Three-Pole Tunable Filters with High Rejection using Mixed Quarter-Lambda and Asymmetric Half-Lambda Resonators

812 Z. Y. ZHAO, J. CHEN, L. YANG, K. H. CHEN, THREE-POLE TUNABLE FILTERS WITH HIGH REJECTION … Three-Pole Tunable Filters with High Rejection using Mixed 4  Resonators and Asymmetric 2  Resonators Zhiyuan ZHAO1,2, Jiang CHEN2, Lin YANG2, Kunhe CHEN2 1 Institute of Communications Engineering, PLA University of Science and Technology, Nanjing 210007, China 2 Nanjing Telecommunication Technology Institute, Nanjing 210007, China [email protected], [email protected] Abstract. A novel three-pole tunable bandpass filter using varactor-loaded quarter-wavelength combline and asymmetric half-wavelength resonators is proposed in this paper. A nearly constant 3-dB absolute bandwidth is 150 ± 13 MHz (10.7%~6.9% fractional bandwidth) within the tuning range of 1.4-2.0 GHz (42.8%). The filter is designed on a Rogers substrate with εr = 2.2 and h = 1 mm with its insertion loss varying from 3.6 dB to 2.8 dB and return loss better than 10 dB over the entire tuning range. The creation of two transmission zeros near the passband edges is analyzed by the even-odd-method. By using dissimilar resonators, the proposed tunable filter could obtain > 33 dB rejection levels at the second harmonics. The measured results show good agreement with the simulated ones. Keywords Three-pole tunable filters, combline resonators, modified combline resonators, constant absolute bandwidth (CABW), transmission zeros (TZs), varactor-tuned. 1. Introduction Electronically tunable or reconfigurable pre-select microwave filters significantly improve the overall performance of multi-bands and multi-functions wireless communication systems, which bring the reduction of the system size, complexity and cost. Planar tunable bandpass filters (BPFs) can be realized by varactor diodes [1], ferroelectric diodes [2], or RF micro-electro-mechanical systems (RFMEMS) devices [3]. However, the varactor-diode filters are widely studied due to the advantages of continuous and high-speed tuning and economical fabrication. Due to compactness and ease of integration, combline and modified combline resonators loaded by varactor diodes, commonly used in small-size tunable filters for the RF front end, have been studied in numerous literatures [4]-[11]. However, the combination of quarter-wavelength (λ/4) combline and asymmetric half-length (λ/2) resonators, especially for realizing a constant absolute bandwidth (CABW) of three-pole tunable filter with high rejection, has not been reported. Hunter and Rhodes firstly described that the optimum electrical length is approximately 53° at the center frequency of the tuning range for achieving the constant bandwidth of the stripline tunable filter [4]. For microstrip-line tunable filter, a systematic approach was presented to choose the tunable filter design parameters [5]. In [6], a tunable combline filter with plural transmission zeros originating from source-load and multi-resonators coupling was realized. Note that most microstrip combline or modified combline filters only have transmission zeros in the lower stopband or upper stopband, and this leads to an asymmetrical transmission response and poor rejection in the stopband without transmission zeros. Yi-Chyun Chiou et. al. proposed a non-adjacent resonator coupling to generate an extra zero at the lower band, except the intrinsic zero at the upper stopband [7]. In [8], there were two transmission zeros at both sides of the passband, respectively, however the source-load coupling structure was complicated. In [9], there were two transmission zeros near the passband due to the tap connections of input and output port, however the rejection level in the stopband was not high enough without adding the bandpass network to the two ends. Therefore, it remains difficult to realize a highrejection tunable filter with CABW and two transmission zeros within a wide tuning range. S P L P 2 L 1 L 5 L 3 L 0 L 4 L Fig. 1. Proposed three-pole tunable BPF using mixed λ/4 combline and asymmetric λ/2 