Draw and explain the equivalent LCR resonant circuit of an oscillating crystal. Write the expression for its series resonant frequency and quality factor. What is the effect of the crystal thickness on its frequency?
An oscillating crystal, such as a quartz crystal, can be modeled as an LCR (Inductor-Capacitor-Resistor) resonant circuit. In this model, the crystal’s mechanical vibration is converted into electrical energy, and the resonant frequency is determined by the electrical characteristics of the circuit.
The equivalent LCR resonant circuit consists of three components:
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