Crystal oscillators are those in which a specially-cut crystal controls the frequency. CRYSTAL-CONTROLLED OSCILLATORS are the standard means used for maintaining the frequency of radio transmitting stations within their assigned frequency limits. A crystal-controlled oscillator is usually used to produce an output which is highly stable and at a very precise frequency.
As stated earlier, crystals used in electrical circuits are thin sheets cut from the natural crystal and are ground to the proper thickness for the desired resonant frequency. For any given crystal cut, the thinner the crystal, the higher the resonant frequency. The "cut" (X, Y, AT, and so forth) of the crystal means the precise way in which the usable crystal is cut from the natural crystal. Some typical crystal cuts may be seen in the figure below.
Quartz crystal cuts.
Transmitters which require a very high degree of frequency stability, such as a broadcast transmitter, use temperature-controlled ovens to maintain a constant crystal temperature. These ovens are thermostatically controlled containers in which the crystals are placed.
The type of cut also determines the activity of the crystal. Some crystals vibrate at more than one frequency and thus will operate at harmonic frequencies. Crystals which are not of uniform thickness may have two or more resonant frequencies. Usually one resonant frequency is more pronounced than the others. The other less pronounced resonant frequencies are referred to as SPURIOUS frequencies. Sometimes such a crystal oscillates at two frequencies at the same time.
of current that can safely pass through a crystal ranges from 50 to 200
milliamperes. When the rated current is exceeded, the amplitude of
mechanical vibration becomes too great, and the crystal may crack.
Overloading the crystal affects the frequency of vibration because the
power dissipation and crystal temperature increase with the amount of
Crystals as Tuned Circuits
A quartz crystal and its equivalent circuit are shown in the figure below, views (A) and (B). Capacitor C2, inductor L1, and resistor R1 in view (B) represent the electrical equivalent of the quartz crystal in view (A). Capacitance C1 in (view B) represents the capacitance between the crystal electrodes in view (A). Depending upon the circuit characteristics, the crystal can act as a capacitor, an inductor, a series-tuned circuit, or a parallel-tuned circuit.
Quartz crystal and equivalent circuit.
Quartz crystal and equivalent circuit.
At some frequency, the reactances of equivalent capacitor C1 and inductor L will be equal and the crystal will act as a series-tuned circuit. A series-tuned circuit has a minimum impedance at resonance (the figure below). Above resonance the series-tuned circuit acts INDUCTIVELY, and below resonance it acts CAPACITIVELY. In other words, the crystal unit has its lowest impedance at the series-resonance frequency. The impedance increases as the frequency is lowered because the unit acts as a capacitor. The impedance of the crystal unit also increases as the frequency is raised above the series-resonant point because the unit acts as an inductor. Therefore, the crystal unit reacts as a series-tuned circuit.
Frequency response of a crystal.
Since the series-tuned circuit acts as an inductor above the resonant point, the crystal unit becomes equivalent to an inductor and is parallel with the equivalent capacitor C1 (view (B) of the previous figure above). At some frequency above the series-resonant point, the crystal unit will act as a parallel-tuned circuit. A parallel-tuned circuit has a MAXIMUM impedance at the parallel-resonant frequency and acts inductively below parallel resonance (the figure above). Therefore, at some frequency, depending upon the cut of the crystal, the crystal unit will act as a parallel-tuned circuit.
frequency stability of crystal-controlled oscillators depends on the Q
of the crystal. The Q of a crystal is very high. It may be more than 100
times greater than that obtained with an equivalent electrical circuit.
The Q of the crystal is determined by the cut, the type of holder, and
the accuracy of grinding. Commercially produced crystals range in Q from
5,000 to 30,000 while some laboratory experiment crystals range in Q up