Compact Absorptive Microstrip Bandpass Filter with Adjustable Bandwidth and Phase

Abstract

In this communication, a compact absorptive bandpass filter (ABPF) characterized by adjustable bandwidth and phase, low group delay (GD), a high absorptive ratio and low insertion loss (IL) is proposed. The presented ABPF consists of a bandpass section that is made of a quarter-wavelength coupled line and four stubs that are basically a lumped resistor in series with a short-circuited quarter-wavelength transmission line. The stubs not only perform the function of absorption but also have the advantage of adjustable bandwidth and phase. To verify the design concept and analysis formulas, an ABPF operating at 2.4 GHz is fabricated and measured; its simulated and measured results are in good agreement.

1. Introduction

Energy that is reflected back to the front end generates a new spectral component at the signal source, which affects the accuracy and stability of the signal [1]. To prevent such reflection and to improve the stability of adjacent active circuits, microwave components with absorptive functionality have been developed rapidly over the years. As the fundamental component in communication systems, a bandpass filter (BPF) is used for radio frequency (RF) energy transmission in the passband. Hence, a BPF should avoid the reflection of out-of-band signals as much as possible. On the other hand, the phase-distortion requisites of digital communications can be the most stringent requirements, as they mostly define the quality of the recovered signal as being limited by inter-symbol interference (ISI) phenomena. In order to prevent the signals from distortion, linearization of the phase frequency response of BPFs is a problem that urgently needs to be solved in modern digital communication systems. Meanwhile, adjustable bandwidth and phase can provide high selectivity for filtering applications. In the literature, various approaches to reflectionless BPFs have been reported so far [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20].

In [2], a symmetrical bandpass filter (BPF) with quasi-absorptive functionality was presented, based on an in-series cascade of several first-order stages. In [3], a distributed and symmetrical all-band quasi-absorptive filter with a matched resistor in series with a short-circuited quarter-wavelength transmission line was proposed to be achievable by cascading more bandpass sections. A set of one-, two- and three-pole quasi-absorptive microstrip bandpass filters were demonstrated in [3]. In [5], using the in-series cascading connection of multiple replicas of an input-reflectionless BPF, input-reflectionless wideband bandpass filters (BPFs) and balun BPFs with quasi-elliptical response were implemented. In [6], a new generic reflectionless filter topology was introduced, with a rigorous design methodology involving closed-form design formulas for distributed-element filters. In [8], a microstrip line symmetrical all-band absorptive bandpass filter (BPF) with arbitrarily prescribed wideband flat group delay (GD) characteristics was proposed; this filter can be easily extended to higher-order designs by cascading several first-order symmetrical quasi-absorptive BPFs. In [18], a quasi-reflectionless BPF composed of a two-stage coupled line and a shunt open-circuited stub is proposed; this filter features the characteristics of wide filtering bandwidth, wide reflectionless bandwidth, high selectivity, flat passband response and high out-of-band rejection.

In this letter, a compact absorptive microstrip bandpass filter with adjustable bandwidth and phase is presented, consisting of a bandpass section implemented using a coupled line and four absorptive stubs. Each absorptive stub consists of a quarter-wavelength short-circuited transmission line in series with a lumped resistor. The constraints imposed by the resistance of the absorptive stubs on the bandwidth, phase and absorptive ratio are revealed by simulations. The proposed absorptive bandpass filter is simulated, fabricated and measured. It features several distinct advantages such as compact size, adjustable bandwidth and phase, low insertion loss, excellent return loss and a high absorption ratio.

2. Analysis

The configuration of the proposed absorptive microstrip coupled-line bandpass filter is depicted in Figure 1. It can be seen that the bandpass filter comprises three blocks: M₁, M₂ and M₃. M₁ and M₃ are connected in parallel with Ports 1 and 2, respectively. They are identical structures that consist of a lumped resistor in series with a short-circuited quarter-wavelength transmission line. The lumped resistor is R_a, and the characteristic impedance and electrical length of the transmission lines are Z_a and θ, respectively. M₂ is a coupled-line section loaded with a stub at its open-circuited ports, respectively. The even- and odd-mode impedances of the coupled line with an electrical length of π/4 are Z_0e and Z_0o. The loaded stubs consist of a lumped resistor of R_b and a short-circuited line with an electrical length of θ and a characteristic impedance of Z_b. As a result, absorptive behavior can be achieved. Ports 1 and 2 are terminated with a load Z₀, which is 50 Ω.

