Wide Stopband Substrate Integrated Waveguide Filter Using Bisection and Trisection Coupling in Multilayer

I.   Introduction

Substrate-integrated-waveguide (SIW) filters perform better than other planar filters in terms of loss, radiation, quality factor, and power capacity, particularly in high-frequency applications [1]–[3]. However, being a cavity-like structure, the spurious passbands of a SIW filter are inherently much closer to the passband and much more concentrated in the upper stopband than those of conventional planar filters, hence degrading the selectivity in the stopband. Even though the selectivity near the passband could be unaffected, this could still be a serious problem given the rapid development of telecommunication items and services with multi-standard/multi-band circuits/systems. Therefore, wide stopbands would be important for the current SIW filters to eliminate the wide-band interference.

In the published literature, there are numerous methods for achieving wide stopband SIW filters. Cascading a lowpass filter is a direct way of suppressing the spurious passband and achieving a wide stopband [4], but it increases the size and insertion loss of the circuit. Utilizing hybrid structures or microstrip-like designs can easily extend the stopband and reduce the size significantly [5]–[10], but they degrade the quality factor and structural shielding, rendering them unsuitable for the high-frequency and high-performance applications. Moreover, one can extend the stopband of a SIW filter by introducing transmission zeros to suppress the spurious passband [11]–[13], staggering the frequency of spurious modes to weaken the spurious passband [14]–[16], employing mixed coupling to counteract the spurious modes [17]–[21], and so forth. However, the stopband extension achieved is limited, and the design procedure is relatively complex.

Comparatively, aligning the coupling structure so that the spurious modes have the weakest coupling is a significantly more efficient method for achieving wide stopband SIW filters [17], [22]–[27], which take advantage of the field distribution of the spurious modes themselves. When this method is used to eliminate the first spurious passband consisting of TE₁₀₂|TE₂₀₁, it 1) does not require additional structure or complex theoretical analysis, 2) does not affect the design of the fundamental passband, and 3) does not degrade the performance of the filters, i.e., it is highly efficient. However, this method is hard to further eliminate higher-order spurious modes when the SIW filter is implemented in a single-layer structure because, in a single-layer SIW filter, the coupling structure significantly degrades the symmetry of the spurious modes, and the resulting asymmetry significantly degrades the efficiency of this method [24], [25]. In [17] and [26], the SIW filters are implemented in multilayer structures, which are capable of removing the asymmetry, but they did not eliminate higher-order spurious modes in addition to TE₁₀₂|TE₂₀₁.

In this article, based on multilayer structures, we will develop this efficient method toward eliminating higher-order spurious modes without degrading its efficiency. To this end, we propose trisection coupling in addition to bisection coupling. For a SIW filter working in the fundamental mode TE₁₀₁ (f₀), all the spurious modes below TE₅₀₅ can be efficiently eliminated; hence, the stopband can be extended up to about 5f₀ in a simple but very efficient design.

The remainder of this paper is organized as follows. Section II will explain its principle, Section III will give two experimental verifications, Section IV will discuss the advantages, and Section V will conclude this article. All the simulations will be performed using the Ansoft HFSS.

II.   Methods

To simplify design and increase efficiency (without requiring a complex analysis of the spurious mode frequencies), all the SIW cavities in this article are made square. Hence, the spurious modes’ frequencies can be calculated as follows:

where ${{f_{{\text{T}}{{\text{E}}_{101}}}} = {f_0}}$ is the fundamental mode’s frequency. Their order with increasing frequency can be easily listed as TE₁₀₁ (the fundamental mode), TE₁₀₂|TE₂₀₁, TE₂₀₂, TE₁₀₃|TE₃₀₁, TE₂₀₃|TE₃₀₂, TE₁₀₄|TE₄₀₁, TE₃₀₃, ...

Reasonably, eliminating these spurious modes in sequence will result in an increasingly wide stopband.

1   Symmetry of the spurious modes

Figure 1 depicts the electric-field distributions of TE₁₀₂ and TE₁₀₃ in a square SIW cavity. Theoretically, when the coupling structures are positioned where the arrows indicate (bisection and trisection along the edge), the coupling/transmission of TE₁₀₂ and TE₁₀₃ will be minimized, and the spurious passband arising from TE₁₀₂ and TE₁₀₃ will be eliminated naturally [17], [24]. However, it should be noted that the coupling structure in turn has an impact on the field distribution, which will affect the elimination.

