Mumbai University > Electronics and telecommunication engineering > Sem 3 > Analog electronics 1

Marks: 5M

Years: May 15, May 16

Principle of crystal oscillators:

Certain materials such as quartz exhibit a unique property called "piezo electric’’ property.

• It states that if mechanical force is applied to a quartz crystal then it generates electric potential.

• Also if electric field is applied to a crystal it vibrates mechanically.

• If we apply mechanical vibrations to a quartz crystal then under proper operating conditions we can obtain electrical oscillations from it.

Frequency stability:

The biggest advantage of using a crystal oscillator is its high frequency stability. The frequency of a crystal oscillator remains stable inspite of changes in temperature, voltage, humidity or other parameters. Equivalent Circuit of a Crystal:

• The ac equivalent circuit of a crystal is as shown in Fig5. It shows that the crystal is equivalent to a resonant circuit.

• In the ac equivalent circuit of a vibrating crystal, the internal frictional losses are represented by a resistance R.

• Mass of the crystal and hence its inertia is represented by L and stiffness under the vibrating condition is represented by capacitor C.

• Due to the mounting arrangement shown in Fig5 the crystal is equivalent to a capacitance denoted by C’ in the equivalent circuit. C' is called as the mounting capacitance.

Resonant frequencies:

• There are two resonant circuits existing in the ac equivalent circuit of the crystal. RLC form a series resonant circuit and RLC in parallel with C' will form a parallel resonant circuit. The resonant frequency of the series RLC series circuit is given by:

$f_s= \frac{1}{(2π√LC)}$

This is with an assumption that quality factor Q is very large. The resonant frequency of the parallel resonant frequency formed by RLC and C’ is given by,

$f_p = \frac{1}{(2π√(LC_eq ))}$

Where, $C_eq =\frac{ CC'}{(C + C')}$