Compact Fixed and Tune-All Bandpass Filters Based on ... - IEEE Xplore

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 6, JUNE 2006

Compact Fixed and Tune-All Bandpass Filters Based on Coupled Slow-Wave Resonators Emmanuel Pistono, Mathieu Robert, Lionel Duvillaret, Jean-Marc Duchamp, Anne Vilcot, Member, IEEE, and Philippe Ferrari

Abstract—A compact topology for bandpass filters based on coupled slow-wave resonators is demonstrated. A study of fixed bandpass filters leads to design rules and equations. Measurements on a 0.7-GHz fixed bandpass filter, consisting of three coupled slowwave resonators, demonstrate the validity of the proposed topology and validate the theory, since the agreement between simulations and measurements is very good. Designed for a -factor of 5, this filter shows a of approximately 5.2. At the center frequency, insertion loss is 0.6 dB and return loss is greater than 20 dB. A 0.7-GHz tune-all bandpass filter is also designed and tested. The performance of this electronically tuned filter, which incorporates semiconductor varactors, is promising in terms of wide continuous center-frequency and bandwidth tunings. For a center-frequency tuning of 18% around 0.7 GHz, the 3-dB bandwidth can be simultaneously tuned between 50 and 78 MHz, with an insertion loss smaller than 5 dB and a return loss greater than 13 dB at the center frequency. The surface areas of the fixed and tunable 0.7-GHz filters are, respectively, 16 and 20 cm2 . Index Terms—Microwave bandpass filter, slow-wave structures, tunable filter, varactors.

I. INTRODUCTION HE DESIGN of compact and efficient bandpass filters constitutes a great challenge [1]. The integration of microwave systems necessitates size reduction of each elementary function (e.g., antenna, filters, and amplifier). In the case of multiband microwave receivers, the use of multiple filters consumes a large surface area and is therefore unacceptable. Thus, tunable bandpass filters showing tunability of both the center frequency and bandwidth, called tune-all bandpass filters, constitute an interesting way to solve this problem, since they can perform over all operating bands. The great number of recent publications demonstrating tunable microwave filters [2]–[17] confirms their importance, in particular, publications concerning tune-all microwave bandpass filters [14]–[17]. In [15] and [16], wide tunability around 0.7 GHz was achieved. However, spurious peaks appeared in the filter behavior, either at low frequencies [15] or at high frequencies [16]. Furthermore, filter sizes at 0.7 GHz were as large as 32 cm [15] or even 105 cm [16].

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Manuscript received October 3, 2005; revised February 17, 2006. E. Pistono and M. Robert are with the Laboratoire d’Hyperfréquences et de Caractérisation, Université de Savoie, 73376 Le Bourget-du-lac, France (e-mail: [email protected]; [email protected]). L. Duvillaret, J.-M. Duchamp, A. Vilcot, and P. Ferrari are with the Institute of Microelectronics Electromagnetism and Photonics, Unité Mixte de Recherche 5130 Centre National de la Recherche Scientifique–Institut National Polytechnique de Grenoble–Université Joseph Fourier, 38016 Grenoble, France (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.874894

To reduce filter size, various slow-wave structures can be used (see, e.g., [9]–[14] and [18]–[21]). Among these, capacitively coupled distributed microelectromechanical-systems (MEMS) transmission lines [9]–[14] constitute an interesting way to obtain not only reduced size (by periodically loading resonators with shunt capacitors to obtain slow-wave behavior) but also filter tunability (by using tuned MEMS varactors instead of fixed capacitors). In such filters, tuning of the bandwidth was either uncontrolled or not well controlled [12], leading to an unwanted shift of the bandwidth. Based on series-coupled half-wavelength resonators [22], the compact tunable bandpass filter topology presented in this paper utilizes capacitively coupled varactor transmission lines, using semiconductor varactors instead of MEMS varactors [9]–[14]. Here, tunability of both the center frequency and bandwidth is achieved since both shunt and series capacitors are replaced by bias-tuned semiconductor varactors. Also, straightforward design equations are obtained. This paper is organized as follows. Section II introduces the filter topology based on coupled slow-wave resonators. Design rules and equations are worked out for filters with fixed bandwidth and working frequency. In Section III, results for two fabricated filters are presented. First, a fixed bandpass filter is designed and measured, showing a good agreement between simulation and measurement, thereby validating the design equations. Next, measured and simulated results for a 0.7-GHz optimized tune-all bandpass filter [17] demonstrate promising continuous tuning of both center frequency and bandwidth, and a comparison with previous works is proposed. Wideband measurements show a large attenuation bandwidth up to eight times the center frequency. Finally, the conclusion summarizes the performance of fabricated filters and suggests future improvements. II. BACKGROUND THEORY Here, we consider ideal lossless transmission lines in order to find equations from which straightforward design principles can be deduced. These design equations provide a first approximation to the desired filter performance as a function of center frequency, bandwidth, and attenuation slopes. As will be shown in Section II-B, the return loss of the calculated filter is inadequate, particularly in filters consisting of more than two coupled resonators. Improvement of the passband return loss and other characteristics requires an optimization. A. Description of the Coupled Slow-Wave Resonator Filters The filters exhibited in this paper consist of series-coupled slow-wave resonators.

