Continuously Tunable Dual-mode Bandstop Filter

IEEE MICRO W A VE AND WIRELESS COMPONENTS LETTERS 1 Continuously T unable Dual-mode Bandstop Filter Amir Ebrahimi, Member , IEEE, Thomas Baum, Me mber , IEEE, James Scott, Member , IEEE, and Kamran Gh orbani, Senior Member , IEEE Abstract —A varactor -b ased tunable bandstop fi lter has b een proposed in this article. Th e p roposed filter is based on a dual- mode circuit developed by introducing ind uctive an d capacitive couplings into a notch fi lter . The frequency tu nability i s achiev ed by usin g varactor diodes instead of the lumped capacitors in the circuit. Next, t he equivalent circuit model has been implemented in planar microstrip technology using thin inductive traces and vara ctor diodes. The fabricated filter prototype sho ws a continuous center frequency tuning range of 0 . 66 − 0 . 99 GHz with a compact size of 0 . 12 λ g × 0 . 16 λ g , where λ g is t h e guided wa velength at the middle frequency of the tuning range. Index T erms —Bandstop filter , dual-mode filter , second-order filter , tun able filter . I . I N T RO D U C T I O N N O W AD A YS, with the ad ven t of wireless standards u sing se veral frequency ban d s, there is an essential requirem e n t in the design of commun ication system s with comp atibility of tuning or reconfigur in g to new freq uency band s [1]. Band sto p or notch filters are useful block s in many of these systems fo r rejecting unwanted ban ds. Thus, there is a particu lar require- ment in design ing tunab le bandstop filter s fo r such systems. V ariety of configur ations and meth ods have bee n developed for tunable b andstop filter s [1]–[8]. T h e filter in [1] incorpo rates λ/ 2 couple d line resonators yielding a large circuit size. In [2], [3], lumpe d -element tunable band stop filters are designed for cognitive radios. Nevertheless, the quality factor o f lumped- elements are limited for higher frequen cy implementations. Furthermo re, thr e e-layer PCB is required for realizing the inductive couplin gs in [3] a nd precise position adju stment should be perfo r med to design the required cou pling betwe e n the in d uctors. In [4], a hig h rejection tunable stopban d filter is designed u sin g multi-lay er circuit boar d. High quality factor is ach iev ed in [5], [6] by using microstrip -line-cou pled cavity resonators tuned by piezo actu ators. However , they require complicated mu ltilayer fabricatio n. Micro -electrome c h anical (MEMS) varactors ar e used in [7] for tu ning distributed coupled - line b andstop filters. Ne vertheless, the coupled li ne configur ations are not compatib le with sm a ll size d evices at lower freq uencies. A tunable ban d stop filter is d e signed by tunable defected gr o und (DG ) r esonators loaded with BST varactors in [8]. Howe ver , this filter suffers f r om a lo w tuning range and high return loss. This paper presents a d ual-mod e varactor tuna b le two-pole bandstop filter . The dual-mo de cir cuit is design ed by in tr o- ducing indu ctiv e and cap acitiv e co u plings into the in/ou tput resonators of a no tch filter . Th in indu ctiv e tr aces are used for implemen ta tio n of ind u ctors. In contrast to th e pr evious designs, th e inductive coup ling is realized b y a third inductor The authors are with the School of Engineering, Royal Melbourne In- stitute of T echnolo gy (RMIT), Melbourne, VIC 3001, Australia (e-mail: amir .ebra himi@rmit.edu.au). C L (a) J 12 C L L M C M L 1 (b) L M C M C 1 90 , Z T Ω L 1 C 1 Fig. 1. Circuit model of the filters. (a) Introduci ng inducti ve and capaciti ve couplin gs to the notch fi lter . (b) T he proposed bandstop filter after repl acing the inducti v e and capaciti ve couplin gs with their equiv alen t circuit model s. embedd e d in the gro und plane of the circuit. This alleviates the need fo r complicated three-laye r fabrication , o ffers mor e flexibility in designing the couplin g coefficient, and saves the top layer circuit area lea ding a m ore com pact size. The filter design procedur e and the oper ation prin c iple are explained in the next