Figure  1.  Electric-field distributions of TE₁₀₂|TE₁₀₃ in a square SIW cavity.

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As for a single-layer SIW filter, the coupling structure can only be positioned on one side of the SIW cavity, which inevitably results in an asymmetric impact on the field and a significant distortion of the field distribution. Consequently, the spurious passband arising from TE₁₀₂ and TE₁₀₃ (let alone higher-order spurious modes) will no longer be naturally eliminated. A compensation design has to be additionally implemented to complete the elimination, and the design complexity will dramatically increase as higher-order spurious modes are involved, i.e., the efficiency significantly degrades.

As for a multilayer SIW filter, the coupling structure can be positioned on both symmetric sides simultaneously. This does not cause an asymmetric impact to significantly distort the field distribution. Consequently, the spurious passband arising from TE₁₀₂ and TE₁₀₃ (and other higher-order spurious modes) can still be naturally eliminated.

2   The filter we proposed (Part-1)

Figure 2 shows the multilayer structure of our proposed wide stopband SIW filter. The SIW cavities are inter-coupling with each other through the coupling slots in the middle layers.

Figure  2.  Multilayer structure of the proposed wide stopband SIW filter.

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The bisection slots in layer-1 will eliminate the transmission of TE₁₀₂ as illustrated above, and this elimination is valid for all TE_10m (m = 2i, i =1, 2, 3, ...). Due to the orthogonality, the centrally positioned ports in the top and bottom layers will simultaneously eliminate the transmissions of TE_n01 (n = 2i, i =1, 2, 3, ...).

Similarly, the trisection slots in layer-3 will eliminate the transmissions of TE_10p (p = 3i, i =1, 2, 3, ...), while, due to the orthogonality, the trisection slots in layer-2 will simultaneously eliminate the transmissions of TE_q01 (q = 3i, i =1, 2, 3, ...).

Additionally, Figure 3 depicts the electric and magnetic field distribution of TE₁₀₅ in a SIW cavity. Both the electric and magnetic field of TE₁₀₅ are almost zero at the positions of the bisection and trisection slots. Consequently, the slots in layer-1 and layer-3 will eliminate the transmission of TE₁₀₅, and, due to the orthogonality, the slots in layer-2 will eliminate the transmission of TE₅₀₁. Based on the same principle, such an elimination is also valid for TE₁₀₆|TE₆₀₁, TE₁₀₇|TE₇₀₁, TE₁₀₈|TE₈₀₁, ...

Figure  3.  Electric- and magnetic-field distributions of TE₁₀₅ in a square SIW cavity.

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As for TE₁₀₁, which is the fundamental mode and determines the fundamental passband, all the bisection and trisection slots can support its transmission well because they are all positioned with the maximum magnetic field of TE₁₀₁ and almost parallel to the magnetic field of TE₁₀₁, as shown in Figure 4. In other words, here the fundamental passband can be designed as usual (as in a conventional multilayer SIW filter with multiple inductive coupling slots). Consequently, as shown in Figure 2, the external quality factor (Q_e) can be adjusted by l_s, which is the length of the out-coupling coplanar waveguide, and the inter-coupling coefficient (k) can be adjusted by l₁, l₂, and l₃, which are the lengths of the bisection and trisection slots. In this article, the prototype filters are designed with a center frequency of 6 GHz and a fractional bandwidth of 3%. The Q_e and k are therefore determined as: Q_e = 39.8, k₁₂ = k₃₄ = 0.0214, k₂₃ = 0.0164 [28], and the l_s, l₁, l₂, and l₃ are adjusted accordingly to meet these specifications.

Figure  4.  Electric- and magnetic-field distributions of TE₁₀₁ in a square SIW cavity.

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As a result, using the structures shown in Figure 2, in a very simple (bisection and trisection coupling slots) but efficient (without requiring additional structure, compensation, or complex theoretical analysis) design, one can get a SIW filter operating in TE₁₀₁ (f₀) whereas eliminating the spurious modes of TE_10m (m =2, 3, 4, ...), TE_20n (n =1, 2, 3, ...), TE_30p (p =1, 2, 3, ...), TE_40q (q =1, 2, 3, ...), and TE_50r (r =1, 2, 3, and 4), which include all the spurious modes below TE₅₀₅.

For verification, Figure 5 shows the extracted coupling coefficients of TE₁₀₁ and several typical spurious modes. Notably, among the remaining spurious modes, the one with the lowest frequency is TE₅₀₅ (5f₀), which will determine the upper limit of the stopband extension of the proposed filter shown in Figure 2.