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PISTONO et al.: COMPACT FIXED AND TUNE-ALL BANDPASS FILTERS BASED ON COUPLED SLOW-WAVE RESONATORS

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Fig. 1. Topology of a single-coupled slow-wave resonator loaded at the near and far ends with series capacitors C .

Fig. 1 shows the topology of a single-coupled slow-wave resonator. This consists of a slow-wave resonator loaded at its near and far ends with series capacitors . The resonator itself is made up of a transmission line of characteristic impedance and electrical length , periodically loaded by shunt capacitors . In this study, only the two-shunt-capacitor case is considered. The electrical length of the unloaded transmission line is defined at frequency as

(1) where is the effective relative permittivity, is the physical length of the unloaded line, and is the vacuum light velocity. At the center frequency , the electrical length is . B. Design Rules By using (cascade) matrices, the equivalent characof a coupled slow-wave resonator can be teristic impedance easily extracted. Let us notice that the coupled slow-wave resonator considered is symmetrical and reciprocal. of a single-coupled slowThe characteristic impedance wave resonator (assuming that the characteristic impedance of ) is shown in Fig. 2 the unloaded transmission line is for three different values (5, 10, and 20) of the resonator-loaded . This is defined as quality factors

(2) where and are the limits of the first frequency band in is purely real, and . which As explained in [23], by using the Bloch-wave method for a periodic structure consisting of an infinite number of coupled slow-wave resonators, we can say that the Bloch-wave charac. Thus, frequency passbands and stopteristic impedance is bands can be deduced. They correspond to frequency bands for which unattenuated propagation can take place, separated by frequency bands in which the wave is attenuated. Also, these frequency bands correspond, respectively, to frequency bands is either purely real or purely imaginary (assuming where lossless circuits). In reality, is not infinite, and the load and source impedances of the pseudoperiodic structure are made must equal 50 . Therefore, to obtain a matched filter, or be close to 50 . This condition can be fulfilled only for , as seen in Fig. 2(d), and (e). Depending on the value of , the frequency ranges for which is purely real give a good estimate of the location of the

Fig. 2. Calculated characteristic impedance Z of single-coupled slow-wave resonators for Z = 170 : (a) Q = 5, (b) Q = 10, and (c) Q = 20. jS j of (d) single-, and (e) two-coupled-slow-wave-resonator filters for Z = 170 , and Q = 5; 10; and 20. C ; C , and  are calculated with the formulas developed below.

passbands. In fact, a good agreement is seen (even when ) between the passbands [see Fig. 2(e)] and the bands that lead

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to real values of [see Fig. 2(a)–(c)]. For , these considerations do not apply, since then the structure is not periodic; hence, no spurious peak appears above in Fig. 2(d). The larger the -factor is, the narrower and higher in frequency the second passband is. This behavior makes wide attenuation bandwidths, free from a spurious peak, possible. Furthermore, these spurious peaks are very narrow. Thus, in practice, even for low values of , the peak spurious levels will be weak due to transmission-line and varactor losses (see Section III-A). Having presented the principle of these filters, we now derive design rules and relations for the calculation of the capaciand . To this end, we solve the two equations corretors at sponding to the first passband, that is, and at . The solution for leads to two solutions for , with opposite signs, with the positive solution being

Fig. 3. Electrical length  of the slow-wave resonator (calculated for Q = = ratio demonstrates the slow-wave phenomenon.

