Abstract:
In one embodiment, a dynamically reconfigurable bandpass filter includes a resonator loop and a microfluidic channel proximate to the resonator loop, the channel containing a conductor, wherein the position of the conductor within the channel can be adjusted to change capacitive loading of the resonator loop and therefore change the frequencies that the filter passes. In another embodiment, a filter includes a second resonator loop having comprising switches located at discrete positions along a length of the second resonator loop, wherein opening and closing of the switches changes the effective length of the second resonator loop to change capacitive loading of the first resonator loop.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application claims priority to U.S. Provisional Application Ser. No. 61/776,229, filed Mar. 11, 2013, which is hereby incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     Radio frequency (RF) filters that can be reconfigured to operate within a broad frequency range are highly desired to address the size requirements of emerging compact and multifunctional RF front-ends. The reconfigurable filter technologies that are currently being investigated mainly rely on material loadings, semiconductor varactor diodes, ferroelectric varactors, RF microelectromehanical system (MEMS) switches, and RF MEMS varactors. The performance of these filters is limited by the frequency tunability and/or power handling of their varactors. For example, the frequency tuning range of varactor diode based filters is typically below 30%. RF MEMS technology enables the fabrication of miniaturized filters, but the frequency tuning range is small unless the tuning is performed in a discrete manner. Evanescent mode cavity resonator filters controlled with MEMS-based actuators have been shown to offer a high frequency tuning range, but these filters generally exhibit large electrical sizes due to their volumetric construction. 
     In view of the limitations of current reconfigurable bandpass filters, it can be appreciated that it would be desirable to have alternative reconfigurable bandpass filters that do not suffer from such limitations. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure may be better understood with reference to the following figures. Matching reference numerals designate corresponding parts throughout the figures, which are not necessarily drawn to scale. 
         FIG. 1A  is a schematic diagram of a first embodiment of a dynamically reconfigurable bandpass filter. 
         FIG. 1B  is a cross-sectional view of the filter of  FIG. 1A  taken along line B-B. 
         FIG. 1C  is a plan view of a bottom resonator loop of the filter of  FIG. 1A . 
         FIG. 1D  is a plan view of a top resonator loop of the filter of  FIG. 1A . 
         FIG. 1E  is a graph that plots Q e  as a function of frequency for the filter of  FIG. 1A . 
         FIG. 2A  is a schematic diagram of a second embodiment of a dynamically reconfigurable bandpass filter. 
         FIG. 2B  is a graph that plots k as a function of frequency for the filter of  FIG. 2A . 
         FIGS. 3A and 3B  are images of components of an experimental dynamically reconfigurable bandpass filter. 
         FIG. 3C  is a graph that plots simulated S-parameters for the filter of  FIGS. 3A and 3B . 
         FIG. 3D  is a graph that plots measured S-parameters for the filter of  FIGS. 3A and 3B . 
         FIG. 4A  is a cross-sectional view of a further experimental dynamically reconfigurable bandpass filter. 
         FIG. 4B  is a graph that plots the measured performance of the filter of  FIG. 5A . 
         FIG. 5A  is a schematic diagram of a third embodiment of a dynamically reconfigurable bandpass filter. 
         FIG. 5B  is a cross-sectional view of the filter of  FIG. 5A  taken along line B-B. 
         FIG. 5C  is a plan view of a bottom resonator loop of the filter of  FIG. 5A . 
         FIG. 6  is a graph that plots the variation of coupling coefficient (K) and external quality factor (Qe) as a function of frequency for Lm=2.5 nH. 
         FIGS. 7A and 7B  are images of components of a further experimental dynamically reconfigurable bandpass filter. 
         FIG. 7C  is a graph that plots simulated insertion and return loss performances for the filter of  FIG. 7A . 
         FIG. 7D  is a graph that plots measured insertion and return loss performances for the filter of  FIG. 7A . 
         FIG. 8A  is a schematic diagram of a fourth embodiment of a dynamically reconfigurable bandpass filter. 
