A quartz crystal is a tuned circuit with a very-high Q, which, along with many other desirable attributes, makes the crystal an excellent component choice for oscillators. Crystal oscillators are recognizable from their LC oscillator counterparts.1 For the Pierce oscillator, the crystal replaces the inductor in the corresponding LC-tuned circuit oscillators and not surprisingly, the crystal appears inductive in the circuit. Refer to the crystal's equivalent circuit in Fig. 5b when reviewing crystal-oscillator operation.

Upon startup, the amplitude of oscillation builds up to the point where nonlinearities in the amplifier decrease the loop gain to unity. During steady-state operation, the crystal, which has a large reactance-frequency slope (Fig. 7), is located in the feedback network at a point where it has the maximum influence on the frequency of oscillation. A crystal oscillator is unique in that the impedance of the crystal changes so rapidly with frequency that all other circuit components can be considered to be of constant reactance, this reactance being calculated at the nominal frequency of the crystal. The frequency of oscillation will adjust itself so that the crystal presents a reactance to the circuit, which will satisfy the Barkhausen phase requirement.2

Figure 9 represents a simplified oscillator circuit drawn with only the RF components, with no biasing resistors and no ground connection. In this design, the inductor has been replaced by a crystal. Looking at the Pierce crystal oscillator, the crystal will appear inductive in the circuit in order to oscillate. The Pierce crystal oscillator (Fig. 10), which is designed to look into the lowest possible impedance across the crystal terminals,3 oscillates just above the series resonant frequency of the crystal.

In the Pierce oscillator, the ground-point location has a profound effect on the performance. Large phase shifts in the resistive-capacitive (RC) networks and the need for large shunt capacitances to ground on each side of the crystal make the oscillation frequency relatively insensitive to small changes in series resistances or shunt capacitances. Additionally, the RC roll-off networks and shunt capacitances to ground provide the circuit with a high immunity to noise minimizing any transient noise spikes.3

At series resonance, the crystal appears resistive in the circuit (Fig. 11) and the phase shift around the circuit is 2-π radians (360 deg.). If the frequency of the circuit shifts above or below the series resonant frequency of the crystal, it increases or decreases the phase shift so that the total is no longer equal to 360 deg., thereby maintaining the steady-state operation at the crystal frequency. However, this only happens in an ideal circuit. Under actual circuit operation (Fig. 12), the phase shift through the transistor is typically more than 180 deg. due to increased delay and the tuned circuit typically falls short of 180 deg. Therefore, the crystal must appear inductive to provide the phase shift needed in the circuit to sustain oscillation.

Thus, the output frequency of the Pierce crystal oscillator is not at the crystal-series resonant frequency. Typically, a parallel resonant crystal is specified by frequency and load capacitance, CL. Capacitance CL is the circuit capacitance required by the crystal for operation at the desired frequency. The circuit-load capacitance is determined by external capacitors C2 and C3, transistor internal capacitance, and stray capacitance, CS. A product-design engineer can select the values of capacitors C2 and C3 to match the crystal CL using:

The printed-circuit-board (PCB) stray capacitance can be assumed to be in the range of 2 to 5 pF; it can be minimized by keeping circuit traces as short as possible. A desirable characteristic of the Pierce oscillator is the effects of stray reactances and biasing resistors appear across the capacitors C2 and C3 in the circuit rather than the crystal. If the circuit-load capacitance does not equal the crystal CL, the operating frequency of the Pierce oscillator will not be at the specified crystal frequency. For example, if the crystal CL is kept constant and the values of C2 and C3 are increased, the operating frequency approaches the crystal-series resonant frequency (i.e., the operating frequency of the oscillator decreases). Care should be used in selecting values of C2 and C3. Large values increase frequency stability but decrease the loop gain and may cause problems during oscillator startup. A trimmer capacitor can be substituted for capacitor C2 or C3 to manually tune the Pierce oscillator to the desired frequency. Capacitors with low temperature coefficients, such as NPO or COG types, should be selected for this purpose.

There is much to learn about crystals and crystal oscillators, and this article only covers the basics in an effort to assist the product design engineer in selecting a crystal. More coverage of this topic is available from the Microchip website at www.microchip.com.4 Readers are encouraged to study the design and operation of crystal oscillators because they are such important components in modern electronic designs. Product-design engineers should also consult with a crystal manufacturer about specific product design needs.

REFERENCES

  1. T.H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, Cambridge University Press, New York, NY, 1998.
  2. M.E. Frerking, Crystal Oscillator Design and Temperature Compensation, Van Nostrand Reinhold Co., New York, 1978.
  3. R.J. Matthys, Crystal Oscillator Circuits, Revised Ed., Krieger Publishing Co., Malabar, FL, 1992
  4. Application Note AN826, "Crystal Oscillator Basics and Crystal Selection for rfPIC™ and PICmicro® Devices," Microchip Technology, Chandler, AZ, Internet: www.microchip.com.