10 and Z = 170 ). The  (3) where at . Equation (3) shows that depends and not on . only on at leads to Similarly, the solution for two solutions for . The unique positive solution is

(4) at . Equation (4) shows that is linked where in a nontrivial way. to both and Fig. 3 shows the slow-wave phenomenon of a typical slowand ), where is wave resonator (here, the electrical length of the slow-wave resonator loaded by shunt (without considering the near- and far-end series capacitors capacitor loads ). Fig. 3 shows that the electrical length of the slow-wave resonator is at . Thus, these slow-wave resonators are halfwavelength resonators coupled at their near and far ends by series capacitors. The slow-wave phenomenon is clearly demonbetween the electrical length of strated, since the ratio the slow-wave resonator and that of the unloaded transmission line is about 15 at the center frequency . This means that the total physical length of a filter composed of such slow-wave resonators is about 15 times smaller than the equivalent filter based on unloaded half-wavelength resonators [22]. ’s of 5 and 20, (assuming For slow-wave resonators with ), the ratios are about 8 and 28, respec-

tively. Consequently, this filter topology is well suited for realizing compact and high- filters. and that depend We next derive simple relations for , the center freonly on the resonator loaded quality factor (at ), and the unloaded quency , the electrical length characteristic impedance of the transmission line. Thus, from and , (2)–(4), we find new expressions for the capacitors given as

(5) and (6), shown at the bottom of this page. The next step is to find an expression for . A suitable method is to calculate the power series expansion of about , to first order, as given in (7), shown at the bottom of the following page. Such an expansion is reasonable in (i.e., ). Moreover, the higher the practice since , the better this assumption is. By imposing the condition at the working frequency , which corresponds to the matching condition, the following straightforward expresis found: sion for

(8) Here again, one sees that, to minimize the electrical length of of the slow-wave resonator, the characteristic impedance the unloaded transmission line must be as large as possible. The is, the smaller the value of is that fulfils higher the value of the matching condition.

(6)

PISTONO et al.: COMPACT FIXED AND TUNE-ALL BANDPASS FILTERS BASED ON COUPLED SLOW-WAVE RESONATORS

Fig. 4. Dependencies of: (a) 2f C and (b) 2f C on the electrical length  of the unloaded slow-wave resonator at f .

We now discuss how the design parameters and depend on , and . Fig. 4 shows how and vary with the electrical length (at ) of the unloaded slow-wave ’s varying between 5 and 20, and varying resonator for between 110–170 . Fig. 4(a) and (b) shows that and both have the same type of dependency on . For a given , the smaller is, the higher and must be to obtain coupled slow-wave , the higher is, the smaller resonators at . For a given must be to obtain a coupled slow-wave resonator matched to is, the 50 at . Finally, as explained above, the higher the will be. smaller

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Fig. 5. Calculated: (a) jS j and (b) jS j for filters consisting of a number n of coupled slow-wave resonators (with Z = 170 ; Q = 10), where n varies from 1 to 5.

Fig. 5 shows and for these filters. These results were obtained by considering a number of coupled slow-wave and ), when resonators (calculated with is varied from 1 to 5. As seen in Fig. 5, as the number of coupled slow-wave resonators increases, the attenuation slope of the filter transmisbecomes the loaded sion increases, and the closer to quality factor of the calculated filter. This is defined as: (9)

(7)

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Fig. 7. 0.7-GHz fixed three-coupled-slow-wave-resonator bandpass filter.

III. RESULTS FOR TWO FABRICATED 0.7-GHZ BANDPASS FILTERS

Fig. 6. jAttenuation slopej of the coupled slow-wave filters for = 170 . from 5 to 20, with

Z

Q

’s varying

where is the filter center frequency, and is the 3-dB bandwidth. So, to a first approximation, to calculate the initial . On the other filter parameters, one can approximate hand, when increases, the matching in the passband degrades (for example, for , the return loss is 5 dB). To improve the matching of the calculated filter in the passband, a simple optimization is required. This can be done with aid of microwave software such as ADS [24] or Ansoft Designer [25]. For this purpose, it is sufficient to slightly modify the near- and far-end resonators and, in particular, the values of each coupling capacitor . Fig. 6 shows the attenuation slope of the filter, calculated from 3 to 30 dB, versus the number of coupled slow-wave and 20, with resonators constituting the filter, for . For a given coupled slow-wave filter, Fig. 6 shows that the attenuation slopes below the low cutoff frequency and above the high cutoff frequency of the bandpass filter are very similar. C. Design Method and Optimization The design of the fixed filters involves two steps. First, by knowing the desired filter behavior (i.e., the attenuation slopes below and above , the , and the center frequency ) and the maximum realizable characteristic impedance in a given technology, one can determine the following: • required number of coupled slow-wave resonators (see Fig. 6); • electrical length of the slow-wave resonators [see (8)]; and [see (5) and (6)]. • capacitor values Second, to improve the return loss in the passband, the param, and of the near- and far-end coupled slow-wave eters resonators must be modified, as we demonstrated previously for low-pass filters [26]. This can be done by using the optimization tools in typical CAD software. In this design step, transmission line losses are taken into account and accurate models must be used for the capacitors. The design method for tunable filters is similar, except that capacitors are replaced by varactors.

