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Many modern wireless systems use resonator tuning schemes for changing communication frequencies. Most methods for changing communication frequencies are predicated upon coupling a voltage-controlled capacitor (varactor) to a resonator in order to change its resonance frequency. The tunable CPW resonator [13] discussed in Section 4.2.4 is an example of such a scheme, although in that case the varactor, implemented with a cantilever beam, is both the capacitor of the LC resonator and the means to effect frequency tuning.

The fundamental disadvantage of varactor-coupled tuning approaches is that the intrinsic parasitic resistance of the varactor introduces losses in the resonator, thus lowering its unloaded Q. The consequence of a reduction in the unloaded Q may be appreciated by examining the carrierto- noise (C/N) ratio in a voltage-controlled oscillator (VCO), where C/N is given by [20] where QL is the loaded Q of the resonator, Loss is the loss factor in the resonator, f0 is the frequency of oscillation, Df is the offset frequency from f0, P0 is the output power of the oscillator, k is Boltzmann?s constant, T is absolute temperature, B is the measurement bandwidth, and NF is the noise figure of the amplifier. Examination of (4.14) reveals that in order to obtain high C/N ratio, the loaded Q must be high. The loaded Q, in turn, is highest when the resonator experiences minimum external loading.

A novel technique to effect resonator tuning, which is enabled by an electrostatically actuated MEM air bridge, is indicated in Figure 4.16. In this scheme, changing the resonator?s resonance frequency is accomplished by varying the capacitor or varactor coupling, rather than by varying the capacitor [21]. In essence, an interferometer, such as a Mach-Zender interferometer [19], is coupled to the resonator. Then, by way of an electrostatically actuated air-bridge disposed over one of its arms, its transmission, and consequently its coupling to the resonator, changes the resonance frequency of the resonator as described below. Using impedance-transforming properties of a transformer, the input to the primary port of a 1:Nt transformer whose secondary is loaded with a capacitor Ctuning or an inductor Lt results in a capacitanceN C t 2 tuning or an inductanceL N t t / 2 , respectively.

To vary the effective coupling Nt, a Mach-Zender interferometer is coupled to dielectric resonator. In Figure 4.16, the Mach-Zender interferometer is implemented as a capacitor, specifically a ring capacitor. Thus, the Mach-Zender interferometer acts as a tunable capacitor and includes a bottom electrode, an air bridge, and a ring branch. Applying an actuation voltage Vt causes the air bridge to deflect towards the ring branch, thus loading the ring branch with variable capacitance, which, in turn, changes the coupling to the ring branch and, as a consequence, the effective capacitance coupled to resonator. The dielectric resonator is coupled to a transmission line having a termination RT at one end and an active element at the opposite end. The active element is coupled to both a feedback element and a matching network that is coupled to a terminating load RL.

Referring to Figure 4.17, assuming balance amplitudes (i.e., |t1| = |t2| = 1), the transmission T, which relates the output-to-input wave amplitude ratio, is given by where k is the propagation constant defined by with w being the frequency and Lr and Cr being the inductance and capacitance per unit length, respectively. L is one-half the mean circumference of the ring. For a given L, T is a function of k1 and k2, and T is a measure of the coupling between input and output when there is an output transmission line.

When there is not an output transmission line, the waves in each branch of the ring simply counter-propagate and T still represents the coupling to the ring. In this case, however, it is more appropriate to consider the reflection from ring R = 1 – T. This coupling can be varied by changing k2 – k1, in particular, by changing Cr on one of the ring branches. Thus, the concept allows the tuning of the resonator yet without deteriorating its Q by the tuning mechanism.