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Novel wideband tunable resonator and the application to frequency-agile bandpass and bandstop filters.

1. INTRODUCTION

In modern wireless communication systems, tunable frequency filters are often used as tracking filters for multiband telecommunication systems, radiometers, and wide-band radar systems. Therefore, extensive studies have been done and many technologies have been considered in this topic. Different tuning components have been employed in the tunable filter designs, i.e., MEMS switches [1-5], semiconductor varactors [6-17]. Barium-strontium-titanate (BST) [18] and yttrium iron garnet (YIG) techniques [19] are also utilized to design tunable filters.

Among the tunable BPFs, the combline and interdigital structures are widely used as BPFs in modern microwave and millimeterwave subsystems due to their compactness, excellent stopband and selectivity performance, and easy integration [20]. Microstrip combline and interdigital tunable bandpass filters have been investigated by many researchers in the past few years [1,2,6-14]. In recent years, tunable BSFs have attracted increasing interests [4,15-19]. Regardless of the tuning methods involved in the aforementioned filter designs, the resonators of these filters are each short-circuited to ground or open at the ends while the opposite ends are terminated in lumped capacitors. The using of the abovementioned resonators either limits the tuning range or increases the insertion loss of the filters.

In this paper, a novel end-loaded resonator is investigated and applied to design tunable BPF and BSF. The novelty of the resonator lies in that two varactors are added to the two ends of the resonator, and then its resonant frequency can be bi-directionally tuned. The resonant frequency of the proposed resonator is derived and simulated. As a result, the theoretical frequency tuning range can be significantly extended to approximately double that of the conventional tunable resonator. The demonstrated tunable interdigital BPF with the proposed resonators can achieve a wide tuning range (52.4%) while retaining minimum degradation (less than 2.4dB) in the passband. The tuning range of the demonstrated tunable BSF using the proposed resonators is 53.5% while the return loss is greater than 10dB in the tuning range.

2. ANALYSIS OF PROPOSED TUNABLE RESONATOR

Figure 1(a) shows the proposed structure of the resonator loaded by one varactor at one end and another at the opposite end. The transmission line can be either uniform or non-uniform. The analysis is focused on the uniform case. The input admittance Yin is given by

[Y.sub.in] = [Y.sub.0][[jb.sub.1] + j[Y.sub.0] tan [[theta].sub.1]/[Y.sub.0] + j([jb.sub.1])tan [[theta].sub.1]] + [Y.sub.0][[jb.sub.2] + j[Y.sub.0] + tan [[theta].sub.2]/[Y.sub.0] + j([jb.sub.2])tan [[theta].sub.2]) (1)

[b.sub.i] = [omega][C.sub.vi] (2)

where [Y.sub.0] is the characteristic admittance of the transmission line, [[theta].sub.i] the electrical length of the transmission lines, bi the admittance of the varactors, Cvi the tunable capacitance of the varactors, and L (= [[lambda].sub.g]/4, [[lambda].sub.g] is the guided wavelength at the resonance frequency) the length of the transmission line. Three typical cases are discussed below.

Case 1: [b.sub.1] (or [C.sub.v1]) is infinite and [b.sub.2] (or [C.sub.v2]) approaches zero, i.e., the end of the transmission line loaded by varactor ([C.sub.v1]) is equivalently shorted and another end loaded by varactor ([C.sub.v2]) is equivalently open, as shown in Figure 1(b). Thus, the resonant condition is that the imaginary part of Yin is equal to zero, namely, Im{[Y.sub.in]} = 0, resulting in

1 - tan [[theta].sub.1] tan [[theta].sub.2]/tan [[theta].sub.1] + tan [[theta].sub.2] = 1/tan([[theta].sub.1] + [[theta].sub.2]) = 0 (3)

Thus, the fundamental resonant frequencies ([f.sub.01]) can be expressed as

[f.sub.01] = c/4L[square root of [[epsilon].sub.e]] (4)

c is the velocity of light speed in free space, [[epsilon].sub.e] is the effective permittivity.