Both fixed and tunable bandpass filters were designed in coplanar waveguide (CPW) technology. The fixed filter was fabricated on a Rogers RO4003 substrate with relative per, dielectric loss , height mittivity mm, and copper thickness m. The tunable filter was fabricated on an RT-Duroid 5880 substrate having , dielectric loss , relative permittivity height mm, and copper thickness m. A. 0.7-GHz Fixed Bandpass Filter An initial three-coupled-slow-wave-resonator bandpass filter was designed and optimized with ADS for a fixed 0.7-GHz of 5. The aim of this first circuit center frequency and a was to demonstrate that the predicted results are not critically dependent on the accuracy of the fixed capacitors loading the leads to a resonators. The 110- characteristic impedance center conductor width mm, a gap width mm, a ground plane width mm, and at 0.7 GHz. American Technical Ceramics capacitors type ATC 600-S were used; these have a low series resistance of 0.15 and a series inductance of 0.8 nH. The capacitance tolerance was between 3.5%– 5% for the values used in this design. A photograph of this filter is shown in Fig. 7. To avoid odd-mode propagation, shunt capacitors must be soldered on each side of the CPW center conductor to maintain symmetry. This means that the value of each shunt capacitor must be . The electrical lengths corresponding to the physical lengths and are 32.4 and 30.9 , respectively. The surface area of 10 , this fixed bandpass filter is 16 cm , that is, 14 is the guided wavelength at the center frequency . where A sensitivity study was carried out by means of a Monte Carlo analysis. Fig. 8 shows simulated -parameters of the realized fixed bandpass filter, assuming a 5% accuracy on the capacitance values. One observes that the filter behavior is not critically dependent on the available capacitor tolerance. Indeed, a tolerance of 5% of the capacitance values induces a 3% center-frequency variation and a 3% bandwidth variation. Moreover, at the center frequency, the return loss remains always better than 24 dB. Then, measurements were done using a Wiltron 360 Vector Network Analyzer and the open-short-through-load (OSTL) calibration procedure. Fig. 9 compares the measured and simulated -parameters of the realized fixed bandpass filter. The narrowband results of Fig. 9(a) show that the measurements agree very well with the simulations. Insertion loss and return loss are, respectively, 0.6 and 24 dB at . The measured

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Fig. 10. Topology of the 0.7-GHz tune-all two-coupled-slow-wave-resonator bandpass filter.

Fig. 8. Monte Carlo analysis of the proposed fixed bandpass filter: simulated jS j and jS j assuming a 5% accuracy on the capacitance values.

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peak appears at about 1.8 times the center frequency . The 20-dB bandwidth of this spurious peak is 10 MHz, and it has a maximal transmission modulus of 16.7 dB at 1.24 GHz. This spurious peak corresponds to the second passband where is real [see Fig. 2(a)]. This peak occurs at a lower frequency than expected theoretically. This is due to the parasitic series inductance of actual capacitors. The wideband measurements of Fig. 9(b) show a second spurious peak in the attenuation bandof 14.6 dB at 7.15 GHz. width with a maximal B. 0.7-GHz Tune-All Bandpass Filter

Fig. 9. 0.7-GHz fixed three-coupled-slow-wave-resonator bandpass filter. (a) Comparison between narrowband measured and simulated S and S . (b) Wideband measured S .

j j

j j

j j

is 5.15, which is very close to the expected value. Low and high attenuation slopes are 211 and 360 dB/decade, respectively. This filter shows a wide 15-dB attenuation bandwidth extending to 7 GHz [see Fig. 9(b)]. However, a narrow spurious

