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Tunable band-pass filter using RF MEMS capacitance and transmission line.


Radio frequency micro electromechanical systems (RF MEMS) technology offers an attractive capability for RF systems, particularly in support of switching, variable capacitance and inductance and tuning functions [1-4]. One such component is the micro electromechanical voltage tunable capacitor, which can enable a wide tuning range and high quality (Q) factors. Compared with solid state varactors, MEMS tunable capacitance and inductance have the advantage of lower loss, low voltage operation and potentially larger tuning range [1]. The interconnection loss and noise can also be less than off-chip solid state RF components. The actuation mechanism for MEMS capacitor is mostly electrostatic, consuming very little power during actuation. A parallel plate tunable capacitor can be fabricated using surface micromachining techniques. In standard filter design at low frequency, the MEMS varactor is used as a lumped element with off-chip inductors. At high frequency, some designs were reported with integrated transmission lines and MEMS capacitors [5,6]. The transmission lines used for these designs are half wavelength or 180[degrees], so the filter will be very long at low frequencies. The tuning range is also not very high for these filters, 3.8% and around 14%, respectively. Also, low-pass and band-pass filters integrating capacitive MEMS switches and short inductive transmission lines have been realized for frequencies above 10 GHz [7-9]. In [7], the change in cut-off frequency was obtained by switching different combinations of inductances and capacitances. In [8,9], the cut-off and center frequencies were tuned by changing the inductance using MEMS switching. However, none of them had the capability of tuning bandwidth.

In this paper, we have presented a design of a band-pass filter with combination of low pass filter and high pass filter. The low pass filter was designed using the stepped impedance transmission line. A preliminary design of the low pass filter was presented in [10]. The low-pass filter was integrated with series coupling capacitors to obtain a 3rd order band-pass filter as presented in [11], is shown in Figure 1. A MEMS shunt capacitor was used to replace the low-impedance transmission line in a stepped impedance filter. The series inductor has been implemented using a short section of high impedance transmission line. The series capacitors work as a high-pass filter and are implemented using inline cantilever capacitive MEMS switches in series configuration. The tuning of both the center frequency and the bandwidth is possible by means of tunable capacitances. The presented band-pass filter is much more compact than filters based on half wave resonators. The center frequency of the band-pass filter can be tuned by shunt capacitors. The bandwidth of the filter can be tuned by changing the series capacitor. The filter has large tuning range, about 30% of its center frequency. Although step impedance filters don't have very sharp roll-off, they can still be useful for certain applications where compact size and wide tuning range are more important than the roll-off. The band-pass filter can be used in harmonic suppression in frequency synthesizer and transceiver system. The high tuning range and bandwidth tuning capability will be very useful in the systems operating in multiple frequencies and varying bandwidth.


Theory of capacitive switch, design of the band-pass filter consisting of a third-order 3dB ripple Chebyshev low-pass filter and series capacitances are described in Section 2. The filter was designed and optimized using the ADS[R] software from Agilent. A simulation of the filter performance is also presented in Section 2. A prototype of the filter is fabricated using our own facility at SINTEF MiNaLab, Oslo, Norway. Three ordinary parallel plate bridges were used as tunable shunt capacitances by actuating different combinations of the bridges. Series cantilevers of two different dimensions are used as series capacitors. The fabrication of the filter is presented in Section 3. The measurement results and re-simulation taking into account the effects of process constraints, are discussed in Section 4. Finally the paper is concluded.


2.1. Theory of Parallel Plate Capacitance

A traditional parallel plate capacitor is shown in Figure 2. According to the theory presented in [11,12], the value of the capacitance between the suspended bridge and center electrode for a deflection x from the initial position of the bridge can be determined by,

C(x) = [[epsilon].sub.0] x [A.sub.e] / ([g.sub.0] - x) + [t.sub.d] / [[epsilon].sub.r] (1)

Here [A.sub.e] ([L.sub.e] x [W.sub.e]) is the overlap area between the suspended beam and the bottom electrode, [t.sub.d] is the thickness and [[epsilon].sub.r] is relative permittivity of the dielectric. [L.sub.e] and [W.sub.e] are length and width of the electrode respectively. [g.sub.0] is the initial gap between the suspended beam and bottom electrode. The deflection x is caused by the attractive electrostatic force [F.sub.e] generated by the applied actuation voltage [V.sub.DC] [12], i.e.,

[F.sub.e] = 1 / 2 [C.sub.a](x)[V.sup.2.sub.DC) / ([g.sub.a0] - x + [t.sub.d] / [[epsilon].sub.r] (2)

