Crystal Oscillator

The crystal oscillator is a quartz crystal used as a frequency selective element. The quartz crystal is also known as piezoelectric crystal. Hence the oscillator circuit containing piezoelectric crystal is called a crystal oscillator. It has two electrodes that supply signals to the crystal. Crystal oscillators have high-frequency stability and a high-Quality factor compared to RC and LC tuned circuit oscillators. It is considered one of the highly stable oscillators suitable for high-frequency applications.

What is a crystal?

A crystal is a solid substance with atoms and molecules tightly packed in a three-dimensional shape. Most solid objects have their resonant and frequency of vibrations. The object made of the elastic material with the resonant and frequency of vibrations is crystal. The resonant frequency also depends on the speed of the sound in a solid object, such as steel. Steel is a metal alloy that has a high speed of sound.

The advantages of using quartz crystals are as follows:

Higher purity
Easy handling
Low cost
Excellent raw material
Good healing power
Easily available

The circuit of a crystal oscillator is shown below:

The quartz crystal is attached in parallel with the resonant circuit of the oscillator. The resonant circuit includes a resistor, capacitor, and an inductor connected in series. Co is the static capacitance associated with the quartz crystal.

Principle

The applied voltage across the crystal helps it to vibrate at its natural frequency. The vibrations produced by the piezoelectric crystal get converted into oscillations.

Working

The input signal is applied to crystal oscillator circuit. It consists of a crystal and the resonance circuit, as shown above. The signal first passes through the electrodes of the quartz crystal. It changes its shape due to the applied voltage. When the voltage is removed, the crystal returns to its original shape. The crystal generates a small voltage before returning to its original position.

The piezoelectric crystal uses the electrical signal to produce vibrations. It means that the crystal converts electrical energy into mechanical energy. The vibrations get converted into oscillations of constant frequency. The other terminal converts the mechanical energy back to electrical energy.

The produced oscillations of constant frequency act like an RLC circuit. Once a crystal is adjusted to a specific frequency and other environmental factors, it starts maintaining a high frequency or high-Quality factor.

The crystal oscillators cover frequencies below 1000 Hz and above 200M Hz.

Static capacitance

C_o is the static capacitance connected in parallel with the RLC combination, as shown above.

The resistor, inductor, and capacitor are connected in series. The impedance can be represented as:

Z(s) = (1/sC₁ + sL₁ + R₁)

Another capacitor Co was connected in parallel.

Z(s) = (1/sC₁ + sL₁ + R₁) || 1/sC_O

Putting the value of ?_s in the above equation, we get:

Where,

?_s is the series resonant angular frequency

?_p in series resonant angular frequency

History

The piezoelectric crystal was first developed by two French physicists P. Curie and Jacques in 1880.
In 1921, the first quartz oscillator was developed by an engineer and an American physicist Walter G Cady. There were also other innovators of the quartz crystal including Louis Essen, an English physicist.
In 1928, Canadian engineer Warren Marrison of the Bell laboratories developed the first quartz crystal clock.
After that, quartz crystal clock was replaced by pendulum clocks, which were further replaced by the atomic clocks in 1950.
The demand for crystals increased during World War II for their use in radios and radar.
The Bell laboratories developed a synthetic way to develop quartz crystals to overcome the rising demand for quartz crystals.
In 1970, most of the crystals used in the electronic industry were synthetic.
In 1968, a photolithographic process was used for manufacturing such crystals. It was developed by Juergen Staudte. It allows the manufacturing of quartz crystals in small size, which were easily portable.

Stability analysis of Crystal oscillators

The frequency stability of a crystal is based on the Quality-factor. The oscillator's Q factor is inversely related to its frequency. The factor that influences the Q-factor includes temperature, mechanical stress, aging, and radiation damage.

Let's discuss these factors in detail.

Temperature

The temperature variations can directly influence the operating frequency of the oscillator. The crystal ovens are used in such cases to stabilize the temperature. The crystal oven is a temperature-controlled chamber that helps the crystal to maintain a constant temperature to avoid any fluctuations in the frequency. Different types of compensators are used along with the crystal ovens, such as microcontroller compensators.

Mechanical Stress

The electrodes, crystal, and bonding materials can generate stress in oscillators. It occurs due to the expansion or contraction of the bonding material, defects or impurities in the crystal, or by the effect of gravity on the crystal. Other types of mechanical stress are vibrations, change in atmospheric pressure, and noise. The careful design and transducers in the oscillator can help overcome mechanical stress.

Aging

The gradual deformation of the crystal with time is known as aging. It results in the frequency changes in the oscillator. The differences in the packaging of the electrodes, diffusion of impurities, etc., are the reasons that cause aging in the oscillator. Various metals are used to prevent aging, such as gold, silver, and aluminum. The gold handles strong mechanical shocks but does not form oxides. Silver and aluminum are used for making electrodes and easily form oxides.

Radiation Damage

The crystals are sensitive to the incident radiations. It can be reduced by heating the crystal at high temperature of about 400 degrees Celsius in an electric field in a hydrogen free environment. Such crystal responds slowly to the incident radiations.

Frequency Accuracy

The frequency accuracy of the crystal oscillator lies between the range 10^-6 and 10^-7. The range includes all other environmental factors, such as temperature changes and aging.

The stabilities of the precision quartz oscillator lie between the range 10^-10 and 10^-12. The precision quartz oscillators are protected from any external environmental disturbances. It also works at a constant temperature with very few frequency fluctuations and long-term accuracy.

Advantages

The advantages of crystal oscillator are as follows:

Inexpensive
It is due to the compact size and low of the quartz crystals used in the oscillator.
Low phase noise
The crystal oscillators vibrate in only one phase and thus have low noise as compared to other oscillators.
High Q factor
The high Q factor signifies the frequency stability and low losses in a circuit. Crystal oscillators have a high Q factor due to the high range of operating frequencies.
High stability
The crystal has high stability due to the presence of quartz crystal.
High operating frequency
It is also due to piezoelectric crystals connected in parallel with the resonance circuit.

Disadvantages

The disadvantages of crystal oscillator are as follows:

The low operating frequency crystals are not readily available.
It is best suitable for high-frequency applications.

Numerical Examples

Example: In the equivalent circuit of the crystal oscillator, L = 2H, C1 = 0.04p Farads, Co =10p Farads, and R = 2000 Ohms. Find the series and parallel resonant angular frequency.

Solution:

Given: L = 2H

C1 = 0.04p Farads

= 0.04 x 10^-12 F

= 4 x 10^-14 Farads

Co =10p Farads

= 10 x 10^-12 F

=10^-11 Farads

R = 2000 Ohms

F_s = Series resonant angular frequency