domingo, 30 de mayo de 2010

Integrated Modeling of Mechanical and RF

Integrated Modeling of Mechanical and RF
Performance of MEMS Capacitive Shunt Switch

Radio frequency Microelectromechanical System (RF MEMS) is an emerging technology, which is envisaged to play a key role in the development of broadband communications, software radio applications and agile radar systems. MEMS shunt capacitive switches can deliver superior RF performance to existing technologies up to 100GHz [1-2]. RF MEMS switches can be integrated into System-on-Chips, offer wider bandwidth, high isolation, low power consumption, low losses and have an excellent linearity, compared to traditional RF front-end switches [3].
The MEMS capacitive shunt switch which is used to demonstrate the integrated modeling approach, consists of a suspended movable metal bridge, which is mechanically anchored and electrically connected to the ground line of a coplanar waveguide (CPW) transmission line. The simplified circuit diagram for the shunt switch is shown in figure 1.

Figure 1. Simple circuit representation of capacitive shunt switch
In operation, a DC bias voltage and an RF signal are superimposed and applied to the signal line. In the RF-On state, i.e. when the DC bias is zero, the bridge remains up, hence the capacitance is small, and hardly affects the impedance of the line. In the RF-ON state the signal freely passes through. By increasing the DC bias voltage the bridge is pulled down onto a dielectric layer placed on the top of the signal line. The switch capacitance increases, causing an RF short to ground, and the switch is in the RF-OFF state. A high down capacitance and a low up-state capacitance results in high isolation and low insertion loss in the RF-OFF and RF-ON states respectively. This paper describes a method of integrating electromechanical and RF simulations. This allows the device designer to optimize both the mechanical and RF performance of the device and enables RF system designers to include device S-parameters in system simulations. This method is demonstrated with simulations of a novel 'curled cantilever' MEMS capacitive shunt switch.
The integrated modeling method is developed to allow the construction of 3D actuated geometries of MEMS devices, from electromechanical modeling results as input to 3D electromagnetic simulation software.

Figure 2. Process flow of integrated modeling and simulation
The mechanical modeling of the MEMS switch is performed in the Coventorware 3D finite element package.
The simulated profile of the switch in both up and down states is exported in 2D format. This 2D data is imported in spline format into CST Microwave Studio. Measured interferometric profiles can also be imported as 2D data into CST. The curve is translated into 3D structure for electromagnetic simulations. The process flow for integrated modeling is shown in figure 2.
The CMOS compatible single layer cantilever switch is fabricated in the Tyndall surface micromachining process with a nominal switch gap of 1.5μm. The switch uses a process-induced stress gradient to achieve 30μm air gaps at the tip of a 350μm long cantilever switch. The switch is built on a high-resistivity silicon substrate, on which a 0.5μm thick silicon oxide is deposited as an isolation layer. The
CPW is fabricated from 0.5μm thick sputtered Al/1%/Si. A
140nm thick PECVD silicon oxide dielectric is deposited as passivation layer between the switch electrodes. The sacrificial layer is formed by a layer of 2.5μm thick polyimide. The switch cantilever is formed from cold sputtered aluminium, which has a tensile stress of approximately 35MPa, and is placed over a 700μm long 110/200/110 G/S/G transmission line. The SEM image in figure 3 shows the fabricated beam after release.

Figure 3. SEM Image of the cantilever showing deflection due to stress Gradient
A. Mechanical modeling
The switch uses thin-film residual stress gradient to deflect the switch cantilever to achieve high air gaps, despite the use of a relatively thin sacrificial layer in the fabrication process. The effect of biaxial stress gradient becomes apparent for wide cantilevers causing transverse bending. Experiments from previous fabrication runs have shown the process gradient averages 51MPa/μm in a 1μm thick aluminium film.
The switch design is optimized in Coventorware to minimize unwanted transverse bending by incorporating a number of 2ìm wide slots in the structure. The slots also allow easy removal of the sacrificial layer. This design modification eliminates transverse bending which can be seen from the simulated cantilever deflection shown in figure 4. To ensure uniform movement of the switch, the beams are linked using 5μm tethers at regular intervals.