section s. I I . F I L T E R D E S I G N A. Synthesis of the F ilter The p roposed filter is designed by app lying inductive and capacitive couplings between the ser ies LC resonator s o f the degenerative-pole notch filter as in dicated in Fig. 1(a) [2]. As explained in [9], introduc in g the couplings separates the two poles of the filter resulting in a d ual-mod e ban dstop filter [9], [10]. T he J 12 in verter can be realized with a 90 ◦ transmission line. By replacin g the indu ctiv e and capacitiv e couplings with their T and π equiv alent circuits resp ectiv ely , the circu it model takes the form shown in Fig . 1(b ). Th e L and C values in Fig. 1 can be synthesized as [11] Z T = Z 0 √ g 0 g 3 , (1) L = Z 0 ∆ ω 0 √ g 1 g 2 , (2) C = 1 ω 2 0 L , (3) where g 0 − g 3 are the element values of th e lowpass filter prototy p e, ω 0 is the central frequ ency of the filter , Z 0 is the termination impeda nce, and ∆ is th e fraction al ban d width. Next, using the standard cou pled-reso nators filter theory , the element values o f the filter in Fig. 1(b) are calculated as [ 1 1] L M = ∆ k L, (4) L 1 = (1 − ∆ k ) L, (5) C M = ∆ k C, (6) IEEE MICRO W A VE AND WIRELE SS COMPONENTS L ETTE RS 2 L 1 L M C a 90 , 50 Ω C C C C C b C a L 1 Fig. 2. Modi fied circu it model to achei ve practical v alues for the varac tors. C 1 = (1 − ∆ k ) C, (7) where k is the n ormalized coupling coefficient b etween the input and outp ut reson ators. B. T u n able F ilter A tu nable b andstop filter is designed by rep lacing the C 1 and C M capacitors with varactor diod e s, where the C 1 , mainly controls the cen ter frequency and C M is used to control the rejection le vel [7]. Howe ver , the circuit in Fig. 1(b) results in very small values of C M that might not be ach iev able using commercia lly av ailable varactors. T o add r ess this challeng e, the circuit in Fig. 2 (a) can be used. In this circuit, series capacitors C C are introduced to acheive more practical values of the capacitor s. By choosing a practically a vailable value for C C , and equatin g the T c o unterp a rt models of the capacitors in Fig. 1(b) and Fig. 2( a ), the C a and C b can be obtain ed as C a = C k C j 2 C k + C j , (8) C b = C 2 k 2 C k + C j , (9) where C k and C j are interme diate variables giv en by C k = (1 + ∆ k ) C C C C C − C (1 + ∆ k ) , (10) C j = 1 − (∆ k ) 2 ∆ k C. (11) The C value is obtained from (3) a n d the L 1 and L M inductanc es are the same in Fig. 2(a) a n d Fig. 1(b). C. Planar Implementatio n of the T unable F ilter The filter in Fig. 2 can be implemented u sing lumped compon ents. But, the achiev able rejection of the filter would be limited due to the low quality factors of commerc ial lumped compon ents. Thu s, a realization using micro strip is preferab le due to lower loss a t h igher freq uencies [9]. An implem entation in microstrip is sho wn in Fig. 3, w h ere th e L 1 inductor s are implemented with two thin meander ed traces with w 1 width. The ground metallization is rem oved b e neath these two traces to enh ance the L 1 inductanc es. Also, L M is rea lize d with the thin metallic trace of t width in the grou nd plan e. Th e D1 varactors ar e considered to imp lement C a variable cap acitors, and the pairs of D2 series varactors act as the variable C b capacitors. A via ho le connects D1 varactors to L M in the groun d plane. Finally , th e microstrip section between the two C C capacitors is designe d to act as a λ/ 4 imped ance inverter . l 1 l 2 C C V 2 Port 1 Port 2 V 1 d 1 d 2 d 3 d 4 d 5 w 1 d 6 w C C D1 D1 D2 D2 C C V 1 t Microstrip Via R bias C DC-block Varactor Fig. 3. Plannar implementati on of the tunable filter in microstri p technology . The top microstrip metalliz ation is shown in orange, whereas the ground metalli zation is gray . The dimensions are: d 1 = 11 . 7 mm, w 1 = 0 . 8 mm, d 2 = d 4 = d 5 = 4 . 2 mm , d 3 = 7 . 1 mm, d 6 = 4 . 2 mm , w = 3 . 5 mm, l 1 = 14 . 4 mm, l 2 = 20 mm, t = 0 . 8 mm , l 3 = 12 . 5 mm, l 4 = 38 . 