Compact Dual-Band Parallel Coupled T-Shaped SIR Filter for WLAN Applications

In this article, a new compact dual-band bandpass filter was introduced. The filter utilized two operating bands centered at 2.45 GHz and 5 GHz widely used for wireless local area network applications. The filter consists of T-shaped sections of step impedance resonator. The structure is an even symmetrical around electrical or magnetic wall, so the operation mechanism of the filter can be analyzed by an even-and odd-mode transmission line theory. The resonator structure is parallel coupled to a pair of 50 Ω input/output ports. Proper feeding and coupling structures can realize at least two transmission zeros around each of the operating band. To enhance the spurs rejection in the out of the band response of the filter, additive transmission zero at 10 GHz was created by adding stub of quarter guided wavelength at a selected distant from the output port edge. The filter is designed and optimized using the full wave Electromagnetic simulator. The center frequency of the designed bands can be easily refined by the filter dimensions. The overall dimension of the filter is g g   48.0 3.0  (where g  is the guided wavelength at the frequency of 2.45 GHz) corresponding to 14.3 mm x 22 mm.


Introduction
Growing expansion of modern wireless communication systems motivates the researchers to concentrate their research topic on compact multi-band operation. Bandpass filters are essential circuit's of microwave structures. Recent trends are towards compact size and high performance resonator structures of printed planar microwave filters.
Stepped impedance resonators (SIR) are one way to dramatically reduce size and miniaturization of microstrip bandpass filters [1]. Sophisticated versions of SIR's have been applied to filter design looking for multi-band, compactness and wide upper stopband behavior [2,3]. Serious and essential work in the design of SIR filters are presented by Makimoto and Yamashita in 1980 [4]. Design formulas for band pass filters using parallel coupled stripline stepped impedance resonators (SIR) are derived. Their formulas take into accounts the arbitrary coupling length as well as quarter wavelength coupling.
A magnetically coupled bandpass filter using two pairs stepped impedance hairpin resonators and magnetically coupling is described in [5]. The result of the filter demonstrates compact size, a very low insertion and spurious response can be suppressed effectively. A compact microstrip cross-coupled bandpass filters realized by miniaturized stepped impedance resonators (SIR's) are proposed by [6]. The proposed cross-coupled filter not only has a compact size but also has high-selectivity and a very wide stopband response.
In [7], a periodic stepped-impedance ring resonator (PSIRR) is proposed to design dualmode bandpass filters with a miniaturized area and desirable upper stopband characteristics. Microstrip triple band tri-section bandpass filter using stepped impedance resonators (SIRs) is designed, simulated, built for the first time using hair pin structure [8]. It is shown that the coupling effect between SIRs can be used as a knob to obtain better performing bandpass filter for the desired frequency band.
A compact dual-band SIR based bandpass filter using a multimode resonator (MMR) is proposed. The MMR is composed of two pairs of short-ended coupled-lines, two pairs of openended coupled lines and four connecting transmission lines [9]. The design is resulting in controllable dual bands and wide upper-stopband suppression. In [10], a multiband band-pass filter based on the resonant characteristics of step-impedance and inter-digital capacitor resonators was proposed. This design leads to compact size and good filter performance.
In [11] a bandpass filter was designed using U shape resonator as hairpin resonator. The bandpass filter has the center frequency of 400 MHz. In this frequency, filter acquires quite a long resonator line, so the compact filter is nedded. In order to reduce the dimension of filter, the filter only two U shape resonators that arranged series with couple feed line were used.
Besides that, the model used via ground holes designed in both of the line resonator and the substrate with higher dielectric constant was used.
Stepped impedance resonators (SIR), in addition to being compact, also are used for harmonics suppressions. In [12], T-Shaped SIR was used for harmonics suppression and their applications for diplexer. In [13], a broadband microstrip bandpass filter with compact size, sharp skirt and wide upperstopband performance was proposed using the triple-mode resonator loaded with two folded stepped-impedance open and short-circuited stub. The resonator can generate one odd mode and two even modes in the desired passband.
This study synthesizes dual-band bandpass filter based on single T-shaped SIR with controllable center frequencies used for wireless local area network (WLAN) applications. Compactness has been achieved by using single SIR to excite dual-band in the resonator. So, the total length of the resonators has been reduced.

Analysis of T-Shaped SIR Resonator
The T-shaped SIR resonator is shown in Figure 1. As the structure of the resonator is symmetrical along the electrical or magnetic wall, then even-odd method can be used for simplifying the analysis of the equivalent circuit as shown in Figure 2. Here, θ 1 and θ 2 are electrical lengths of the two sections, and Y 1 and Y 2 are the characteristic admittances corresponding to the sections impedances Z 1 and Z 2 respectively. As depicted in Figure 1 When ino Y enforced to zero, then the odd mode analysis of Figure 2 (2) and (3), the transmission zeros of the circuit in Figure 1 can be calculated according to: It seems clearly that the locations of transmission zeros depend on the transmission line impedances (Z 1 and Z 2 ), the electrical lengths ( 1 and  2 ). By proper selection of these parameters, transmission zeros can be found and located as they are the roots of (4). This may be simply achieved using full wave Electromagnetic Simulators.

Design of Dual-Band Band Pass Filter Using T-Shaped SIR Resonator
The proposed filter configuration is shown in Figure 3. The filter consists of single Tshaped resonator parallel coupled to 50 Ω feeding ports. The filter is designed and optimized using the full wave Electromagnetic Simulator.

Figure 3. Proposed filter configuration based on T-shaped SIR resonator
The substrate used in the design of the filter is Rogers RO3210 with relative dielectric constant of 10.8 and thickness of 1.27 mm. Based on the circuit analysis given in the previous section, a dual-band BPF shown in Figure 3 is constructed in the full-wave simulator SONNET. The related circuit parameters at the center frequency of 2.45 GHz are listed in Table 1.

Simulation and Results
The structure of the filter is optimized using the Electromagnetic Simulator. The final dimensions in (mm) are: Figure 4 shows the simulated frequency response of the filter. Four transmission zeroes around the bands are clearly observed at 0.1, 1.1, 3.05, 5.75 and 7.95 GHz with a return loss of -38.12, -48.74, -38.92, 51.07 and -22.45 dB respectively. The response has two transmission bands at 2.45 and 5 GHz with return loss of -18.47 and -31.43 dB respectively. To enhance the out-of-the band rejection, transmission zeroes may be added in the frequency range from 5.7 GHz to 10 GHz. The transmission zero at 9.4 GHz was created by adding stub of quarter guided wavelength at the selected frequency and a width of 0.3 mm located at 1.4 mm from the outer edge of port 2.
The effect of adding an extra zero to the frequency response of the filter is shown in Figure 5. The additive zero Tz6 reduce the effects of spurs in the region from 5.75 to 10 GHz.

Conclusion
A T-shaped SIR resonator has been presented and analyzed for dual-band bandpass filter design. Even and odd modes of the resonator structure are allocated in the first and second passband using full wave Electromagnetic simulator. The results from circuit modeling and simulating a dual-band filter show the creation of five transmission zeros caused in a skirt shape response around each of the two bands. Clearing the out of the band region from spurs was achieved by addition of an extra zero in a selected location of the filter frequency response. The filter was compact size, simple shape and low profile with dual-band operation suitable for many wireless applications.