**7. Miniaturized and selective SIW bandpass filter with S-shaped broadside-coupled complementary split-ring resonators (BC-CSRR)**

This work [15] proposes the design of a substrate integrated waveguide (SIW) bandpass filter (BPF) incorporated with a novel broadside-coupled complementary split-ring resonator (BC-CSRR). The complementary double S shape as metamaterial is carved on the top and broad bottom walls of SIW with orientation 180<sup>o</sup> to each other. The proposed filter is designed for X band using substrate alumina with a relative permittivity of 9.8 and height of 0.508 mm. Further, the width of the SIW, WSIW is set to 5.4 mm to keep the nominal cutoff frequency of the waveguide to 10 GHz using SIW design equations.

#### **7.1 Analysis and design of metamaterial**

For designing the proposed S-shaped metamaterial, a double S-shaped structure was placed one above the another in an antisymmetrical manner over a dielectric layer forming a shape of 8 [16]. S on both sides of the dielectric forms metamaterial that simultaneously provides negative permeability and permittivity. The side length of the S shape is kept equal to λg/4 (A = 2.25 mm), and thickness T is kept equal to 0.35 mm, as shown in **Figure 22**.

#### **Figure 23.**

*Geometry of double "S"-shaped structure with microstrip line at the bottom.*

**Figure 23** depicts the setup to get S parameters of complementary S-shaped metamaterial using HFSS. For this, two-layered dielectric substrates (alumina) having relative permittivity 9.8 of thickness 0.508 mm are stacked over each other. The Sshaped structure is placed on the opposite side of the top dielectric substrate one above the other (in a complementary manner) to form **Figure 8**. A 50 Ω microstrip line is provided at the bottom of the lower substrate.

In HFSS, first, simulate the metamaterial structure by providing the solution frequency. Then get S-parameters (S11, S21) in tabular form as follows:

Result- > Create Modal Simulation Data Report - > Data Table.

Create a data table for S(1,1) containing magnitude and angle in rad (phase). Similarly, create a data table for S (2,1). These files have extension .csv (commaseparated values).

Export these .csv files to the same folder where MATLAB code is kept. Now, call these files S(1,1).csv and S(2,1).csv in parameter extraction MATLAB code [17] in function referred as DATA\_READ specifying the path locations of files.

*Analysis and Design of Miniaturized Substrate Integrated Waveguide CSRR Bandpass Filters… DOI: http://dx.doi.org/10.5772/intechopen.104733*

**Figure 24.** *Graph of real values of μ and ε.*

Successful execution of MATLAB code [17] for the parameter extraction results led to permittivity and permeability, as shown in **Figure 24**. The graph indicates that the permeability and permittivity are negative simultaneously for the frequency range between 7.25 GHz and 9.15 GHz. It illustrates that the structure has metamaterial characteristics for the frequency range between 7.25 GHz and 9.15 GHz.

#### **7.2 Design of single-stage SIW BC-CSRR bandpass filter**

**Figure 25** shows single-stage BC-CSRR BPF, which has a pair of identical "S" shaped etched on the SIW top and broad bottom walls but at 180° to each other. A tapered microstrip feed line has been used for exciting the SIW. The design parameters are taken as: WSIW = 5.4 mm, LSIW = 4.2 mm, P = 1.6 mm, D = 0.8 mm, LT = 4 mm, WT = 2 mm, LM = 2 mm, WM = 0.50 mm, A = 2.25 mm, and T = 0.35 mm.

**Figure 26** shows the equivalent circuit of the single-stage BC-CSRR BPF. The equivalent circuit of the S-shaped SRR structure is given by [18], in which S-SRR is modeled by a series L-C circuit in each half ring of the eight-shaped structure through a common capacitor. Since CSRR is complementary to the SRR structure, the

**Figure 25.** *Schematics of single-stage SIW BC-CSRR BPF.*

**Figure 26.**

*Equivalent circuit of BC-CSRR BPF.*

**Figure 27.** *Frequency response (S11) of an equivalent lumped circuit of single-stage BC-CSRR SIW filter.*

**Figure 28.** *Frequency response of single-stage BC-CSRR SIW filter.*

*Analysis and Design of Miniaturized Substrate Integrated Waveguide CSRR Bandpass Filters… DOI: http://dx.doi.org/10.5772/intechopen.104733*

equivalent circuit of single unit BC-CSRR will be dual of S-SRR. The metallic vias of the SIW are modeled as Lv.

