Miniaturized Dual-Band Bandpass Filter Using T-Shaped Line Based on Stepped Impedance Resonator with Meander Line and Folded Structure

Abstract

A stepped impedance resonator (SIR) is suitable for designing a dual-band bandpass filter (BPF) that can be adjusted to reject spurious bands. A BPF is proposed using an SIR T-shaped meander line and folded structure. The BPF mainly comprises a meander line, a folded structure, and a T-shaped line. A novel BPF is used for the T-shaped line, which operates as a band-stop filter connecting to the center of the BPF. As a result, the complete BPF enables dual-band operation. The insertion and return losses of the first frequency passband (f₀₁) are 0.024 and 17.3 dB, respectively, with a bandwidth of 46% at a center frequency of 2.801 GHz (2.2–3.48 GHz). The insertion and return losses of the second frequency passband (f₀₂) are 0.026 and 17.2 dB, respectively, with a bandwidth of 10% at a center frequency of 4.351 GHz (4.13–4.55 GHz). The proposed BPF provides low loss, a simple structure, and a small size of only 4.29 × 4.08 mm, and it can be integrated into mobile communications systems.

1. Introduction

The passive bandpass filter (BPF) is an essential component in a mobile communications system and commonly used in receivers and transmitters [1]. Important design characteristics of BPFs include their response, frequency selectivity, transmission zero, and cost [2]. A popular low-cost BPF design is a microstrip line for dual-band operation [1]. In fact, dual-band BPFs are widely used for reception and transmission in mobile communications systems [3]. In general, a dual-band BPF is composed of a BPF and a band-stop filter (BSF) connected to series and shunt components [4]. However, the overall BPF size is large. Alternatively, a stepped impedance resonator (SIR) can be adopted in a dual-band BPF, which can then be adjusted to reject spurious bands [5,6,7,8,9,10,11]. Nevertheless, many SIR-based dual-band BPFs are large and should be used with a via hole, which increases the insertion and return losses. In [12,13], the SIR is connected to the two BPFs through various multistage components, increasing the size of the design. To miniaturize a device, a high-dielectric (ε_r) substrate can be used, but its cost is high [14]. In this article, a dual-band BPF is proposed using an SIR with a meander line and a folded structure. The meander line is integrated with a T-shaped line.

2. Design Method and Analysis

The proposed BPF features the SIR meander line, a folded structure, and a T-shaped line, as shown in Figure 1a, and the Figure 1b shows the equivalent circuit of the proposed BPF. From the Figure 1a, the SIR structure is expressed as open stubs with low and high impedances. The SIR presents a symmetric structure on both the left side (part a) and right side (part b). Z₁ and Z_j represent the low impedances of the meander line, and Z_s represents the low impedance of the folded structures. In addition, Z₂ and Z_i represent the high impedances corresponding to the T-shaped lines, and Z_t represents the high impedance of the T-shaped line. θ₁ and θ_j represent the electrical lengths of the meander lines, and θ_s represents the electrical length of the folded structure. In addition, θ₂ and θ_i represent the electrical lengths corresponding to the T-shaped lines, and θ_t represents the electrical length of the T-shaped line.

Figure 1. (a) Structure and (b) equivalent circuit of proposed BPF.

The input admittance (Y_in) of parts a and b is given by Equations (1) and (3) [15], which can be expressed using an equivalent circuit.

$${\mathrm{Y}}_2-{\mathrm{Y}}_1\frac{{\mathrm{Y}}_2+{\mathrm{jY}}_1\tan {\mathsf{\theta }}_1}{{\mathrm{Y}}_1+{\mathrm{jY}}_2\tan {\mathsf{\theta }}_1} , {\mathrm{Y}}_{\mathrm{i}}-{\mathrm{Y}}_{\mathrm{j}}\frac{{\mathrm{Y}}_{\mathrm{i}}+{\mathrm{jY}}_{\mathrm{j}}\tan {\mathsf{\theta }}_{\mathrm{j}}}{{\mathrm{Y}}_{\mathrm{j}}+{\mathrm{jY}}_{\mathrm{i}}\tan {\mathsf{\theta }}_{\mathrm{j}}}$$

(1)

$${\mathrm{Y}}_2-{ \mathrm{Y}}_1+{\mathrm{jY}}_{\mathrm{s}}\tan {\mathsf{\theta }}_{\mathrm{s}}$$

(2)

$${\mathrm{Y}}_2-\frac{{\mathrm{jY}}_2({\mathrm{jY}}_2\tan {\mathsf{\theta }}_2+{\mathrm{Y}}_{\mathrm{s}}\tan {\mathsf{\theta }}_{\mathrm{s}}) }{{\mathrm{Y}}_2+{\mathrm{Y}}_{\mathrm{s}}\tan {\mathsf{\theta }}_2\tan {\mathsf{\theta }}_{\mathrm{s}}}$$

(3)