Case 2: [b.sub.1] (or [C.sub.v1]) is infinite and [b.sub.2] (or [C.sub.v2]) is finite, i.e., the end of the transmission line loaded by varactor ([C.sub.v1]) is equivalently shorted, as shown in Figure 1(c). Similarly, the fundamental resonant frequency ([f.sub.02]) for this case can be derived easily as

[f.sub.02] = [arctan([Y.sub.0]/2([pi][f.sub.02][C.sub.V2]))] x c/2[pi]L[square root of [[epsilon].sub.e]] (5)

When [C.sub.v2] [approximately equal to] 0, meaning the end of the transmission line loaded by varactor ([C.sub.v2]) is equivalently open-circuited, so (5) is equal to (4). It is easy to see that [f.sub.02] may be tuned towards lower frequency as [C.sub.v2] varies from small to large capacitance with the bias voltage ([V.sub.2]) of the tuned varactor, while the voltage ([V.sub.1]) of the other varactor ([C.sub.v1]) is fixed, as shown in Figure 2(a).

Case 3: [b.sub.1] (or [C.sub.v1]) is finite and [b.sub.2] (or [C.sub.v2]) approaches zero, i.e., the end of the transmission line loaded by varactor ([C.sub.v2]) is equivalently open-circuited, as illustrated in Figure 1(d). Similarly, the fundamental resonant frequency ([f.sub.03]) for this case can be expressed as

[f.sub.03] = [[pi] - arctan(2[pi][f.sub.03][C.sub.V1]/[Y.sub.0])] x c/2[pi]L[square root of [[epsilon].sub.e]] (6)

When [C.sub.v1] [right arrow] [infinity], implying that the end of the transmission line loaded by varactor ([C.sub.v1]) is equivalently short-circuited, then (6) is equal to (4). In this way, [f.sub.03] may be tuned towards upper frequency as [C.sub.v1] decreases with the reverse-biased voltage ([V.sub.1]), while the voltage ([V.sub.2]) of [C.sub.v2] is kept unchanged, as shown in Figure 2(b).

Based on the above analyses, the proposed resonator can find some potential applications in tunable filters. For validation purposes, the filters are implemented using microstrip technology due to the fabrication simplicity. The substrate used is Rogers RO4000 ([[epsilon].sub.r] = 3.38, substrate thickness h = 0.813mm, loss tangent = 0.0027). The silicon varactors involved in the designs are ISV232 and JDV2S71E from Toshiba, and the capacitance ratios of the varactors are 10.5 and 11.5, respectively.

3. DESIGN OF TUNABLE FILTERS USING PROPOSED RESONATOR

3.1. Design of Tunable Interdigital Bandpass Filter

As the coupling coefficients of interdigital structure is larger than that of combline structure [21], the interdigital filter is easer to be fabricated and welded with larger coupling space. In this section, a tunable interdigital BPF is designed to verify the application of the proposed end-loaded resonators in tunable BPFs. When the ends of the resonator with [C.sub.v1] (large enough) are equivalently shorted to ground, the configuration and equivalent circuit of the BPF are shown in Figures 3(a) and (b). The transmission-line segment is modeled as the equivalent distributed inductor. The coupling between the resonators is denoted as the impedance inverter [K.sub.01]. When the ends with [C.sub.v2] (small enough) are equivalently open-circuited, the configuration and equivalent circuit of the BPF are shown in Figures 3(c) and (d). The transmission-line segment ([[theta].sub.1]) is modeled as the capacitor ([C'.sub.1]). The transmission-line segment ([[theta].sub.2]) and varactor ([C.sub.v1]) are equivalent to the serial-connected inductor (L) and variable capacitor ([C'.sub.v1]). The couplings between the resonator lines are also denoted as the impedance inverter [K'.sub.01].

Figure 4(a) shows the structure and design parameters of the filter using three straight microstrip lines. The input and output feeding lines (50 [OMEGA]) are tapped at the first and last microstrip lines in which two capacitors ([C.sub.3]) are embedded and function as DC block. Two different varactors are serially connected at the ends of each microstrip line through the capacitors ([C.sub.1] and [C.sub.2], functioning as DC block, their selections have been analyzed in [22], and they also service as voltage dividers to give a lower AC voltage swing across the varactors and better linearity). The RF chokes are connected to reduce the impact on the DC power.

