IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES VOL

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2566 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 8, AUGUST 2005 A 12–18-GHz Three-Pole RF MEMS Tunable Filter Kamran Entesari , Student Member, IEEE, and Gabriel M. Rebeiz , Fellow, IEEE Abstract This paper presents a state-of-the-art RF microelec- tromechanical systems (MEMS) wide-band tunable filter designed for the 12–18-GHz frequency range. The coplanar-waveguide filter, fabricated on a glass substrate using loaded resonators with RF MEMS capacitive switches, results in a tuning range of 40% with very fine resolution, and return

loss better than 10 dB for the whole tuning range. The relative bandwidth of the filter is 5.7 0.4% over the tuning range and the size of the filter is 8 mm mm. The insertion loss is 5.5 and 8.2 dB at 17.8 and 12.2 GHz, respec- tively, for a 2-k sq bias line. The loss improves to 4.5 and 6.8 dB at 17.8 and 12.2 GHz, respectively, if the bias line resistance is in- creased to 20 k sq. The measured IIP level is 37 dBm for 200 kHz. To our knowledge, this is the widest band planar tunable filter to date. Index Terms Coplanar-waveguide (CPW) filter, loaded res- onators,

microelectromechanical systems (MEMS), RF MEMS, wide-band tunable filter. I. I NTRODUCTION F microelectromechanical systems (MEMS) tunable fil- ters have been developed in the past few years for multi- band communication systems, radars, and wide-band tracking receivers [1]. MEMS switches and varactors have very low loss, therefore, resulting in relatively high- designs. RF MEMS also offer outstanding linearity with a measured overall 40–50 dBm [2]–[4]. Electrostatic RF MEMS switches do not require any dc current and, therefore, offer a very low power approach for tuning

applications. There are two different types of frequency-tuning methods for MEMS-based filters: analog and digital. Analog tuning is relatively easy with MEMS varactors and provides continuous frequency variation, but the tuning range has been limited to 5%–15% [3]. In digital-type tuning, where a capacitor is switched in and out of the circuit, discrete center frequencies and wide tuning ranges are possible (20%–60%), and several designs are currently available at 0.1–10 GHz [4]–[6]. The main advantage of digital-type designs is that they are less sensitive to bias and Brownian noise

[2], and the center frequency is well known (little drift with temperature). However, due to the size of the switching capacitor bank, it has been hard to design filters using the digital approach above 8 GHz. Recently, a 2-bit (four states) 10–14-GHz MEMS filter was presented with Manuscript received September 23, 2004. This work was supported by the National Science Foundation under Contract ECS9979428. K. Entesari is with the Radiation Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan at Ann Arbor, Ann Arbor, MI 48109-21222 USA

(e-mail: kentesar@umich.edu). G. M. Rebeiz was with the Radiation Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan at Ann Arbor, Ann Arbor, MI 48109-21222 USA. He is now with the Electrical and Computer Engineering Department, University of California at San Diego, La Jolla, 92037 CA USA (e-mail: rebeiz@ece.ucsd.edu). Digital Object Identifier 10.1109/TMTT.2005.852761 excellent performance [7], but the filter results in four separate frequency responses, which are not contiguous. There is a need for a completely contiguous

filter design at 8–18 GHz, and this paper addresses this problem. In this paper, we present a three-pole RF MEMS digital tun- able filter with 40% tuning range from 12.2 to 17.8 GHz. The frequency band is covered by 16 filter responses (states) with very fine frequency resolution so as to behave as a continuous- type filter. To achieve this high tuning resolution, a novel 4-bit MEMS distributed capacitor bank is used in the resonator. A nonlinear study of the tunable filter is presented in Section IV. II. F ILTER ESIGN A. Topology Fig. 1 presents the circuit

model for a three-pole loaded resonator tunable filter. Each coplanar-waveguide (CPW) resonator is periodically loaded by four switched MEMS capacitors pairs (eight in total), which results in a slow-wave structure with a smaller effective wavelength and lower char- acteristic impedance in comparison to the unloaded resonator. Every switched capacitor is built as a series combination of a MEMS switch with a capacitance ratio of 30–40 and a fixed metal–air–metal (MAM) capacitor The loaded MEMS resonators are coupled through inductive impedance inverters and form a three-pole

