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Variable capacitors, or varactors, were discussed at length in Chapter 3. In this chapter, we revisit the subject of varactors, but in the context of implementations that emphasize their application in circuits other than voltagecontrolled oscillators (e.g., filters).

The Binary Capacitor:

The binary capacitor function, a capacitance that is made to change between two values, is embodied by the shunt capacitive MEM switch. Indeed, as is well known [7], the operation of the shunt capacitive MEM switch is predicated upon the fact that, when it is in the up state, the capacitance from the bridge to the center conductor of the CPW line is very small; whereas when it is in the down state, that capacitance is very large. Thus, when examined, not from the insertion loss/isolation perspective, but from the perspective of the equivalent RF behavior of the structure, it may be readily characterized as a binary capacitor and exploited for tuning/reconfigurability purposes. Recently, Peroulis et al. [8] employed the serpentine-spring-supported lowvoltage capacitive MEM switch [9] to demonstrate just such a binary capacitor . The structure?

s intrinsic capacitance is given by where A is the area of overlap of the bridge with the center conductor of the CPW line, d is the bridge-to-substrate distance, td is the thickness of the dielectric protecting the bottom electrode, er is its relative dielectric constant, and Cfringing is the fringing capacitance. Depending on the particulars of the implementation  and the intended application, however, it is worth pointing out that there may be other parasitic elements that would blur the simple capacitive behavior implied by (4.3), and thus they must be included in its model. For example, Peroulis et al. [8] found that for applications of the binary capacitor in filters, the extra elements. must be included. These elements include (1) the resistance and inductance of the bridge, denoted Rp and Lp, respectively, and obtainable from full-wave simulations; (2) the loss in the dielectric insulator coating the bottom electrode, Gp, and given by [8] where tan d is the loss tangent of the dielectric; and (3) the short access lines of length lL and lR, as represented by their effective series resistance and inductance, RSL and LSL, respectively. Peroulis et al.

[8] pointed out that the parasitic inductance is particularly important in the model because its values are comparable to those found in actual filters. Under the short line approximation, assumed by Peroulis et al. [8], the parasitic elements are given bywhere a represents the line attenuation constant, usually obtained experimentally,.