resonators. This paper proposes a new three-pole tunable filter with two transmission zeros using mixed λ/4 combline and asymmetric λ/2 resonators, as shown in Fig. 1. The design RADIOENGINEERING, VOL. 23, NO. 3, SEPTEMBER 2014 813 aim is to maintain the absolute bandwidth constant and obtain high rejection. It consists of an asynchronously varactor-tuned λ/4 combline resonator between the two varactor-loaded asymmetric λ/2 resonators. Parallelcoupled-lines are selected as the external coupling structure to achieve impedance matching across a wide tuning range without any other tuning components [10]. By properly controlling the bias voltages, a high-rejection tunable filter with nearly constant absolute bandwidth within a wide frequency tuning range can be realized. This paper is organized as follows. The characteristic of the proposed filter topology is introduced and design theory is analyzed in Section 2. In Section 3, experimental results of a built prototype are shown. Finally, the conclusions of this work are drawn in Section 4. 2. Tunable Filter Theory 2.1 Bandwidth Characteristic of the Coupled Resonators 1 P 2 P 2 0   10   202    101    ,eo yy  1  ' 1 C ' 2 C 1 L 2 L (a) (b) Fig. 2. (a) Coupled varactor-loaded combline and modifiedcombline resonators, and (b) its equivalent circuit. The design is based on varactor-loaded 4  combline resonator and varactor-loaded asymmetric 2  modifiedcombline resonators [9]. Fig. 2 presents a coupled-resonator section of the proposed tunable filter and its simplified equivalent circuit. The lumped-element capacitances are '' 1c1 CCC   and '' 22 // a CCC  , and the inductances are 1 L and 2 L , where 1 L and ' c C are the equivalent inductor and capacitor of the 4  combline resonator, respectively, 2 L and ' a C are the equivalent inductor and capacitor of the asymmetric 2  modified-combline resonator, respectively [11]. The coupling coefficient of the equivalent coupled resonators model in Fig. 2 is calculated by energetic coupling approach [12]. Assuming weak coupling condition (1 ME kk ), the coupling coefficient is determined as '' 02 01 01 01 02 02 '' 01 01 01 02 02 ( )[cos cos( )] (2 sin2 )(2 sin2 ) 2( ) sin (2 sin2 )(2 sin2 ) LC ME LC kk kk k kk               (1) 02 01     (2) where, ' L kand ' C k are the inductive and capacitive coupling coefficients per unit length in the coupling region. 01  (01 4    ) and 02  (02 2    ) indicate electrical lengths of the 4  combline resonator and the asymmetric 2  resonator, respectively. Using the standard differentiation procedure, given 02 01 4   , it can be calculated that the optimum electrical length of 01  in the midband of the tuning range. The crude optimum electrical length of the 4  combline resonator corresponds to the frequency at which the bandwidth is maximized. Fig. 3. Normalized bandwidth of the proposed architecture using quasi-TEM resonators. Fig. 3 is a plot of normalized coupling bandwidth 12   ( 12 0 k    ) versus 01  according to (1) when quasiTEM resonators are used, with 001   . If the allowed percentage change of bandwidth is ±10%, a wide center frequency tuning range ( 01  ,02  ) can be obtained to fulfill the bandwidth requirement [Δωmax – Δ, Δωmax]. Due to the linear relationship between electrical length and frequency, the plot shows the bandwidth dependence on the tuning frequency. The electrical length corresponding to Δωmax is the optimum resonator length ( 01  = 39°) at the midband. 2.2 Analysis of the Coupled Resonators A P B P Fig. 4. The three coupled-resonators without I/O coupling structure. In the analysis of the three coupled-resonators of the proposed tunable filter, the Y-parameter is adopted. Fig. 4 is three coupled-resonators without I/O coupling structure. The reference ports ( A Pand B P) are added for deriving the admittance matrix, the Y-parameter matrix of the two asynchronously coupled-resonators is calculated as 814 Z. Y. ZHAO, J. CHEN, L. YANG, K. H. CHEN, THREE-POLE TUNABLE FILTERS WITH HIGH REJECTION … 13 31 13 32 11 12 33 0 33 0 13 32 23 32 21 22 33 0 33 0 tan tan tan tan yy yy yy yjY yjY Yyy yy yy yjY yjY                      (3) And the four-port Y parameters of the parallel coupled-line are [13], 11 22 33 01 ()cot 2ro re j yyy YY    , (4a) 12 21 01 ()cot 2ro re j yy YY    , (4b) 13 31 01 ()csc 2ro re j yy YY    , (4c) 23 32 01 ()csc 2ro re j yy YY    (4d) where Yre, Yro are the evenand odd-mode characteristic admittances of the parallel coupled-line, respectively. The resonant angular frequency ω0 can be found by the following equation, (i = 1, 2). 