Figure 4. Coventor simulation of a cantilever switch incorporating 2μm wide stress release slots. This modification eliminates transverse bending and increases tip deflection.
The cantilever switch design presented here has a 350μm x 200μm x 1μm structure, consisting of 10 cantilever beams, each 18μm wide and separated by a series of 2μm slots. The shape of the released switch agrees well with the simulations, and little or no transverse warping is observed. The measured deflection of the cantilever structure shows the tip deflection of 30.7μm which agrees with the simulated deflection of 28.5μm, which can be seen in the surface profile, figure 5.
The slight offset is most likely due to the effects of the beam anchor and errors in the assumption that the stress gradient is linear across the metal thickness.

Figure 5. Measured surface profile shows the tip deflection is 30.7μm, which agrees with the simulated, for a stress gradient of 51MPa/μm.
B. Radio frequency modeling
The RF operation of the switch consists of a grounded metallic beam suspended over a passivated CPW on high resistivity silicon of thickness 500μm. The simulated profile from the mechanical modeling of the deflected cantilever was imported to CST Microwave Studio [6]. The curve was swept to 1μm thickness along the path of profile and the width of 200μm to get the exact 3D structure of the cantilever with stress gradient induced tip deflection after release. The constructed model of the cantilever switch can be seen in figure 6. The 3D structure in the down state can be constructed from the simulated MEMS profile in the down state. The structure is simulated by enclosing it in an air box with imposed radiation boundary conditions.

Figure 6. The up state model of the cantilever built in CST MWS for RF Simulations
The RF measurements were performed using an HP8722D Vector Network Analyzer (VNA) by wafer probing on a Cascade station using Ground-Signal-Ground (GSG) coplanar probes. The full two-port Short-Open-Load-Thru (SOLT) calibration was performed using the Impedance Standard Substrate (ISS) prior to the device measurement. The frequency range used during the calibration and measurement was 0.5GHz to 20GHz with 401 points. The bias voltage required for the switch actuation was provided from a Keithley 237 high-voltage source connected to the DC port of the VNA. This enables a DC bias to be superimposed with a -10dBm-power microwave signal that is applied to the device. The two-port S-parameters of the switch in the open and closed state were recorded and then the Insertion Loss and Isolation were calculated from the S21 parameter, respectively. The S21 is defined as a signal transmission coefficient between the input and output port. To actuate the switch a voltage of 24V is used. When no bias is applied and the switch stays in the openstate, the RF signal is almost fully transmitted between the input and output port with the maximum measured and simulated loss of -0.4dB at 20GHz. The insertion Loss of the switch is shown in figure 7.

Figure 7. Measured and simulated Insertion loss of the switch.
However, when a voltage is applied and the switch is closed, the RF signal is attenuated and only a small portion passes between the ports. The switch capability for the RF signal attenuation is called the switch Isolation and the maximum value in our device is -30dB at 12.3GHz for simulation and measurement.
Ideally the switch would have 0dB Insertion Loss and infinite Isolation. However, presented values can be classified as a good switching performance. A very good agreement in the characteristic shape between the measurement and the simulation is seen in case of the Isolation. The characteristics and resonance frequencies (ƒr=12.3GHz) are almost overlapped as shown in figure 8.

Figure 8. Measured and simulated isolation of the capacitive switch.