**Figure 27** shows the simulated result of the equivalent lumped circuit using ADS. **Figure 28** shows the frequency response of single-stage BC-CSRR incorporated SIW filter. The figure shows that by etching the S structure in SIW, a passband is obtained with a center frequency of 8.2 GHz and 3-dB bandwidth of 0.15 GHz. The maximum return loss is 21.55 dB, and insertion loss is 0.32 dB at the center frequency. It can be seen that the resonant frequency of the SIW BC-CSRR element is well below the cutoff frequency of the original SIW, causing its miniaturization.

#### **7.3 Design of two-stage SIW BC-CSRR bandpass filter**

In order to improve roll-off factor and order of filter, cascaded connection [19] of two identical BC-CSRR structures is used to form two-stage BPF. **Figure 29** shows the

**Figure 29.** *Schematics of two-stage SIW BC-CSRR BPF.*

**Figure 30.** *Parametric analysis of return loss for varying side length "a."*

structure of two-stage BC-CSRR BPF with design parameters taken as:WSIW = 5.4 mm, LSIW = 4.2 mm P = 1.6 mm, diameter of via D = 0.8 mm, LT = 4 mm, WT = 2 mm, LM = 2 mm, WM = 0.50 mm, A = 2.25 mm, T = 0.35 mm, and L = 4.25 mm.

The distance (L) between two BC-CSRRs has a vital influence on the performance of the proposed two-stage filter. **Figure 30** shows the parametric analysis of return loss with varying values of L (for L = 3.25, 3.75, 4.25, 4.75, 5.25 mm). It is clear from **Figure 30** that the filter shows optimum performance for L = 4.25 mm. For other small or big values of L, its response becomes undesirable.

**Figure 31a** and **b** depicts the current distribution in passband and stopband, respectively. As seen from the current distribution, it is clear that when the filter is passing the signal, the center resonator is resonant and has a large current that couples the signal through to the output.

**Figure 32** shows the frequency response of two-stage BS-CSRR. From the response, it can be observed that a passband with 3-dB bandwidth of 0.385 GHz is obtained. The simulated insertion loss is 0.32 dB, and the simulated roll-off rate at the lower and upper edge of the passband is calculated to be 78.26 dB/GHz and 65.5 dB/ GHz, respectively. The maximum return loss value is 24.85 dB at the center frequency of 8.4 GHz with a 3-dB bandwidth of 0.38 GHz.

**Figure 31.** *Current distribution in (a) passband and (b) stopband.*

**Figure 32.** *Frequency response of single-stage BC-CSRR SIW filter.*

*Analysis and Design of Miniaturized Substrate Integrated Waveguide CSRR Bandpass Filters… DOI: http://dx.doi.org/10.5772/intechopen.104733*

**Figure 33.**

*(a) Top and (b) bottom view of the fabricated bandpass filter.*

**Figure 34.** *Comparison of (a) the simulated and measured result S parameters and (b) VSWR.*

### **7.4 Fabrication and results**

The proposed filter is fabricated using substrate material alumina with a relative dielectric constant of 9.8, tan δ = 0.001, and thickness of 0.508 mm to validate the result. **Figure 33a** and **b** shows the photograph of the top and bottom layer of the assembled filter with overall dimensions as 10 mm (length excluding transition) 8.5 mm (width).

The scattering parameters of the fabricated filter are measured by a vector network analyzer Anritsu S 820E. A two-port SOLT (short- open- load and thru) calibration has been done to consider cable losses between the VNA and the DUT. The measured and HFSS simulated results are compared and depicted in **Figure 34a**. It can be seen that the measured passband of the filter is from 8.20 GHz to 8.74 GHz with 3-dB bandwidth of 0.54 GHz. The maximum return loss value is 17.2 dB with an insertion loss of 0.92 dB in almost the entire passband. It achieves good attenuation (>20 dB) in the upper stopband. The measured roll-off rate is 58.5 dB/GHz and 60.2 dB/GHz at the lower and upper edge of the passband, respectively. **Figure 34b** depicts the simulated and measured VSWR plot for the entire range.
