Influence of series reactance on quartz-crystal resonators

This paper analyses the equivalent circuit of a quartz-crystal resonator in series with both capacitive and inductive reactances, in order to demonstrate the effect of these components on the observed resonances of the circuit¿the principal interest being in the design of series-resonant oscillators operating in both the fundamental and overtone mode. It is shown that there are severe limitations on the pulling range of a quartz crystal if significant overall circuit performance degradation is to be avoided. Finally, a series of expressions are presented as design guidelines for circuit engineers.