A Tunable Constant-Absolute-Bandwidth Bandpass Filter with Switchable Ability

Abstract

This paper presents a tunable bandpass filter (BPF) with constant absolute bandwidth (CABW) and switchable properties. The BPF is performed by using a tri-mode cross-shape resonator (CSR) loaded with varactors. The CABW and switchable ability are achieved by adjusting the resonant frequencies. Meanwhile, the two transmission zeros (TZs) produced by center-loaded stubs strengthen the skirt selectivity in the on-state and the isolation in the off-state. For demonstration, a tri-pole switchable BPF with three control voltages is implemented and verified, and the control mechanism is simple. In the on-state, it exhibits a 120 MHz, 3 dB CABW with the measured insertion loss (IL) of 2.2–2.5 dB in the tuning range of 0.816–1.188 GHz. In the off-state, the measured isolation is better than 27 dB.

1. Introduction

Modern wireless communication systems require multifunctional RF front-ends in which reconfigurable filters play an essential role for easy integration. Additionally, a number of filters with tunability of center frequency (CF), bandwidth (BW) or TZs have been reported [1,2,3,4,5,6,7]. Furthermore, reconfigurable filters with switchable ability have attracted the attention of researchers since they are able to form switched filter banks and expand the tuning range of the filter [8,9,10,11].

By utilizing pin diodes as switches to tunable BPFs, a BPF which can switch the low- or high-tunable passband in on-state is proposed in [11], and a BPF which can switch the tunable passband in the on- or off-state is proposed in [12]. However, the use of pin diodes will make the design bulky and the control complex. To overcome this problem, intrinsically switched tunable BPFs are proposed, and the switching function is performed by using the filters’ own tuning elements without additional switches. Through controlling the coupling coefficients between resonators to be zero [9,10,13], adjusting the TZs to suppress the passband [14,15,16], and employing transversal filter structures based on multimode resonators and modifying the resonant frequencies of odd- and even-mode to be the same [17,18], the tunable filters have the ability to switch the passband in the off-state.

On the other hand, the tunable BPFs with CABW property, which can replace a number of fixed filters and reduce the size of the communication systems, have also attracted lots of attention. By compensating the coupling coefficient with the inter-resonator varactors [19,20,21], choosing a proper coupling region [22,23], and maintaining the separation between resonant frequencies [18,24], tunable BPFs with CABW property have been reported.

In this letter, a tunable CABW BPF with switchable ability is proposed based on a novel CSR. The tunable CABW is accomplished by adjusting the resonant frequencies and maintaining their separations simultaneously. Moreover, the switchable ability of the passband is achieved by using its transversal filter structure. By utilizing the transmission zeros of the resonator, the skirt selectivity of the on-state and the isolation of the off-state are improved [25]. As a demonstration, a prototype of a switched tunable 120 MHz 3-dB CABW BPF with a tuning range of 0.816–1.188 GHz is developed and characterized. Experimental and simulated results are in good agreement.

2. Filter Design and Analysis

2.1. Analysis of CSR

The proposed tri-mode CSR shown in Figure 1a consists of a half-wave resonator and two shunt stubs, where Y₁, Y₂ and Y₃ are the characteristic admittances and θ₁, θ₂ and θ₃ are the electrical lengths. For tuning the resonant frequencies, three types of varactors (C₁, C₂ and C₃) are added in the resonator.

Due to the symmetrical structure, the odd- and even-mode equivalent circuits can be expressed as shown in Figure 1b,c, respectively [26]. The input admittances of the proposed resonator can be derived as follows.

For odd-mode

Y_o = −jY₁cotθ₁ + j2πfC₁,

(1)

The odd-mode resonant frequency f_o can be determined according to Im (Y_o) = 0.

For even-mode

Y_e1 = −jY₁cotθ₁ × 2πfC₁/(−Y₁cotθ₁ + 2πfC₁),

(2)

Y_e2 = Y₂ (j2πfC₂ + jY₂tanθ₂)/(2Y₂ − 4πfC₂tanθ₂),

(3)

Y_e3 = Y₃ (j2πfC₃ + jY₃tanθ₃)/(2Y₃ − 4πfC₃tanθ₃),

(4)

Y_e = Y_e1 + Y_e2 + Y_e3,

(5)

The two even-mode resonant frequencies f_e1 and f_e2 can be deduced by Im (Y_e) = 0.

Based on Equations (1)–(5), Figure 2 shows the tuning range of f_o with variation of C₁, and Figure 3 plots the f_o, f_e1 and f_e2 dependence on C₂ and C₃ for C₁ = 1 pF. It can be observed that the odd-mode resonant frequency f_o is only controlled by C₁, and the even-mode resonant frequencies f_e1 and f_e2 are varied around f_o by tuning C₂ and C₃ when C₁ is fixed, that is to say, the specified frequency space between f_e1/e2 and f_o can be obtained by tuning C₂ and C₃. Note that there is a set of C₂ and C₃ makes f_e1 = f_o = f_e2 for fixed C₁ (f_o), and this feature can be used for switching off the passband, which will be discussed in Section 2.2.