The T-shaped line (Z₂ and Z_s) operates as a wide-bandwidth BSF in the null-frequency range between the first and second frequency bands, as shown in Figure 1b. θ₂ and θ_s lead to 30° and 45° in the null-frequency range [16]. Next, Z₂ and Z_s can be solved in Equation (4) using θ₂:

$${\mathrm{Z}}_2={\mathrm{Z}}_0\cot {\mathsf{\theta }}_2 , {\mathrm{Z}}_{\mathrm{s}}={\mathrm{Z}}_0\frac{{\cos }^2{\mathsf{\theta }}_2}{1-2{\sin }^2{\mathsf{\theta }}_2}$$

(4)

where θ₂ must be above 0° and below 45° (2θ₂ < θ₂ = 90°). If θ₂ is more than 45° (θ₂ < 90°), Z_s reaches infinity, as shown in Figure 2a. As the shunt stub is −jZ_s cot θ_s = ∞, the T-shaped structure acts like an open stub. Z₂ and Z_s are 86.6 and 75 Ω, respectively, and θ₂ and θ_s are 30° and 45°, respectively. Figure 2b shows the simulation results for the BSF response between the first and second frequency bands using a T-shaped structure.

Figure 2. Simulation results for parameter responses. (a) Variation of impedance (Z₂ and Z_s) according to θ₂ and (b) BSF, (c) first frequency band, and (d) second frequency band responses.

The simulated insertion losses are 0.09 and 0.11 dB, respectively, and the simulated return losses are 24.8 and 23.4 dB at the first and second center frequencies of 3.85 and 5.95 GHz in the BSF, respectively.

The calculated impedance and electrical length of the equivalent circuit are listed in Table 1. Figure 2c,d shows the simulated passbands of the first and second frequency ranges for the proposed dual-band BPF, respectively. The simulated first and second center frequencies are 2.8 GHz (2.15–3.43 GHz) and 4.3 GHz (4.08–4.5 GHz), with bandwidths of 46% and 10%, respectively. The insertion losses of the first and second frequency bands are 0.024 and 0.023 dB, respectively, and the return losses of the first and second frequency bands are 18.6 and 19.6 dB, respectively. The BPF performs a dual-band operation when the T-shaped line is connected between parts a and b, as shown in Figure 1b.

Table 1. Calculated electrical parameters.

Parameter	Value	Parameter	Value
Zi	46.0 Ω	θ1(f–j)	0.65°
Z1, Z2, Zj, Zs	117 Ω	1/θ2	3.06°
θi	9.02°	θs1, θs2	4.26°
θ1 (a–e), θs3	1.21°	θj1, 4, θj2	5.52°

Parts a and b (Figure 1a) operate in the first and second frequency bands, respectively, and the T-shaped line serves as a BSF. More specifically, the filter for the design in the proposed BPF is integrated into a BPF and a BSF (a). Next, the BPF used an SIR resonator and the BSF feature a T-shaped-line structure. The BPF features a two-stage structure, in which the two stages are symmetrical. The SIR resonator is divided into a-part and b-part, and a coupling structure (g) is coupled between the a-part and the b-part. The coupling structure serves to connect the a-part and the b-part. At this point, a-part acts as a resonator for operating the first frequency band (1st), as shown in Figure 3, and b-part plays a role in the operation of the second frequency band (2nd).

Figure 3. Frequency band response for 2 stage (a and b parts) SIR.

The a-part and b-part SIR resonators are composed of high impedance (Z_j) and low impedance (Z_i). At this point, when the impedance difference between Z_j and Z_i is provided in the SIR of the a-part and the b-part, the impedance ratio (Δ) must be adjusted to be greater than 1 (Δ > 1) [17]. The reason is that when Δ = Z_j < Z_i, the position of the harmonic of the SIR resonator changes, resulting in a dual-band resonant phenomenon. Therefore, a dual-band is formed due to the combination of two SIR resonators, and this filter constitutes a filter in dual mode [18,19].

The BSF operates through the structure of a T-shaped line. In general, the BPF features a π-type equivalent circuit. However, the BSF features a T-shaped equivalent circuit. BSFs are constructed with an electrical length within 90° of series (transmission line of Z₂) and within 45° of parallel (open stub of Z_s) within 90° of series for ease of design due to impedance and physical length or width. The transmission line (Z₂) is symmetrical and functions as equivalent to 90° by calculating 30° to reduce the size, and the transmission line plays a role in transmitting the incident power to the output side. The stub cuts off the desired band in the process of transmitting power and, at this point, when the electrical length is 45° and 30°, the cut-off band can be adjusted.

In the T-shaped line, the meander-line corresponding to the impedance Z₁, plays a micro-tuning role to reduce the insertion and return loss in the T-shaped BSF, and the size of the loss changes according to the change in the length of the transmission line.

The parallel open stub of the T-shaped line corresponding to the impedance of Z_t serves as a clear boundary between the bandpass filter and the BSF so that the SIR BPF and the BSF of the T-shaped line can operate, respectively. At this point, it also serves as an intermediate connection for integrating the BPF and the BSF.