The ABCD transmission matrix of the proposed absorptive bandpass filter can be expressed as

$$\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]=N_1{N}_2{N}_3$$

(1)

N₁, N₂ and N₃ represent the ABCD matrices of M₁, M₂ and M₃, respectively. They can be obtained from Figure 1 as

$$N_1=N_3=\left[\begin{array}{cc}1& 0\\ Y_A& 1\end{array}\right]$$

(2)

where

$$Y_A=1/Z_A=1/\left(R_a+j{Z}_a\tan \theta \right)$$

(3)

The ABCD matrix of M₂ is

$$N_2=\left[\begin{array}{cc}{A}_1& B_1\\ C_1& D_1\end{array}\right]$$

(4)

which can be expressed by the following equations, derived from the impedance matrix of the conventional four-port parallel-coupled-line structure [21]:

$$A_1=D_1=\left(\begin{array}{l}{K}_1{Z}_{0e}{Z}_{0o}\sin 2\theta +K_1{Z}_B^2\sin 2\theta +\\ j{K}_1^2{Z}_B{\sin }^2\theta -j4Z_{0e}{Z}_{0o}{\cos }^2\theta \end{array}\right)/Y$$

(5)

$$B_1=\left(\begin{array}{l}2K_1{Z}_{0e}{Z}_{0o}{Z}_B\sin 2\theta +j4{\left(Z_{0e}{Z}_{0o}\sin \theta \right)}^2+\\ j\left(K_1^2-4Z_{0e}{Z}_{0o}\right)Z_B^2-j{\left(K_1{Z}_B\cos \theta \right)}^2\end{array}\right)/Y$$

(6)

$$C_1=\left(\begin{array}{l}2K_1{Z}_B\sin 2\theta +j4Z_B^2{\sin }^2\theta \\ +j{K}_1^2{\sin }^2\theta -j4Z_{0e}{Z}_{0o}\end{array}\right)/Y$$

(7)

where K₁ = Z_0e + Z_0o, K₂ = Z_0e − Z_0o and

$$Z_B=1/\left(R_b+j{Z}_b\tan \theta \right)$$

(8)

$$Y=2K_2\left({Z^2}_A-Z_{0e}{Z}_{0o}\right)\sin \theta$$

(9)

We can then substitute (2) and (4) back into (1) to obtain

$$\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]=\left[\begin{array}{cc}{A}_1+Y_A{B}_1& B_1\\ C_1+Y_A\left(2A_1+Y{B}_1\right)& A_1+Y_A{B}_1\end{array}\right]$$

(10)

When Ports 1 and 2 are terminated with a load Z₀, which is set to 50 Ω in this letter, the expressions of the S-parameters of the absorptive passband filter can be derived from (10).

$$S_{11}={\displaystyle \frac{B-C{Z}_0^2}{A{Z}_0+B+C{Z}_0^2+D{Z}_0}}$$

(11)

$$S_{21}={\displaystyle \frac{2Z_0}{A{Z}_0+B+C{Z}_0^2+D{Z}_0}}$$

(12)

After that, the absorptive ratio and group delay can be obtained.

$$AR=1-{\left|S_{11}\right|}^2-{\left|S_{21}\right|}^2$$

(13)

$$\tau ={\displaystyle \frac{d\angle S_{21}}{d\omega }}$$

(14)

From the above analysis, it is evident that the 3 dB fractional bandwidth (FBW) for ∆S_21-3dB, the absorptive ratio and the group delay of the proposed circuit is determined by Z_a, Z_b, R_a, R_b, Z_0e, Z_0o and θ.

To achieve good characteristics for the bandpass section, when Ports 1 and 2 are terminated with a load Z₀ = 50 Ω and without four stubs, Z_0e and Z_0o can be estimated to be 157.66 Ω and 57.1 Ω in [9], respectively. The S-parameters and group delay of the coupled line are then plotted in Figure 2 using the substrate with ε_r = 3.00 and tanδ = 0.0013. As illustrated in Figure 2b, there is a depression at the center frequency, and there is a bump at each edge of the passband.

In order to better demonstrate the characteristics of the proposed absorptive bandpass filter with adjustable bandwidth and phase, Figure 3 shows the numerical results of the ABPF’s bandwidth, return loss, absorptive ratio and phase in terms of the design parameters using the substrate with ε_r = 3.00 and tanδ = 0.0013. Let R_a and R_b be equal to R and Z_a and Z_b equal to Z. When Z = 58.17 Ω, Z_0e = 157.66 Ω and Z_0o = 57.1 Ω, it can be seen from Figure 3a that the 3 dB fractional bandwidth (FBW) for ∆S_21-3dB increases from 25.8% to 42.5% as R goes from 50 Ω to 180 Ω. As observed from Figure 3b, the return loss is better than 10 dB from 1 GHz to 4 GHz as R increases from 50 Ω to 180 Ω. Meanwhile, at 1 GHz and 4 GHz, the absorption rate is better than 90%, and it changes from low to high and then to low as R increases in Figure 3b. In addition, the smaller R is, the flatter the group delay is, as shown in Figure 3c. As can be seen by comparing Figure 3c with Figure 2b, the structure has the effect of pulling low and limiting high for the group delay.

