Frequency Stability Analysis of Transistorized Crystal Oscillator

This paper gives an analysis of a modified Pierce oscillator for frequency variation due to changes in the circuit or transistor. The magnitudes of the frequency shifts due to parameter changes are computed in relation to each other. The analysis has been verified by testing the oscillator circuit with several transistors which had significantly different measured parameters. Computed frequency shifts were compared with measured frequency shifts. The agreement between experimental and calculated data is <8×10-9 with a 5 Mc, fifth overtone quartz crystal in the circuit. A general equation relating frequency changes to changes in circuit parameters has been derived and is applicable to any operating frequency as long as the y parameters of the transistor and the circuit elements of the oscillator are known.