bandpass filter. The inductive impedance inverters are T-combinations of a shunt inductor and two series transmission lines with negative lengths [3]. The response of the filter can be tuned over a wide fre- quency range by changing the effective electrical length of the resonators using 16 different combinations (4-bit) of pairs of MEMS switches in the up- and down-state positions. Due to the filter topology, the shape and fractional bandwidth of the filter is approximately fixed over the tuning range, and the inductive couplings between the resonators compensate

the increasingly capacitive behavior of the resonators when they are tuned toward the lower frequencies [9]. It is also known that the in- ductive coupling along with capacitive loading provides closer spurious passbands and lower rejection at higher frequencies [1], [8]. However, for a loaded resonator, this negative effect is not observed because the second resonance is eliminated due to loading effect at the center of the resonator. B. Resonator Design The circuit model of a capacitively loaded resonator is shown in Fig. 2 The loading capacitors are placed in a symmetrical fashion around

the middle of the resonator and are actuated in pairs. This results in a symmetrical shape of the standing-wave voltage on the loaded resonator and, therefore, for each state, the maximum voltage level always occurs at the middle point 0018-9480/$20.00  2005 IEEE
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ENTESARI AND REBEIZ: 12 18-GHz THREE-POLE RF MEMS TUNABLE FILTER 2567 Fig. 1. Circuit model of a three-pole loaded resonator tunable lter. Fig. 2. Circuit model of a capacitive resonator loaded with eight capacitive MEMS switches. TABLE I ESONATOR IRCUIT ODEL LEMENT ALUES XTRACTED ROM ADS S IMULATIONS of the

resonator. For example, to change the resonant frequency from State-0000 (all the switches are in the up-state position) to State-0001, the two MEMS switches, which are in series with MAM capacitor are pulled down. Table I shows the values for the MEMS capacitors in up- and down-state positions ( and ) and the MAM capacitors . The largest loading unit cells (MAM capacitors in series with the MEMS switches) are placed close to the middle of the resonator and can shift the resonant frequency from 18 GHz to around 14 GHz when they are pulled down. The smallest loading unit cells are placed

farther from the middle of the resonator and are for ne tuning. All loading unit cells have the same elec- trical distance from each other with an unloaded t-line impedance of 78 . This distance is simulated to be 4.4 (or 120 m) at the design frequency (18 GHz) with Agilent s ADS when a lumped capacitor model is used as a loading unit cell. A practical realization of a unit cell is shown in Fig. 3, and the physical length of each unit cell is 140 m. The nite width of the bridge and MAM capacitors and the current path over the bridge result in a phase delay, which reduces the effective Agilent

Technol. Inc., Palo Alto, CA, 2002. Fig. 3. Circuit model and practical realization of a unit cell in a loaded resonator. The biasing resistance is grounded in the simulations. physical length of a unit cell to 100 m, and the spacing between two adjacent unit cells is 20 m and, hence, mat 18 GHz. Table I also shows the electrical length of the unloaded sections for each resonator simulated in ADS . The real physical lengths of the unloaded sections will be reduced in the practical realization due to the negative t-line lengths of the inductive inverters. All resonators are simulated using

Sonnet with CPW dimen- sions of 70/120/70 m on a 500- m glass substrate ( and at 18 GHz). The dimensions of the CPW line are chosen to minimize the conductor loss [11]. The measured unloaded CPW line parameters are , and dB/m at 18 GHz with 2- m electroplated gold. Table II shows the transmission-line parameters for the four different loaded sections of the resonator [3]. and are the equivalent capacitor values for each loading cell and are calculated from (1) Sonnet 8.52, Sonnet Software Inc., Syracuse, NY, 2003.
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2568 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL.