         FIG. 8B  is a cross-sectional view of the filter of  FIG. 8A  taken along line B-B. 
     
    
    
     DETAILED DESCRIPTION 
     Although various reconfigurable bandpass filters have been developed, their performance is often limited in terms of size, frequency tuning range, and power handling. Disclosed herein are dynamically reconfigurable bandpass filters that provide significantly enhanced frequency tuning ranges and power handling capabilities from a compact device size. The filters comprise single or multiple resonator loops whose effective lengths can be dynamically adjusted to tune the frequencies that pass. In some embodiments, the effective length of the resonator loop is adjusted by moving a conductor, such as a volume of conductive liquid or a conductive plate, through a microfluidic channel so as to change the degree to which the conductor capacitively couples to a further resonator loop of the filter. In other embodiments, the effective length of the resonator loop is adjusted using micromechanical (MEMS) switches. 
     In the following disclosure, various specific embodiments are described. It is to be understood that those embodiments are example implementations of the disclosed inventions and that alternative embodiments are possible. All such embodiments are intended to fall within the scope of this disclosure. 
     As described above, reconfigurable bandpass filters are disclosed that comprise resonator loops whose effective lengths can be adjusted to tune the frequencies that the filter passes. Described first is a filter having resonator loops whose, effective length can be adjusted using a conductive liquid, such as a liquid metal. More particularly, described is broadside-coupled split-ring resonators (BC-SRRs) having a microfluidic channel that defines the length and shape of one of the resonator&#39;s loops. Frequency tuning can be accomplished by adjusting the amount of conductive liquid that is present within the channel. With this configuration, the tuning range is limited by the physical separation of the loops of the BC-SRR. Because this distance can be made very small, wideband tunability can be accomplished. The filter is promising for high-power radio frequency (RF) applications because of the highly linear nature of its tuning mechanism. Moreover, the filter is suitable for small applications because the filter can be fabricated to have a miniature footprint. 
       FIG. 1A  illustrates an embodiment of a dynamically reconfigurable bandpass filter  10  that is configured as a BC-SRR. As shown in that figure, the filter  10  comprises a resonator  12  that includes a bottom resonator loop  14  and a top resonator loop  16 , each of which being an open loop resonator. The top loop  16  is positioned above the bottom loop but spaced therefrom by a layer of dielectric material (see  FIG. 1B ). For clarity, each loop  14 ,  16 , is separately illustrated in  FIGS. 1C and 1D , respectively. In the illustrated embodiment, the loops  14 ,  16  are generally rectangular. Regardless of their shapes, however, the loops  14 ,  16  have similar dimensions and configurations. Each loop  14 ,  16  includes a gap  18 ,  20  along one of its sides such that the loops are open. As is apparent from  FIGS. 1A, 1C, and 1D , the gaps  18 ,  20  are positioned on opposite sides of the resonator  12  (i.e., displaced 180° from each other) so that they do not overlap. The bottom loop  14  comprises a solid element (e.g., trace) that is made of an electrically-conductive material, such as copper. The top loop  16 , however, comprises a microfluidic channel through which conductive liquid can be driven. The size of the loops  14 ,  16  can be varied to fit the application. As an example, however, each side (arm) of the loops  14 ,  16  can have a length, l, that is approximately 19 mm and a width, w, that is approximately 1.2 mm ( FIGS. 1C and 1D ), and the gaps  18 ,  20  can be approximately 2.6 mm wide. 
       FIG. 1B  shows a cross-section of the filter  10  taken along line B-B in  FIG. 1A . As indicated in  FIG. 1B , the filter  10  can comprise a stack of materials that includes a ground plane  22 , a substrate  24 , and a polymer layer  26 . As is further indicated in the drawing, the bottom loop  14  is formed in the substrate  24  and the top loop  16  is formed on the polymer layer  26 . By way of example, the polymer layer  26  can be approximately 13 mil thick, in which case the distance between the loops  14 ,  16  is approximately 13 mil. 
     As shown in  FIG. 1C , the filter  10  also comprises an RF input port  28 . In the illustrated embodiment, the input port  28  is coupled to a feed line  30  of the bottom loop  14  with a coupling inductor  32 . 