2.2. Coupling Matrix Analysis

Figure 4 shows the transversal topology architecture of the proposed filter, which consists of a tri-mode CSR, source, load and external quality factor Q_e. The denormalized coupling matrix can be expressed as [18]

$$\left[m_{\mathsf{\Delta }}\right]=\left[\begin{array}{ccc}{m}_{\mathrm{e}1\mathrm{e}1}& 0& 0\\ 0& m_{\mathrm{oo}}& 0\\ 0& 0& m_{\mathrm{e}2\mathrm{e}2}\end{array}\right],$$

(6)

where m_e1e1/oo/e2e2 = f_d/f_e1/o/e2 − f_e1/o/e2/f_d, f_d is the frequency-mapping element.

The external quality factor can be expressed as [27]

Q_e = (Q_exe1 + Q_exe2 + Q_exo)/3,

(7)

Q_{exe1/exe2/exo} = f_e1/e2/o/Δf_{e1/e2/o±90°},

(8)

where Q_{exe1/exe2/exo} and Δf_{e1/e2/o±90°} are the external quality factor and BW of the three resonant modes, respectively.

By separately tuning the parameters of the coupling matrix and Q_e, the theoretical response curves with f_d = 1 GHz are given in Figure 5, Figure 6 and Figure 7 [18,28]. Figure 5 displays the theoretical response curves varying m_e1e1, m_oo and m_e2e2 considering a fixed Q_e = 28. As can be seen, center frequency tuning behavior with CABW property can be obtained by purposely changing the variable elements in the coupling matrix. As shown in Figure 6, the specified 3 dB BW can be achieved by adjusting the frequency space between f_e1/e2 and f_o, and BW_3dB ≈ f_e2 − f_e1 when f_e2 > f_o > f_e1. In particular, when m_e1e1 = m_e2e2 = m_oo = 0 (i.e., f_e1 = f_o = f_e2), the passband is switched off. Figure 7 illustrates the calculated frequency responses when Q_e is tuned from 40 to 10 but the elements of the coupling matrix are fixed as m_e1e1 = −m_e2e2 = 0.15 and m_oo = 0. The return loss (RL) of the passband increases when Q_e decreases, and the 3 dB BW of the passband is almost independent of Q_e when Q_e varies from 40 to 20, but as Q_e continues to decrease, the 3 dB BW becomes narrower and cannot be estimated as f_e2 − f_e1. As a conclusion, the specified BW and off-state of the passband can be controlled by f_e1, f_o and f_e2, and a range of Q_e provide controllable BW with a RL of the passband better than a certain value.

2.3. Analysis of TZs

The two shunt stubs taped with C₂ and C₃ can produce two TZs, respectively. The input admittances of the two stubs are as below.

Y_d = Y₂ (j2πfC₂ + jY₂tanθ₂)/(Y₂ − 2πfC₂tanθ₂),

(9)

Y_u = Y₃ (j2πfC₃ + jY₃tanθ₃)/(Y₃ − 2πfC₃tanθ₃),

(10)

The frequencies of the two TZs f_z1 and f_z2 can be deduced by Y₂ − 2πfC₂tanθ₂ = 0, and Y₃ − 2πfC₃tanθ₃ = 0, respectively [29]. As can be seen, f_z1 and f_z2 are controlled by C₂ and C₃, respectively.

In Figure 8, the weak coupling transmission responses are investigated when Y₁ = Y₂/2 = Y₃/2 = 1/75 S, θ₁ = 65°, θ₂ = 60° and θ₃ = 35° at 1 GHz. Seen from Figure 8, the condition of f_z1 < f_e1 < f_o < f_e2 < f_z2 can be realized, and the two TZs can be utilized to improve the out-of-band rejection. By increasing C₂ and decreasing C₃, the BW (f_e2 − f_e1) becomes narrower and the two TZs follow the variations of f_e1 and f_e2. When f_e1 = f_o = f_e2 is realized by tuning C₂ and C₃, the two TZs are also tuned to the same frequency as f_o and can be used to enhance the isolation of the off-state.

2.4. Schematic Diagram of the Filter and the External Quality Factor

Figure 9 presents the schematic diagram of the reconfigurable BPF based on the CSR proposed in this paper. The BPF consists of a CSR and a pair of feedlines. The three resonant modes of the CSR are utilized to form the three poles of the filter, and the two transmission zeros of the CSR are used to improve the skirt selectivity of the filter in on-state and the isolation in off-state. The variable capacitors are realized by varactors, and several lumped components are employed for DC blocks (C_b = 30 pF) and DC bias (R_b = 10 kΩ). The voltages V₁, V₂ and V₃ are utilized to tune the capacitances of the varactors. Due to the influence of C_b, the relationship between C_i in Figure 1 and C_vi (i = 1, 2, 3) in Figure 9 are C₁ = C_v1, C₂ = C_bC_v2/(C_b + C_v2) and C₃ = C_bC_v3/(C_b + C_v3).