Cesar Augusto Suarez 
CI 17394384

MEMS Electromagnetic Modeling

MEMS Electromagnetic Modeling

 Applications of micro-electromechanical systems (MEMS) in automobiles are fairly recent. The two most common examples of MEMS use in automobiles are in crash sensing for airbag deployment, and in manifold absolute pressure sensing. There are, however, several other areas where MEMS devices are expected to replace more traditional technologies within the next few years. MEMS devices/systems (e.g. sensors and actuators) have several vital advantages over more traditional technologies. Because of highly reliable batch processing techniques, large volumes of highly uniform devices can be produced at relatively low unit cost. Since MEMS have virtually no moving parts to wear out, they are extremely reliable and long lasting. With the advent of microprocessor compatibility imposed on many automotive sensor/actuator applications, silicon based MEMS sensors will have a very efficient interaction with the controlling microprocessors.
With increasing use of MEMS devices in automotive applications, modeling and simulation of these devices will become more and more important. Although CAE has a very important place in the development cycle of the automobile, the CAE needed for MEMS has some significant differences. Because of the much smaller dimensions of MEMS devices, forces that are normally neglected in macro-structural CAE cannot be neglected any more. Behavior of material in bulk form is quite different from that in thin film form. MEMS devices exhibit the interaction of mechanical, electrical, magnetic, thermal, and other physical phenomena, and therefore simulation of these devices has to be able to capture this multi-physical interaction. This paper will discuss all these important issues that need to be addressed in MEMS modeling and illustrate them through actual simulation cases of MEMS devices.

MEMS is an acronym that stands for micro-electromechanical systems. MEMS contain components of size ranging from 1 micrometer to 1 millimeter. The core elements in MEMS generally consist of two main types of components: sensors and actuators. Actions of these devices are initiated by chemical, thermal, electrical, or magnetic means. Thus, two characteristics that separate MEMS systems from more traditional engineering systems are their size and the multi-physical governing principles.
Applications of MEMS devices can be found in a variety of industries such as biomedical, aerospace, instrumentation, automotive, etc. New developments and applications in the MEMS field are finding their way into many of these industries everyday. Good performance-cost ratios are responsible for the popularity of industrial MEMS devices in today's market. They are innately faster as speed usually scales with size. Most MEMS devices operate on very little power so a high level of power consumption is not an issue. These devices also reflect high levels of accuracy, reliability, and reproducibility. In the manufacturing of MEMS, Batch Microfabrication techniques have led to newly developed effects and products in the MEMS market all over the world.
In the automotive industry MEMS applications hold a lot of promise. Automotive components need to be produced in very large volumes not only from a demands point of view, but also from the necessity of recovering the initial investments. Operating lifetimes of up to 10 years along with very low unit prices are also required. These qualities are inherent in MEMS devices. Due to the progress made in batch manufacturing of MEMS, large volumes of highly uniform devices can be created at relatively low cost.
Also, since MEMS devices have very few or no moving parts, they don't wear out and as a result are very reliable.
Two areas where MEMS devices are currently being used in automobiles are in engine control and airbag deployment. Manifold absolute pressure sensors are used in engine control of many vehicles and silicon accelerometers are used to trigger airbags. Apart from these two MEMS devices that are on production vehicles today, there are many devices that are at various stages of development. Some of these will be used on production vehicles in the very near future. Application areas where MEMS devices may be seen in standard production include wheel speed sensing, yaw-rate sensing, active safety and steering, navigation, seatbelt pre-tensioning, road condition monitoring, etc.
Modeling and simulation of MEMS devices is an important step in the design, development and successful application of MEMS products. While modeling techniques for large devices and systems are well established and tested, modeling and simulation of microdevices pose some unique challenges. Thus, engineers trained in modeling traditional automotive components need to be aware of these vital differences when they try to model MEMS devices. In the next few sections, some of these challenges are highlighted and some of the commonly used modeling tools for MEMS work are described. In the end, two very commonly used MEMS devices are analyzed for their behavior in response to external input. The devices chosen are common components in many MEMS applications and are also useful for automotive MEMS devices.