In this tunable BPF design, the first step is to design a high performance BPF using the conventional quarter-wavelength microstrip lines as the resonators. The design is similar to that of the interdigital filter [21]. The center frequency of the passband is decided by the length of the microstrip resonator, while the tap position ([L.sub.3]) and gap (g) affect the external quality factor and coupling coefficient [21]. Therefore, the frequency response may be obtained by choosing appropriate [L.sub.3], g and microstrip line length. Figure 4(b) shows the simulated response when [W.sub.1] = 1.9 mm, [W.sub.2] = 1.8 mm, [L.sub.1] = 59.3 mm, [L.sub.2] = 56.3 mm, [L.sub.3] = 42.6 mm, g = 0.8 mm.

When the ends of the microstrip resonators are end-loaded with the loading elements, as shown in Figure 4(a), the center frequency, external quality factor and coupling coefficient would change. To realize good performance for the filter in the tuning range, [C.sub.1], [C.sub.2], [W.sub.2], [L.sub.1], [L.sub.2] and [L.sub.3] were optimized. The optimized parameters are listed in Figure 4(a). The frequency response of the tunable BPF is discussed as follow.

Initially, the reverse-biased voltage (Vi) of the ISV232 ([C.sub.v1]) is fixed at 0V, i.e., the capacitance of ISV232 ([C.sub.v1]) is large and the ends with which are equivalently short-circuited. The fundamental passband frequency decreases with the reverse-biased voltage ([V.sub.2]) of JDV2S71E ([C.sub.v2]) from 14.5 to 0V (i.e., the capacitance of JDV2S71E ([C.sub.v2]) varies from small to large capacitance). The simulated and measured results in cases of several bias voltages are plotted in Figurea 5(a), (b). The tendency of the tuned frequency in Figures 5(a), (b) corresponds well to that in (5). The center frequency can be continuously tuned from 572.9 to 777.1MHz (featuring fractional tuning range of 30.3%), while the measured passband insertion loss over the tuning range varies from 2.14 to 2.4 dB, including the loss of the SMA connectors. The passband return loss is better than -12 dB within the tuning range. For each tuning state, a transmission zero is found to locate at the upper edges of the fundamental passband, which improve the roll-off rate.

When the bias voltage ([V.sub.2]) of the JDV2S71E ([C.sub.v2]) is fixed at 14.5 V, i.e., the capacitance of JDV2S71E is small and the ends connecting JDV2S71E ([C.sub.v2]) are equivalently open-circuited, the fundamental passband frequency increases with the bias voltage ([V.sub.1]) of ISV232 ([C.sub.v1]) from 0 to 16.5 V (i.e., the capacitance of ISV232 ([C.sub.v1]) varies from large to small). The simulated and measured results for different bias voltages are shown in Figures 5(c), (d), agreeing well with the results from (6). The center frequency can be continuously tuned from 777.1 to 979.3MHz (23.8%). The measured insertion loss of the passband over the tuning range varies from 2.4 to 1.44 dB. The passband return loss is better than -10 dB within the tuning range. A transmission zero is also located at the upper edges of the fundamental passband within the tuning range, and high selectivity is obtained.

The implemented filter is shown in Figure 6 with the size of 0.21[[lambda].sub.g] x 0.07[[lambda].sub.g] (59.3mm x 19.6mm), which includes the diodes and the soldering pads, where [[lambda].sub.g] is the guided wavelength at the lowest passband frequency. The frequency can be tuned from 572.9 to 979.3 MHz (52.4%) with the insertion loss less than 2.4dB. For comparison, Table 1 summarizes the comparison of the proposed BPF and other work. We may see that the proposed filter has the advantages of compact size, wide tuning range and minimum degradation.

