Crystal Oscillator Working And Resonant Frequency
What Is Crystal Oscillator
To maintain constant frequency, piezoelectric crystals are used with the LC or RC oscillators (or) in the place of LC or RC circuits. Oscillators of this type are called crystal oscillator
Effects Of Crystal Oscillator
Due to the following effects, the LC and RC oscillators do not produce more stable oscillations
1) The value of R, L, and C which are frequencydetermining factors in these circuits, will changewith temperature.
(2) If any component in the feedback network ischanged, it will shift the operating frequency of the oscillator.
Piezo Electric Effect
The crystal has a peculiar property known as piezo electric effect, which is expressed as
(1) when mechanical stress is applied across its twofaces, the crystal vibrates and an ac voltage is produced.
(2) when an ac voltage is applied across its crystal,the crystal vibrates at the frequency of the applied voltage.
The frequency of the vibration is equal to the resonance frequency of the crystal
The equivalent electrical circuit of the crystal is mentioned as
1)when the crystal is not vibrating it is equivalent to the capacitance Cm known as mounting capacitance
2) when a crystal vibrates it is equivalent to RLC series circuit
It is actually a colpitts Oscillator modified into a crystal Oscillator. The crystal replaces the inductor in the colpitts Oscillator the resistance R1 and R2 provide base bias and RE with CE provide stabilization
Crystal Oscillator Working

The natural frequency of the LC circuit is made nearly equal to the natural frequency of the crystal
When the supply is switched ‘ON’, the capacitor C1 is going to charge. When the capacitor C1 is fully charged, it discharges through crystal which produces oscillation.
The frequency of the oscillation depends upon the values of C1, C2, and the RLC equivalent values of crystal. If the frequency of the oscillation is equal to its crystal resonant frequency, the circuit produces more stable oscillation.
The crystal frequency is independent of temperature.The C, feedback network, provides 180° phase shift, and also the CE amplifier provides another 180° phase shift. Hence the total phase shift is 360°, which provides positive feedback.
Therefore, continuous undamped oscillation is produced.A crystal oscillator always generates high frequency oscillations, range from 20KHz to 20MHz
Crystal Oscillator Resonant Frequency

Series Resonant Frequency
When the XL is equal to XC of the RLC circuit the impedance is equal to the resistance R [smaller]
Fs=1/2π√LCs
Parallel Resonant Frequency
When the reactance of RLC series circuit is equal to the reactance of capacitor Cp the crystal offers a very high impedance to the external circuit
Fp=1/2π√LCeq
Ceq=Cs Cp/Cs+Cp
The crystal oscillator has a very high value of Q — factor
The extremely high values of the Q factor of a crystal produces oscillations with high frequency values
Quality factor of a crystal
Q=wL/R
Crystal Oscillator Symbol

Advantages of crystal Oscillator
- Excellent frequency stability
- simple circuit
- High quality factor
Disadvantages of crystal Oscillator
- Crystal is fragile type hence it is used only in low power circuits
- Not used as tuned Oscillator
Crystal Oscillator Applications
- Phase control and timing circuit
- Trigger Circuit