Keywords

1 Introduction

Dual-band RF and microwave bandpass filters (DBBPFs) are subject of interest in recent days due to the growing demand for dual-band appliances. A DBBPF is an essential component in such systems. A conventional DBBPF can be designed by cascading two different bandpass filters (BPFs) having separate passbands, by embedding a different resonator into the primary resonator of the BPF and by the separation of various resonant modes generated by a multimode resonator. The first method is very straightforward and easy to implement, but such kind of DBBPF circuits is greater in size compared to others, and therefore, they are very rarely used nowadays. The second and third methods are prevalent for DBBPF designing. Some recent research articles related to different DBBPFs are shown in [1,2,3,4,5,6,7,8,9], which are implemented using [1] parallel-coupled stepped impedance resonators (SIRs), [2] microstrip line resonator loaded with an open-loop ring in one end which acts as an embedded resonator, [3] multimode E-shaped resonator, [4,5,6] dual-mode resonators, [7, 8] spiral resonators and [9] end-coupled resonators loaded with metallic via holes, respectively.

Although undoubtedly enormous research is already conducted on DBBPFs, further research is still required for the implementation of cost-effective and compact DBBPFs with good dual passband performance. In this paper, a novel and compact DBBPF is proposed using a dual-mode resonator, folded single-mode resonator and an etched ground structure (EGS). The dual-mode resonator generates the first passband near 2.4 GHz, and the folded microstrip line resonator produces the second passband near 3.5 GHz. The insertion loss in both of the passband is reduced by incorporating an EGS in the ground plane, which improves the cross-coupling between the resonators and feedline. All the resonators are analyzed using classical odd–even-mode technique. The proposed DBBPF is simulated in IE3D with RO4003C substrate (\( \varepsilon_{r} \) = 3.38, \( h \) = 0.508 mm, \( \tan \theta \) = 0.0018), which provides less than 1-dB insertion loss in both of the passbands and more than 20-dB rejection level up to twice the midband frequency.

2 Design and Analysis of the Proposed BPF

The proposed DBBPF is depicted in Fig. 1. All the labeled dimensions of the BPF are listed in Table 1. The BPF only consumes 18.75 × 9.55 mm2 core layout area. The coupling architecture of the DBBPF is illustrated in Fig. 2. The source and load are directly coupled to each other, whereas they are in cross-coupling mode with the dual-mode resonator (resonator 1) and folded SIR (resonator 2).

Fig. 1
figure 1

a Proposed DBBPF; b EGS (bottom)

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Table 1 DBBPF dimensions
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Fig. 2
figure 2

Coupling architecture of the proposed BPF

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The proposed DBBPF is constructed using a fundamental dual-mode resonator of Fig. 3 and a microstrip line SIR of Fig. 4. Using classical transmission line and odd–even-mode techniques [10], the resonant frequencies of the dual-mode resonator in Fig. 3 are approximately calculated from its odd–even-mode equivalent circuits, which are shown in Eqs. (1) and (2), respectively.

Fig. 3
figure 3

a Dual-mode resonator; b odd-mode circuit; c even-mode circuit

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Fig. 4
figure 4

Odd- and even-mode resonant characteristics

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$$ f_{1odd} = \frac{c}{{4\left( {l_{1} + 2b_{1} + b} \right)\sqrt {\varepsilon_{e} } }} $$
(1)
$$ f_{1even} = \frac{c}{{4\left( {l_{1} + 2b_{1} + b + b_{2} } \right)\sqrt {\varepsilon_{e} } }} $$
(2)

[where ‘\( c \)’ is the velocity of light, ‘\( \varepsilon_{e} \)’ is the effective dielectric constant, and \( \left( {l_{1} + 2b_{1} + b} \right) \) and \( \left( {l_{1} + 2b_{1} + b + b_{2} } \right) \) are average lengths of the odd- and even-mode resonators.]

From Eqs. (1) and (2), the odd- and even-mode resonant characteristics are extracted by considering RO4003C microstrip transmission line, which are depicted in Fig. 4. It can be found that the resonant frequencies f1odd and f1even are closely spaced, and they can be separated by increasing the length of the dimension ‘b2.’

The second resonator of Fig. 1 is the folded version of a basic SIR shown in Fig. 5. The resonance frequency of the SIR is approximately calculated by using the transmission line techniques mentioned in [10], which is shown in Eq. (3). The tunability characteristic of the resonance frequency is depicted in Fig. 6, which indicates a monotonical decay of the resonance frequency as the average resonator length is increased.

Fig. 5
figure 5

Stepped impedance resonator (SIR)

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Fig. 6
figure 6

Resonant characteristic of the SIR

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$$ f_{2} = \frac{c}{{2\left( {l_{2} + 4c_{1} + 2c_{2} } \right)\sqrt {\varepsilon_{e} } }} $$
(3)

3 Results and Discussion

The simulated scattering response of the proposed DBBPF (Fig. 1) in the presence and absence of EGS is depicted in Fig. 7. The initial dimensions of the DBBPF are extracted using Eqs. (1)–(3), and thereafter, some manual optimization is performed to get better results. At first, the resonant modes f1odd and f1even are set near to 2.4 GHz by adjusting the dimensions L1, L2, w2, a and the radius R of the dual-mode resonator of Fig. 1. The center frequency of the second passband is set near to 3.5 GHz by adjusting the dimensions L3, L4 and w4, respectively.

Fig. 7
figure 7

Simulated scattering parameters

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Figure 8 depicts the zoomed view of the DBBPF scattering response in the presence and absence of EGS. Although it can be found that the transmission zero locations are somewhat changed due to the inclusion of EGS in the ground plane, its effect in the passband can be more accurately observed in Fig. 8. The insertion loss in both of the passband is reduced near to 0.7 dB, which was around 1.2 dB for the previous case. The fractional bandwidth (FBW) in the passbands is 4.2% and 2%, respectively, which ensures achievement of high selectivity in both of the passbands.

Fig. 8
figure 8

Simulated scattering parameters zoomed view

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This improvement in the passband performance can be explained by the current distribution patterns illustrated in Fig. 8. It can be found that the unused resonator in each of the frequency bands is properly deactivated due to the inclusion of EGS and therefore more power is transmitted in that specified passband. The folded SIR at 2.4 GHz is better deactivated in Fig. 9c compared to Fig. 9a. On the other hand at 3.5 GHz, the dual-mode resonator in Fig. 9d is better deactivated compared to Fig. 9b; thereby, more power transfer in each of the passband is obtained.

Fig. 9
figure 9

Current distribution: a at 2.4 GHz without EGS; b at 3.5 GHz without EGS; c at 2.4 GHz with EGS; d at 3.5 GHz with EGS

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4 Conclusion

In this paper, a compact and novel DBBPF based on dual-mode resonator, folded SIR and EGS is proposed. The simulated DBBPF provides high selectivity in the both of the passbands with 20-dB outside-band isolation and less than 1-dB insertion loss in the operating frequencies (2.4, 3.5 GHz). The proposed BPF is suitable for WLAN (2.4 GHz) and WiMAX (3.5 GHz) applications.