3 mm. (a) P1 P2 P1 P2 L M t 1 l 1 l 2 C C C a P1 P2 w 1 Via t 1 l 2 l 1 P1 P2 L 1 + L M C eq ω z 2 = 1 , ( L 1 + L M ) C eq C eq = C a C C C a + C C (b) Fig. 4. (a) Inucti ve trace in ground plane reali zing L M and it’ s circ uit model. (b) Circuit for optimizing the dimensions of the L 1 trace. |S 21 | (dB) Frequency (GHz) Frequency (GHz) |S 11 | (dB) 0.4 0.6 0.8 1.0 1.2 -40 -30 -20 -10 0 C a = 1.1 pF C b = 0.21 pF C a = 1.9 pF C b = 0.5 pF C a = 4.9 pF C b = 3.25 pF 0.4 0.6 0.8 1.0 1.2 -40 -30 -20 -10 0 EM Sim. Cir. Sim. Fig. 5. Comparison between the E M and circuit model simulations of the designed tunable bandstop filter for three differe nt value s of C a , and C b . The design starts b y ob taining the element values of the circuit in Fig. 2 using ( 1)-(11). The filter sh o uld be designed for the center freq u ency of the tuning band. Then, th e tunin g is achieved by using varactors instead of the lumped cap acitors. The in itial dimensions of the metallic trace implementing L M are obtain e d u sin g the closed- form equatio ns fo r microstrip inductor s in [12]. Then, the dimensions ar e optimized by simulating the structu r e in Fig. 4(a) u sing AD S Momen tum , where th e L M is found f rom the susceptan ce slope. The n ext step is to find the dimensions of the th in trac e implementin g L 1 . Likewise, equation s in [ 12] ar e used a s initial values. Then, the dimensions are optimized by simulating the structure in Fig . 4(b) and findin g the tr ansmission zer o frequen cy ω z , wher e L 1 is fo und by kn owing L M , C a and C C . For validation, a Butterworth ban d stop filter is designed with a center frequ ency of 0 . 83 GH z and ∆ = 1 8 %. The equivalent circuit mod el para m eters by con sidering C C = 2 . 2 p F are IEEE MICRO W A VE AND WIRELE SS COMPONENTS L ETTE RS 3 (a) (b) Fig. 6. The fabricat ed filter prototype. (a) Front vie w , and (b) Back view . Frequency (GHz) Frequency (GHz) S 21 (dB) S 11 (dB) 0.4 0.6 0.8 1.0 1.2 -40 -30 -20 -10 0 0.4 0.6 0.8 1.0 1.2 -40 -30 -20 -10 0 Case 1 Case 2 Case 3 Case 4 Case 5 Fig. 7. Comparison between the simulated (solid line) and measured (dashed line) S-parameters of the filter . The ( V 1 , V 2 ) value s for dif ferent cases are: ( 15 V , 35 V ) for Case 1, ( 8 . 5 V , 30 V ) for Case 2, ( 6 V , 11 V ) for Case 3, ( 4 . 2 V , 5 V ) for Case 4, ( 1 . 7 V , 0 . 2 V ) for Case 5. L 1 = L 2 = 27 nH, L M = 3 . 1 nH with C a = 1 . 9 pF , and C b = 0 . 5 pF . The layo ut dimensions are then op timized b y curve fitting of the EM and circu it simulation s in the Ke ysight ADS software by considerin g a R og er s RO 435 0 sub strate with ǫ r = 3 . 48 and 1 . 524 mm thick ness. A com parison between the EM and circuit model simu latio ns provided in Fig. 5 shows a g ood ag r eement validating the design proce - dure. Th e com p arison is p erforme d fo r the center f requen cies of 0 . 6 6 GHz and 0 . 99 GHz as well, with the correspon ding C a and C b values g iven in the inset of Fig. 4 (a), where all the other cir cuit parameters are kept unch anged. The se results verify the tunab ility o f the de signed filter by varying the C a , and C b capacitance values. I I I . E X P E R I M E N TA L V A L I DA T I O N A N D R E S U LT S A pro totype of the proposed filter is fabricated and tested for validation. Fig. 6 shows the fro nt and back views of the fabricated filter . The Infin eon BB837 surface-m o unted diode s are u sed as varactors. Th e b ia sin g networks are made of R = 10 k Ω resistors, and C DC-block = 1 00 pF capacitors. Fig. 7 shows the EM simu lated and measured S-par ameters of the filter, where the series p arasitic r e sistance of the varactor f rom the mau factur er’ s SPICE model is considered in simulations [1 3]. The filter shows a con tin uous tuning of the center f requen cy from 0 . 66 GHz to 0 . 9 9 GHz with an almost constant − 3 dB stopban d fraction al bandwidth of 18 %. The measured stopban d return loss ( SB RL) of the filter is less th an 0 . 8 dB, whereas the p assband insersion loss (PB IL ) is less than 0 . 