Active Q Factor Analysis for Non-uniform Microstrip Stub Colpitts FET Oscillators

Abstract

This paper presents Q factor analysis for FET oscillators employing distributed-constant elements. We replace the inductor of a lumped constant Colpitts circuit by a shorted microstrip transmission line for high frequency applications. Involving the FET's transconductance and the transmission line's loss due to both conducting metal and dielectric substrate, we deduce the Q factor formula for the entire circuit in the steady oscillation state. We compared the computed results from the oscillator employing an uniform shorted microstrip line with that of the original LC oscillator. For obtaining even higher Q factor, we modify the shape of transmission line into nonuniform, i.e., step-, tapered-, and partially-tapered stubs. Non-uniformity causes some complexity in the impedance analysis. We exploit a piecewise uniform approximation for tapered part of the microstrip stub, and then involve the asymptotic expressions obtained from both stub's impedance and its frequency derivatives into the active Q factor formula. Applying these formulations, we calculate out the value of capacitance for tuning, the necessary FET's transconductance and achievable active Q factor, and then finally explore oscillator performances with a microstrip stub in different shapes and sizes.