Fig. 10 shows the topology of the optimized tune-all bandpass filter. This compact tune-all bandpass filter consists of two coupled slow-wave resonators. Near- and far-end high impedance transmission line segments called “tapering sections” are used. The characteristic impedance of these tapering sections is , as for is optithe slow-wave resonators, but their electrical length mized to improve the filter return loss in the passband. To obtain a tunable filter, capacitors are replaced by varactors. As a first approximation, we consider that center-frequency tunability is obtained by tuning the shunt varactors, since then the loaded of the slow-wave resonators is modified, electrical length leading to resonator-frequency tuning. Bandwidth control is obtained by tuning the series varactors . Simulations and optimizations for this tunable filter were carried out using Ansoft Designer. Commercially available reverse-biased Schottky diodes M/A-Com MA46H071 and , and MA4ST1240 were used to realize series varactors . Here again, shunt capacitors of values shunt varactors must be soldered on each side of the CPW center conductor to maintain symmetry. The characteristic is 170 , leading to a center conductor width impedance mm, a gap width mm, a ground plane mm, and at 0.7 GHz. Physical width lengths (electrical lengths) of the slow-wave resonators and mm (24.7 ) and the tapering sections are, respectively, mm (22.7 ). This leads to a filter length of and a surface area of . Measurements were done using a Wiltron 360 Vector Network Analyzer and the through-reflect-line (TRL) calibration procedure. Fig. 11 compares the measured and simulated -parameters of the realized tune-all bandpass filter for the two bandwidths of 50 and 78 MHz. Shunt and series varactor bias and are indicated in Fig. 11. They vary voltages from 0 to 2 V and from 0 to 5.9 V, respectively. Fig. 11 shows that the simulated and measured insertion losses are in good agreement. These simulations were carried out for the following:

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Fig. 12. Loss contribution of the series resistance of the shunt and series varactors. Simulated S of the bandpass filter for the typical case corresponding to a 78-MHz bandwidth at f =0.57 GHz. Biases are V (C ) = 0:5 V and V (C ) = 0 V.



j j

Fig. 11. Simulated and measured jS j and jS j for the tune-all bandpass filter. (a) Center-frequency tuning for a 50-MHz bandwidth. (b) Center-frequency tuning for a 78-MHz bandwidth.





• shunt varactors with junction capacitance (V) , varying from 3.2 to 8.8 pF, series resistance series inductance nH, and case capacitance pF; (V) varying • series varactors with junction capacitance nH, and from 0.7 to 2.5 pF, pF. The measured return loss is better than expected from the simulation and is always better than 13 dB at . The center-frequency tunability of this tune-all bandpass filter reaches 24% for a 50-MHz bandwidth, with insertion loss 5 dB at , and 18% for a 78-MHz bandwidth, with insertion loss 3.8 dB at . Simulations demonstrating the major contribution of the varactor series resistance to the total insertion loss at are shown in Fig. 12. These simulations correspond to the filter behavior V and V and are premeasured for sented in Fig. 11(b). In Fig. 11(b), the return loss is better than 20 dB at , and thus we deduce that insertion loss is due only to CPW losses and varactor losses. and For the actual varactors, which have , insertion loss at is 3.6 dB. The simulations reveal

Fig. 13. Measured bandwidth tuning of the filter for a fixed shunt-varactor bias V (C ) = 1:5 V and a variable series-varactor bias V (C ) in the range 0.33–3.9 V.

that insertion loss at the center frequency is mainly due to the series resistance of the varactors, and especially to that of the shunt varactors. For ideal varactors with no series resistance, insertion loss would be 0.3 dB. This corresponds to the CPW losses since the device is well matched in this configuration, dB. Furthermore, the simulation for with and suggests that the series resistance of the series varactors has a minor impact on the insertion loss at . For , corresponding to the series resisthe case tance of the MA46H071 varactors, the insertion loss (1.85 dB) would be half the actual value. Fig. 13 shows the measured tunable bandwidth of the filter V for the shunt varactors and a for a fixed bias variable series-varactor bias in the range 0.33–3.9 V. For a mean center frequency (around 0.7 GHz) and maintaining insertion loss below 5 dB, the bandwidth can be tuned between 50 MHz ( -factor of 14.5) and 150 MHz ( -factor

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TABLE I PERFORMANCE OF PRIOR TUNABLE FILTERS BASED ON CAPACITIVELY COUPLED VARACTOR TRANSMISSION LINES

Fig. 14. Wideband measured jS j of the filter when the shunt and series varactors biases are set to V (C ) = 0 V and V (C ) = 0 V.