Here [C.sub.a](x) is the total capacitance between the bridge and the actuation electrodes. For traditional parallel plate capacitance, the suspended beam can move up to one third of it's initial position before it collapses to downstate. When x = [g.sub.0], the beam touches the centre electrode and the downstate capacitance becomes,

[C.sub.d] = [[epsilon].sub.0][[epsilon].sub.r] [A.sub.e] / [t.sub.d] (3)

Equation (3) is applicable for an ideal scenario, where both suspended beam and bottom dielectric surface are smooth. In practice, there may be some roughness present on the dielectric surface and also on the beam. The capacitance in this case is given by [12],

[C.sub.dr] = [[epsilon].sub.0][A.sub.e] / 2 (1 / [t.sub.r] + [t.sub.d] / [[epsilon].sub.r] + [[epsilon].sub.r] / [t.sub.d]) (4)


Here [t.sub.r] is amplitude of the total roughness.

2.2. Theory of the Stepped-impedance Filter

It is well known [13, 14], that if the length of the transmission line is short ([beta]l < [pi]/4) and the characteristic impedance is high the transmission line can be represented by the equivalent circuit, as shown in Figure 3, where the reactance is given by,

[X.sub.l] = [Z.sub.0][beta]l (5)

Here the characteristic impedance of the line is [Z.sub.0], the length is l and the propagation constant is [beta]. So a series inductor can be represented by a short length of high characteristic impedance transmission line.



2.3. A Band Pass Filter with Third-order Low-pass Filter Topology and Optimization in ADS

A band pass filter topology, with 3rd order low pass filter and series capacitor is shown in Figure 4. The basic filter elements are extracted from the Chebyshev equal ripple low pass filter prototype [11,13].

The normalized filter elements for a 3dB ripple Chebyshev are given by [g.sub.1] = 3.3487, [g.sub.2] = 0.7117, [g.sub.3] = 3.3487, and [g.sub.4] = 1.00 is the load impedance [13]. A 3dB ripple design is used to obtain a sharp roll-off above the cut-off frequency. A nominal center frequency of 5.8 GHz was chosen for this the filter, considering the use at C band. The proposed filter was fabricated on a 280 [micro]m think high resistivity silicon substrate. The relative dielectric constant of the substrate was 11.9 and the resistivity was 8000 [OMEGA]-cm. For an 80[OMEGA] CPW transmission line, the dimensions were 160 [micro]m/53 [micro]m/160 [micro]m (G/W/G). After tuning the filter performance in ADS [15], the nominal shunt and series capacitor and 80[OMEGA] transmission length were optimized to 1.1 pF, 370 fF and 1467 [micro]m (30.7[degrees]). Due to finite impedance, the high impedance transmission line would introduce certain amount of shunt capacitance, and reduce the required amount shunt capacitance. A higher value of impedance, such as 100[OMEGA] or more, could be chosen for the series inductance. This would make the transmission line very narrow, which may introduce high loss in the pass band. To compensate the loss, a very thick metal layer would require for transmission line.

2.4. Simulation of the Filter Performance, Tuning Centre Frequency and Bandwidth

A schematic view of the band pass filter with transmission line and MEMS capacitance are shown in Figure 5. The following parameters were used for simulation in ADS. The 80 [OMEGA] transmission line length was 1467 [micro]m. The series capacitances in each side were 370 fF. The shunt capacitance is varied from 0.60 pF to 1.40 pF. The simulation results are shown in Figure 6. It can be seen that the center frequency is tuned from 6.80 GHz to 5.00 GHz when the shunt capacitance varies from 0.60 pF to 1.40 pF. The center frequency shifts to 4.80 GHz when the shunt capacitance value becomes 1.80 pF. For bandwidth tuning, the shunt capacitance was fixed at 0.8 pF and the series capacitance is varied from 370 fF to 700 fF. The simulation results are shown in Figure 7. It can be seen that the bandwidth (-3dB) is changed from 1.6 GHz to 3 GHz when the series capacitance vary from 370 fF to 700 fF.