     With reference back to  FIG. 1A , provided within the microfluidic channel of the top loop  16  is a continuous volume of conductive liquid  34 . The conductive liquid  34  can be a liquid metal, such as mercury or a eutectic alloy comprising gallium, indium, and tin (e.g., Galinstan™). Also provided within the channel at each end of the volume of conductive liquid  34  is a dielectric fluid  36 , such as a polytetrafluoroethylene (PTFE) solution (∈ r =2.2), which is used to adjust the location of the volume of conductive liquid within the channel. When the dielectric fluid  36  is driven along the channel, for example by a micropump (not shown), the top loop  16  can be completely filled with, partially filled with, or completely emptied of the conductive liquid  34 . Accordingly, the effective length of the top loop  16  can be adjusted to change the capacitive loading between the top loop and the bottom loop  14  and, therefore, change the frequencies that can be passed by the filter  10 . With the dimensions described above, the resonator  12  resonates at approximately 850 MHz when there is no conductive liquid  34  in the top loop  16  (i.e., when the effective length of the loop is zero). When the top loop  16  is completely filled with conductive liquid  34  and it has its maximum effective length, however, the resonator  12  resonates at its lowest frequency of approximately 630 MHz. Frequencies between these two extremes can be tuned by partially filling the top loop  16  with the conductive liquid  34 . 
     The required external quality factor Q e  and coupling coefficient k of a second-order Butterworth coupled resonator filter can be calculated from its low-pass lumped circuit prototype (g0=g3=1, g1=g2=1.4142) as Q e =g0·g1/FBW=28 and k=FBW/sqrt(g1·g2)=0.0354 for a fractional bandwidth (FBW) of 5%. Such a filter can exhibit a well-matched, constant FBW performance if Q e  and k are relatively constant over the tuning range of the resonator. As depicted in  FIG. 1E , the Q e  of the conductive liquid-based BC-SRR shown in  FIG. 1A  significantly decreases as it is tuned to higher frequencies. This behavior is independent of the tapping location t. The coupling inductor (LM)  32  shown in  FIG. 1A  stabilizes the variation in Q e  over the tuning range. The reactance of the inductor  32  is proportional to the frequency and counteracts the reduction in Q e  at higher frequencies. 
     Parametric studies were conducted using Agilent&#39;s Advanced Design System (ADS) and a tapping location of t=0 mm with LM=5.5 nH was determined to provide a relatively constant Q e  over the operational band. These studies were performed by simultaneously considering five different conductive liquid locations (d=d1=0, d2=7, d3=16.5, d4=26, d5=35.5 mm), which are identified as data points in the design curves presented in the graphs of  FIGS. 1B, 2B, 3B, and 3C . It is possible to tap the conductive liquid resonator with different layout arrangements (such as using multiple circuit elements and alternative tapping locations) to provide other types of desired performance variations (such as constant absolute bandwidth) as the operation frequency is tuned. 
     To achieve a constant FBW response over the frequency range, a relatively constant coupling coefficient k is needed. This can be achieved with the 180°-rotated configuration shown in  FIG. 2A . In  FIG. 2A , a dynamically reconfigurable bandpass filter  40  comprises two resonators  12  that are positioned such that they are 180° out of phase from each other. Each resonator  12  has a configuration similar to that described above in relation to  FIGS. 1A-1D  and, therefore, comprises a bottom resonator loop  14  (conductor trace) and a top resonator loop  16  (microfluidic channel). As is apparent from  FIG. 2A , the top loops  16  of both resonators  12  are formed by the same continuous microfluidic channel  42 , which contains two independent volumes of conductive liquid  44  that are separated by a dielectric fluid  46 . With such a configuration, the amount of conductive liquid  44  in each top loop  16  can be simultaneously controlled. The channel  42  forms a closed-loop system that, in some embodiments, can be dynamically reconfigured using series-connected micropumps controlled with a microprocessor (not shown). By way of example, the resonators  12  can be separated by approximately 1.8 mm to ensure that the minimum filter bandwidth is at least 5% over the tuning range. In such a case, k is 0.035 at the edges and 0.04 at the middle of the operation band. 