Modeling and simulation methods for MEMS can be broadly divided into three different levels of approximation. The lowest level, sometimes called the "Geometry level" (see Figure1), is closest to reality. At this level the physical phenomena are described through partial differential equations. Numerical solution of these equations is achieved through techniques such as the finite element method or the boundary element method. When done right, these methods yield very accurate results of residual stresses, heat distribution, distortions, natural frequencies, etc. Because these methods also require considerable computational resources, they are used only when detailed data about the MEMS structures are needed. At a higher level of abstraction, models used are called "network models." Examples of network models are circuit simulators or multi-body simulators. 

Figure 1: Different levels of MEMS modeling
These can be used to represent all the MEMS subcomponents and are represented through sets of ordinary differential equations. The solutions of these equations provide information about the transient behavior of the system. At this level, the physical behavior of the system and the interrelation of its subcomponents are still well captured.
At the highest level of abstraction, MEMS models use block diagrams with signal inputs and outputs (similar in approach to signal processing and controls). The level to be used in a particular situation is determined by the kind of results one is expecting to obtain. For the rest of this paper we will talk most about the "Geometry level" modeling.
There are a lot of discussions related to MEMS modeling and simulation in the industry, and one of the reasons is because it involves many diverse problems with varying spatial and temporal scale. Moreover, simulating MEMS devices as a whole gets complicated especially in a new design. The design might involve unfamiliar physics, such as lumped models and continuum approximations and might be difficult to handle as one piece. There are several commercial tools available for modeling the behavior of MEMS devices at the geometry level. In these tools, analysis methods such as the Finite Element, Boundary Element or the coupled Finite and Boundary element method are usually used. CAD tools nowadays give the user the option of choosing the standard MEMS fabrication process involved, such as Bulk Micromachining, Surface Micromachining, LIGA, etc. With this information, the standard process template is retrieved and along with the planar geometry information from the mask layout editor – a three dimensional structure is created. Simulation of any problem is now possible, such as thermomechanical, electrostatic, and completely coupled thermo-electromechanical analysis. In the next few paragraphs some of the CAD tools are discussed. The list considered here is by no means complete. There are other tools which we are not able to mention here.
For many decades IntelliSense Software Corporation provided design and development services as well as software tools to MEMS developers. Intellisuite, a product of IntelliSense, is a dedicated software for a total MEMS solution. With MEMaterial, AnisE, IntelliMask, and IntelliFAB, it consists of a whole suite of process tools comprising of material databases, process characterization and optimization tools, anisotropic etch modeling, layout, and process design. The analysis modules include thermoelectromechanical, Packaging, PiezoMEMS, ElectroMagnetic & RF MEMS, and BioMEM & Microfluids. But the underlying FEA solver is ABAQUS, linking to IntelliSense Software's in-house code for coupled analysis. By incorporating process templates, thin-film material engineering, mask layout, and device analysis within a single tool, IntelliSuite enables MEMS engineers to optimize devices prior to fabrication, reducing prototype development time and cutting manufacturing costs.
MEMSCAP provides MEMS Pro that enables designers to create designs and couple them with electronic systems that drive the parts. ANSYS Multiphysics  allows for coupled energy domain modeling and simulation with applications in microfluidics technology, high-frequencyelectromagnetics, and electrostatic-structural coupling. ABAQUS Piezo allows the modeling of piezoelectric behavior in MEMS devices. Since the fields that need to be addressed in MEMS modeling are as diverse as the devices that operate on their principles, MEMS modeling in different industries is yet to be standardized.
