Crystal Oscillator and Series Resonance Frequency

Crystal Oscillator
A crystal oscillator is an electronic circuit that uses the mechanical resonance of a vibrating crystal of piezoelectric material to create an electrical signal with a precise frequency. It is widely used in various applications, including digital clocks, microprocessors, and communication systems, where accurate and stable frequency signals are required.

Series Resonance Frequency
The series resonance frequency (wS) is the frequency at which a circuit resonates when the inductive reactance (XL) and capacitive reactance (XC) cancel each other out, resulting in the circuit behaving like a purely resistive circuit. At this frequency, the impedance of the circuit is at its minimum, and the current through the circuit is maximum.

Crystal Oscillator Behavior
When the frequency of oscillation of a crystal oscillator is less than the series resonance frequency, the crystal oscillator acts as a capacitor. This means that the crystal behaves like a capacitor in the circuit, contributing capacitive reactance (XC) to the overall impedance of the circuit.

Explanation
When the frequency of oscillation is less than the series resonance frequency, the inductive reactance (XL) of the crystal is dominant over the capacitive reactance (XC). The crystal behaves like an inductor, which opposes changes in current flow. As a result, the crystal oscillator acts as an inductor in the circuit.

However, when the frequency of oscillation is greater than the series resonance frequency, the capacitive reactance (XC) of the crystal becomes dominant over the inductive reactance (XL). The crystal behaves like a capacitor, which stores and releases electrical energy as the voltage across it changes. In this case, the crystal oscillator acts as a capacitor in the circuit.

Therefore, when the frequency of oscillation is less than the series resonance frequency, the crystal oscillator acts as a capacitor. It contributes capacitive reactance (XC) to the overall impedance of the circuit, affecting the behavior and characteristics of the oscillator.

In conclusion, the crystal oscillator acts as a capacitor when the frequency of oscillation is less than the series resonance frequency. It is essential to consider this behavior when designing and using crystal oscillators in electronic circuits.