Crystal Oscillator |
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Crystal Oscillators
One of the most important features of an oscillator is its Frequency Stability, or in other words its ability
to provide a constant frequency output under varying conditions. Some of the factors that affect the frequency stability of an oscillator
include: temperature, variations in the load and changes in the power supply. Frequency stability of the output signal can be improved by
the proper selection of the components used for the resonant feedback circuit including the amplifier but there is a limit to the stability
that can be obtained from normal LC and RC tank circuits. For very high stability a
quartz crystal is generally used as the frequency determining device to produce another types of oscillator circuit known
generally as Crystal Oscillators.
When a voltage source is applied to a small thin piece of crystal quartz, it begins to change shape producing a characteristic
known as the Piezo-electric Effect. This piezo-electric effect is the property of a crystal by which an electrical charge
produces a mechanical force by changing the shape of the crystal and vice versa, a mechanical force applied to the crystal produces an electrical
charge. Then, piezo-electric devices can be classed as
Transducers as they convert energy of one kind into energy of another.
This piezo-electric effect produces mechanical vibrations or oscillations which are used to replace the LC tank circuit
and can be seen in many different types of crystal substances with the most important of these for electronic circuits being the quartz minerals
because of their greater mechanical strength.
The quartz crystal used in Crystal Oscillators is a very small, thin piece or wafer of cut quartz
with the two parallel surfaces metallized to make the electrical connections. The physical size and thickness of a piece of quartz crystal
is tightly controlled since it affects the final frequency of oscillations and is called the crystals "characteristic frequency". Then once
cut and shaped the crystal can not be used at any other frequency. The crystals characteristic or resonant frequency is inversely proportional
to its physical thickness between the two metallized surfaces. A mechanically vibrating crystal can be represented by an equivalent electrical
circuit consisting of low Resistance, large Inductance and small Capacitance as shown below.
Quartz Crystal
A quartz crystal has a resonant frequency similar to that of a electrically tuned tank circuit but with a much higher
Q factor due to its low resistance, with typical frequencies ranging from 4kHz to 10MHz. The cut of the crystal
also determines how it will behave as some crystals will vibrate at more than one frequency. Also, if the crystal is not of a parallel or
uniform thickness it have two or more resonant frequencies having both a fundamental frequency and harmonics such as second or third
harmonics. However, usually the fundamental frequency is more stronger or pronounced than the others and this is the one used. The equivalent
circuit above has three reactive components and there are two resonant frequencies, the lowest is a series type frequency and the highest a
parallel type resonant frequency.
We have seen in the previous tutorials, that an amplifier circuit will oscillate if it has a loop gain greater or equal to 1
and it has positive feedback. In a Crystal Oscillator circuit the oscillator will oscillate at the crystals fundamental series
resonant frequency as the crystal always wants to oscillate when a voltage source is applied to it. However, it is also possible to "tune" a
crystal oscillator to any even harmonic of the fundamental frequency, (2nd, 4th, 8th etc.) and these are known generally as
Harmonic Oscillators while Overtone Oscillators vibrate at odd multiples of the fundamental frequency,
3rd, 5th, 11th etc). Generally, crystal oscillators that operate at overtone frequencies do so using their series resonant frequency.
Colpitts Crystal Oscillator
The design of a Crystal Oscillator is very similar to the design of the
Colpitts Oscillator we looked at in the previous tutorial,
except that the LC tank circuit has been replaced by a quartz crystal as shown below.
Colpitts Crystal Oscillator
These types of Crystal Oscillators are designed around the common emitter amplifier stage of a
Colpitts Oscillator. The input signal to the base of the transistor is inverted at the transistors output. The output
signal at the collector is then taken through a 180o phase shifting network which includes the crystal operating in a series
resonant mode. the output is also fed back to the input which is "in-phase" with the input providing the necessary positive feedback.
Resistors, R1 and R2 bias the resistor in a
Class A operation and resistor Re
is chosen so that the loop gain is slightly greater than unity.
Capacitors, C1 and C2 are made as large as possible in order that
the frequency of oscillations can approximate to the series resonant mode of the crystal and is not dependant upon the values of these
capacitors. The circuit diagram above of the Colpitts Crystal Oscillator circuit shows that capacitors,
C1 and C2 shunt the output of the transistor and which reduces the feedback signal.
Therefore, the gain of the transistor limits the maximum values of C1 and C2. The output
amplitude should be kept low in order to avoid excessive power dissipation in the crystal otherwise could destroy itself by excessive vibration.
Pierce Oscillator
Another common design of crystal oscillator is that of the Pierce Oscillator. The Pierce oscillator is
a crystal oscillator that uses the crystal as part of its feedback path and therefore has no resonant tank circuit. The Pierce Oscillator
uses a JFET as its amplifying device as it provides a very high input impedance with the crystal connected between the output Drain terminal
and the input Gate terminal as shown below.
Pierce Crystal Oscillator
In this simple circuit, the crystal determines the frequency of oscillations and operates on its series resonant frequency
giving a low impedance path between output and input. There is a 180° phase shift at resonance, making the feedback positive. The amplitude of
the output sine wave is limited to the maximum voltage range at the Drain terminal. Resistor, R1 controls the amount
of feedback and crystal drive while the voltage across the radio frequency choke, RFC reverses during each cycle.
Most digital clocks, watches and timers use a Pierce Oscillator in some form or other as it can be implemented using the minimum of components.
Microprocessor Clocks
We can not finish a Crystal Oscillators tutorial without mentioning something about Microprocessor clocks.
Virtually all microprocessors, microcontrollers, PICs and CPU's generally operate using a Crystal Quartz Oscillator as its frequency
determining device to generate their clock waveform because as we already know, crystal oscillators provide the highest accuracy and frequency
stability compared to Resistor/Capacitor or Inductor/Capacitor oscillators. The CPU clock dictates how fast the processor can process the data
and a microprocessor having a clock speed of 1MHz means that it can process data internally 1 million times a second at every clock cycle.
Generally all that's needed to produce a microprocessor clock waveform is a crystal and two ceramic capacitors of values ranging between 15 to
33pF as shown below.
Microprocessor Oscillator
Most microprocessors, microcontrollers and PICs have two oscillator pins labelled OSC1 and
OSC2 to connect to an external quartz crystal, RC network or even a Ceramic resonator.
In this application the Crystal Oscillator produces a train of continuous square wave pulses whose frequency is controlled
by the crystal which inturn regulates the instructions that controls the device. For example, the master clock and system timing.
Example No1
A series resonant crystal has the following values after being cut, R = 1kΩ,
C = 0.05pF and L = 3H. Calculate the fundamental frequency of oscillations
of the crystal.
The frequency of oscillations for Crystal Oscillators is given as:
Then the fundamental frequency of oscillations for the crystal is given as 411 kHz
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