Important issues in MEMS modeling
As has been mentioned before, two critical aspects of MEMS are their small length scales and their multi-physics nature. As a result, in modeling MEMS devices one needs to be careful about issues that don't receive any attention in the traditional approaches of modeling continuum material.
MEMS devices function by converting one or more physical or chemical conditions into electrical signals (in case of sensors) or vice versa (in case of actuators). For example, a pressure sensor may convert the change in pressure into an output voltage and micropumps convert a voltage into output pressure. Modeling of these devices, say for example a cantilever plate or pressure membrane, may involve electrostatic, electromagnetic, and piezoelectric phenomena to name a few. These characteristics are often coupled with static or dynamic mechanical response of the micro-structure .
In MEMS modeling of electrostatically actuated devices such as beams, diaphragms, comb-drives, and nano-tweezers [13], one has to be wary of proper calibration [14] of the device according to the pull-in voltage. The maximum deflection achieved before the onset of the instability is referred to as the pull-in distance. Because this distance is so small, this value is a limiting factor in the design of all systems of this kind.
In modeling micro fluidic devices such as micro pumps or micro valves, one needs to account for both compressible and incompressible fluid dynamics in the micron size-domain. Compressible fluid in that regime may no longer be considered continuum flow. Therefore, simulation algorithms for viscous flow and/or low-pressure damping are needed to assist the design of these devices.
Most commercial Finite element codes are developed using the concepts of continuum mechanics and are tested for bulk material (properties). They cannot be directly applied for MEMS devices. Many MEMS devices are electroactive or magnetoactive in nature. For example, mechanical responses of piezoelectric materials are a result of applied voltage. These types of behavior are not modeled within most general-purpose commercial software packages. MEMS materials are rarely a continuum, because they often consist of layers of thin films that are bonded to dissimilar materials. Thin-film material databases are very important to any MEMS designer. They give people ready access to material properties such as Young's Modulus and dielectric constants. These differ from properties of bulk materials and tend to vary significantly as a function of machine settings from which they are being fabricated. Sometimes faulty designs and structural or particle misbehavior may take place because MEMS structures are more sensitive to faulty material properties than bulk structures. Even with a correct model simulation, results received may be severely inaccurate upon the use of incorrect material data.
Microfabrication processes play an important role in the behavior of MEMS devices. In many cases fabrication related device feature affects the performance quite significantly. Fabrication may induce residual stresses and/or other effects on MEMS devices that cannot be ignored (like bulk materials) due to the size of such devices. That is why, in modeling the behavior of these devices, the effects of the fabrication process through a process model needs to be considered as well. MEMS fabrication  can be of different types such as micromachining, MUMPs (Multi-User MEMS processes), etc. Micromachining is the bulk anisotropic etching of crystalline silicon. The angle between crystalline planes or the etching angle is naturally 54.74 degrees. It is a combination of fabrication processes that are used for example to create MEMS devices and Lab-on-chip systems. Today, complex systems such as micromirrors, comb-drives, cantilever arrays, microgears, and microfluidic flow sensors are all created using a few of these basic techniques. For resistors, diodes, and transistors, dopants are introduced to form electrically active regions. Bulk micromachining has been the standard for producing capacitive and piezoresistive pressure sensors. MUMPs is a program that provides MEMS fabrication processes to the industry. PolyMUMPs is a three-layer polysilicon surface micromachining process. MetalMUMPs is an electroplated nickel process, and SOIMUMPs is a silicon-on-insulator micromachining process.