The prototype of the filter was fabricated using traditional parallel plate capacitors. We have used three parallel bridges for each shunt capacitance. The variation of the capacitance can be obtained by actuating individual bridge, or combination of bridges. Each shunt capacitance is a combination of two 12 wide (on the two sides) and one 15 [micro]m wide (middle) shunt bridge. The width of the centre conductor for the 50 [OMEGA] transmission lines is 140 [micro]m with a gap of 80 [micro]m each side in CPW configuration. The thickness of the centre electrode dielectric ([Si.sub.3][N.sub.4]) is 220 nm. For each series capacitance, two equal cantilevers are used in parallel. Sputtered gold was used as a suspended beam. A negative stress gradient was present in the sputtered gold. Therefore, cantilevers of different beam widths were used for the capacitance variation in the fabricated prototype. For the cantilevers the electrode length is 25 [micro]m. Due to lack of actuation facility, we have used two sets of cantilever, each set contain two cantilever in parallel, with width of 22 [micro]m, 30 [micro]m for each prototype.

A four-mask process was used to fabricate the proposed filter. The cross-sectional view of the process flow of the capacitive bridges is shown in Figure 8. A 280 [micro]m thick silicon wafer with 4-8k[OMEGA]-cm resistivity (specified by supplier) was used for the fabrication. A 500 nm thick oxide was grown on the silicon wafer to reduce loss (A). Then 500 nm thick aluminium layer was deposited by sputtering and patterned by wet etching (B). A 220 nm thick [Si.sub.3][N.sub.4] was deposited as dielectric by plasma-enhanced chemical vapour deposition (PECVD) and patterned by dry etch (C). HiPR 6517 photoresist was used as a sacrificial layer. The resist thickness was 2.55 [micro]m and patterned by standard lithography and special baking methods (D) as described in detail in [16]. Then 1.1 [micro]m thick gold was sputtered and patterned by wet etch (E). The gold was sputtered with very low power and a pressure of 20 m Torr to give a low tensile stress, as described in [17]. A 50 nm thick NiCr layer was used as an adhesive layer between gold and aluminium. When the gold was sputtered, the transmission line was also sputtered with 1.1 [micro]m additional gold on aluminum. Low tensile stress ensures a low actuation voltage and gives better reliability. Finally the switches and filters were released and dried in a critical point dryer [17].


A SEM image of the fabricated band-pass filter is shown in Figure 9. An enlarged image at the capacitance region is also shown in Figure 10. The actuation electrodes are separated from the RF signal electrode, and each bridge and cantilever have their own set of actuation electrodes. In Figure 9 the centre narrow line is the 80 Ohm transmission line, which is equivalent to a series inductor. The capacitors are at both ends of the 80 Ohm transmission line shunting a 50 Ohm transmission line. The cantilevers at the end of the bridge form the series capacitances. In the Figure 10, the three parallel bridges of shunt capacitors and the two parallel cantilevers for series capacitor can be seen. The extended 50 Ohm transmission lines are used for measurement purpose with a CPW probe.



The fabricated filters were measured at Norwegian University of Science and Technology (NTNU), high frequency measurement lab, using a vector network analyser from Agilent. The filter characteristic was measured up to 30 GHz. Standard Line-Reflect-Reflect-Match (LRRM) methods were used for calibration of the network analyser. The actuation voltage was around 15 volt for shunt bridge and 8 volt for cantilevers. The measured filter S parameters are shown in Figure 11. We have measured the filter characteristics with one bridge down (15 [micro]m wide centre bridge) red line, and 2 bridges down (15 [micro]m and 12 [micro]m wide bridges) blue line, both with two 22 [micro]m wide cantilevers down. We have also measured the band-pass filter performance with 1 bridge (15 [micro]m wide) down and two 30 [micro]m wide cantilevers down (black line). From Figure 11, it can be seen that both center frequency and bandwidth change with shunt and series capacitance. There is an upward shift in the center frequency from the simulation results. This happened as a result of a decrease in the capacitances owing to electrode roughness, over etching, non planarity of the bridge and other non ideal effect during fabrication. These effects were considered, re-simulated the filter performance in ADS and presented below.


After fabrication the filters were inspected in an optical interferometer to measure the actual width and height of the bridge. The actual initial heights of the bridges were 2.25 [micro]m and the width was reduced on average 1 [micro]m from each side owing to over-etching. The roughness was measured in an atomic force microscopy (AFM). Gold is usually smooth and it was found that the average roughness of the gold was 7 nm. The [Si.sub.3][N.sub.4] average roughness was 9 nm on aluminum. But the main contribution to the roughness was from aluminum. This is because of the high temp (300[degrees]C) [Si.sub.3][N.sub.4] deposition. From AFM measurement, it was found that the height of the aluminum bumps was about 80 nm. As the nitride was deposited on aluminum, the total amplitude of roughness for the downstate capacitance was 96 nm. The dielectric constant of the [Si.sub.3][N.sub.4] is 7.5. Considering the overetch and roughness, according to Equation (4), the downstate capacitance became 0.38 pF for the 15 [micro]m bridge ([W.sub.e], 13 [micro]m real width) and 0.30 pF for the 12 [micro]m bridge ([W.sub.e], 10 [micro]m real width). In all cases, the length of the electrode, [L.sub.e] was 140 [micro]m. Using the same roughness, the downstate capacitance for a 22 [micro]m wide cantilever beam became 0.19 pF and for 30 [micro]m wide cantilever beam became 0.285 pF. The filter was re-simulated with the above parameters.


