Design considerations for high-frequency crystal oscillators

The deleterious effects of crystal shunt capacitance and series resistance on the performance of series-mode oscillators are discussed. When the parasitic capacitance across the crystal significantly modifies the transconductance of the amplifying stage the circuits can become susceptible to a parasitic second mode of oscillation above the series-resonance frequency of the crystal. A simple model that can sufficiently describe such crystal oscillator circuits was developed and used to derive simple design equations that can accurately predict the behavior of these circuits. The design equations should be especially useful for a reliable design in cases when it is not practical to use an additional inductor to compensate for the parasitic shunt capacitance of the crystal. It is shown theoretically that the inclusion of this capacitance in the feedback path reduces the total effective capacitance in the tank circuit, which is tuned to the desired overtone frequency. This creates a second mode of oscillation frequency which is higher than the desired crystal resonance frequency. The ranges of loop-gain and tank resistance values that can prevent this parasitic mode of oscillations are derived. It is also shown that the useful loop gain for the desired oscillations to start is restricted to a similar region by the crystal shunt capacitance and series resistance