Based on the discussion in Section 2.2, the desired Q_e for realizing a BPF with 120 MHz 3 dB BW in the frequency range of 0.8–1.2 GHz is illustrated in Figure 10, where Q_emax is the maximum external quality factor, with which the RL of the passband is better than 10 dB, and Q_emin is the minimum external quality factor, with which the 120 MHz 3 dB BW of the passband can be estimated by f_e2 − f_e1. Therefore, Q_e between Q_emin and Q_emax can be utilized to realize a passband with following characteristics: dB|S₁₁| < −10 dB and BW_3dB ≈ f_e2 − f_e1 = 120 MHz.

Q_e curves with different distance s in the frequency range of 0.8–1.2 GHz are extracted by Equations (7) and (8) and shown in Figure 10. When frequency is changed from 0.8 to 1.2 GHz, the Q_e curve changes from increasing to decreasing, and when s is adjusted from 0.15 to 0.25 mm, the Q_e curve moves from a small value to large. Apparently, Q_e (s = 0.2 mm) is in the range between Q_emin and Q_emax in the frequency range of 0.8–1.2 GHz and can be used to design the tunable BPF with 120 MHz 3 dB BW.

3. Experimental Verification

The reconfigurable BPF is fabricated on a 0.508 mm RO4003C substrate with a relative dielectric constant of 3.55 and a loss tangent of 0.0027. The EM simulator SONNET is employed for the physical dimension optimization, and the final physical parameters of the filter are determined as in

Table 1. Physical parameters of the proposed filter.

Parameter	Value (mm)	Parameter	Value (mm)
l1	31.6	w1	0.5
l2	33.6	w2	1.5
l3	19.2	w3	1.5
l4	28.8	w4	0.5
s	0.18	w5	1.1

. C_b = 30 pF and R_b = 10 kΩ are used as DC block and DC bias, respectively. The varactors Ma46H201 from M/A COM are employed as C_v1s, the varactors Ma46H202 from M/A COM are employed as C_v2 and C_v3, and the voltages V₁, V₂ and V₃ are utilized to control the capacitances of C_v1s, C_v2 and C_v3, respectively. The photography of the fabricated reconfigurable BPF is presented in Figure 11. The size of the filter is approximately 0.09 λg × 0.18 λg, where λg is the guided wavelength on the substrate at 0.816 GHz.

The measurement is performed with a Rohde & Schwarz ZVA24 analyzer. The measurement results are compared with the simulation results as shown in Figure 12 and Figure 13. Figure 12 shows the results of the filter as a CABW tunable filter with a 3 dB BW of 120 MHz. The center frequency can vary from 0.816 to 1.188 GHz and the measured 3 dB BW of the filter is 120 ± 2 MHz, the measured IL is 2.2–2.5 dB, and the measured RL is better than 10 dB over the tuning range. The IL is dominated by the parasitic resistances of the varactors [3]. Two TZs on either side of the passband improve the skirt selectivity. Figure 13 shows the results of the filter in the off-state. As can be seen, the measured isolation is better than 27 dB. A comparison with other tunable CABW BPFs presented in previous studies is provided in

Table 2. Comparisons with previously reported tunable CABW filters.

Ref No.	Filter Order	Number of Control Voltages	IL in Passband (dB)	Off-State	Isolation in Off-State (dB)	Size $\left({\mathit{\lambda }}_{\mathbf{g}}^2\right)$
[20]	2	3	1.2–2.3	No	-	0.0042
[23]	2	1	1.34–2.92	No	-	0.0224
[12]	2	3	2.52–4.08	Yes	>43	0.0183
[17]	2	2	1–3	Yes	>10	0.0121
[18]	2	4	≤3.8	Yes	>20	0.0211
This work	3	3	2.2–2.5	Yes	>27	0.0162

. The tunable CABW BPFs proposed in [20,23] have no switchable ability. The switchable ability of the filter proposed in [12] is realized by using PIN diodes, therefore, extra bias voltages are needed in the design and the IL is poor. The number of the control voltages is the same as the order of the proposed filter in [17], which makes its control simplistic, however, the isolation of its off-state is poor. The two-pole tunable CABW filter in [18] presents a minimum 20 dB isolation of its off-state, but the number of the control voltages is four. In this study, the tunable CABW filter presents low IL in the on-state and high isolation in the off-state, and the tri-pole BPF with switchable ability using only three bias voltages, which simplifies the control complexity.

4. Conclusions

This letter proposed a tri-pole reconfigurable CABW BPF with switchable ability. The CSR loaded with varactors is employed to make the tunable element, and the center-loaded stubs in the CSR are utilized to generate the two TZs and improve the selectivity of the filter. Coupling matrix analysis of the transversal filter structure shows that center frequency tuning CABW and switchable ability can be achieved through adjusting the resonant frequencies. The weak coupling transmission-line responses demonstrate that the TZs can be used to improve the isolation of the off-state. Center frequency tuning, CABW maintenance, and switchable ability of the tri-pole filter are realized by using only three control variables, which simplifies the control complexity. The proposed filter has the potential to be applied in switched filter banks to reduce control complexity.