of 4.7). Insertion loss is minimal (2.55 dB) at when the bandwidth is maximal ( 150 MHz). In this example, bandwidth control is obtained by varying only the series-varactor bias . The center frequency remains almost unchanged during the bandwidth tuning. In fact, while tuning the over its full range, the relative center-frequency tuning shift has an upper bound of only 4%. Fig. 14 depicts the measured wideband insertion loss of the filter when the shunt and series varactors biases are set to V and V. Fig. 14 shows that there is no spurious peak (greater than 30 dB) in the filter response for frequencies below ten times the 0.7-GHz working frequency. C. Brief Comparison of Tunable Filters Based on Capacitively Coupled Varactor Transmission Lines To show the improvements of our design, Table I summarizes performance of up to now tunable filters based on capacitively coupled varactor transmission lines. Filters are compared in terms of: 1) loaded factor; 2) bandwidth fluctuation (the achievement of a wide center-frequency tuning generally induces unwanted variations of the bandwidth over the tuning range); 3) center-frequency tuning; 4) maximal insertion loss, and 5) surface area. To compare the surface area, we consider the , where is the surface of the filter (in surface factor m ). Thus, the more compact the device is, the higher this factor is. The effective relative permittivity is not considered in this surface factor, for two reasons, which are: 1) only a few papers give this parameter and 2) the technological constraints may forbid the transfer of a filter topology to another technology. The unwanted bandwidth fluctuation is defined as the ratio between the minimal and maximal 3-dB bandwidths of the center-frequency tunable filter over its whole tuning range. Filters presented in [12] and [13] show very interesting results in terms of center-frequency tuning range. However, achievement of these wide center-frequency tuning ranges induces wide bandwidth fluctuations for these two filters. Our design allows obtaining wider center-frequency tuning ranges than in [12] and

[13] for similar loaded factors, with insertion loss comparable to that in [12] or better than that in [13]. Moreover, our topology of tune-all bandpass filter allows a very good control of bandwidth fluctuations over the whole tuning range. Finally, this design exhibits a much higher surface factor than previous tunable filters based on capacitively coupled varactor transmission lines. IV. CONCLUSION A topology for compact bandpass filter has been demonstrated. Design rules and equations have been derived to provide straightforward tools for the designer. First, a fixed three-coupled-slow-wave-resonator bandpass filter showing a -factor of 5 was used to validate the theory. Measurements and simulations are in very good agreement. At the center frequency, insertion loss is 0.6 dB and return loss is 24 dB. . This filter is very compact with a surface area of 14 10 Second, a tune-all bandpass filter has been designed, showing very promising performance in terms of wide continuous tuning of both bandwidth and center frequency. The center-frequency tuning is achieved by varying the electrical length of the slow-wave resonators by means of the shunt varactors. Bandwidth tuning is obtained by coupling varactors in series with the resonators. The relative center-frequency tuning of the fabricated filter is 18% around 0.7 GHz for a bandwidth variation from 50 to 78 MHz and an insertion loss below 5 dB. Narrower bandwidths can be obtained, but at the cost of increased insertion loss. This insertion loss is mainly due to the series resistances of the shunt varactors. It is apparent that the use of MEMS varactors, which have a low series resistance, would improve the performance of this filter topology, especially at the higher working frequencies. The compactness of these circuits will allow designers to integrate such filters on high-resistivity substrates for higher frequency operation. ACKNOWLEDGMENT The authors would like to thank Prof. R. G. Harrison, Department of Electronics, Carleton University, Ottawa, ON, Canada, for his advice and discussions. REFERENCES [1] K. Hettak, N. Did, A.-F. Sheta, and S. Toutain, “A class of novel uniplanar series resonators and their implementation in original applications,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 9, pp. 1270–1276, Sep. 1998.