     While the resonators  12  in  FIGS. 1A and 2A  are shown having square loops, it is noted that non-rectangular resonator shapes can be employed with lumped coupling capacitors to realize different tunable bandwidth characteristics, such as increasing, decreasing, or constant absolute bandwidth. Such shape modifications may also provide better Q e  and k stability over frequency. It is further noted that while BC-SRR resonators have been explicitly illustrated and discussed, other resonators can be similarly adjusted using conductive liquid. For example, the effective length of a single open loop resonator can be altered using conductive liquid. 
       FIGS. 3A and 3B  show components of an experimental dynamically reconfigurable bandpass filter that was constructed using polytetrafluoroethylene (PTFE) tubing to form the top loops of the BC-SRR. The PTFE tubing had a 16 mil (0.4064 mm) inner radius and a 6 mil (0.1524 mm) wall thickness. The bottom loops of the resonator were formed by 50Ω microstrip lines having a 1.2 mm width. The PTFE tubing was accurately aligned and positioned over the bottom loops by milling cut-outs through low-loss 1.575 mm thick Rogers 5880 substrate (∈ r =2.2, tan δ=0.0009). The tubes were stabilized in their locations using Scotch™ tape. Mercury and Galinstan™ are two types of liquid metals that can be employed for the filter. Although Galinstan™ can be sticky because of oxidation, it can still be moved through the PTFE tubing with the aid of Teflon™ solution (AF 400S2-100-1, 1% Teflon™ powdered resin dissolved in 3M FC-40, acquired from DuPont). Because of its non-toxicity, Galinstan™ (δ=3.46×10 6 ) was selected for the experimental verifications. 
     The liquid metal and Teflon™ solutions were controlled with two syringes, as depicted in  FIG. 3A . The ADS simulations of the overall filter for various d values using LM=5.5 nH coupling inductors resulted in a return loss that was not well matched (&lt;8 dB). To alleviate this issue, a parametric sweep was carried out over the complete filter models. For t=0 mm, increasing the coupling inductors to LM=12 nH was found to provide a return loss performance greater than 10 dB over the whole frequency range, as shown in  FIG. 3C . The inductors were acquired from the Coilcraft 0805CS series and were modeled to exhibit a Q of 50 at 850 MHz. The simulated insertion loss was about 2 dB throughout the operation band. The inductor-, dielectric-, and conductor-based insertion losses were 0.26 dB, 0.29 dB, and 1.49 dB, respectively, at the lowest frequency of operation. As compared to a copper-based implementation, the additional insertion loss because of Galinstan™ was simulated to be 0.59 dB. 
       FIG. 3D  shows the measured performance of the filter. LM=10 nH was experimentally determined to provide the best greater than 10 dB return loss performance. The measured filter responses were about 20 MHz higher than the simulated data. The measured insertion loss was 3 dB at the lowest frequency and 1 dB higher than the simulated performance. The resonance frequency deviation can be associated with the dielectric constant tolerances, overlaid substrate used for guiding the tubing, and undesired air gaps that may have existed between the tubing and the printed loops. The insertion loss deviation was likely because of the unaccounted loss of the PTFE tubing, overlaid substrate, and Scotch™ tape. The filter exhibited a measured tunability from 650 to 870 MHz with near constant 5% −3 dB FBW. The footprint of the resonators was about 20×40 mm 2 . 