53, NO. 8, AUGUST 2005 TABLE II NIT ELL IRCUIT ODEL LEMENT ALUES XTRACTED ROM ADS S IMULATIONS AT 18 GHz ( =78 ; =2 ; =42 dB/m, =65 Fig. 4. Simulated: (a) unloaded quality factor and (b) resonant frequency for a tunable loaded resonator. The quality factor for an unloaded resonator is calculated from (2) and is 65 at 18 GHz for the unloaded CPW resonator. For the loaded sections, the quality factor is calculated in the up- or down-state positions using [10] (assuming (3) These values all are presented in Table II. Fig. 4(a) and (b) shows the simulated unloaded quality factor of the loaded

res- onator and the resonant frequency for 16 different combinations of the switches, respectively. This is done using a single res- onator, which is weakly coupled to the input and output ports, and the simulated resonant frequency and quality factor for each different state is obtained using ADS based on the values on Table I. C. Complete Filter Design and Simulations The nal section of the lter design is the inductive inverter implementation. The goal is to design a three-pole 6% 0.1-dB ripple Chebyshev lter. Canonical equations result in input and output inverters with pH and interstage

inverters with pH at 18 GHz. The series transmission lines with negative electrical lengths are absorbed in the unloaded sections of each resonator [3] ( at 18 GHz). The physical realization of shunt inductors in CPW transmission lines is shown in Fig. 5. The length and width of the inductive short-circuit slots are found using a full-wave simulation (Sonnet). Fig. 6 shows the simulated insertion loss for 16 different states with sq, and is 5.4 and 8 dB at 17.8 and 12.2 GHz, respectively. The higher insertion loss at 12.2 GHz is due to the higher loss factor of a loaded transmission line and

the low-resistivity bias line, which has a strong loading effect when all the switches are in the down-state position. III. F ABRICATION AND EASUREMENT A. Fabrication, Implementation, and Biasing The tunable lter is fabricated on a 500- m glass substrate and ) using CPW lines and MEMS switches with a standard RF MEMS process developed at The University of Michigan at Ann Arbor [12]. The MEMS capac- itive switch is based on a 8000- sputtered gold layer and is suspended 1.4 1.6 m above the pull-down electrode. The di- electric Si layer is 1800- thick and the bottom electrode thickness is 6000

(underneath the bridge). The MAM capaci- tors are suspended 1.5 m above the rst metal layer. The CPW conductor, bridge anchor, and top plate of the MAM capacitors are electroplated to 2- m thick using a low-stress gold solution. The bias lines are fabricated using an 800- -thick SiCr layer with a resistivity of approximately 2 k /square. The width, length, and thickness of the MEMS bridge are 60, 280, and 0.8 m, respectively, and the gap is 1.5 m for the bridge and MAM capacitors [see Fig. 3]. The bottom plate of one of the MAM capacitors is connected to the thin- lm resistor to bias the

bridge. The release height of the MEMS bridge and MAM capacitor is 1.5 m measured by a light-interferometer microscope. The measured pull-in voltage is V, with a corresponding spring constant of N/m, and a residual stress of MPa. The mechanical resonant frequency and quality factor of the switch are kHz and respectively [2]. The photograph of the complete 12 18-GHz lter is shown in Fig. 5. It is composed of three resonators, each one loaded with eight unit cells, two inductive inverters at the input and output of the lter, and two inductive inverters between loaded resonators. Each switch has

a separate SiCr dc-bias line for
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ENTESARI AND REBEIZ: 12 18-GHz THREE-POLE RF MEMS TUNABLE FILTER 2569 Fig. 5. Complete 12 18-GHz lter fabricated on a glass substrate. Fig. 6. Simulated: (a) insertion loss and (b) return loss of the tunable three-pole 12 18-GHz lter. independent control. The center conductor of the coplanar loaded resonators is connected to the dc ground pad through the RF probe using a bias tee. The lter is excited using ground signal ground (GSG) single-ended probes with a pitch of 150 m. B. Measurements The tunable lter is measured using CPW probes and TRL

calibration. The measured results are shown in Fig. 7 for 16 dif- ferent states. The insertion loss [see Fig. 7(a)] is 5.5 and 8.2 dB at 17.8 and 12.2 GHz, respectively, and the relative bandwidth Fig. 7. Measured: (a) insertion loss and (b) return of the tunable three-pole 12 18-GHz lter. is approximately xed for the whole tuning range, as expected from the simulation results. The return loss [see Fig. 7(b)] is better than 10 dB over the whole tuning range. The measured center frequency and loss for each of the 16 different states is presented in Fig. 8(a). Fig. 8(b) shows the relative

bandwidth variation for all responses, and is 6.1% at 17.8 GHz (State 0), and 5.3% at 12.2 GHz (State 15). Fig. 9 compares the mea- sured and simulated insertion loss for three arbitrary states at 17.8 (State 0), 14 (State 8), and 12.2 GHz (State 15), and the
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2570 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 8, AUGUST 2005 Fig. 8. (a) Measured center frequency and loss. (b) Measured relative bandwidth of the 16- lter responses 5.7 0.4% Fig. 9. Comparison between the measured and simulated insertion loss for three arbitrary states at 12.8 (State 15), 14.0

