An algebraic formulation of frequency stability against supply voltage variation of quartz crystal oscillator
✍ Scribed by Takahiro Shoji; Takehiko Adachi
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 240 KB
- Volume
- 83
- Category
- Article
- ISSN
- 8756-663X
No coin nor oath required. For personal study only.
✦ Synopsis
With widespread use of portable communication equipment, the stability of quartz crystal oscillators used as a frequency source has become important. In this paper, an algebraic formulation of the stability of the voltage source of a quartz crystal oscillator is derived and its effectiveness is verified. First, a nonlinear approximation model of a transistor in large signal operation is derived, leading to an algebraic expression of the equivalent capacitance of the active circuit in the oscillator. Next, by using the obtained expression, an algebraic formula for the stability of the frequency power supply voltage in steady-state oscillation is derived. Finally, for circuit examples including the design range used in practice, the analysis of frequency supply voltage stability is carried out and is compared with the simulation. The discrepancy is only 10%, so that the analysis is usable in practice. From the obtained analytical equation, the variation of the oscillation frequency due to supply voltage variation is found to be caused by variation of the basecollector junction capacitance and the baseemitter junction capacitance of the transistor. Also, a quantitative analysis of the frequency variation and the capacitance parameters of the transistor as well as the circuit element values becomes possible.