A simple way of characterizing high Q oscillators

A simple and accurate theory is presented for the design of high-Q tuned circuit oscillators. The crystal is considered separately from the active oscillator, and all high-Q approximations are handled before the design begins. Previously published concepts (OSCI-LLATOR, negative resistance) are rigorously used as a basis for the final formulas. Technology-independent equations for the oscillation build-up time constant and accurate frequency determination are given along with validity checks on the calculations. The final result is that high-Q oscillator design is reduced from a two-port to a one-port network problem. All remaining mathematical complexity comes from the design of the active impedance and is not a part of crystal oscillator theory. The derived equations were experimentally verified to reasonable measurement accuracy. Pierce and Miller oscillator design methods based on the theory are demonstrated, and SPICE runs are made to demonstrate the theory's application.<>