ABSTRACT

In this paper, a combination of slot ring and complementary split ring resonators has been proposed to achieve quad band bandpass filter response in waveguide. The resonators have been formed on a Roger RO 4350 substrate with their common centre at the middle of the substrate. Two such structures have been placed on the transverse plane of a WR–90 waveguide at a distance of 8.41 mm to achieve the dual pole quad band response. Necessary simulations have been carried out using Ansoft HFSS (version 14). Measured result shows a quad band bandpass response with centre frequencies at 8.51/9.46/10.47/12.05 GHz and 3-dB bandwidth 0.256/0.2287/0.445/ 0.755 GHz, respectively. Approximate equivalent circuit of the filter is also proposed. The filter is 10 mm long.

KEYWORDS

Bandpass filter; Complementary split ring resonator (CSRR); Quad band; Split ring resonator (SRR); Waveguide

1. INTRODUCTION

Due to their numerous advantages like high power handling capability, low loss, etc. waveguide filters are still in use in radar and satellite communication systems. However, they are relatively heavy and bulky. To get rid of these disadvantages, recently, much attention has been paid on the design compact, light-weight waveguide fil- ter. In addition, since present day radio frequency (RF) systems are becoming multifunctional, multiband filter response is also in demand.

In order to achieve compactness in waveguide filter, E- plane metal septa was first proposed by Konishi and Uenakada [1]. Later, E-plane substrate insert technology was used to design compact single and dual band bandpass filter [2,3]. Split ring resonators (SRRs) complementary split ring resonators (CSRRs) were also used in rectangular waveguide to design compact, dual band bandstop and bandpass filters [4–12].

In order to achieve multiple passband in waveguide, many techniques have been proposed by many researchers. Dual band bandpass response was achieved by using coupling matrix [13] and cascading wideband filter with a narrowband bandstop filter [14]. In line type and conical type dual band elliptic waveguide filters were reported in [15,16]. Dual mode was also used to achieve dual band response [17]. Frequency transformation was investigated to design multi-band bandpass filters [18].

This paper presents a compact quad band waveguide bandpass filter based on a planar structure insert. The structure consists of two slot rings and three CSRRs, and has been formed on Roger RO 4350 substrate with their common centre at the middle of the substrate. Two such planar inserts have been placed on the transverse plane of a WR–90 waveguide at 8.41 mm distance to achieve the dual pole quad band response. The measured response shows a quad band bandpass response with centre frequency at 8.51/9.46/10.47/12.05 GHz. The total length of the filter is 10 mm.

2. RESONATOR DESIGN AND ANALYSIS

Schematic diagram of the proposed planar insert and its placement in WR–90 rectangular waveguide is shown in Figure 1. The resonator has been designed on Roger RO 4350 dielectric substrate of thickness 0.762 mm, copper thickness 0.035 mm, relative dielectric constant 3.66, and loss tangent 0.004.

Since both the CSRR and slot ring resonator behave as parallel LC resonator in shunt of a transmission line, the equivalent circuit of the proposed structure can be represented by a series connection of five parallel LC resonators and coupling inductances and capacitances between them. The presence of large number of resonators and their coupling inductances and capacitances makes the equivalent circuit complicated and difficult to analyse.

Figure 1: Schematic diagram of (a) combination of CSRRs and slot ring resonator with its dimensions: R0 = 2.1, R1 = 2.4, R2 =

2.7, R3 = 3, R4 = 3.3, R5 = 3.6, R6 = 3.9, R7 = 4.2, R8 = 4.5, R9 = 4.8, W1 = 4.4, W2 = 3.8, W3 = 2 (all are in mm), and (b) placement

of the CSRRs and slot ring resonator into the transverse plane of WR–90 waveguide

In order to simplify the circuit, weak coupling case may be approximated where it is assumed that the couplings between these CSRR and slot ring resonators are weak. Under such circumstances, the equivalent circuit of the proposed resonator reduces to a series connection of five parallel LC resonators in shunt of a transmission line, as shown in Figure 2.

For 500 Ohm (characteristic impedance of waveguide at 10 GHz) impedance system, the values of L and C can be calculated using the relations provided in [11,12] after frequency scaling, which is given by

Table 1: L and C values for the desired data

In the above equations, Z0i and j S21ðjv0Þ j represents the characteristic impedance of the waveguide and magnitude of S21 at the resonance frequency f0, respectively. B3dBi represents the 3-dB bandwidth of the passband. The calculated lumped element values are tabulated in Table 1.