00 Im[ ( )] 0 ii i YC    (5) For the filter composed of two varactor-loaded asymmetric λ/2 resonators, their fundamental resonant frequency is f0, and the second-order spurious response is at the frequency higher than 2f0. Furthermore, that composed of a varactor-loaded λ/2 combline resonator has spurious passband far from 3f0. Therefore, the rejection level of the second harmonics of the proposed filter in Fig. 1 can be improved significantly. The coupling coefficient of the coupled resonators is [11] 12 0 12 12 0 1 2 Im[ ( )]YBW kbb f g g   (6) where BW is the 3-dB absolute bandwidth, g1, g2 are the element values of low-pass prototype filter, respectively. And the slope parameter b1 and b2 are derived as [13] 0 00 Im[ ] 22 ii i i YC b        . (7) 2.3 Transmission Zeros Creation 3 Y 1 Y 2 Y 1 Y 3 Y A P B P Fig. 5. Equivalent circuit model of the three coupledresonators. As was explained in the past literatures, adding I/O coupling structure shifts the transmission zero at infinite frequency downwards, but it does not really add a zero. For facilitating the analysis of the TZs’ location, the I/O matching networks are not calculated. Since the topology is symmetrical to the center plane, the S-parameter of the three coupled resonators can be calculated by using the even-odd-mode method [13]. It is assumed that the evenand odd-mode electrical lengths of the parallel symmetrical pair of coupled-lines are identical to the value of θ01, and the parasitic effects of the grounded via-holes and the line discontinuity due to the DC block capacitor Cb are ignored. Fig. 5 presents the exact equivalent circuit model of the three coupled-resonators in Fig. 4. In this circuit, Y1 = Y22 – Y3, Y2 = Y11 – Y3, Y3 = –Y12, where Yij is the element of the Y matrix in (3). C2 3 Y 1 Y 2 /2Y C1/2 Even-mode A P  3 Y 1 Y A P (a) (b) Fig. 6. (a) Its equivalent even-mode circuit, and (b) its equivalent odd-mode circuit in Fig. 5. Fig. 6 is the equivalent evenand odd-mode circuit obtained by placing a short or open circuit at the symmetric plane. The evenand odd-mode input admittance YAe and YAo seen from port PA can be respectively solved by (8) and (9) 32 1 21 23 1 () 2 Ae YY jC YjCY YYjC       , (8) 213Ao YjCYY   . (9) By superposition, the transfer function S21 can then be written as [13] 0 21 00 () ()() Ae Ao Ae Ao YY Y SYYYY   (10) where Y0 is terminal admittance. Enforcing S21 = 0 or YAe – YAo = 0, the two transmission zero frequencies can be solved. As can be seen in the above transcendental equations, it is not easy to obtain the explicit solution of the TZs’ location. The transmission response is obtained by feeding the three coupled resonators at PA and PB, and the S21 response indicates that the filter possesses three poles (fp1 through fp3) and two transmission zeros (fz1 and fz2), as shown in Fig. 7. One transmission zero appears at the lower stopband, and the other appears at the upper stopband. The TZs creation is usually due to the multiple coupling paths, which means several signals cancel each others at a certain frequency. According to (8)-(10), the transmission zero is a function of the loading capacitance, so they move with the center RADIOENGINEERING, VOL. 23, NO. 3, SEPTEMBER 2014 815 frequency of the filter varied by controlling the biasing voltages. Fig. 7. S21 response of Fig. 4 with weakly capacitive coupling at its two ports. 