Fig. 1.
Different steps to design the third-order bandpass hexagonal SIW filter with cross-coupling.
Table 1.
Hexagonal SIW filter's target specifications.
| Parameter | Value |
|---|---|
| Filter order | 03 |
| Center frequency | 8.15 GHz |
| −3 dB bandwidth | 375 MHz |
| Insertion loss (IL) | < 0.1 dB |
| Passband ripple | 0.0431 |
| Passband return loss | −20 dB |
| FZT (Frequency of zero transmission) | 8.241 GHz |
| Filter function | Tchebychev |
| g0 | g1 | g2 | g3 | g4 |
| 1 | 1.0316 | 1.1474 | 1.0316 | 1 |
Table 2.
Values of capacitance C1, inductance L1, impedance Zi.
| Zi | L1, C1 | f |
|---|---|---|
| Z = 50 Ω | L1 = 56.67 nH | 7.9 GHz |
| Z23 = 62.09 Ω | C1 = 0.0071 pF | |
| Z12 = 62.09 Ω |
Fig. 2.
Total equivalent circuit of the third-order bandpass hexagonal SIW filter with cross-coupling.
Fig. 3.
Optimal EM response for a single-band BPF with a single TZ in the upper stopband.
Fig. 4.
Initial configuration of a first-order hexagonal SIW filter.
Table 3.
Dimensions of the first-order hexagonal SIW filter.
| Parameters | d | p | Ifeed | wfeed | wgap | Lz | Wsiw |
|---|---|---|---|---|---|---|---|
| Values [mm] | 2 | 2.98 | 2.9 | 2.6 | 1.5 | 8.4 | 15.98 |
Fig. 5.
Group delay of the first hexagonal SIW resonator after optimization (p = 1.05 mm, d = 5 mm, wgap = 1.5 mm, Ifeed = 2.8 mm, Wfeed = 2.8 mm, Lz = 8.4 mm).
Fig. 6.
Quality factor of a resonator Qe versus wfeed of the first hexagonal SIW resonator.
Fig. 7.
Representation of the electric field distribution of the fundamental modes in a hexagonal cavity resonator at f = 8 GHz, (a) φ = 90°, (b) φ = 65°, (c) φ = 45°.
Fig. 8.
The second-order bandpass hexagonal SIW-DGS filter employing mixed coupling (Lz = 8.4 mm, Ifeed = 1.5 mm, wfeed = 2.8 mm, wgap = 1.5 mm, d = 0.6 mm, p = 1 mm, g13 = 5 mm, L = 10 mm, w = 0.5 mm, s = 0.45 mm).
Fig. 9.
S-parameters of the proposed conventional SIW-DGS filter.
Fig. 10.
Extracted coupling coefficient K versus g12 for the second-order bandpass hexagonal SIW-DGS filter.
Table 4.
Coupling and iris widths gij of the third-order hexagonal SIW-DGS bandpass filter.
| Mi,i+1 | K | gij [mm] |
|---|---|---|
| M12 = M23(0.0453) | 0.0465 | g12 = g23 = (5.22) |
| M13(0.0621) | 0.0623 | g13 = (5.6) |
Fig. 11.
Representation of the electric field distribution of the second-order hexagonal SIW-DGS filter at f = 8 GHz, (a) φ = 0°, (b) φ = 45°, (c) φ = 90°, (d) φ = 180°.
Table 5.
The initial dimensions of the third-order passband hexagonal SIW-DGS filter.
| Parameters | Symbol | Value [mm] |
|---|---|---|
| Microstrip line | Width | W50 = 1.2 |
| L50 = 5.6 | ||
| SIW characteristics | Width | Wsiw = 15.98 |
| Pitch of vias | p = 1 | |
| Diameter | d = 0.5 | |
| Iris characteristics | Distance | g12 = 5.2 |
| g13 = g23 = 5.6 |
Fig. 12.
The third-order bandpass hexagonal SIW-DGS filter design with cross-coupling.
Fig. 13.
EM response for the third-order bandpass hexagonal SIW-DGS filter with cross-coupling.
Fig. 14.
Comparison of the EM response of the third-order bandpass hexagonal SIW-DGS filter extracted using CM and HFSS.
Fig. 15.
Simulated electric field distributions at the resonance frequency at f = 8 GHz, (a) φ = 0°, (b) φ = 45°, (c) φ = 90°, (d) φ = 180°.
Fig. 16.
The photograph of the implemented third-order bandpass hexagonal SIW-DGS filter, (a) top view and (b) bottom view.
Fig. 17.
Measured vs simulated results of the third-order bandpass hexagonal SIW-DGS filter with (a) insertion loss and (b) return loss.
Table 6.
Comparison of calculated, simulated, and measured results for the developed third-order hexagonal SIW filter.
| Operation | Calculation | Simulation | Measurement |
|---|---|---|---|
| Center frequency [GHz] | 7.9 | 7.903 | 7.898 |
| Lower −3dB Cut-off [GHz] | 0.1 | 1.58 | 1.62 |
| Bandwidth [MHz] | 279.66 | 270 | 272 |
Table 7.
Comparison of the designed third-order hexagonal SIW-DGS filter to other reported filter designs.