The simulated scattering parameters of the structure in Figure 1(b) and its equivalent circuit in Figure 2 are compared in Figure 3. The figure reveals that the responses are very close to the each other, which justifies the weak coupling approximation, made earlier, and the equivalent circuit in Figure 2.

To understand the appearance of the bands, the surface current distribution on the structure has been studied

Figure 4: (a–d) Surface current distribution on the unit cell at 8.52, 9.46, 10.52, and 12.09 GHz

and plotted in Figure 4. Figure 4(a) reveals that at 8.52 GHz, maximum surface current is distributed around the two outermost CSRR, while there are negligible surface current on the rest of the CSRR and slot ring resonators. This signifies that the two outermost CSRR are responsible for the band at 8.52 GHz. Similarly, by observing the surface current distributions in Figure 4

(b) – (d), it can be said that second and third outermost CSRRs are responsible for the band at 9.46 GHz, innermost CSRR and outermost ring resonators are responsible for the band at 10.52 GHz, and both the ring resonators are responsible for the band at 12.09 GHz. The figure also reveals that as we move towards the higher frequency resonances, the excitation shifts towards the inner slot ring resonators from outermost CSRRs.

Once the structure has been characterized, the next step is to arrange them to develop a dual pole, quad band waveguide bandpass filter. To do this, two of such planar inserts have been placed on the transverse plane of a WR–90 waveguide at an optimized distance (“l”) 8.41 mm, as shown in Figure 5(a). In the figure “h” represents the thickness of the dielectric substrate. In practice, the design of the filter requires that there should be a quarter wavelength (90o) separation between the inserts (or resonators) so that an inverter is formed between them. Since the guided wavelength of TE10 mode at 10 GHz with Roger RO 4350 as dielectric is 15.68 mm, the substrate thicknesses (0.762 mm) contribute 16.69o to the 90o electrical length of the inverter. Therefore, the rest of 73.31o must be provided by the air dielectric section. The guided wavelength of TE10 mode at 10 GHz with air dielectric is 39.75 mm, which requires that the physical length of the air dielectric section should be 8.09 mm. However, due to the presence of the higher

Figure 5: Proposed dual pole quad band bandpass filter (a) 3D view of the proposed filter and (b) lumped element equivalent circuit (characteristics impedance of transmission line inverter = 500 Ohm at 10 GHz)

order modes around the resonator and around substrateair dielectric boundary requires some optimization in length which resulted l = 8.41 mm. The lumped element equivalent circuit of the structure is shown in Figure 5(b).

3. RESULT AND DISCUSSION

The proposed waveguide filter has been simulated using Ansoft HFSS (version 14). To validate the simulation result, next, it has been fabricated and measured. The measurement has been carried out using calibrated Keysoft PNA vector network analyzer (Model No: N5221A). The photograph of the fabricated insert and its integration into the WR–90 waveguide is shown in Figure 6.

Simulated and measured frequency responses of the magnitude of scattering parameters of the proposed filter have been plotted and compared in Figure 7. To validate the equivalent circuit model, the simulated scattering parameters (magnitude) of the circuit

Figure 6: Photograph of (a) fabricated combination of CSRRs and slot ring resonator, and (b) integration into WR–90 rectangular waveguide

Figure 7: Simulated and measured frequency response of the proposed dual pole quad band bandpass filter

Table 2: Comparison of the simulated and measured resonant frequency, 3-dB bandwidth in band insertion and return loss

of Figure 5(b) also have been plotted in the same figure. The responses are in good agreement which validates the simulation as well as the equivalent circuit model. The results are summarized in Table 2. The slight deviations in the simulated and measured results are due to probable errors in the placement and alignment of the inserts inside the waveguide and losses in N-type coaxial to waveguide adaptors, used in the measurement.

A comparison of the characteristics of proposed quad band bandpass filter with few other reported filters is tabulated in Table 3.

4. CONCLUSION

This paper presents a compact dual pole, quad band waveguide bandpass filter using a new type of insert. The insert consists of two slot rings and three CSRRs. The literature survey reveals that up to dual band bandpass frequency response has been achieved using CSRR loading in waveguide. In that respect, the proposed structure introduces two more passbands. The design procedure and equivalent circuit model have been presented and explained. The measured results show that the four bands are centred at 8.51, 9.46, 10.47, and 12.05 GHz, respectively, and hence the filter may find applications in radiolocation systems, airborne, and naval radars. The total length of the proposed filter is 10 mm long which is compact as compared to other reported filters.

ACKNOWLEDGMENTS

The authors will like to thank the Department of Science and Technology (DST), Government of India for their instrumental support through FIST Project.