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[2] C. Rauscher, “Reconfigurable bandpass filter with a three-to-one switchable passband width,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 2, pp. 573–577, Feb. 2003. [3] B. W. Kim and S. W. Yun, “Varactor-tuned combline bandpass filter using step-impedance microstrip lines,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 4, pp. 1279–1283, Apr. 2004. [4] A. Pothier, J.-C. Orlianges, G. Zheng, C. Champeaux, A. Catherinot, D. Cros, P. Blondy, and J. Papapolymerou, “Low-loss 2-bit tunable bandpass filters using MEMS DC contact switches,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 354–360, Jan. 2005. [5] C. D. Nordquist, C. L. Goldsmith, C. W. Dyck, G. M. Kraus, P. S. Finnegan, F. Austin IV, and C. T. Sullivan, “ -band RF MEMS tuned combline filter,” Electron. Lett., vol. 41, pp. 76–77, Jan. 2005. [6] K. Entesari and G. M. Rebeiz, “A differential 4-bit 6.5–0-GHz RF MEMS tunable filter,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 1103–1110, Mar. 2005. [7] E. Pistono, P. Ferrari, L. Duvillaret, J.-M. Duchamp, and R. G. Harrison, “Hybrid narrow-band tunable bandpass filter based on varactors loaded electromagnetic-bandgap coplanar waveguides,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 8, pp. 2506–2514, Aug. 2005. [8] C. Siegel, V. Ziegler, U. Prechtel, B. Schönlinner, and H. Schumacher, “Very low complexity RF-MEMS technology for wide range tunable microwave filters,” in Proc. 35th Eur. Microw. Conf., Paris, France, Oct. 2005, pp. 637–640. [9] Y. Liu, A. Borgioli, A. S. Nagra, and R. A. York, “Distributed MEMS transmission lines for tunable filter applications,” Int. J. RF Microw. Comput.-Aided Eng., vol. 11, no. 5, pp. 254–260, Sep. 2001. [10] A. Abbaspour-Tamijani, L. Dussopt, and G. M. Rebeiz, “A millimeterwave tunable filter using MEMS capacitors,” in Proc. 32nd Eur. Microw. Conf., Milan, Italy, Sep. 2002, pp. 813–815. [11] ——, “Miniature and tunable filters using MEMS capacitors,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 7, pp. 1878–1885, Jul. 2003. [12] G. M. Kraus, C. L. Goldsmith, C. D. Nordquist, C. W. Dyck, P. S. Finnegan, F. Austin IV, A. Muyshondt, and C. T. Sullivan, “A widely tunable RF MEMS end-coupled filter,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2004, vol. 2, pp. 429–432. [13] K. Entesari and G. M. Rebeiz, “A 12–8-GHz three-pole RF MEMS tunable filter,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 8, pp. 2566–2571, Aug. 2005. [14] D. Mercier, J.-C. Orlianges, T. Delage, C. Champeaux, A. Catherinot, D. Cros, and P. Blondy, “Millimeter-wave tune-all bandpass filters,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 4, pp. 1175–1181, Apr. 2004. [15] M. Sanchez-Renedo, R. Gomez-Garcia, J. I. Alonso, and C. Briso-Rodriguez, “Tunable combline filter with continuous control of center frequency and bandwidth,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 191–199, Jan. 2005. [16] B. E. Carey-Smith, P. A. Warr, M. A. Beach, and T. Nesimoglu, “Wide tuning-range planar filters using lumped-distributed coupled resonators,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 2, pp. 777–785, Feb. 2005. [17] E. Pistono, P. Ferrari, L. Duvillaret, J.-M. Duchamp, and A. Vilcot, “A compact tune-all bandpass filter based on coupled slow-wave resonators,” in Proc. 35th Eur. Microwave Conf., Paris, France, Oct. 2005, pp. 1243–1246. [18] L.-H. Hsieh and K. Chang, “Slow-wave bandpass filters using ring or stepped-impedance hairpin resonators,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 7, pp. 1795–1800, Jul. 2002. [19] C. K. Wu, H. S. Wu, and C. K. Tzuang, “Electric–magnetic–electric slow-wave microstrip line and bandpass filter of compressed size,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 8, pp. 1996–2004, Aug. 2002. [20] Y.-K. Kuo, C.-H. Wang, and C. H. Chen, “Novel reduced-size coplanar-waveguide bandpass filters,” IEEE Microw. Wireless Compon. Lett, vol. 11, no. 2, pp. 65–67, Feb. 2001. [21] J. Sor, Y. Qian, and T. Itoh, “Miniature low-loss CPW periodic structures for filter applications,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 12, pp. 2336–2341, Dec. 2001. [22] D. F. Williams and S. E. Schwarz, “Design and performance of coplanar waveguide bandpass filters,” IEEE Trans. Microw. Theory Tech., vol. MTT-31, no. 7, pp. 558–566, Jul. 1983. [23] R. E. Collin, Foundations for Microwave Engineering, 2nd ed. New York: McGraw-Hill, 1992. [24] Advanced Design System (ADS). ver. 2004A, Agilent Technol., Palo Alto, CA, 2004. [25] Ansoft Designer. ver. 2.0, Ansoft Corporation, Pittsburgh, PA, 2004.