3.2. Design of Tunable BSF

In this section, a tunable BSP is designed to verify the application of the proposed end-loaded resonators in tunable BPFs. When the ends of the resonator with [C.sub.v1] (large enough) are equivalently shorted to ground, the configuration and equivalent circuit of the proposed BPF are shown in Figures 7(a) and (b). The coupling region is denoted by the admittance inverter J01. The resonator is equivalent to the parallel-connected inductor L and capacitor [C.sub.v2]. When the ends with [C.sub.v2] (small enough) are equivalently open-circuited, the configuration and equivalent circuit of the proposed BPF are shown in Figures 7(c) and (d). The transmission-line segment ([[theta].sub.3]) is modeled as the capacitor ([C'.sub.2]). The transmission-line segment ([[theta].sub.2]) and varactor ([C.sub.v1]) are equivalent to the serial-connected inductor (L') and variable capacitor ([C'.sub.v1]). The coupling between the resonator lines is also denoted by the admittance inverter [J'.sub.01].

Figure 8(a) shows the structure and design parameters of the BSF. The basic structure consists of two coupled-line sections and a transmission line in the middle. In each coupled-line section, the resonator is coupled to the main line, forming a bandstop structure. Two capacitors ([C.sub.2]) are embedded in the feeding lines (50 [OMEGA]) functioning as DC block. The varactors (ISV232) are serially connected at the ends of each resonator directly, while the varactors (JDV2S71E) are serially connected at the opposite ends of each resonator through the capacitors (C1, functioning as DC block). The RF chokes are connected to reduce the impact on the DC power.

In this tunable BSF design, the first step is also to design a high performance BSF using the conventional quarter-wavelength microstrip lines as the resonators. The design procedures are similar to that of the BSF [21]. Therefore, the frequency response may be obtained by choosing the appropriate length of the microstrip resonator, the length and gap of the coupled-line section. Figure 8(b) shows the simulated response when W = 1.9 mm, [W.sub.1] = 0.4 mm, [W.sub.2] = 1 mm, [W.sub.3] = 2 mm, s = 0.2 mm, [L.sub.1] = 17.8 mm, [L.sub.2] = 12.95 mm, [L.sub.3] = 9.2 mm, [L.sub.4] = 0.1 mm, [L.sub.5] = 11.55 mm, [L.sub.6] = 7.8 mm, [L.sub.7] = 3 mm, [L.sub.8] = 2 mm, [L.sub.9] = 5 mm. It is interesting to notice that there are two transmission zeroes in the stopband, owing to the different length of the two resonators. When the ends of the microstrip resonators are end-loaded with the loading elements, the optimized parameters are listed in Figure 8(a).

Following the same way with the aforementioned BPF, Figures 9(a), (b) illustrates the simulated and measured results for several typical bias voltages ([V.sub.2]) of JDV2S71E from 15 to 0 V as the reverse-biased voltage ([V.sub.1]) of the ISV232 ([C.sub.v1]) is fixed at 0 V, which agree fairly with each other. The results show that the fundamental stopband frequency can be continuously tuned from 608.6 to 781 MHz (24.8%). The measured maximum attenuation levels are better than 16.6dB. The passband insertion loss is better than 0.4 dB, and the return loss is greater than 10 dB for each tuning state. For each tuning state, two transmission poles are near the stopband edges, which improve the roll-off rate.

In the case of the bias voltage ([V.sub.2]) of JDV2S71E ([C.sub.v2]) fixed at 15 V, the simulated and measured results for several typical bias voltages (V1) of ISV232 from 0 to 30 V are depicted in Figures 9(c), (d), which are in reasonable agreement. The results show that the fundamental stopband frequency can be continuously tuned from 781 to 1053 MHz (29.6%). The measured maximum attenuation levels are better than 16.6dB. The passband insertion loss is better than 0.4dB, and the return loss is greater than 10 dB for each tuning state. Two transmission poles are near the stopband edges, high selectivity is thus obtained. There are two zeroes in the stopband, guarantying the in-band performance.

The implemented filter is shown in Figure 10. The whole size of this filter is less than 0.115[[lambda].sub.g] x 0.147[[lambda].sub.g] (30.9mm x 39.5 mm). The center frequency can be changed from 608.6 to 1053 MHz (53.5%) with the return loss better than 10 dB. A comparison with other reported BSFs is given in Table 2, which shows that the proposed filter using only two unit cells has good characteristics with wide tuning range and better in-band performance.

According to the above descriptions, we can summarize the design procedures of the frequency-agile filters using the proposed tunable resonators as follows.

