A Cascaded Triplet SIW Bandpass Filter

A substrate integrated waveguide (SIW) bandpass filter is proposed in this article, which uses proximity coupling structures and slot loaded quarter SIW resonators to implement a cascaded triplet (CT) filter. Electrical coupling is realized with the novel proximity coupling structure, while the size of a quarter SIW resonator (QSIWR) is reduced by 43 percent, when loaded with a slot. By introducing magnetic cross coupling into the electric main coupling path, a C-Band CT filter is designed, which has a transmission zero at the upper stopband. The measured results show good performance and agree well with the simulated results.

Since the proposal of the substrate integrated waveguide (SIW) technique, many kinds of SIW filters have been designed, among which SIW cavity coupled filters are in the majority.^1-3 Such filters have the advantages of high Q, light weight, easy fabrication and simple integration with planar circuits. However, they are relatively large in size, compared with their microstrip counterparts, especially in the lower microwave frequency band. To alleviate this problem, some miniaturized SIW filters have been proposed based on half mode substrate integrated waveguide (HMSIW),⁴ substrate integrated folded waveguide (SIFW)⁵ and their variants.^6-11 The quarter SIW resonator (QSIWR) is one of these miniaturized structures, first proposed by Zhang,⁹ whose size is only a quarter of an SIW cavity resonator. The electric field distribution of a QSIWR’s fundamental resonant mode is shown in Figure 1, compared with that of a rectangular SIW cavity.

In this article, it will be shown that the size of a QSIWR can be further reduced when loaded with a carefully designed slot. In addition, a proximity coupling structure will be proposed. Unlike traditional magnetic coupling between SIW resonators, which are mostly realized by an aperture in the common wall of two neighbored SIW cavities, electrical coupling is adopted and can be readily realized by the proximity coupling structure. With electrical coupling in the main path and magnetic coupling in the cross coupling path, a CT filter is designed, which operates at 5.9 GHz, with a fractional bandwidth of 7 percent and has a transmission zero point at approximately 7 GHz.

Filter Design

The configuration of the proposed CT filter is shown in Figure 2. It is a cross coupled filter with three slot loaded QSIWRs. The center frequency of the filter is determined by the resonant frequency of the constitutional resonators, while the bandwidth is mainly affected by the coupling strength. Besides, the cross coupling between resonator 1 and resonator 3 determines the location of the transmission zero point. The input and output ports are two tapped 50 V microstrip lines, which determine how the filter is coupled with external circuits. The filter is specified to work at 5.9 GHz with a fractional bandwidth of 7 percent and a transmission zero at 7 GHz. Thus the coupling matrix and external quality factors are synthesized to be:12

where M_ij denotes the coupling coefficient between resonator i and resonator j, M_ii denotes the fractional frequency deviation of resonator i from the center frequency of the filter, Q_e1 and Q_e3 represent the input and output external quality factors.

Slot Loaded QSIWR

A slot loaded QSIWR has a slot etched off along the diagonal of its upper metal plane. Due to the effect of the slot, the resonant frequency of a slot loaded QSIWR is affected not only by l₁ and l₂ (in our design l₁ = l₂) but also by the dimensions of the slot. A parametric dependence of the resonant frequency is shown in Figure 3 for a slot loaded QSIWR built on a Rogers 5880 substrate with ε_r = 2.2 and tanδ= 0.0009. It is observed that the resonant frequency decreases as the slot becomes longer and wider, which means that to achieve the same resonant frequency, the cavity length l₁ of a slot loaded QSIWR can be shorter than that of a QSIWR and thus the size of the filter is further reduced.

To explain the effect of the slot on lowering the resonant frequency of a QSIWR, an analysis on the surface current distribution is done by HFSS. As shown in Figure 4, the surface current of a slot loaded QSIWR has to detour around the slot, which stretches the effective current path in contrast to QSIWR and results in a lower resonant frequency. To implement an asynchronous resonance, as required by the coupling matrix, a gap is opened in the grounded via wall of both resonator 1 and resonator 3, as denoted by g in Figure 2 (a).