55 dB within the tunin g ran ge. A relatively low SB RL and PB I L a r e attributed to the larger bandwidth of the T ABLE I C O M PA R I S O N OF V A R I O U S T U N A B L E B A N D S TO P F I LT E R S Ref. T un. mech. Rej. (dB) T un. Range (GHz) ∆ (%) Size ( λ 2 g ) SB RL (dB) PB IL (dB) [1] V aract or 50 1.75–2.2 (11.4%) 10 0 . 18 2 0 . 65 [2] V aract or 17 0.47–0.73 (43%) 4.5 0 . 0004 3 0 . 4 [3] V aract or 23 0.6-0.99 (49%) 10 0 . 005 N. G. 1 [4] V aract or 40 0.76-1.05 (32%) 8 0 . 034 2 1 . 52 [5] Piezo Act. 45 2.77–3.57 (25.2%) 0.9 0 . 5 2 2 . 4 [6] Piezo Act. 30 2.7–3 (10.5%) 1.5 0 . 15 1 . 8 2 T . W . V aract or 27 0.66-0.99 (40%) 18 0 . 019 0 . 8 0 . 55 designed filter with re spect to th e pr evious one s, using thin meander e d micro strip inductors instead of th e lumped on es, and using λ/ 4 micr ostrip stub as an impedan ce in verter instead of lum ped indu ctor . A com parison between the perfor mance of the design ed filter and state-of- a rt designs in T able I reveals that the d e sig ned filter is m ore co mpact co m pared to the to pologies implemen ted with m icrostrip inducto rs or distributed resonato rs. More over, the table shows a com petitive perfor mance of the pro posed filter in terms of the tuning rang e, and rejection. I V . C O N C L U S I O N A second -order tunable bandstop filter has been pr esented based on a combinatio n of lumped elem e nts and microstrip - based com p onents. An equivalent circuit-b ased desig n method has been d ev elop ed fo r synthesizing th e element values of the filter . The pro posed top ology o ffers com pact size, h igh rejection le vel, and a wide co ntinuou s tuning range. R E F E R E N C E S [1] X. Y . Zhang, C. H. Chan, Q. Xue, and B.-J. Hu, “RF tunabl e bandstop filters with constant bandwidth based on a doublet configuration, ” IEEE T rans. Indus. Electr . , vol. 59, no. 2, pp. 1257–1265, 2012. [2] Y .-C. Ou and G. Rebeiz, “Lumped-element fully tunable bandstop filters for cogniti ve radio applicati ons, ” IEE E T rans. Micr ow . Theory T ec hn. , vol. 59, no. 10, pp. 2461–246 8, Oct 2011. [3] C.-H. Ko, A. Tran, and G. Rebeiz , “T unable 500-1200-MHz dual-band and wide bandwidt h notch filters using RF transformers, ” IEEE T rans. Micr ow . Theory T echn. , vol. 63, no. 6, pp. 1854–1862, June 2015. [4] Y . H. Cho and G. M. Rebeiz, “Tuna ble 4-pole dual-not ch filters for cogniti v e radios and carrier aggrega tion systems, ” IEEE T rans. on Micr ow . Theory T ech. , vol . 63, no. 4, pp. 1308–1314, April 2015. [5] E. J. Naglich, J. Lee, D. Peroulis, and W . J. Chappell, “ A tunabl e bandpass-to -bandstop reconfigurable filter w ith indepen dent bandwidths and tunable response shape, ” IEE E T rans. Micr ow . Theory T echn. , vol. 58, no. 12, pp. 3770–377 9, 2010. [6] J. Lee, E. J. Naglic h, H. H. Sigmarsson, D. Peroulis, and W . J. Chappell , “Ne w bandstop fi lter circuit topo logy and its applicati on to design of a bandstop-t o-bandpass switcha ble filter , ” IEEE Tr ans. on Micr ow . Theory T echn. , vol. 61, no. 3, pp. 1114–1123, 2013. [7] I. Reines, S.-J. Park, and G. M. Rebeiz, “Compact low-l oss tunable X - band bandstop filte r with m iniatu re RF-MEMS switche s, ” IEEE T rans. Micr ow . Theory T echn. , vol. 58, no. 7, pp. 1887–1895, 2010. [8] Y .-H. Chun, J.-S. Hong, P . Bao, T . Jackson, and M. Lancaster , “Tunab le slotted ground struct ured bandstop filter with bst v aract ors, ” IET Micr ow . Antennas & Pro pag. , vol . 3, no. 5, pp. 870–876, 2009. [9] A. Ebrahimi, W . W ithaya chumnankul, S. F . Al-Sara wi, and D. Abbott, “Compact second-orde r bandstop filter based on dual-mode complemen- tary split-ring resonator , ” IE EE Micr ow . W irel ess Compon. Lett. , vol. 26, no. 8, pp. 571–573, Aug 2016. [10] A. Ebrahimi, W . W ithay achumnankul, S. F . Al-Sara wi, and D. Abbott, “Dual-mode behavio r of the complement ary electric-LC resonat ors loaded on transmission line: Analysis and applicat ions, ” J . Appl. Phys. , vol. 116, no. 8, 2014, art. no. 083705. [11] A. I. Zvere v , Handbook of F ilter Synthesis . Wil ey , 1967. [12] J.-S. G. Hong and M. J. Lancaster , Micr ostrip filters for RF/micr owave applica tions . John W iley & Sons, 2004, vol. 167. [13] Infineon , (2017). [Online]. A v ailable : https:/ /www .infineon.com