(State 8), and 17.8 GHz (State 0). simulated and measured responses agree very well. For the case of sq , the simulated insertion loss is 1.0 dB better at 17.8 GHz, 1.4 dB better at 14 GHz, and 2.2 dB better at 12.2 GHz, as compared with the measurements with sq. The measured response of a fabricated lter without any bias lines also con rms that the insertion loss improves by 0.8 dB at 17.8 GHz (all the switches are electroplated in the up-state position) to 2.0 dB at 12.2 GHz (all the switches are electroplated in the down-state position). IV. N ONLINEAR HARACTERIZATION The nonlinear analysis

of MEMS switches, varactors, and tunable lters has been presented in [13]. For high level RF signals, this analysis shows that the MEMS bridge capacitance self-pull-down results in a nonlinear behavior of the tunable Fig. 10. Experimental setup for intermodulation measurements (
Fig. 11. Nonlinear measurements at =0 V: the fundamental and intermodulation components versus the input power, and the two-tone IM versus the beat frequency. lter. In the case of two RF signals, third-order intermodulation is generated. To measure the intermodulation components at the output of the tunable lter, the

setup shown in Fig. 10 is used. Fig. 11 shows the measured output power for the fundamental and intermodulation components for several values of . The measured is 37 dBm for kHz. The measurement is in the up-state position since this state gives the worse products. Tunable lters with diode var- actors have much lower values of (12 dBm in [14] and 28 dBm in [15]). Fig. 11 also shows the intermodulation compo- nent versus the difference frequency between input tones for dBm (no bias voltage on the bridges). The inter- modulation component follows the mechanical response of the bridge, and the

level drops by 40 dB/decade for which is in agreement with theory [13]( is the mechanical res- onant frequency). This means that is 77 dBm at a differ- ence frequency of 2 MHz, which is very hard to measure and is quite impressive. V. C ONCLUSION The paper has demonstrated a wide-band tunable lter on a glass substrate from 12.2 to 17.8 GHz (40% tuning range). Four different unit-cell pairs (MEMS capacitive switches in se- ries with high- MAM capacitors) have been used to load the CPW resonators to reduce their effective length and make them tunable in a very wide range. This resulted in a

tunable lter with very ne tuning resolution. The return loss is better than 10 dB over the whole band, and it is possible to achieve a better return loss, especially at lower frequencies, if the inductive in- verters are made tunable. The measured results are very close to full-wave simulations. This study has shown that RF MEMS
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ENTESARI AND REBEIZ: 12 18-GHz THREE-POLE RF MEMS TUNABLE FILTER 2571 tunable lters are excellent for wide-band designs and result in very low intermodulation levels. EFERENCES [1] G. L. Matthaei, E. Young, and E. M. T. Jones, Microwave Filters,

Impedance-Matching Networks, and Coupling Structures . Norwood, MA: Artech House, 1980. [2] G. M. Rebeiz, RF MEMS Theory, Design, and Technology . New York: Wiley, 2003. [3] A. Abbaspour-Tamijani, L. Dussopt, and G. M. Rebeiz, Miniature and tunable lters using MEMS capacitors, IEEE Trans. Microw. Theory Tech. , vol. 51, no. 7, pp. 1878 1885, Jul. 2003. [4] K. Entesari and G. M. Rebeiz, A differential 4-bit 6.5 10-GHz RF MEMS tunable lter, IEEE Trans. Microw. Theory Tech. , vol. 53, no. 4, pp. 1103 1110, Mar. 2005. [5] R. M. Young, J. D. Adam, C. R. Vale, T. T. Braggins, S. V. Krish- naswamy,