2.4 Extraction of k12 and Qe of the Tunable Filter As the center frequency of the filter is varied, all of the filter parameters change. Thus, the coupling coefficients between resonators are always changed. To assure CABW, the desired coupling coefficient must satisfy the conditions described in [3]. The gap S1 is chosen so that the two asynchronously tuned resonators are coupled through a suitable coupling coefficient k12. The coupling coefficient k12 of the coupled resonators can be calculated by [13] 22 22 21 22 02 01 02 01 12 22 22 01 02 2 1 02 01 1()()() 2 pp pp ff ff ff kff ff ff      (11) where f01, f02 are resonant frequencies of each single resonator, fp1 and fp2 are frequencies of the two peaks. The choice of the sign in (4) depends on the definition of electric and magnetic coupling. To maintain nearly constant absolute bandwidth, the external quality factor Qe should increase as the frequency shifts upward. This can be realized by using the parallelline structure as shown in Fig. 1. The geometrical dimensions and capacitance of the matching capacitor Cm of the I/O structure can be determined by matching the singly loaded Q. The required Qe for a 3-pole filter is given by [13] 0010 90 e f ggf Q f BW    (12) where 90 f   is determined from the frequency at which the phase shifts ±90° with respect to the absolute phase at f0. 3. Design and Experimental Verification of Tunable Filter A nearly CABW three-pole tunable filter with high rejection using λ/4 combline and asymmetric λ/2 resonators is presented in this section to verify the analysis above. A full-wave electromagnetic simulator, Computer Simulation Technology (CST2009) Microwave Studio and Design Studio software packages are employed for the circuit dimensions of final filter simulation. The designed filter is simulated and fabricated in microstrip technology with the following specifications: Frequency tuning range: 1.4-2.0 GHz; Passband bandwidth: 150 ± 10 MHz; Number of poles: three; Type: 0.04-dB ripple Chebyshev at 1.7 GHz. 3.1 Design Procedure Step 1). Subjecting to the specifications, select the three-pole low-pass prototype with elements gi, i =0,…4. Then calculate the external quality factors and coupling coefficient according to (6) and (12). Step 2). Determine the dimensions of the proposed tunable resonators. The electrical length of the combline resonator is set to be 39° (θ01 = 39°, θ02 = 4θ01 = 156°) at 1.7 GHz. The characteristic impedance of combline filter is traditionally 71 or 72 Ω to obtain the optimum unloaded Q [11]. For minimizing the size of the circuit, especially the asymmetric half-wavelength resonator, we choose a little higher characteristic impedance (W1 = 1 mm). The gap S1 between λ/4 combline resonator and asymmetric λ/2 resonators can then be determined to satisfy k12. The parameters of the I/O structure are typically chosen to be a high impedance line for tight coupling. The matching capacitor Cm, the gap S2, and the width W2 of the line are then chosen to satisfy Qe. Step 3). Finally, the optimization of circuit dimensions of filter is employed CST2009 EM simulator. The electrical length of the comb-line resonator is optimized to be 8 mm (27°) at 1.7 GHz because of the additional equivalent electrical lengths of grounding via-holes, grounding pads and components of DC blocking capacitor and varactor. According to the extraction method of coupling coefficient and external quality factor in [13], the k12 and Qe versus different center frequencies of the tunable filter is extracted and plotted in Fig. 8 with the desired values for the constant absolute bandwidth. Due to the inconsistency between the simulated k12, Qe and the desired ones, the ripple of the filter will change and the absolute bandwidth will vary as the frequency shifts downward or upward from the mid-band. For the optimized resonators, the capacitance of the loading varactors C1 and C2 corresponding to the resonant frequency is plotted in Fig. 9 for comparison. The simulated results agree well with the calculated ones by (5). The filter is designed on Rogers RT5880 substrate (εr = 2.2, h = 1 mm, and tanδ = 0.0009) with overall size of ~40 × 36 mm2, as shown in Fig. 10. 