Current advances in modern wireless communication systems have created the demand for smaller, more reliable and low cost microwave components. Meanwhile, many communication systems operate in dual-bands, which necessitate complicated technologies to realize such components. Dual-wideband bandpass filters (BPF) are one of the most popular components increasingly investigated in most recent studies. On one hand, these should be designed to realize a wide passband and, on the other hand, they should provide dual-band behavior. This duality makes the design of these elements so complicated that designers have to use a complex technology or a multi-layered one.1-3

Several investigations have introduced many dual-band BPFs using different topologies. However, they show a narrow bandpass and still occupy a relatively large area.4,5 Additionally, several techniques have been proposed to design such components, which can provide dual-band behavior but with complicated technologies, including short-circuited stubs.6,7

One of the recent classes of wideband components, using a multi-mode resonator, is the best candidate to realize wideband structures.8,9 However, it is not able to demonstrate a dual-band. While complementary split ring resonators (CSRR) are the best ones to realize dual-band components that may provide dual-wideband BPFs in combination with multi-mode ones, in the structures of these wideband components, there is no capacitive coupling to combine with CSRRs. However, it should be noted that there is a coupling structure between the feed and the quarter-wavelength transmission lines in the layout of these multi-mode ones. Simulation shows that this combination with CSRRs not only does not provide dual-band behavior, but also reduce their performance by reducing their zeros near the center frequencies.

In this article, a novel combination of a multi-mode resonator with CSRR is proposed, in which an extra coupling structure is used to combine with the second resonator. The developed structure consists of a pair of λ/4 transmission lines similar to the basic topology of these resonators, as well as a loaded transmission line with two balanced spiral-shaped, high impedance, transmission lines instead of the conventional λ/2. In addition to providing a dual-band performance, the overall size of these multi-mode resonators is significantly reduced, accompanied with wider passbands, using this proposed topology. A novel compact dual-wideband BPF was designed and fabricated, based on this technique, on a 0.755 mm thick substrate with εr = 2.56. The measured frequency response of the proposed filter agrees closely with the simulated one.

Design Procedure

Figure 1 (a) Schematic of the conventional multi-mode resonator and (b) proposed layout for the λ/2 transmission line of the conventional one.

Capacitive Gap Structure (CGS) of the Multi-Mode Resonator
As stated, to utilize CSRRs for the realization of a dual-wideband BPF, it is necessary to have a capacitive gap structure in the layout of multi-mode resonators. Here, the layout of these resonators is initially developed in order to provide a CGS and afterward, a CSRR is used to ascertain the idea. To get an analytical view of the design of the proposed dual-band BPF, the structure of the recent multi-mode resonator is initially followed as shown in Figure 1. Observing the structure of the conventional multi-mode resonator, including two pairs of quarter wavelength and a loaded λ/2 transmission lines, the only coupling structure of this topology is between the feed and the quarter wavelength transmission line, for which EM simulation shows that it does not provide dual-band passband in combination with CSRRs. As indicated in the figure, this conventional layout is modified to realize a capacitive coupling structure. As demonstrated, two balanced high impedance transmission lines are added to the λ/2 transmission line of the structure as the main resonator to realize capacitive gaps between their ends and the main resonator.

By considering the reactance X for the coupling structure, it can be shown by calculating the ABCD matrix of the layout that the C component of this matrix can be expressed as follows:

where A is a coefficient in terms of the structure's parameters and the denominator values are provided in the diagram schematic given in Figure 1.

According to Equation 1, to determine the zeros of the structure near the center frequency f0, the denominator is equated to zero, which implies the following equation:

To simplify the analysis, if ZS is chosen to be equal to 2ZL, the following equation is derived:

where X is the reactance created by the coupling structure. Similarly and according to Equation 1, by choosing θ1 + θ2 = 2θ, and simplifying the equation, it can be demonstrated that the zeros near the resonant frequency can be specified as fz1 = f0/2 and, fz2 = 3f0/2, which are exactly located at the lower and upper sides of the center frequency.

Figure 2 (a) Combination of the proposed multi-mode and complementary split-ring resonators and (b) equivalent circuit model.

By replacing the layout of the recent conventional multi-mode resonator with the proposed one, it can be shown that this structure realizes a wider BPF in passband, with a notable size reduction in comparison with a conventional one.9 It is demonstrated that this compact multi-mode resonator realizes a dual-wideband BPF in combination with a simple CSRR.

Dual-Wideband Bandpass Filter

As indicated in the previous section, the capacitive gap structures can be created in the structure of the conventional multi-mode resonator to utilize complementary split ring resonators and subsequently realize a dual-wideband bandpass filter. As indicated in the schematic diagram provided in Figure 2, the CSRR is placed exactly at the bottom of the CGS in the proposed multi-mode resonator. Its dimensions are: L = 6.8 mm, L1 = 2.6 mm, W = 0.2 mm, S = S1 = 0.2 mm.

The equivalent circuit of the proposed model can be derived as indicated in Figure 2, where the L and C represent the inductor and capacitor created by the high impedance spiral-shaped TL with a characteristic impedance ZS and the CGS, respectively, and other elements represent the LC equivalent circuit of the CSRR. Needless to say, the bandwidth of two bands of the filter is directly proportional to these parameters. It is shown that the proposed compact multi-mode resonator realizes a dual-wideband BPF with better performance than that of the conventional ones.