Figure  5.  Extracted coupling coefficients of TE₁₀₁, TE₁₀₂, TE₁₀₃, and TE₁₀₅ under use of the bisection and trisection coupling slots.

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3   The filter we proposed (Part-2)

In practical design, the definition of “bisection” is clear, which is exactly the center of the edge. However, because the equivalent width of a SIW cavity is frequency-dependent [29], [30], the definition of “trisection” could be a little bit different for different spurious modes.

Specifically, the practical positions of the trisection slots are subject to a compromise of different equivalent widths between TE₃₀₁ and TE₃₀₅. Figure 6 shows the simulated results of the proposed filter. When the trisection slots are designed according to the equivalent width of TE₃₀₁|TE₁₀₃, the spur arising from TE₃₀₁ is eliminated well, but the spur arising from TE₃₀₅|TE₅₀₃ cannot be eliminated well, and vice versa.

Figure  6.  Responses of the proposed filter using different definitions of trisection to respectively eliminate TE₃₀₁ and TE₃₀₅.

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Finally, we designed two prototype filters. The first one (Filter-1) overlooks the elimination of TE₃₀₅|TE₅₀₃, the design of trisection slots concentrates on eliminating TE₃₀₁|TE₁₀₃. Subsequently, the stopband can only be extended to 4.12f₀, which is the frequency of the remaining TE₃₀₅|TE₅₀₃ according to equation (1).

The second one (Filter-2) makes a compromise between the eliminations of TE₃₀₁|TE₁₀₃ and TE₃₀₅|TE₅₀₃, which are designed with equal weights. As a result, the stopband can be ideally extended to 5f₀ (TE₅₀₅) as expected, but it inevitably degrades the suppression in the stopband in comparison to that of Filter-1.

III.   Results

In this section, the experimental verifications are provided. We fabricate and measure Filter-1 and Filter-2 to verify our proposed technique. Their fabrication is based on substrate of 0.508mm Rogers RT/duroid 5880 (ε_r = 2.2 and tanδ = 0.0009). Their measurement is performed using a network analyzer (Agilent N5227A) with two 2.4 mm end launch connectors (Southwest Microwave).

The two filters’ dimensions are listed in Table 1 and Table 2. Their sizes of the core components are both 2.39 × 2.39 cm² (f₀ = 6 GHz). The filter’s photograph is shown in Figure 7, which is mounted with screws.

Table  1.  Dimensions of Filter-1

Param.	Value (mm)		Param.	Value (mm)		Param.	Value (mm)
$w_1$	23.9		$l_1$	3.4		$d_1$	10.6
$w_2$	24.1		$l_2$	2.4		$d_2$	10.5
$w_{\rm{p}}$	1.58		$l_3$	2.7		$d_3$	10.3
$w_{\rm{s}}$	0.6		$l_{\rm{s}}$	4.7		$ld_1$	8
width	0.6		$b_{01}$	7.1		$ld_2$	8

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Table  2.  Dimensions of Filter-2

Param.	Value (mm)		Param.	Value (mm)		Param.	Value (mm)
$w_1$	23.9		$l_1$	3.36		$d_1$	10.6
$w_2$	24.1		$l_2$	2.38		$d_2$	10.65
$w_{\rm{p}}$	1.58		$l_3$	2.76		$d_3$	10.65
$w_{\rm{s}}$	0.6		$l_{\rm{s}}$	4.6		$ld_1$	7.6
width	0.6		$b_{01}$	7.1		$ld_2$	8

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Figure  7.  Photo of the proposed filter (Filter-2).

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The measured responses are depicted in Figure 8 and Figure 9. Their insertion loss are both about 2.8 dB with a bandwidth of 2.5%. Agreeing well with the simulation, their measured stopbands are respectively extended to 24.9 GHz (4.15f₀) and 29 GHz (4.83f₀) with more than 33 dB and 25.5 dB suppression. Their upper limits of stopband extension agree well with expectations, which are almost equal to the frequencies of TE₃₀₅|TE₅₀₃ and TE₅₀₅, respectively.

Figure  8.  Responses of Filter-1.

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Figure  9.  Responses of Filter-2.

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Figure 10 and Figure 11 compare the passband and wideband responses with those of a classic single-layer SIW filter, showing that our proposed technique significantly extends the stopband without increasing the insertion loss or degrading the superiority of the SIW filter.