[26] D. Kaddour, E. Pistono, J.-M. Duchamp, L. Duvillaret, A. Jrad, and P. Ferrari, “Compact and selective low pass filter with spurious suppression,” Electron. Lett., vol. 40, pp. 1344–1345, Oct. 2004.

Emmanuel Pistono was born in Gap, France, in 1978. He received the Electronics and Microwaves Engineer degree and M.Sc. degree from the Institut National Polytechnique de Grenoble (INPG), Grenoble, France, in 2002 and 2003, respectively, and is currently working toward the Ph.D. degree University of Savoie, Le bourget-du-lac, France. He is currently with the Laboratoire d’Hyperfréquences et de Caractérization (LAHC), Université de Savoie. His research interest is the design and realization of hybrid fixed and tunable microwave

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Mathieu Robert was born in Chambéry, France, in 1982. He received the Radiofrequency and Microwaves M.Sc. degree from the University of Lille 1, Lille, France, in 2005. He is currently with the Université de Savoie, Le Bourget-du-Lac, France.

Lionel Duvillaret was born in Thonon-les-bains, France, in 1966. He received the Ph.D. degree in physics from the University of Paris XI-Orsay, Paris, France, in 1994. From 1990 to 1994, he was involved in research on electrooptic sampling with the Institute of Fundamental Electronics (IEF), Orsay, France. In October 1993, he joined the Laboratoire d’Hyperfréquences et de Caractérization (LAHC), Université de Savoie, Le-Bourget-du-Lac, France, where he was an Assistant Professor of physics. Since October 2005, he has been an Associate Professor with the National Polytechnical Institute of Grenoble (INPG), Grenoble, France, where he continues his research with the Institute of Microelectronics, Electromagnetism and Photonics, INPG. His current research interests include terahertz time-domain spectroscopy, electrooptic characterization of electric fields, and electromagnetic bandgap materials. He has authored or coauthored over 75 journal papers and international conference proceedings.

Jean-Marc Duchamp was born in Lyon, France, on April 10, 1965. He received the M.Sc. degree from the University of Orsay, Orsay, France, in 1988, the Engineer degree from Ecole Supérieur d’Electricité (ESE), Gif/Yvette, France, in 1990, and the Ph.D. degree from the Université de Savoie, Le Bourget-dulac, France, in 2004. From 1991 to 1996, he was a Research Engineer with Techmeta, Pringy, France. He is currently with the Laboratoire d’Hyperfréquences et de Caractérization (LAHC), Université de Savoie, where he teaches electronics and computer sciences. His current research interests include nonlinear microwave and millimeter-wave circuits analysis and design like nonlinear transmission lines, periodic structures, and tunable impedance transformers.

PISTONO et al.: COMPACT FIXED AND TUNE-ALL BANDPASS FILTERS BASED ON COUPLED SLOW-WAVE RESONATORS

Anne Vilcot (M’90) received the Engineer grade in electronics from the National High School in Electronics and Radioelectricity of Grenoble of the National Polytechnical Intitute of Grenoble (INPG), Grenoble, France, in 1989, and the Ph.D. degree in microwaves from the Laboratory of Electromagnetism Microwaves and Optoelectronics (LEMO), Grenoble, France, in 1992 In 1989, she joined the LEMO. Since then, she has been involved with the optical control of microwave devices. She is currently a Professor with the INPG and the Vice-Director of the Institute of Microelectronics, Electromagnetism and Photonics, Grenoble, France.

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Philippe Ferrari was born in Ugine, France, in 1966. He received the B.Sc. degree in electrical engineering and Ph.D. degree from the Institut National Polytechnique de Grenoble (INPG), Grenoble, France, in 1988 and 1992, respectively. In 1992, he joined the Laboratory of Microwaves and Characterization, Université de Savoie, Le Bourget-du-Lac, France, as an Assistant Professor of electrical engineering. From 1998 to 2004, he was the Head of the laboratory project on nonlinear transmission lines and tunable devices. Since September, 2004, he has been an Associate Professor with the University Joseph Fourier, Grenoble, France, and he continues his research with the Institute of Microelectronics Electromagnetism and Photonic (IMEP), INPG. His main research interest is the conception and realization of tunable devices such as filters, phase shifters, and power dividers, and also new circuits based on periodic structures such as filters and phase shifters. He is also involved in the development of time-domain techniques for the measurement of passive microwave devices and the moisture content of soil.