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Introduction to Quartz Frequency Standards

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Introduction to Quartz Frequency Standards - Oscillator Basics

Figure 1 is a greatly simplified circuit diagram that shows the basic elements of a crystal oscillator [1-3]. The amplifier of a crystal oscillator consists of at least one active device, the necessary biasing networks; and may include other elements for band limiting, impedance matching, and gain control. The feedback network consists of the crystal resonator, and may contain other elements, such as a variable capacitor for tuning.

Figure 1
Figure 1. Crystal Oscillator - simplified circuit diagram.

The frequency of oscillation is determined by the requirement that the closed loop phase shift = 2np, where n is an integer, usually 0 or 1. When the oscillator is initially energized, the only signal in the circuit is noise. That component of noise, the frequency of which satisfies the phase condition for oscillation, is propagated around the loop with increasing amplitude. The rate of increase depends on the excess loop gain and on the bandwidth of the crystal network. The amplitude continues to increase until the amplifier gain is reduced, either by the nonlinearities of the active elements (in which case it is self limiting) or by an external level-control method.

At steady state, the closed-loop gain = 1. If a phase perturbation Df occurs, the frequency of oscillation must shift by a Df in order to maintain the 2np phase condition. It can be shown that for a series-resonance oscillator

Equation 1
where QL is the loaded Q of the crystal in the network [1]. ("Crystal" and "resonator" are often used interchangeably with "crystal unit," although "crystal unit" is the official name. See references 3 to 6 for further information about crystal units.) Crystal oscillator design information can be found in references 1, 2, 5 and 7. The abbreviation for crystal oscillator is XO.