Proximity Coupling in the Main Coupling Path

An SIW resonator is closed by grounded vias on all sides and the inter-resonator coupling is generally realized through an aperture in the common via wall between neighbor SIW cavities.^1,2 QSIWRs and slot loaded QSIWRs have two additional open boundaries by contrast and thus may have different coupling structures besides aperture coupling. Figure 5 illustrates the configuration of the proposed proximity coupling structure.Since the resonant frequency of the odd mode is lower than that of the even mode, the coupling is electric in nature.¹² Aperture coupled SIW resonators implement magnetic coupling easily, but have difficulty implementing electric coupling.² However, with the proposed proximity coupling structure, electric coupling is readily realized, which facilitates the design of cross coupled SIW filters.

The coupling coefficient is primarily determined by the space between two resonators and can be extracted by the following formulation.¹²

Where f₁ and f₂ correspond to the resonant frequencies of the odd mode and the even mode, while f₀₁ and f₀₂ correspond to the resonant frequencies of uncoupled resonators.

Cross Coupling

Figure 6 shows the cross coupling structure when the resonators are apart, o₁₃<0 (a) or overlap, o₁₃>0 (b). The cross coupling is weak when the resonators are apart from each other, whereas it gets stronger when they are overlapped. However, in both cases, the resonant frequency of the even mode is lower than that of the odd mode, indicating the cross coupling to be magnetic in nature.¹² The cross coupling strength is dependent on the parameter o₁₃, which is defined to be negative in Figure 6a and positive in Figure 6b. As demonstrated in Figure 7, the transmission zero point gets closer to the passband as the cross coupling grows stronger.

External Coupling

The external quality factors are influenced by the offset distance of input and output microstrip lines, which can be extracted from the group delay of S₁₁ at resonance:¹²

Filter Synthesis

The coupling coefficient and the external quality factor are extracted according to Equations 2 and 3, as demonstrated in Figure 8. Then the initial dimension parameters of the filter can be determined, which are tuned afterward for better performance. The final dimensions are l₁ = l₂ = 9.25 mm, slot_l = 9.5 mm, slot_w = 0.3 mm, s = 0.4 mm, o₁₃ = −0.15 mm, g = 1.4 mm, offset = 0.8 mm, w₅₀ = 1. 5 mm, d = 0.5 mm, p = 1 mm. It is noticed that the size of a slot loaded QSIWR (l₁ = l₂ = 9.25 mm) is further reduced by 43 percent, compared with that of a QSIWR (l₁ = l₂ = 12.25 mm).

Experimental Results

The filter was fabricated by a single layer printed circuit board (PCB) process on a 20 mil thick Rogers 5880 substrate with permittivity of 2.2 and loss tangent of 0.0009. The total size of the filter including feeding lines is 31 by 31 mm. A photograph of the filter is shown in Figure 9. Figure 10 shows the measured results from 4 to 8 GHz compared with the simulated results by HFSS and the ideal responses synthesized by the coupling matrix. The measured insertion loss is approximately 1.77 dB and the return loss is better than 23 dB from 5.7 to 6.03 GHz. The transmission zero point, at approximately 7 GHz, considerably improves the selectivity of the upper stop band. Figure 11 shows the measured results from 3 to 20 GHz. It is observed that the spurious passband is far above the operating band.

Conclusion

A proximity coupling structure for QSIWRs is proposed in this article, which readily realizes electrical coupling and facilitates the design of cross coupled filters. To further reduce the filter size, slot loaded QSIWRs are utilized and a 43 percent reduction in size is achieved, compared with QSIWRs. With electrical coupling in the main path and magnetic coupling in the cross coupling path, a compact C-Band CT filter has been designed, which shows good performances of low insertion loss, high selectivity and wide-spaced spurious passband.

Acknowledgment

The authors would like to thank Star-wave Communications Technology Corp. for measurement of the filter.

References

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