     As noted above, the tuning range of a BC-SRR filter such that described in relation to  FIG. 2A  is limited by the physical separation between the loops of the BC-SRR. The tunability range of such filters can be significantly extended using microfabrication techniques that bring the liquid metal physically closer to the bottom loop of the BC-SRR. Testing was performed utilizing a 2 mil (i.e., 50.8 μm) thick liquid crystal polymer (LCP) layer as the insulator between the liquid metal loop and the printed loop of a BC-SRR. The configuration of the dynamically reconfigurable bandpass filter is shown in  FIG. 4A . As indicated in this figure, the filter  50  comprised a ground plane  52 , a bottom substrate  54 , the liquid crystal polymer layer  56 , and a host substrate  58  made of polydimethylsiloxane (PDMS). The bottom loop  14  was formed in the bottom substrate  54  and the top loop  16  was formed in the host substrate  58 . As shown in  FIG. 4B , a tunability range of 2:1 was experimentally verified from 400 MHz to 800 MHz with Q factors greater than 50. The Q factor can be further improved by utilizing an ultra-thin low-loss insulator such as benzocyclobutene (BCB). Further Q improvements can be accomplished by preparing the channel mold within a lower loss substrate, such as quartz instead of PDMS. Specifically, the numerical simulations predict greater than 4:1 frequency tunability with Q factors greater than 100 over the majority of this wide tuning range when a quartz and 1 mil (i.e., 25.4 μm) thick BCB-based implementation is pursued over alumina substrate. The resonators can be enclosed within a cavity to achieve more improvements in their Q factor. 
     Although slower than semiconductor- and MEMS-based implementations, the tuning speeds of conductive liquid filters such as those described above can be less than milliseconds by using ultra-thin microfluidic channels. Piezoelectric-based micropumps can be utilized for convenient control of the tuning mechanism. The design can also be generalized to higher order tunable filters that are controlled only with a single micropump. 
       FIGS. 5A-5C  illustrate a dynamically reconfigurable bandpass filter  60  that is similar in many ways to the BC-SRR-based filter  40  shown in  FIG. 2A  described above. Accordingly, the filter  60  comprises two resonators  62 , each including a bottom resonator loop  64 . One of these loops  64  is shown in  FIG. 5C . As indicated there, the loop  64  comprises a continuous trace (e.g., of copper) that defines a rectangle having a gap  64  along one side. With reference back to  FIG. 5A , the two loops  64  are inverted relative to each other in the filter  60  so that the gaps  66  are provided on opposite sides of the filter. By way of example, each side (arm) of the loops  64  can have a length, l, that is approximately 10 mm and a width, w, that is approximately 2 mm ( FIG. 5C ). The loops  64  can be spaced from each other a distance, c, of approximately 0.4 mm ( FIG. 5A ). The gaps  66  can be approximately 2 mm wide ( FIG. 5C ). As shown in  FIGS. 5A and 5C , each loop  64  further comprises an extension  68  that serves as an RF input port or an RF output port, depending upon the loop  64 . Each of these extensions  68  comprises a coupling inductor  70 . 
     Rather than comprising a compete top resonator loop, the resonators  62  each comprise a top conductor  72 , which each can be considered to form a partial resonator loop. The conductors  72  can be moved relative to the bottom loops  64  to capacitively load them and change the frequencies that can be passed by the filter  60 . In some embodiments, the conductors  72  comprise volumes of conductive liquid that can be driven through a continuous microfluidic channel  74  that passes over portions of the bottom loops  64 . In other embodiments, the conductors  72  comprise conductive plates that can be driven through the microfluidic channel  74 . Irrespective of the nature of the conductors  72 , the degree to which the conductors capacitively load their bottom loops  64  depends upon the extent to which the conductors overlap the loops and, more particularly, the extent to which the conductors overlap the gaps  66  of the loops. Although the conductors  72  do not overlap the bottom loops  62  to the same degree to which the upper loops  16  can overlap the bottom loops  14  of the filter  40  in  FIG. 2A , nearly the same level of capacitive loading can be achieved. 
     When the top conductors  72  comprise conductive plates, they can be metal plates. Alternatively, the conductive plates can comprise non-metal plates upon which metal has been deposited. For example, the conductive plates can be metallized glass plates. Regardless, the conductive plates can be driven through the microfluidic channel  74  using a suitable dielectric fluid  76 , such as PTFE solution. In such a case, the microfluidic channel  74  can comprise an inlet  78  and an outlet  80  through which the fluid can flow under the driving force of a micropump (not shown). 
