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A Dual-Band Waveguide Bandpass Filter with Adjustable Transmission Zeros

Fig. 9. Dual-pole dual-band bandpass ¯lter.

Fig. 10. Simulated frequency responses of the dual-band dual-pole waveguide bandpass ¯lter.

frequencies around 8.41 GHz and 11.06 GHz and respective 3 dB bandwidths of 00.54 GHz and 0.58 GHz.

3. Introduction of Transmission Zeros

Frequency responses Fig. 10 show poor passband to stopband transition, especially at lower and higher frequency ends. To improve these transitions, two asymmetrical slots have been introduced in the structure, as shown in Fig. 11. Simulated S-parameters of the resonators in Fig. 5 (without asymmetric slot pair) and Fig. 11 (with asymmetric slot pair) are plotted and compared in Fig. 12. The ¯gure reveals that two additional TZs have been introduced in the responses at the lower and higher frequency ends due to the insertion of the asymmetric slots.

The introduction of asymmetric slots in the structure introduces two additional parallel LC resonators in series with the equivalent circuit of Fig. 7. Thus the

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A. Bage & S. Das

Fig. 11. Proposed resonator structure.

Fig. 12. Comparison of the simulated frequency responses of the resonators in Figs. 5 and 11.

structure in Fig. 11 behaves as a series of four parallel resonators. Since a parallel resonator behaves as an inductor/capacitor at a frequency other than the resonance frequency, the equivalent circuit of the structure behaves as a series combination of four inductors and/or capacitors (or as a series LC network) at frequencies other than the resonance frequencies of the four parallel resonators. At resonance, the equivalent series LC network results in a shunt short-circuit path and introduces TZ in the response. It may be noted that the values of the inductance and capacitance of the equivalent series LC network are not constant throughout the band; instead they depend upon the inductive/capacitive behavior of the individual parallel resonator. As the frequency crosses the resonance frequency of a parallel resonator, its behavior changes between inductive and capacitive and the L, C values of the equivalent series LC network change. Therefore a new TZ is obtained.

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A Dual-Band Waveguide Bandpass Filter with Adjustable Transmission Zeros

(a)

(b)

(c)

Fig. 13. Demonstration of the independent control of the transmission zeros when (a) L4 varies

(L1 ¼ L2 ¼ 6; G1 ¼ 0:7, G3 ¼ 0:6; G4 ¼ 1; L3 ¼ 4:35 and L5 ¼ 7:8), (b) L5 varies (L1 ¼ L2 ¼ 6, G1 ¼ 0:7, G3 ¼ 0:6, G4 ¼ 1, L3 ¼ 4:35 and L4 ¼ 13:5) and (c) G4 varies (L1 ¼ L2 ¼ 6, G1 ¼ 0:7, G3 ¼ 0:6, L3 ¼ 4:35, L4 ¼ 13:5 and L5 ¼ 7:8). All dimensions are in mm.

To demonstrate the independent control of the TZs, the parametric analysis of the structure has been carried out for di®erent slot dimensions (L4, L5 and G4). The results are plotted in Fig. 13. Figure 13(a) reveals that with the increase in L4, the upper and middle TZs remain almost constant at 11.7 GHz and 9.8 GHz, respectively, but the lower TZ varies from 8.97 GHz to 7.8 GHz. Figure 13(b) reveals that with the increase in L5, the lower and middle TZs remain almost constant at 8.5 GHz and 9.9 GHz, respectively, but the upper TZ varies from 11.06 GHz to 12.95 GHz. Finally, Fig. 13(c) reveals that as G4 varies from 0.3 mm to 1.5 mm, the lower and upper TZs are almost constant at 8.9 GHz and 11.1 GHz, respectively, whereas the middle transmission zeros vary from 9.9 GHz to 10.4 GHz.

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A. Bage & S. Das

4. Results and Discussion

To construct dual-pole waveguide bandpass ¯lter with multiple TZs, two symmetrical C-shaped resonators loaded with stubs and asymmetrical slot resonators have been analyzed. The simulation results of di®erent types of resonator have been shown in Fig. 14. The numerical simulation has been carried out using CST Microwave Studio (version 14). Based on these, Table 1 has been provided with the relevant information of both the resonators.

Once these two di®erent resonators have been analyzed, next step is to integrate them into standard WR-90 rectangular waveguide to achieve a dual-pole dual-band with multiple TZs. The 3D model of the proposed ¯lter is shown in Fig. 15. The ¯gure reveals that resonators have been placed on the transverse plane of a WR-90 waveguide at an optimized distance of 8.41 mm. The fabricated picture of the proposed ¯lter is shown in Fig. 16.

The fabricated ¯lter has been measured for its scattering parameters using a calibrated Keysight PNA vector network analyzer (model: N5221A). Magnitude responses of the simulated and measured scattering parameters have been plotted

(a) (b)

Fig. 14. Simulated results of (a) ¯rst resonator and (b) second resonator.

Table 1. Resonators' dimensions with their S-parameter characteristics.

					Resonant
Resonator			Dimensions (mm)	TZs location (GHz)	frequency (GHz)
First resonator	L1	¼ L2	¼ 6, L3 ¼ 4:35; L4 ¼ 16,	8.0433/9.8683/11.892	8.7927/11.011
		L5 ¼ 7:8, G1 ¼ 0:6, G2 ¼ 0:7,
		G3 ¼ 1, G4 ¼ 1, W1 ¼ 0:3, W2 ¼ 1
Second resonator	L1	¼ L2	¼ 6, L3 ¼ 4:35; L4 ¼ 13:5;	8.5541/9.8485/11.67	8.7834/11.031

L5 ¼ 8:1, G1 ¼ 0:6; G2 ¼ 0:7;

G3 ¼ 1, G4 ¼ 1; W1 ¼ 0:3; W2 ¼ 1

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A Dual-Band Waveguide Bandpass Filter with Adjustable Transmission Zeros

Fig. 15. The 3D model of proposed ¯lter.

Fig. 16. Photograph of the fabricated ¯lter.

Fig. 17. Measured and simulated frequency responses of the proposed ¯lter.

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