ANALYSIS AND DESIGN OF CRYSTAL OSCILLATORS, PART 1

The approach developed in this report appears to satisfy all the major requirements that must be placed on a unifying technique for oscillator analysis and design. As demonstrated on specific examples, the conditions for oscillation in a generally valid form can be processed to determine a the amplitude of oscillation in relation to the characteristics of the active device, b the requirements on the feedback network to operate the crystal unit according to its specifications, c the changes in frequency of oscillation in response to variations in any one of the circuit components and hence the values required for these components to obtain maximum stability, and d the output power in proportion to the power dissipated in the crystal unit. The key to this approach lies in a graphical method for solution of the oscillator phase equation in the impedance plane. The impedance diagrams obtained thereby open the way to a thorough qualitative understanding of the cause-effect relationships in oscillator performance and provide the guidelines to bring the analytic expressions into a convenient form for quantitative work. Detailed discussions are carried out for the Pierce oscillator and the bridged-T oscillator to illustrate the practical application of the approach.