816 Z. Y. ZHAO, J. CHEN, L. YANG, K. H. CHEN, THREE-POLE TUNABLE FILTERS WITH HIGH REJECTION … Fig. 8. Desired and simulated coupling coefficients and Qe of the proposed filter. Fig. 9. Calculated and simulated capacitance of the loading varactors for the optimized resonators. Fig. 10. Photograph of the fabricated 3-pole tunable filter including biasing circuits. 1 W/2 W 0 L/1 L/2 L/3 L/4 L/5 L 1 S/2 S m C(pF) / b C(pF) 1 / 0.1 2 / 8 / 6/10.6 / 2.5 / 5.5 2 / 0.1 5.6 / 15 Tab. 1. Dimensions for the filter (Dimensions are in millimeters). The physical dimensions of the filter are summarized in Tab. 1. The matching capacitor Cm and DC blocking capacitor Cb are realized by ATC 600S series capacitors. The DC blocking capacitor has a high self-resonant frequency of over 2.5 GHz, which works as open circuit at DC frequency and short circuit at RF frequency. The capacitors C1 and C2 are implemented by MA46H202-1088 GaAs diodes. MA46H202 varactor diodes (C1 or C2 = 0.6-11 pF, Rs = 0.2-0.9  , over a 22 V reverse bias range) are selected as D1 and D2 for frequency tuning, respectively. The biasing circuits are realized using two 100-kΩ resistors to minimize RF signal leakage. 3.2 Measurements (a) (b) Fig. 11. Measured and simulated S-parameters of the proposed tunable BPF. (a) S11. (b) S21. The measured frequency responses of the designed filter with the center frequency tuning obtained by using Agilent N5230A network analyzer are in good agreement with the simulation results, as shown in Fig. 11. The measured return loss (|S11|) is worse than the simulation results due to the inconsistency of the varactor diodes biased by only one bias voltage for the asymmetric λ/2 resonators, however better than 10 dB for all states. The 3-dB absolute bandwidth is maintained nearly constant about 150 MHz (150 ± 13 MHz) over the entire center frequency tuning range from 1.4 GHz to 2.0 GHz (a wide tuning range of 42.8%). The bandwidth slightly increases at the midband frequency and decreases at the both ends of the tuning range. The characteristic of bandwidth variation is consistent with that of Fig. 3. Because of the effect of the RADIOENGINEERING, VOL. 23, NO. 3, SEPTEMBER 2014 817 package inductances of the varactor diodes and parasitic inductance coupling among the via-holes, the passband bandwidth has slight variation between simulation and measurement. Its insertion loss (|S21|) varies from 3.6 dB to 2.8 dB due to the low overall unloaded Q of the resonators by using varactors [14]. The insertion loss improves as the center frequency is tuned to the higher end of the tuning range, and it is related to the characteristic of the varactor diodes under different bias condition and the variation of fractional BW (10.7% at lower end and 6.9% at higher end). The discrepancies mainly result from fabrication tolerance in the implementation and the simulation error between SPICE models and actual varactor diodes. Note that the two transmission zeros near to passband are shifted with the center frequency varied, and the rejection of the lower and upper stopbands remains high with the tuning. Furthermore, the extra zero appears at the higher side due to the package inductance of the varactor diodes, which can enhance the rejection of the second harmonics (> 33 dB). By using dissimilar resonators [15], the rejection level is > 20 dB in the stopband from 1.07f0 to 2.85 f 0. The nonlinear distortion performance is another important figure of merit due to the involvement of the varactor. The measured 1-dB compression point at the filter input is higher than 8 dBm over the tuning frequency. The measured IIP3 is ranging from 33 dBm to 38 dBm for Δf = 1 MHz, meeting most of the requirements for software-defined radio applications. The summary of the measured results is shown in Tab. 2. f0 (GHz) I.L. (dB) BW (MHz) P1 (dBm) IIP3 (dBm) Vb1 (V) Vb2 (V) 1.4 3.6 150 8 33 5.45 0.5 1.7 3.0 163 9 38 8.65 6.0 2.0 2.8 137 8.5 36 13.2 14.9 Tab. 2. Measured results of the tunable filter. 