Crystal Oscillator: Circuit, Frequency & Working Principle

In the previous lecture, we discussed what oscillators are and the types of oscillators in detail. Now in this lecture, we discuss the Crystal Oscillator in very detail. So let’s see it.

The principle of Crystal Oscillator

Certain materials such as quartz exhibit a unique property called piezoelectric property.

It states that if mechanical force is applied to a quartz crystal then it generates electric potential. Also if the 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 of Crystal Oscillator

The biggest advantage of a crystal oscillator is its high-frequency stability. The frequency of a crystal oscillator remains stable in spite of changes in temperature, voltage, humidity, or other parameters.

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Equivalent Circuit of a Crytal Oscillator

The AC equivalent circuit of a crystal oscillator is shown in the figure below. 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.

The 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 the above figure, the crystal is equivalent to a capacitance denoted by C’ in the equivalent circuit. C’s is called the mounting capacitance.

Resonant Frequencies:

These are two resonant circuits existing in the AC equivalent circuit of the crystal RLC that form a series resonant circuit and RLC in parallel with C’ will form a parallel resonant circuit. The resonant frequency of the series R-L-C series circuit is given by:

\mathbf{f_s = \frac{1}{2\pi \sqrt{LC}}}

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

\mathbf{f_p = \frac{1}{2\pi \sqrt{LC_{eq}}} \; where, C_{eq}= \frac{CC'}{(C + C')}}

Note: The parallel resonant frequency fp can be varied by varying the value of C'. The parallel resonant frequency fp is always higher than the series resonant frequency fs.

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Also Read: What is Oscillator? Types of Oscillators

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Types of Crystal Oscillator

The two types of crystal oscillators which we are going to study are:

1. Pierce crystal oscillator
2. Miller crystal oscillator

Pierce crystal oscillator

The crystal is made to operate as an inductance. This is possible if the frequency of oscillations ω is adjusted between ω_s and ω_p as shown in the figure below.

The basic operation of the Pierce crystal oscillator is the same as that of Colpitt’s oscillator.

RFC is a radio frequency choke that connects the DC supply to the circuit but isolates the DC supply from the high-frequency oscillations generated in the tank circuit (feedback network).

Miller crystal oscillator

If the Hartley oscillator circuit is modified by replacing one of the inductors with a crystal then we get the Miller crystal oscillator configuration shown in the below figure.

The crystal acts like an inductor as the frequency of oscillations ω is adjusted between ω_s and ω_p as shown in the below figure.

The Miller Crystel oscillator using FET is also shown in the below figure.

C_gd is the gate to drain the capacitance of FET. The biggest advantage of the Pierce and Miller crystal oscillator is the frequency stability.

The frequency will remain absolutely stable in spite of variations in the supply voltage or temperature, or the parameters of the active device.

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Also Read: Barkhausen Criterion for Oscillation

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Modes of Operation in Crystal Oscillator

The piezoelectric crystals can oscillate in one of the following two modes.

1. Fundamental Mode of crystal oscillator
2. Overtone Mode of crystal oscillator

Fundamental Mode of crystal oscillator

• In the fundamental mode, the crystal oscillator oscillates at the fundamental crystal frequency.
• The fundamental frequency depends on the crystal’s mechanical dimensions, type of cut, and other factors. It is inversely proportional to the thickness of the crystal slab.
• If we want to increase the fundamental frequency we have to reduce the thickness of the crystal slab.
• However, a crystal slab can not be cut too thin due to the possibility of fracturing. Hence there is an upper limit on the fundamental frequency.
• For most crystals, the maximum fundamental frequency is about 20 MHz.

Overtone Mode of crystal oscillator

• For higher frequencies than 20 MHz, we can not use the fundamental mode so the crystal is operated in the overtone mode.
• Overtones are approximately integer multiples of the fundamental frequency. For example twice, three times, and four times the fundamental frequency.
• The overtone frequencies are usually the odd multiples of the fundamental frequency. However, this is not always true.

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Advantages of Crystal Oscillator

Following are some of the advantages of crystal oscillators.

• Very high-frequency stability.
• Very low-frequency drift due to changes in temperature and other parameters.
• It is possible to obtain very high, precise, and stable frequencies of oscillations.
• The Q is very high.
• It is possible to obtain frequencies, higher than the fundamental frequency by operating the crystal in the overtone mode.

Disadvantages of Crystal Oscillator

• These are suitable for high-frequency applications.
• Crystals of low fundamental frequencies are not easily available.

Applications of Crystal Oscillators

• As a crystal clock in microprocessors.
• In the frequency synthesizers.
• In the radio and TV transmitters.
• In special types of receivers.

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