Crystal oscillator - Basics, Working, Frequency Response, Pros & Cons

Crystal oscillator Tutorial:

In this post let us discuss about the basics of crystal, How it works in electronics circuit?, equivalent circuit, frequency response and its application as a oscillator in detail….Before proceeding further, it is good to refresh about the basics of oscillator circuits how tank circuit produces oscillations?

Quartz Crystal Basics:

What is piezoelectric effect? What is piezoelectric crystal?

  • When an AC voltage is applied across certain crystalline materials like Rochelle salt, Quartz and tourmaline they will vibrate at the frequency of applied voltage.
  • Conversely when they are placed under mechanical strain to vibrate, they produce an AC voltage.
  • This effect is known as piezoelectric effect.
  • The crystals which exhibit such effect is known as piezoelectric crystals.
  • Quartz is the most commonly used piezoelectric crystal as they are readily available in nature (inexpensive).
  • Quartz crystals have great mechanical strength and simplicity in manufacture.
  • The quartz crystal can be cut in different ways. Crystal cut perpendicular to x axis is known as x-cut crystal. Crystal cut perpendicular to y axis is known as y –cut crystal. The piezoelectric properties of crystal depend upon its cut.
  • The natural frequency of the crystal is given by 

    f= \frac{K}{t}

    Here K = Constant depends upon the cut

    t = thickness of the crystal.
  • From the equation, thinner the crystal, the natural frequency is greater and vice versa.



Quartz Crystal Working:

To use in the electronic circuits, the crystal is placed in between two metal plates.
This setup will form as a capacitor with crystal as the dielectric medium. When the ac voltage is applied across the plates, the crystal will vibrate at the frequency of applied voltage. When the frequency of applied voltage is made equal to the natural frequency of crystal, resonance will take place and crystal vibrates at maximum value.

Crystal Equivalent Circuit:

  • As shown below, the crystal action can be represented by an equivalent electrical circuit.
  • When the crystal is not vibrating, it is equivalent to capacitance Cm.
    (Because it has two metal plates separated by a dielectric medium). This capacitance is called as mounting capacitance.
  • When the crystal vibrates, it is equivalent to R- L-C series circuit. Here
    L = electrical equivalent of crystal mass,
    C = electrical equivalent of elasticity,
    R = electrical equivalent of mechanical friction,
    Cm = Mounting capacitance.

Frequency Response of the Crystal:

  • In lower range of frequencies, the crystal impedance is controlled by high values of XCm and XC. (Remember that

    Xc = \frac{1}{2\pi fC}

     

    {X_{L}} = 2\pi fL

  • It means, at lower frequencies, the circuit impedance is high and capacitive in nature.
  • As the frequency is increased, R-L-C branch approaches its resonant frequency.
  • At some point, the reactance XL will be equal to XC (ie, impedance is very low).
  • Now the crystal acts as a resonant circuit. This frequency is called as series resonant frequency fs. It is given by 

    f_{s}=\frac{1}{2\pi \sqrt{LC}}


    Further increasing the frequency, the net reactance of branch RLC becomes inductive and equal to XCm. The crystal now acts as a parallel resonant circuit and provides very high impedance. This frequency is known as parallel resonant frequency fp.

    f_{s}=\frac{1}{2\pi \sqrt{LC_{T}}}


    C_{T}=\frac{C\times Cm}{C+Cm}

Transistor Based Crystal Oscillator:




The following figure shows the transistor crystal oscillator.
It is the modification of collpit’s oscillator. (ie, the inductor is replaced with the crystal). Here the crystal acts as a parallel tuned circuit. At parallel resonance the crystal impedance is maximum. So there is maximum voltage drop across C1 and will allow max energy transfer through feedback circuit at fp.

Note that, transistor provides 180° phase shift and capacitor voltage divider will provide further 180° phase shift ( positive feedback)

Advantages of Crystal Oscillator:

  1. They have a high order of frequency stability
  2. Crystal is having very high quality factor (Q). The Q factor of the crystal may be as high as 10000 compared to about 100 LC tank.

Disadvantages of Crystal Oscillator:

  1. They are fragile. So they can only be used in low power circuits.
  2. The frequency of oscillations cannot be changed appreciably.

Thanks for reading about crystal oscillator.... Please leave your comments below....


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