       FIG. 5B  shows a cross-section of the filter  60  taken along line B-B in  FIG. 5A . As indicated in  FIG. 5B , the filter  60  can comprise a stack of materials that includes a ground plane  82 , a substrate  84 , an LCP layer  86 , and a polymer layer  88 . The bottom loop  64  is formed in the substrate  84  and the microfluidic channel  74  is formed in the polymer layer  88 . By way of example, the LCP layer  86  is be approximately 25.4 μm thick. 
     Because the filter  60  uses an ultra-thin layer between the bottom loops  64  and the top conductors  72 , the frequency tuning range of the filter is increased. In embodiments in which the top conductors  72  are conductive plates, long-term reliability, insertion loss performance, and associated power handling capability are also increased. When the filter  60  has the dimensions described above, it can operate from approximately 0.9 to 1.5 GHz with a constant FBW. As such, the frequency tuning range is greatly improved as compared to the above-described embodiments. In addition, the filter exhibits an IL less than 1.7 dB across its tuning range, which is approximately 1.3 dB better than the filter described in relation to  FIGS. 4A and 4B . 
     The filter  60  is tuned by moving the conductors  72  over the gaps  66  of the bottom loops  62 , as indicated by the arrows illustrated  FIG. 5A . The conductors  72  create a capacitive loading effect across the gaps  66  and therefore cause a shift in the resonance frequency of the bottom loops  64 . Depending on the position of the conductors  72 , the amount of capacitive loading varies and gets maximized (i.e., C max ) when the conductor  72  is centered over the loop&#39;s side (arm). Most importantly, this capacitive loading can be completely removed (i.e., C min =0) by retracting the conductors  72  out of the gaps  66 . This enables an extended range of tuning capability as compared to varactors. By using a 25.4 μm thick LCP insulator between the bottom loops  64  and the conductors  72 , the tuning range was reduced to 0.9 GHz. 
     The conductors  72  need to be precisely moved over the bottom loops  64  to obtain a reconfigurable, constant-FBW response. Positioning the leading edge of the conductor  72  approximately 10 mm from the edge of the bottom loop  64  causes zero capacitive loading and the filter  60  operates at 1.5 GHz. On the other hand, when the leading edge of the conductor  72  is approximately 4 mm from the edge of the bottom loop  64 , the capacitive loading increases and the filter  60  operates at 0.9 GHz, providing 50% frequency tuning range. As expected, the insulator layer thickness significantly affects the tuning range of the filter. For example, increasing the insulator thickness from 25 μm to 50 μm decreases the frequency tuning range by more than half. 
     To design a two-pole Chebyshev bandpass filter with 5% FBW, the required external quality factor (Qe) and coupling coefficient (K) were calculated from its lowpass lumped circuit prototype (g0=1, g1=0.6648, g2=0.5445, g3=1.2210) to be 13.296 and 0.0831, respectively. To maintain a constant FBW, it is necessary to keep the Qe and K relatively constant over the frequency tuning range. The ADS studies were performed by simultaneously considering five different configurations in which the leading edge of a metallized plate was respectively spaced 4, 4.5, 4.7, 6, and 10 mm from the edge of the bottom loop. These are locations identified as data points in the plots of  FIGS. 6 and 7 . The tapping location that resulted in the required quality factor was found to be T=6.1 mm. The lumped inductors  70  were utilized to stabilize the variation of Qe over the frequency tuning range. The values of these inductors  70  were determined by utilizing an iterative approach involving ADS schematics and Momentum layouts. The value that provided the required coupling across the entire frequency range was found to be 2.5 nH. The ADS simulations of the overall filter for various P values using the 2.5 nH coupling inductors resulted in a return loss that is not well matched (&lt;8 dB). A parametric sweep was carried out over the complete filter model. Increasing the coupling inductors to 7 nH was found to provide a return loss performance great than 10 dB over the whole frequency range. However, this resulted in 8% constant FBW performance. Due to the proof-of-concept nature of the work, no further optimizations were pursued to lower the FBW back to 5%. The IL was less than 1.3 dB over the entire frequency tuning range. 