1. First, calculate the physical dimensions of a conventional quarter-wavelength resonator according to the design requirements. Second, with the help of ADS, the initial physical parameters of the filter can be attained. Last, the optimized physical parameters can be achieved by using the EM simulator, e.g., HFSS.

2. Select the suitable loading elements such as the DC block capacitors, the varactors and the chokes according to the frequency response of the above filter using the conventional quarter-wavelength resonators and then add the loading elements to the filter. In order to decrease the insertion loss and obtain a wide tuning range, the capacitance ratio and the resistance of the varactors should be larger and smaller respectively.

3. The structural model is built in the EM simulator such as HFSS and the lumped elements are built in ADS. Through the co-simulation, the frequency response can be attained from the simulation results of ADS. By optimizing the physical dimensions and lumped elements a tunable filter with high performance can be got.

4. CONCLUSIONS

This paper presents a novel tunable resonator, which is end-loaded by two different varactors. The resonant condition is analyzed and simulated. This kind resonator is employed to design the frequency-agile BPF and BSF. The simulated results and experimental verifications have been provided, agreeing well with the theoretical predictions, and also indicates that the filters consisting of the proposed resonators have a wider tuning range than the conventional tunable filters, while retaining better performance, e.g., better passband insertion loss or stopband return loss etc.. For the tunable BPF, a wide tuning range (52.4%) has been achieved with the insertion loss less than 2.4dB. A transmission zero is near the upper passband edges and the selectivity is improved for each tuning state. With regard to the tunable BSF, a wide tuning range (53.5%) has been achieved with the return loss better than 10dB. For each tuning state, two transmission poles are near the stopband edges and two transmission zeroes are located in the stopband. With these features, this kind of tunable BPF and BSF using the proposed end-loaded resonators can be very useful in multiband and wideband reconfigurable systems.

ACKNOWLEDGMENT

The authors would like to thank the financial support from the National Natural Science Foundation of China (60971013), the 2009 Innovative Graduate Projects of Jiangsu Province and the Program for New Century Excellent Talents in University (NCET-11-0993).

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Y.-L. Ma (1, 2), W.-Q. Che (1), *, J.-X. Chen (3), and J.-R. Mao (1)

(1) Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

(2) Faculty of Mathematics and Physics, Huaiyin Institute of Technology, 1 Meisheng Eastern Road, Huaian, Jiangsu 223001, China

(3) School of Electronics and Information, Nantong University, 9 Seyuan Road, Nantong, Jiangsu 226019, China

Received 24 September 2012, Accepted 2 November 2012, Scheduled 5 November 2012

* Corresponding author: Wenquan Che (yeeren_che@163.com).

Table 1. Comparisons of several BPFs.

Ref.        Constant                 Size                    Loading
            bandwith                                        elements

[12]          Yes        0.06[lambda]g x 0.2[lambda]g      Si varactor
[13]          Yes      > (0.15[lambda]g x 0.13[lambda]g    Si varactor
[14]           No        0.25[lambda]g x 0.11[lambda]g     Si varactor
this work      No        0.15[lambda]g x 0.07[lambda]g     Si varactor

Ref.        Tuning      Maximum
            range     insertation
                          loss

[12]         18%         -3.5dB
[13]         15%     [approximately
                     equal to] -6dB
[14]         60%          -5dB
this work   52.4%        -3.3dB

Table 2. Comparisons of several BSFs.

Ref.        Constant     Loading     Tuning    Passband      Passband
            bandwith    elements     range    return loss   insertion
                                                               loss

[15]           No      Si varactor    25%      < -20 dB        0 dB
[16]           No      Si varactor   13.2%        --            --
[17]          Yes      Si varactor   23.9%     < -10 dB     > -2.92 dB
this work      No      Si varactor   53.5%     < -10 dB     > -0.4 dB

Ref.         Stopband     Transmission   Transmission   Unit
            attenuation      poles          zezos       cell
               level

[15]         < -14 dB          2              2          3
[16]         < -20 dB          --             1          1
[17]         < -55 dB          3              2          6
this work   < -16.6 dB         2              2          2
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Date:Jan 1, 2013
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