Figure  10.  Passband comparison with a classic single-layer SIW filter on the same substrate.

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Figure  11.  Wideband comparison with the classic single-layer SIW filter.

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Table 3 provides a performance comparison with state of the art, which includes the ones cascading a low-pass filter [4], the ones using hybrid structures [6]–[10], the ones introducing transmission zeros [11], [13], the ones staggering spurious modes [15], the ones employing mixed coupling [17]–[21], and the ones aligning the coupling structure [22]–[24]. In addition to the small footprints and simple but very efficient designs, our proposed filters present the widest stopbands.

Table  3.  Comparison with state of the art

Ref.	$f_0$ (GHz)	Order	FBW (%)	IL (dB)	Size (λr2)	Stopband extension and suppression
[4]	12	3	3	2.85	3.3	2.5$f_0$, 20 dB
[6]	3.7	3	6.7	1.49	0.32	2.65$f_0$, 20 dB
[7]	3.95	4	9.87	2.1	0.16	2.25$f_0$, 20 dB
[8]	8	3	11	0.9	0.124	1.96$f_0$, 23 dB
[10]	4	4	26.6	0.8	0.088	2.08$f_0$, 34 dB
[11]	20	3	10	0.8	3.3	1.57$f_0$, 40 dB
[13]	20	4	2.75	2.78	2.8	1.9$f_0$, 50 dB
[15]	10	3	1.51	2.91	1.86	2.1$f_0$, 25 dB
	10	4	1.97	3.08	2.87	2.5$f_0$, 25 dB
[17]	13	2	4.55	1.5	0.69	2.39$f_0$, 20 dB
	13.2	2	4.5	1.7	0.47	2.27$f_0$, 20 dB
[18]	10.5	2	3.1	–	2.14	2$f_0$, 20 dB
[19]	9.55	2	2.95	2.62	3.56	2.1$f_0$, 20 dB
[20]	5.8	4	2.1	3.2	0.46	4.03$f_0$, 30 dB
[21]	9	3	2.1	2.8	0.46	4.02$f_0$, 27 dB
[22]	6.96	3	5.53	2.29	0.46	2.77$f_0$, 24 dB
[23]	15	5	4	2.3	3	1.96$f_0$, 55 dB
	15	6	4.3	2.6	3.5	1.99$f_0$, 60 dB
[24]	7.55	2	1.92	2.52	1.23	2.51$f_0$, 25 dB
	7.55	3	1.84	3.22	1.61	3.85$f_0$, 20 dB
This work	6	4	2.5	2.8	0.46	4.15$f_0$, 33 dB
	6	4	2.5	2.8	0.46	4.83$f_0$, 5.5 dB
Note: IL: insertion loss; FBW: fractional bandwidth.

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IV.   Discussion

Regarding the multilayer SIW filters in [17]–[22] and [26], despite their diverse underlying principles, all of their inter-couplings are fundamentally bisection couplings. This is the underlying reason behind their limited stopband extension, even though their multilayer structures do have the ability to go further.

In addition to bisection coupling, we propose trisection coupling in this article. Hence, it is capable of eliminating a greater number of spurious modes than before and achieving a wider stopband. Intriguingly, based on this approach, one can further propose 1/5 coupling, 1/7 coupling, 1/9 coupling, etc. in the future to reach a much wider stopband.

Notably, SIW filters using hybrid structures or microstrip-like designs could achieve wider stopbands or smaller footprints than the proposed filters, but their quality-factor and structural-shielding will degrade inevitably, rendering them unsuitable for the high-frequency and high-performance applications. The filtering technique proposed in this article, on the other hand, does not degrade the filters’ quality-factor or structural-shielding, thus it is suitable for the high-frequency and high-performance applications.

V.   Conclusion

This article reports a highly efficient method for achieving wide stopband SIW filters. For a multilayer SIW filter working in TE₁₀₁, using the proposed trisection slots in addition to the bisection slots as inter-coupling structures, all spurious modes below TE₅₀₅ could be eliminated without requiring additional structures or complex theoretical analysis, without affecting the fundamental passbands’ design, and without degrading the filters’ performance. Two prototype filters with small footprints are provided with wide-stopbands of up to 4.15f₀ and 4.83f₀. The proposed method should become a competitive candidate for developing high performance wide stopband SIW filters in wireless/microwave circuits and systems.