Fig. 20 (a): two resonators coupled by an iris opening. Each resonator consists of an SIW square cavity with a circular hole etched on the top of the metal layer. Then, using equation (8) for each variation of the iris opening d 12 with the conditions D = 0.2 mm, P = 0.5 mm, W SIW1 = L SIW1 = 4 mm, R 1 = 1.624 mm, W M = 0.28 mm, and L M = 0.88 mm, we can present the evolution of M 12 as a function of d 12 (Fig. 20 (b)). The results presented in Fig. 19 (b) and Fig. 20 (b) make it possible to deduce the initial dimensions to be applied for the coupling elements (L CPW and d 12 = d 23 ). The configuration and the dimensions of the filter, after optimization by HFSS, are shown in Fig. 21 and Table  6, respectively.
The simulated frequency response by HFSS (Fig. 22) shows that the fractional bandwidth (FBW) is 38% at the centre frequency (CF) of 6.9 GHz and the return loss is better than 16 dB from 5.72 to 8.22 GHz. Thus, the minimum insertion loss (IL) is 1.26 dB and the ripple in the pass band is less than 0.18 dB. Compared with the filters using high-K ceramic [42], [43] as list in Table 7, it can clearly be seen that the proposed filter (Fig. 21) has better performances, including very low ripple, lower insertion loss und greater fractional bandwidth. Also, the proposed design gets a more compact circuit size than other designs.

CONCLUSION
New miniature third-order SIW bandpass filters on a high-permittivity ceramic substrate for the C-band are presented in this article. The use of a ceramic substrate with a relative permittivity of 90 allowed us to reduce the surface area of the SIW filter by nearly 92% compared to the SIW filter on alumina substrate (ε r = 9.9). The simulations results also demonstrate that this reduction in size does not influence the performances of the filter, that is to say without strong degradation of the insertion losses, and from here we conclude that such particularly high-permittivity ceramics are very attractive for frequency applications between UHF and C-band. We have also proved that the use of a cross-coupling between the resonators allows improvement of the rejection. Then, we have proposed a novel miniature C-band super-wide bandpass SIW filter by using a high-permittivity ceramic substrate and circular holes etched on the top of the metal layer. The simulation results of the proposed filters are encouraging and filled the design criteria for radio frequency (RF) such as low insertion losses, ease of fabrication, and integration with other RF circuits in communications systems. The solution proposed in this research work is based on a ceramic substrate with a permittivity of 90, which allowed us to reduce size and make SIW even more attractive. This confirms the feasibility of a SIW solution with a high-permittivity ceramic substrate for the design of filters intended to equip the payload of a satellite. Since C-band is mostly used for satellite and Radar applications. So, proposed SIW filter may be a good candidate to enhance the performance of Satellite application devices. Futures works will be interesting in SIW for coupled interlinked split ring resonator based epsilon negative metamaterial with high effective medium ratio for multiband satellite and radar communications. This work (Fig. 21) High-K Ceramic (ε r =90)/SIW 3 6.9 38 1.26 0.18 13.96×4.36