Cesar Augusto Suarez 
CI 17394384

sábado, 29 de mayo de 2010

Dual Coupled Resonator Local Oscillator

Dual Coupled Resonator Local Oscillator
Local oscillators are used in most radio transmitters and receivers. Any phase noise produced by this local oscillator will add to the noise received at the antenna. For low errors in the decoded data, the phase noise of the local oscillator must thus be far less than the other noise sources in a receiver. The local oscillator should be able to be produced at a low cost, since most applications are very cost sensitive. Realising the resonators, which determine the oscillating frequency, as microstrip transmission lines on the same PCB as the active elements of the oscillator results in low cost designs. An oscillator consists of an amplifier and a feedback network containing a frequency selective network, such that positive feedback is obtained at the desired frequency, causing the circuit to oscillate. Many oscillator topologies, such as Colpitts, Hartley, Crystal and Dielectric Resonator oscillators, have a single resonator frequency selective network and are described in standard electronics texts [1]. The frequency selective networks attenuate all signals at frequencies not corresponding to the required oscillation frequency. They have little attenuation and have the required phase shift to cause the positive feedback at the desired oscillation frequency. The primary factors determining the phase noise of the oscillator are the Q of the resonant network, the noise figure of the amplifier and its output power [2]. Leeson's [3] simplified model for phase noise shows the phase noise is inversely proportional to the square of the Q of the resonator.
Fig. 1 shows the block diagram of a typical oscillator. One can determine if this oscillator will oscillate by opening the switch and applying a signal A, at the desired oscillating frequency, to the input of the amplifier and measuring the signal B that is obtained as the feedback signal. When B>A and B is in phase with A then the oscillator will oscillate when the switch is closed. If the real part of the loop gain, being the ratio of B/A, is greater than one, the circuit will oscillate. A frequency selective network with a higher Q has a higher rate of change of phase of the loop gain versus frequency, and a quicker reduction in the real part of the loop gain, as one deviates from the centre frequency. Since the amount of phase noise of the oscillator is directly related to the real part of the loop gain, the higher the rate of change of phase of the loop gain at the oscillation frequency, the smaller the phase noise of the oscillator. The group delay, being the rate of change of phase, of the frequency selective network, is thus an important parameter.

The Q of the frequency selective network is determined by its components. A typical LC resonator has a Q of less than 200 and a Quartz Crystal has a Q of several thousand. The microstrip transmission line resonators used in the designs presented here have a Q of 191.
It is difficult to obtain as high a Q as possible for planar resonators, such as microstrip lines. Laute [4], uses a printed circuit inductor with a Q of 9 for a 900 MHz VCO. Lee [5] describes an oscillator which uses a single resonator. The coupling into the resonator is adjusted to minimize the loading of the resonator and thus maintain as high a Q as possible. It is possible to minimize loading the resonator using tap coupling and that is very suitable for the operating frequencies used in mobile communication systems. In this paper the use of a dual coupled resonator is proposed. Since the Q is defined for single resonator only, the group delay is a better measure of the frequency selective nature of the both the single and coupled resonator network.

In order to accurately compare the phase noise performance of the single and dual coupled resonators, Microwave Office computer simulations are carried out on the oscillators.
Initially a linear simulation is carried out to ensure that the circuit operates at the correct frequency and has a loop gain greater than one, to ensure that oscillations will occur.
Subsequently nonlinear simulations using harmonic balance are carried out to determine the exact oscillating frequency, power output and phase noise of the oscillator designs. To verify those simulations, hardware has been constructed and its performance measured.

Figure 2. Microwave Office circuit of tapped single microstrip resonator.

Fig. 2 shows the Microwave Office circuit model of the microstrip resonator used in the single resonator oscillator design presented in this paper. One end of the resonator is connected to ground and the other end is an open circuit. The input and output signals are coupled to the resonator using
20Ω resistors, connected to the resonator at a specified distance from the ground connection. The resistance value and tapping point are selected to provide a good match at all frequencies into the 50 Ω input and output impedances of the amplifier used and provide a low insertion loss at the desired oscillating frequency. This ensures that the oscillator does not oscillate at other than the designed frequency. The tapping point is chosen to ensure that the loaded Q of the resonator is just sufficient to cause a loop gain greater than one, thus ensuring oscillations.
Fig. 3 shows the Microwave Office circuit model of a tapped two resonator coupled network, which would typically be used in a two resonator filter. To be able to make a good comparison with the single resonator of Fig. 2, the same line widths and the same coupling resistors are used for both these resonators. To obtain a good impedance match at the operating frequency, slightly different tapping points, Ltaps in
Fig. 2 and Ltapd in Fig. 3 were used. Fig. 4 shows the insertion loss and group delay of the two resonators.
The insertion loss and group delay of the dual coupled resonator are governed by the coupling between the two resonators. The bigger the coupling gap, the bigger the insertion loss and the bigger the group delay. To clearly demonstrate the effect of the resonator group delay on the oscillator phase noise, the amount of coupling used for Fig. 4 is such that insertion loss (red curves) for the dual resonator is the same of that for the single resonator, so that the amplifier used for the single resonator oscillator can also be used for the dual coupled resonator oscillator without any changes. It can be seen that the group delay (blue curves) of the dual resonator network is higher than that for the single resonator network. This difference can be increased much more by reducing the coupling between the resonators, however that increases the insertion loss of the dual resonator compared with the single resonator, so that the amplifier gain then needs to be increased for the dual resonator oscillator.