     The meandered microfluidic channel layout shown in  FIG. 5A  was can be employed to enable simultaneous turning of the resonators  62  and can a single micropump. As shown in  FIG. 5A , one of the bottom loops  64  was shifted downward relative to the other loop to prevent the conductors  72  from overlapping both loops at the same time. Detailed curves depicting the variation of the external quality factor and the coupling coefficient as a function of frequency are provided in  FIG. 6 . 
     A dynamically reconfigurable bandpass filter having a configuration similar to that shown in  FIG. 5A  was fabricated for testing purposes. During the fabrication, microfluidic channels were fabricated in PDMS utilizing a micromolding technique. Metallized glass plates were positioned inside the channels prior to the bonding the PDMS to an LCP layer. The PDMS mold was bonded to the LCP layer using an APTES (3-aminopropyltriethoxysilane) treatment. The PDMS and LCP bond was then aligned with a printed circuit board (PCB) using the alignment holes. Plastic screws and clamps were utilized to hold the PCB and channel layers together. Cubic pieces of PDMS were utilized as microfluidic connectors to interface PTFE tubes with the channels. To move the plates inside the channels, a two-syringe system was implemented to flow Teflon™ solution inside the channels. The final filter stack comprised a 1.27 mm thick PCB board, a 25.4 μm thick LCP layer, and a 2 mm thick PDMS substrate with 250 μm deep and 2.1 mm wide channels with 1.9 mm wide metallized glass plates. 
     The layers of the fabricated filter are shown in  FIGS. 7A and 7B . 6.8 nH Coilcraft inductors from the 0805CS series were utilized at the input and output of the filter. As shown in  FIGS. 7C and 7D , the measured insertion and return loss performances were in good agreement with the simulated results. A frequency tunability range of 50% (1.5 GHz to 0.9 GHz) was accomplished by moving the metallized glass plates a distance of 6 mm (i.e., P 1  to P 5 ) over the open loop resonators. The worst case insertion loss was found to be 1.7 dB at the lowest frequency, which differed from the simulation results by 0.4 dB. The difference in IL between the simulations and measurements was due to the lower Q of the inductors, which was modeled as 50 in ADS simulations. The FBW was measured to vary between 8% and 10% from 0.9 GHz to 1.5 GHz. Increasing the number of poles of the filter would help stabilize FBW variation as lower coupling and external quality factors will be required. The overall footprint of the filter was 24.4×12.4 mm 2 , which is 0.073×0.037λ 0   2  (λ 0 =free space wavelength) at the lowest frequency. 
     A functionality similar to that described above can be achieved by using switches positioned at discrete positions around a loop of a resonator.  FIGS. 8A and 8B  illustrate an example of such a resonator  90 . The resonator  90  is configured as a BC-SRR having a bottom resonator loop  92  and a top resonator loop  94 . Instead of comprising conductive liquid or a conductive plate that moves through a microfluidic channel, however, the top loop  94  is a conductive trace that includes multiple MEMS switches  96  that span gaps  98  positioned along the length of the trace. By individually controlling the switches  96 , the effective length of the top loop  94  can be adjusted. As an example, if all of the switches  96  are closed, the effective length of the loop  94  is the entire trace. If the first (leftmost) switch is opened, however, the effective length of the loop  94  will be halved. 
       FIG. 8B  shows a cross-section of the filter  90  taken along line B-B in  FIG. 8A . As indicated in  FIG. 8B , the filter  90  can comprise a stack of materials that includes a ground plane  100 , a substrate  102 , and an LCP layer  104 . As is further indicated in the drawing, the bottom loop  92  is formed in the substrate  102  and the top loop  94  is formed on the LCP layer  104 . By way of example, the LCP layer  104  can be approximately 8 mil thick. 
     Using switches in the manner shown in  FIG. 8A  provides the advantage of faster tuning because the switches can be operated nearly instantaneously. However, the filter  90  may have greater insertion losses because of the presence of the switches.