Numerical results for the ABPF’s bandwidth, return loss, absorptive ratio and phase in terms of the design parameters using the substrate with ε_r = 3.00 and tanδ = 0.0013 are displayed in Figure 4. When R = 80 Ω, Z_0e = 157.66 Ω and Z_0o = 57.1 Ω, it can be seen from Figure 4a that the bandwidth for ∆S_21-3dB increases from 19.2% to 51.6% as Z goes from 32.91 Ω to 100.7 Ω. The return loss is better than 12 dB from 1 GHz to 4 GHz as Z increases from 32.91 Ω to 100.7 Ω, as shown in Figure 4b. Meanwhile, at 1 GHz and 4 GHz, the absorption rate is higher than 90%, and it changes from low to high, then to low again as Z increases, as seen in Figure 4c. In addition, the larger Z is, the lower the group delay is at the center frequency, as shown in Figure 4d. As can be observed from Figure 3 and Figure 4, there is a trade-off among the BPF bandwidth, return loss, phase and absorptive ratio. Therefore, it should be pointed out that the physical parameters should be designed according to the specified bandwidth, return loss, phase and absorption rate for a particular application.

3. Design, Fabrication and Results

An absorptive microstrip coupled-line bandpass filter having input and output impedances of 50 Ω and operating at a center frequency of 2.4 GHz was designed based on the absorptive BPF model in Figure 1. The layout of the filter using Rogers RO3003 (Rogers Corporation, Rogers, CT, USA) substrate (ε_r = 3.00 and tanδ = 0.0013) with a thickness of 0.762 mm is displayed in Figure 5a. The physical dimensions of the absorptive filter, as shown in Figure 5a, were obtained by means of simulations using ANSYS HFSS v15.0. The optimum circuit parameters of the absorptive filter for the required specification are given as Z_0e = 157.66 Ω, Z_0o = 57.1 Ω, Z = 50.59 Ω and R = 100 Ω.

In order to demonstrate the performance of the presented absorptive bandpass filter, the circuit was realized in a microstrip line and was fabricated for verification. A photo of the fabricated absorptive BPF with a circuit size of 0.27λ₀ × 0.51λ₀ is shown in Figure 5b; its scattering parameters and group delay performances were measured using an Agilent vector network analyzer and are shown in Figure 5b,c. It is clear that the circuit size can be reduced to at least 0.27λ₀ × 0.25λ₀. The calculated power absorption ratio is plotted in Figure 5d. It can be seen that the measured results of the fabricated absorptive BPF are in excellent agreement with the simulated ones.

From the measured results, a group delay less than 0.72 ns was observed at f₀ = 2.4 GHz, and the variation was quite small over the frequency range from 0.5 GHz to 4 GHz, as seen in Figure 5b. As can be observed in Figure 5c, the measured ∆S_21-3dB of the fabricated filter was determined to be 27.8%. The insertion loss (IL) at f₀ = 2.4 GHz was estimated to be 0.20 dB, and the experimental input and output return loss results at f₀ = 2.4 GHz were 25.81 dB and 25.34 dB, respectively. Meanwhile, the measured in-band and out-of-band return loss results of the ABPF were higher than 21.26 dB and 20.73 dB, respectively. Moreover, as displayed in Figure 5d, the minimum stopband power absorption ratio was observed to be 98.96%, and the minimum passband absorption ratio was 2.5% in the passband. As observed from Figure 3, Figure 4 and Figure 5, the numerical analysis, simulations and measurements agree well with each other.

Table 1. Comparison of recently published absorptive BPFs.

Reference	${\mathit{f}}_0$ (GHz)	IL (dB)	RL (dB)	∆S21-3dB (100%)	GD (ns)	Absorption Ratio (100%)	Circuit Size
[2]	2.45	2.2	14.8/10	6	4	NG/NG	1.25${\lambda }_0$ × 0.42${\lambda }_0$
[3]	2.45	0.60	40/13	22.5	1.10	NG/NG	0.71${\lambda }_0$ × 0.46${\lambda }_0$
[6]	2.0	NG	NG/12	50	1.5	NG/NG	0.56${\lambda }_0^2$
[8]	3.5	0.91	NG/6	8.71	1.72	NG/NG	0.28${\lambda }_0$ × 0.70${\lambda }_0$
This work	2.4	0.26	21.26/20.73	27.8	0.72	98.21/2.5	0.27${\lambda }_0$ × 0.51${\lambda }_0$

RL: minimum inside- and outside-passband return loss; NG: never given.

provides a detailed comparison of our proposed absorptive bandpass filter and other recently reported designs.

4. Conclusions

In this letter, a compact dual-port absorptive microstrip bandpass filter with adjustable bandwidth and phase has been proposed. A combination of four absorptive stubs with resistors has been utilized to produce the dual-port absorption; the bandwidth and the phase of the filter can be adjusted by changing the resistance values. The proposed absorptive BPF features compact size, tunable bandwidth, good return loss, low insertion loss and good symmetric reflectionless properties; this filter may have a wide range of applications in microwave and RF circuits and systems, such as antenna feeds, power dividers and baluns.