# 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