Figure 3 Layout of the dual wideband BPF.

Based on the schematic diagrams provided, the final layout of the proposed dual-wideband BPF is prepared as shown in Figure 3 without the CSRR. The dimensions are: L = 3.1 mm, L1 = L2 = 4.2 mm, L3 = 5.4 mm, L4 = 11.37 mm, L5 = 0.5 mm, W = 0.2 mm, W1 = 0.4 mm, W2 = 0.85 mm, W3 = 0.1 mm, W4 = 1.5 mm, S = S1 = S2 = 0.05 mm. Observing the layout, the quarter wavelength lines coupled with the feed lines are bent to distance the two ports from each other, in order to avoid isolation problems and affect the performance of the filter.

Simulation and Measurements

According to the specifications given in the previous sections, a compact dual-wideband BPF was designed and simulated. The design process of the filter is obvious, where the electrical length of the input lines (θ) coupled with the feed ones is initially chosen to be λ/4 for the given center frequency. Then, to make a simple analysis and have two zeros near the center frequency, the condition of θ1 + θ2 = 2θ is introduced, where the electrical length of θ1 and θ2 are chosen to be 50° and 110°C for size reduction and wideband properties, respectively.

Figure 4 Performance of the proposed dual-wideband BPF (a) scattering parameters, (b) and (c) group delay at the first and second bands.

It can be shown, by simulation and according to Equation 2, that the characteristic impedance ZL plays a crucial role in the increase or decrease of the bandwidth of this filter, where the bandwidth is directly enhanced by increasing or decreasing this parameter. In the conventional investigations,8,9 this parameter has usually been chosen with a low value as indicated in Figure 1. However, here it is chosen to be greater than the conventional ones and be approximately 84 Ω, for wideband properties. Additionally and based on the foregone approximation, ZS is chosen to be equal to 2ZL and subsequently as Equation 3 enforces, the reactance X is a high value, which can be practically realized by closing the ends of spiral-shaped TLs to the main resonator.

After the implementation of the proposed layout with initial values, a fine tuning process is carried out with an EM simulation tool (ADS software) to optimize the dimensions of the proposed BPF given previously for the CSRR and the multi-mode resonators, respectively.

The scattering parameters of the proposed dual-wideband BPF, measured with an Agilent 8722ES network analyzer over the frequency range from 1 to 25 GHz, are given in Figure 4. The measured central frequencies are 6 and 18.1 GHz with 3 dB bandwidths of 75.83 percent (from 3.62 to 8.17 GHz) and 15.47 percent (from 16.6 to 19.4 GHz), respectively. Notably, the bandwidth of the first band of the proposed BPF is much wider than that of the conventional ones designed using multi-mode resonators,8,9 presented as wide single band BPFs as well as the dual-band ones proposed by Chin and Zhu.6,7 Additionally, the proposed dual-wideband BPF occupies an active circuit area approximately 17.6 × 11.5 mm on its substrate in comparison with the conventional ones,7,9 whose sizes have been reported as 32.8 × 15.8 mm and 24 × 24 mm. In addition, the measured group delay is linear and flat in the passband for both two bands.

Figure 5 Frequency response of the proposed dual-wideband BPF for different values of ZL.

Dual-wideband BPF with Different Bandwidth

According to the equations obtained in the previous section, the performance of the dual-wideband BPF directly depends on the specified parameters of the structure. The frequency response of the dual-wideband bandpass filter can be examined for different values of some parameters. The performance of this filter was evaluated for different values of the characteristic impedance ZL of the main resonator. Based on Equation 1, the zeros of the structure are derived by equating the denominator to zero. Since the impedance ZL plays a crucial role in determining the zeros and subsequently the bandwidth of the filter, the performance of the filter was simulated for different values of this parameter. By keeping fixed the optimized values of the other parameters except S1, ZL is varied from 41 to 95 Ω and the frequency response of the proposed filter is simulated. Figure 5 provides the performance of this filter for these different values.

Observing the performance of the proposed structure, it is obvious that the more ZL is reduced, the more the bandwidth of the first band is reduced and the center frequency of the second band is also shifted toward the higher frequencies. According to this, it can be concluded that the zeros of this structure can be tuned and controlled by varying the impedance ZL.

Conclusion

A compact dual-wideband bandpass filter (BPF) has been designed and proposed using spiral-shaped multi-mode and complementary split ring resonators. The diagram schematic of the proposed dual-band BPF has been reported to consist of a pair of λ/4 transmission and a loaded transmission line with two balanced spiral-shaped high impedance transmission lines instead of the conventional λ/2, which leads to a high level of size reduction in such components. Following, a complementary split ring resonator has been utilized to realize a dual-wideband BPF. A compact dual-wideband BPF has been designed, analyzed and tested, where two transmission zeros at both the lower and upper stopbands of each band guarantee a high level of suppression in the rejection bands with sharp skirts. The size of this filter has been reported to be decreased by approximately 64.86 percent and 60.94 percent in comparison with that of the conventional dual-band7 and single wideband,9 respectively, with a wider bandwidth.

Acknowledgment

The authors would like to thank Mr. Hosseini and Mr. Akhlaghpasandi, Iran Telecommunication Research Center, for their assistance with the measurement setup.

References

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