4. Conclusions In this paper, we proposed a novel three-pole tunable filter topology with high rejection by using mixed varactorloaded λ/4 combline and asymmetric λ/2 resonators. A 1.4-2.0 GHz three-pole microstrip-line tunable filter with a nearly constant 3-dB absolute bandwidth of 150 ± 13 MHz and the rejection level > 33 dB at the second harmonics is simulated, fabricated, and measured. The measured results agree well with the simulated ones. Acknowledgements This work was supported by Key Pre-research Foundation of PLA university of Science and Technology under grant. KY63ZLXY1301. The authors would like to thank M/A-COM Corporation for the high-performance varactor diodes and Rogers Corporation for the low-loss substrate. References [1] WONG, P. W., HUNTER, I. C. Electronically tunable filters. IEEE Microwave Magazine, 2009, vol. 10, no. 6, p. 46–54. [2] HONG, J. S. Reconfigurable planar filters. IEEE Microwave Magazine, 2009, vol. 10, no. 6, p. 73–83. [3] REBEIZ, G. M., REINES, I. C., EL-TANANI, M. A., ET AL. Tuning in to RF MEMS. IEEE Microwave Magazine, 2009, vol. 10, no. 6, p. 55–72. [4] HUNTER, I. C., RHODES, J. D. Electronically tunable microwave bandpass filters. IEEE Transactions on Microwave Theory and Techniques, 1982, vol. 30, no. 9, p. 1354–1360. [5] TORREGROSA-PENALVA, G., LOPEZ-RISUENO, G., ALONSO, J. I. A simple method to design wide-band electronically tunable combline filters. IEEE Transactions on Microwave Theory and Techniques, 2002, vol. 50, no. 1, p. 172–177. [6] SANCHEZ-RENEDO, M. High-selectivity tunable planar combline filter with source/load-multiresonator Coupling. IEEE Microwave Wireless Components Letter, 2007, vol. 17, no. 7. [7] CHIOU, Y. C., REBEIZ, G. M. A quasi elliptic function 1.75-2.25 GHz 3-pole bandpass filter with bandwidth control. IEEE Transactions on Microwave Theory and Techniques, 2012, vol. 60, no. 2, p. 244–249. [8] EL-TANANI, M. A., REBEIZ, G. M. A two-pole two-zero tunable filter with improved linearity. IEEE Transactions on Microwave Theory and Techniques, 2009, vol. 57, no. 4, p. 830–839. [9] ZHANG, X. Y., XUE, Q., CHAN, C. H., ET AL. Low-loss frequency-agile bandpass filters with controllable bandwidth and suppressed second harmonic. IEEE Transactions on Microwave Theory and Techniques, 2010, vol. 58, no. 6, p. 1557–1564. [10] PARK, S. J., REBEIZ, G. M. Low-loss two-pole tunable filters with three different predefined bandwidth characteristics. IEEE Transactions on Microwave Theory and Techniques, 2008, vol. 56, no. 5, p. 1137–1148. [11] MATTHAEI, G. L., YOUNG, L., JONES, E. M. T. Microwave Filters Impedance-Matching Networks, and Coupling Structures. Norwood, MA: Artech House, 1980. [12] GUYETTE, A. C. Alternative architectures for narrowband varactor-tuned bandpass filters. In Proceedings of the 39th European Microwave Conference. Rome (Italy), 2009, p. 1828–1831. [13] HONG, J. S., LANCASTER, M. J. Microstrip Filters for RF/Microwave Applications. New York: Wiley, 2001. [14] BROWN, A. R., REBEIZ, G. M. A varactor tuned RF filter. IEEE Transactions on Microwave Theory and Techniques, 2000, vol. 48, no. 7, p. 1157–1160. [15] LI, Y. C., ZHANG, X. Y., XUE, Q. Bandpass filter using discriminating coupling for extended out-of-band suppression. IEEE Microwave Wireless Components Letter, 2010, vol. 20, no. 7, p. 369–371. About Authors ... Zhiyuan ZHAO was born in 1986. He received his bachelor's degree from Lanzhou University in 2008, and received his master’s degree from PLA University of Science and Technology in 2011. He is now a Ph. D candidate in the Institute of Communications Engineering, PLA University of Science and Technology, Nanjing, China. His research interests include microwave and RF tunable filters. 818 Z. Y. ZHAO, J. CHEN, L. YANG, K. H. CHEN, THREE-POLE TUNABLE FILTERS WITH HIGH REJECTION … Jiang CHEN was born in 1965 and he is now a professor in Nanjing Telecommunication Technology Institute, Nanjing, China. His research interests include RF power amplifiers and RF filters. Lin YANG was born in 1974 and he is now an engineer in Nanjing Telecommunication Technology Institute, Nanjing, China. His research interests include RF power amplifiers. Kunhe CHEN was born in 1975 and he is now an engineer in Nanjing Telecommunication Technology Institute, China. His research interests include RF tunable filters.