C. E. Freidhoff, S. H. Talisa, E. Capelle, R. Tranchini, J. R. Fende, J. M. Lorthioir, and A. R. Torres, Low-loss bandpass RF lter using MEMS capacitance switches to achieve a one-octave tuning range and independently variable bandwidth, in IEEE MTT-S Int. Microwave Symp. Dig. , Jun. 2003, pp. 1781 1784. [6] J. Brank, J. Yao, A. Malczewski, K. Varian, and C. L. Goldsmith, RF MEMS-based tunable lters, Int. J. RF Microwave Computer-Aided Eng. , vol. 11, pp. 276 284, Sep. 2001. [7] A. Pothier, J. C. Orlianges, E. Zheng, C. Champeaux, A. Catherinot, D. Cross, P. Blondy, and J. Papapolymerou, Low

loss 2-bit bandpass lters using MEMS DC contact switches, IEEE Trans. Microw. Theory Tech. vol. 53, no. 1, pp. 354 360, Jan. 2005. [8] I. Hunter, Theory and Design of Microwave Filters . London, U.K.: IEE, 2001. [9] G. L. Matthaei, Narrow-band, xed-tuned, and tunable bandpass lters with zig zag hairpin-comb resonators, IEEE Trans. Microwave Theory Tech. , vol. 51, no. 4, pp. 1214 1219, Apr. 2003. [10] N. S. Barker, Distributed MEMS transmission lines, Ph.D. disserta- tion, Dept. Elect. Eng. Comput. Sci., The Univ. Michigan at Ann Arbor, Ann Arbor, MI, 1999. [11] K. C. Gupta, R. R. Garg, I. I.

Bahl, and P. P. Bhartia, Microstrip Lines and Slotlines. , 2nd ed. New York: Artech House, 1996. [12] J. S. Hayden and G. M. Rebeiz, Very low loss distributed -band and Ka -band MEMS phase shifters using metal air metal capacitors, IEEE Trans. Microw. Theory Tech. , vol. 51, no. 1, pp. 309 314, Jan. 2003. [13] L. Dussopt and G. M. Rebeiz, Intermodulation distortion and power handling in RF MEMS switches, varactors and tunable lters, IEEE Trans. Microw. Theory Tech. , vol. 51, no. 4, pp. 1247 1256, Apr. 2003. [14] S. R. Chandler, I. C. Hunter, and J. C. Gardiner, Active varactor tunable

bandpass lters, IEEE Microw. Guided Wave Lett. , vol. 3, no. 3, pp. 70 71, Mar. 1993. [15] A. R. Brown and G. M. Rebeiz, A varactor-tuned RF lter, IEEE Trans. Microwave Theory Tech. , vol. 48, no. 7, pp. 1157 1160, Jul. 2000. Kamran Entesari (S 03) received the B.S. degree in electrical engineering from Sharif University of Technology, Tehran, Iran, in 1995, the M.S. degree in electrical engineering from Tehran Polytechnic University, Tehran, Iran, in 1999, and is currently working toward the Ph.D. degree in electrical engineering (with an emphasis on applied electro- magnetics and RF

circuits) at The University of Michigan at Ann Arbor. His research area includes RF MEMS for microwave and millimeter-wave applications, mi- crowave tunable lters, and packaging structures. Gabriel M. Rebeiz (S 86 88 SM 93 97) re- ceived the Ph.D. degree in electrical engineering from the California Institute of Technology, Pasadena. He is a Full Professor of electrical engineering and computer science (EECS) with the University of California at San Diego, La Jolla. He authored RF MEMS: Theory, Design and Technology (New York: Wiley, 2003). His research interests include applying MEMS) for the

development of novel RF and microwave components and subsystems. He is also interested in SiGe RF integrated-circuit (RFIC) design, and in the development of planar antennas and millimeter-wave front-end electronics for communication systems, automotive collision-avoid- ance sensors, and phased arrays. Prof. Rebeiz was the recipient of the 1991 National Science Foundation (NSF) Presidential Young Investigator Award and the 1993 International Sci- enti c Radio Union (URSI) International Isaac Koga Gold Medal Award. He was selected by his students as the 1997 1998 Eta Kappa Nu EECS Professor of

the Year. In October 1998, he was the recipient of the Amoco Foundation Teaching Award, presented annually to one faculty member of The University of Michigan at Ann Arbor for excellence in undergraduate teaching. He was the corecipient of the IEEE 2000 Microwave Prize. In 2003, he was the recipient of the Outstanding Young Engineer Award of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S). He is a Distinguished Lecturer for the IEEE MTT-S.