 Figure 3. Microwave Office circuit of dual coupled microstrip resonator

Figure 4. Group delay and insertion loss of single and dual resonators.

Cesar Augusto Suarez 
CI 17394384

An X-Band to Ku-Band RF MEMS

An X-Band to Ku-Band RF MEMS
Switched Coplanar Strip Filter

Reconfigurable microwave circuits have generated great interest for both military and commercial applications because these networks allow increased system functionality with lower weight and cost than existing systems. Due to their low-loss and other attractive characteristics, radio frequency microelectromechanical systems (RF MEMS) are key to meeting these objectives. One of the most critical elements enabled by RF MEMS is the tunable filter, of which there have been several examples. These filters have included both lumped designs and distributed designs at frequencies ranging from L-band to millimeter-wave. However, there have been few examples of RF MEMS-enabled filters in the 8 to 18 GHz range where numerous radar and communications applications reside. In this work, we present an RF MEMS switched filter operating in this important frequency range.

This filter design is enabled by a low-loss RF MEMS switched capacitor. The device used in this work is optimized for low loss and high- at microwave frequencies. To enable post-processing on arbitrary substrates ranging from quartz to InP MMICs, the device was fabricated using a low-temperature surface micromachining process described in detail previously [10]. This process uses a polymer sacrificial layer and evaporated gold films to fabricate the capacitor, and a low-temperature dry etch process to release the devices. In the future, we anticipate adding thin-film resistors using a high-resistivity layer to allow individual biasing of the switches, enabling more complex and higher-order filter designs.
The switched capacitor consists of a 1.2 m-thick gold cantilever suspended 5 m over a ground pad coated with silicon oxynitride dielectric. A cantilever device is used to reduce sensitivity due to thermal mismatches between the substrate and device, but has not been characterized over a broad temperature range. The device is switched by increasing the actuation voltage until the plate pulls down onto the substrate at approximately 15 V. The up-state capacitance is approximately 150 fF while the down-state capacitance is approximately 400 fF at 20 V. Additionally, the downstate capacitance can be tuned between approximately 350 and 400 fF by varying the holding voltage between the pull-off voltage of 10 V and maximum voltage of 20 V, allowing approximately 10% tuning in the downstate. Even though this slight tuning is possible, in this filter application the device is used as a two-state switch for improved stability and reproducibility in the presence of vibration or bias voltage noise. This MEMS capacitor has a -factor of over 100 through the entire band of operation up to 25 GHz, and an extrapolated minimum self-resonant frequency of over 60 GHz in the highest capacitance state. Additionally, switching times between the down-state and up-state were measured to be under 100 s. Finally, while the device has been operated to over a billion cycles without any charging or stiction-related failures, during the lifetime test the pull-in voltage gradually shifted from 15 to 7 V due to metal fatigue at the anchor. This reliability limitation will be addressed in
future designs.


