Pierce oscillator

The Pierce oscillator is a type of electronic oscillator particularly well-suited for use in piezoelectric crystal oscillator circuits. Named for its inventor, George W. Pierce (1872–1956), the Pierce oscillator is a derivative of the Colpitts oscillator. Virtually all digital IC clock oscillators are of Pierce type, as the circuit can be implemented using a minimum of components: a single digital inverter, one resistor, two capacitors, and the quartz crystal, which acts as a highly selective filter element. The low manufacturing cost of this circuit and the outstanding frequency stability of the quartz crystal give it an advantage over other designs in many consumer electronics applications. If the circuit consists of perfect lossless components, the signal on C1 and C2 will be proportional to the impedance of each, and the ratio of the signal voltages at C1 and C2 will be C2/C1. With C1 and C2 equal size (a common configuration), the current in C1 to C2 would be exactly equal, but out of phase, requiring no current from the amplifier or voltage gain from the amplifier, and allowing a high output impedance amplifier, or the use of an isolating series resistance in the amplifier output. Normal crystals are lossless enough to make this a reasonable approximation: the amplifier does not drive the resonant circuit, but merely stays in sync with it, providing enough power to match losses. A series resistor is occasionally shown in the amplifier output. When used, a series resistor reduces loop gain, and amplifier gain must be increased to restore total loop gain to unity. The purpose of using such a resistor in the amplifier circuit is to increase phase shift at startup, or when the crystal circuit is pulled out of phase by loading, and to eliminate the effects of amplifier non-linearity and of crystal overtones or spurious modes. It is not part of the basic operation of the Pierce topology. R1 acts as a feedback resistor, biasing the inverter in its linear region of operation and effectively causing it to function as a high-gain inverting amplifier.