The tuning of center frequency and comparison between simulation and measurement results of the fabricated filter as shown in Figure 12. For one bridge down and the 22 [micro]m wide cantilevers down, the shunt capacitance becomes 0.38 pF and total series capacitance becomes 0.38 pF (2 cantilevers in parallel). For two bridges down and the 22 [micro]m cantilevers down, the shunt capacitance becomes 0.68 pF and the series capacitance becomes 0.38 pF. For clarity, the [S.sub.11] is not included in the comparison and also the frequency range is reduced. It can be seen that the measured results agree well with the re-simulated results, including the effect of over-etching and roughness. There is a slightly higher center frequency in the measured filter. This can happen because of reduced capacitance owing to non-planarity of the bridge and the cantilever at downstate, which will further reduce the downstate capacitance.

The tuning of the bandwidth and comparison between re-simulation and measurement results of the fabricated filter are shown in Figure 13. For one bridge down and the 22 [micro]m cantilevers down, the shunt capacitance becomes 0.38 pF and the series capacitance becomes 0.38pF (two equal cantilevers in parallel). For one bridge down and the 30 [micro]m cantilevers down, the shunt capacitance becomes 0.38 pF and the series capacitance becomes 0.57 pF (two equal cantilevers in parallel). From Figure 13, it can be seen that the measured results agree well with the re-simulated results, given the effect of over-etching and roughness. Again the measured filter has a slightly higher center frequency for the reason discussed above.



At high frequency an increase in insertion loss and return loss occurs in the filter performance. The smaller value of series capacitance may increase the return loss at higher center frequency. Capacitive tuning with an inductive inverter can be used to reduce the return loss for the entire tuning range [18,19]. Simultaneous tuning of both capacitance and inductance with stub can also be used to reduce return loss and insertion loss for the entire operating range of the filter [20]. The filter roll-off is not very sharp, however can be improved by the use of a high-impedance transmission line and a higher order of the filter. As only the capacitance is used for tuning and the inductance is fixed, this will reduce the tuning range of the filter significantly.


We have presented a tunable band-pass filter design with transmission line and MEMS capacitances. Parallel plate capacitances were used as series and shunt capacitance and fabricated using surface micromachining technique. The tuning of the center frequency has been obtained by actuation of various parallel shunt bridges. The tuning of the band-width has been obtained by actuating different combinations of series cantilevers. The operating frequency shifted upward to some extent from the designed parameters due to reduced capacitance. The capacitance was decreased owing to roughness, over etching and non planarity of the suspended bridge. The measured results agree well with the simulated result considering the fabrication effects. The filter has the flexibility of tuning both center frequency and bandwidth simultaneously. The filter is very compact and has very good control of the tuning frequency.


Authors are grateful to Norwegian Research Council for sponsoring the work through SMiDA project (No. 159559/130) and IRRFT project (No. 159259/I40). Authors also like to thank MiNa Lab personnel for their support in the clean room and Mr. Tjrie Martinsen from IET/NTNU for his help during S parameter measurement.

Received 6 July 2011, Accepted 25 August 2011, Scheduled 31 August 2011


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S. C. Saha (1,4), *, U. Hanke (2), H. Sagberg (3), T. A. Fjeldly (1), and T. Saether (1)

(1) Department of Electronics and Telecommunications (IET), Norwegian University of Science and Technology (NTNU), Trondheim NO-7491, Norway

(2) Institute for Microsystems Technology, Vestfold University College, Tonsberg 3103, Norway

(3) Department of Microsystems and Nanotechnology, SINTEF ICT, P. O. Box 124, Blindern, Oslo NO-0314, Norway

(4) Electronics and Nanoscale Engineering, University of Glasgow, G12 8LT, UK

* Corresponding author: Shimul Chandra Saha (
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Author:Saha, S.C.; Hanke, U.; Sagberg, H.; Fjeldly, T.A.; Saether, T.
Publication:Progress In Electromagnetics Research C
Article Type:Report
Geographic Code:4EXNO
Date:Jun 1, 2011
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