The filter was designed as a second-order capacitively-loaded interdigital filter. The resonators were grounded at one end by a large grounding capacitor for bias isolation, their lengths were chosen to be approximately 45 long at the center frequency of 12.5 GHz to allow for maximum tuning range, and the tap locations were chosen for optimum filter characteristics at 12.5 GHz. The filter elements, to take full advantage of the high performance of the switched MEMS capacitor, were fabricated in a coupled coplanar strip (CPS) configuration on a GaAs substrate. Coplanar technology, rather than microstrip, was 

Fig. 1. Optical micrograph of the RF MEMS switched filter with an inset showing a simple equivalent circuit model of the filter. The filter dimensions are 1.5 _2.2 mm.

chosen both for process simplicity and the ability to fabricate these components on arbitrary substrates. This filter differs frompreviously reported RF MEMS switched CPS-filters [9] in that this design is switched by changing the loading capacitors rather than by physically changing the length of the line. This approach allows for a filter layout that is up to 50% smaller at a given frequency than previous examples.
After using standard filter design techniques and software to design a 15% bandwidth, 0.25-dB ripple filter, the layout accuracy was verified with a commercial 2.5D method-of-moments simulator and a commercial three-dimensional (3-D) finite element simulator. An optical micrograph of the filter, which occupies only 1.5 2.2 mm of chip area, is shown in Fig. 1, which also includes a simple sketch of the equivalent circuit as an inset. The coplanar waveguide (CPW) feedlines are designed for 50 impedance, while the CPS resonators are 80 m wide with a 35 m gap between the signal line and the ground plane, producing a characteristic impedance of 58 and an effective dielectric constant of 6.85. The resonators are
1100- m long and separated by 450 m, producing even and odd mode impedances of approximately 62 and 52. The switched capacitors are 300 300 m with an initial air gap of
5 m. Because of the short resonators (about 45 ), this filter occupies less than half the chip area as earlier designs.

 The filter was tested using coplanar Cascade probes and an HP8510C network analyzer from 50 MHz to 25 GHz. For testing, wirebonds were added across the CPW feed to suppress spurious modes at the feed junctions. The control voltage, ranging from 0 to 20 V, was introduced to the CPW

Fig. 2. Measured and modeled transmission and return loss of the switched filter.

center conductor through the internal bias tees on the network analyzer. The transmission and return loss properties of the filter at voltages of 0 and 20 V are shown in Fig. 2, which also shows the circuit model response. At 0 V, the filter's center frequency is 15.5 GHz, with a bandwidth of 2.2 GHz. The minimum passband loss is approximately 1.4 dB in that state, with the return loss better than 20 dB in the passband. When the switches are pulled in at 20 V, the filter center frequency is
10.7 GHz with 1.8 GHz bandwidth. In this state, the insertion loss is less than 2 dB, with in-band return loss better than 10 dB.
This 37% center frequency switching is achieved with only two simple RF MEMS devices.
The rejection of the filter at two bandwidths above the center frequency is greater than 15 dB for both of the states, as expected for a two-pole filter. In similar filters operating at lower frequency, we have observed a slight decrease in stop-band rejection at three times the center frequency, but the rejection of this particular filter remains greater than 20 dB because of the electrically short resonators.
While the measured and modeled responses correspond well, there is a discrepancy between the measured and modeled bandwidths which can be accounted for by several factors.
First, the circuit-level simulation does not accurately account for the coplanar-strip tees, which impact the performance of the resonators. Second, accurately accounting for the coupling between the coplanar strip resonators and end ground planes requires full 3-D electromagnetic simulation. Finally, the resonator grounds are not exactly fixed at the end of the resonator, but instead distributed across the large area of the grounding capacitor. All of these effects were captured by full electromagnetic simulation and considered in the final design, but were not incorporated into the circuit model.
The filter properties change with frequency because the physical locations and lengths of the resonators and taps are fixed.
Therefore, as the filter is switched, the effective tap position and coupling coefficient vary, deviating from the ideal desired filter response. The filter was optimized for a response at 12.5 GHz, resulting in larger insertion and return losses at lower frequencies and merging of the poles at the upper frequency. Except for these slight departures from an ideal filter shape, the filter response is symmetric about the center frequency. The loss of the filter is limited by the low (30–40) of the coplanar strip line, rather than by losses in the switched capacitors. By using a transmission line technology with improved unloaded , the los of this filter can be significantly improved.

Cesar Augusto Suarez 
CI 17394384