# Pierce oscillator

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Pierce oscillator

The Pierce oscillator is a type of electronic oscillator circuit particularly well-suited for implementing 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, two resistors, two capacitors, and the quartz crystal, which acts as a highly selective filter element. The low manufacturing cost of this circuit, combined with the outstanding frequency stability of the quartz crystal, give it an advantage over other designs in many consumer electronics applications.

Operation

Biasing resistor

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.To see this, assume the inverter is ideal, with infinite input impedance and zero output impedance; this resistor forces the input and output voltages to be equal. Hence the inverter will neither be fully on nor off, but in the transition region where it has gain.

Resonator

The crystal in combination with "C"1 and "C"2 forms a pi network band-pass filter, which provides a 180 degree phase shift and a voltage gain from the output to input at approximately the resonant frequency of the crystal. To understand the operation of this, it can be noted that at the frequency of oscillation, the crystal appears inductive; thus it can be considered a large inductor with a high Q. The combination of the 180 degree phase shift (i.e. inverting gain) from the pi network and the negative gain from the inverter results in a positive loop gain (positive feedback), making the bias point set by R1 unstable and leading to oscillation.

Isolation resistor

A second resistor could be used between the output of the inverter and the crystal to isolate the inverter from the crystal network. This would also add additional phase shift to "C"1.PDF| [http://www.fairchildsemi.com/an/AN/AN-340.pdf Fairchild Semiconductor Corporation, HCMOS Crystal Oscillators: Fairchild Semiconductor Application Note 340, May 1983, pp. 1-2] |45.4 KiB ]

The total capacitance seen from the crystal looking into the rest of the circuit is called the "load capacitance". When a manufacturer makes a "parallel" crystal, a technician uses a Pierce oscillator with a particular load capacitance (often 18 or 20 pF) while trimming the crystal to oscillate at exactly the frequency written on its package.

To get the same frequency performance, one must then make sure that the capacitances in the circuit match this value specified in the crystal's data sheet. Load capacitance "C"L can be calculated from the series combination of "C"1 and "C"2, taking into account "C"i and "C"o, the input and output capacitance of the inverter, and "C"s, the stray capacitances from the oscillator, PCB layout, and crystal case (typically 3-9 pF): [cite web
url=http://www.abracon.com/Support/qtzcry_glossary.pdf
title=Quartz crystal glossary of terms
accessdate=2007-06-06
format=PDF
publisher=Abracon Corporation
] [cite web
url=http://www.euroquartz.co.uk/pdf/cx-6v-sm-800k.pdf#page=2
title=CX miniature crystals
accessdate=2007-06-06
format=PDF
publisher=Euroquartz
] [ [http://www.foxonline.com/tech3031.htm Fox Electronics Technical Information ] ] [cite web
accessdate=2008-08-26
format=PDF
publisher=Crystek Crystals Corp.
]

: $C_L = \left\{ \left[C_1 + C_i\right] imes \left[C_2 + C_o\right] over \left[C_1 + C_i + C_2 + C_o\right] \right\} + C_mathrm\left\{S\right\}$

When a manufacturer makes a "series" crystal, a technician uses a different tuning procedure.When such a crystal is used in a Pierce oscillator,the Pierce oscillator (as always) drives the crystal at nearly its parallel resonance frequency.But that frequency is few kilohertz higher than the series resonant frequency printed on the package of a "series" crystal.

Increasing the "load capacitance" slightly decreases the frequency generated by a Pierce oscillator, but never enough to reduce it all the way down to the series resonant frequency.

References

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