3. Design and Fabrication

The proposed BPF was designed as shown in Figure 4a, and the Figure 4b shows the fabricated a proposed BPF. In the Figure 1a, the parameters l₁ (a–e) and l₁ (f–j) are 0.26 and 0.14 mm, respectively, and 1/l₂ and l_t are 0.66 and 3.82 mm, respectively. In addition, l_j1 (=l_j4), l_j2, and l_j3 are 0.93, 1.19, and 0.13 mm, respectively, while l_s1, l_s2, and l_i are 0.14, 0.78, and 1.84 mm, respectively.

Figure 4. (a) Design layout and (b) fabricated BPF.

The parameters w_i and w₁ (w₂ = w_j = w_s) are 1.69 and 0.26 mm, respectively, and w_t, g, and s are 0.13, 0.12, and 0.14 mm, respectively, where s and g establish coupling structures and form the gap size. Parameters l_T and W_T are the total horizontal and vertical dimensions of 4.57 and 4.08 mm, respectively. Figure 4b shows the proposed BPF fabricated on a Teflon substrate with a low dielectric constant of 2.54 and a height of 0.54 mm. The size of the fabricated BPF is 24.0 × 16.4 mm.

4. Experimental Results

The simulation and measurement results for the proposed BPF are shown in Figure 5 The simulation results for the insertion and return losses of the first frequency passband (f₀₁) are 0.024 and 18.3 dB, respectively, with a bandwidth of 46% at the center frequency of 2.8 GHz (2.15–3.43 GHz), and the insertion and return losses of second frequency passband (f₀₂) are 0.023 and 18.2 dB, respectively, with a bandwidth of 10% at the center frequency of 4.35 GHz (4.08–4.5 GHz).

Figure 5. Experimental results for proposed BPF.

In a fabricated BPF, the measurement results for the insertion and return losses of the first frequency passband (f₀₁) are 0.042 and 17.3 dB, respectively, with a bandwidth of 46% at a center frequency of 2.8501 GHz (2.2–3.48 GHz), and the insertion and return losses of the second frequency passband (f₀₂) are 0.026 and 17.2 dB, respectively, with a bandwidth of 10% at a center frequency of 4.3501 GHz (4.13–4.55 GHz).

Table 2 lists the characteristics, including bandwidth, insertion loss, and total size, of the proposed BPF and similar filters.

Table 2. Characteristics of proposed BPF and similar filters.

Ref.	Center Frequency (GHz)		IL (dB)		RL (dB)		BW (%)		Size (λg)
	f01	f02	f01	f02	f01	f02	f01	f02
This work	2.8501	4.3501	0.042	0.026	17.30	17.20	46.00	10.00	0.28 × 0.108
[5]	1.78	4.00	0.42	0.37	15.00	15.00	7.000	5.500	0.23 × 0.33
[6]	1.75	3.64	-	-	-	-	2.000	5.000	0.14 × 0.27
[7]	2.43	5.06	3.80	4.40	19.80	14.30	83.80	18.80	0.67 × 0.68
[8]	2.4	4.00	1.41	1.00	-	-	8.000	39.00	0.48 × 0.09
[9]	2.21	3.85	0.59	1.36	18.40	22.40	20.40	5.00	0.21 × 0.26
[10]	2.44	3.50	2.17	1.71	10.32	10.32	5.370	5.85	0.45 × 0.19
[11]	1.21	2.41	0.19	1.29	28.29	21.36	89.08	31.90	0.30 × 0.14
[13]	3.70	5.80	0.70	1.00	-	-	31.00	13.00	0.39 × 0.25

IL, insertion loss; RL, return loss; BW, bandwidth.

In this paper, a designed BPF can be applied as a sensor suitable for use in chemicals, agriculture, medicine, and petroleum [20]. In particular, the frequency response characteristic of the filter is changed by a change in the capacitance value related to coupling. Therefore, biosensor applications are possible because the filter can detect specific substances on tissues [21].

5. Conclusions

A dual-band BPF using an SIR meander line, folded structure, and T-shaped line was proposed. The T-shaped line operates as a BSF, and the BSF divides the first and second frequency passbands on the BPF to achieve dual-band operation. The proposed BPF provides low insertion and return losses, a simple structure, and a compact size. In existing dual-band BPFs, a BSF is configured in addition to the BSF, or a BSF is integrated using the defected ground structure. However, these designs increase the size and deteriorate the filtering characteristics owing to the ground plane concentration loss. By contrast, the proposed design integrates a T-type structure at the center of the BPF. Therefore, size increase is avoided, and the ground-plane concentration loss is prevented. The measured insertion and return losses of the first frequency passband (f₀₁) are 0.042 and 17.3 dB with a bandwidth of 46% at a center frequency of 2.8501 GHz (2.2–3.48 GHz), and the insertion and return losses of the second frequency passband (f₀₂), are 0.026 and 17.2 dB, with a bandwidth of 10% at a center frequency of 4.3501 GHz (4.13–4.55 GHz). The proposed BPF is suitable for mobile communications systems owing to its planar structure.