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AN826

Crystal Oscillator Basics and Crystal Selection for rfPICTM and PICmicro® Devices

Microchip Technology 

AN826

FIGURE 7: COLPITTS OSCILLATOR

The Colpitts oscillator functions differently from the

Pierce oscillator. The most important difference is in the

biasing arrangement. Transistor biasing resistors can

increase the effective resistance of the tuned circuit

(LC or crystal) thus reducing its Q and decreasing the

loop gain [5].

The parallel resonant circuit formed by L1 in parallel

with C2 and C3 determines the frequency of the oscil-

lator.

CRYSTAL BASICS

The discussion up to this point has been on basic oscil-

lators using inductors and capacitors for the tuned cir-

cuit. The main disadvantage of LC oscillators is that the

frequency can drift due to changes in temperature,

power-supply voltage, or mechanical vibrations. Plac-

ing a LC oscillator on frequency sometimes requires

manual tuning.

We now look at how a quartz crystal operates internally

and later we will see how they operate in crystal oscil-

lators. Understanding how the quartz crystal operates

will give the design engineer an understanding of how

they behave in an oscillator circuit.

Quartz crystals have very desirable characteristics as

oscillator tuned circuits. The natural oscillation fre-

quency is very stable. In addition, the resonance has a

very high Q ranging from 10,000 to several hundred

thousand. In some cases values of 2 million are achiev-

able. The crystal merits of high Q and stability are also

its principle limitations. It is difficult to tune (pull) a crys-

tal oscillator [3] (more on the topic of crystal pulling

later).

The practical frequency range for Fundamental mode

AT-cut crystals is 600 kHz to 30 MHz. Crystals for fun-

damental frequencies higher than 30 to 40 MHz are

very thin and therefore fragile. Crystals are used at

higher frequencies by operation at odd harmonics

(overtones) of the fundamental frequency. Ninth over-

tone crystals are used up to about 200 MHz, the prac-

tical upper limit of crystal oscillators [3]. This

Application Note will limit our discussion to Fundamen-

tal mode crystal operation.

Piezoelectric Effect

Quartz is a piezoelectric material. When an electric

field is placed upon it, a physical displacement occurs.

Interestingly enough, we can write an equivalent elec-

trical circuit to represent the mechanical properties of

the crystal.

Equivalent Circuit

The schematic symbol for a quartz crystal is shown in

Figure 8 (A). The equivalent circuit for a quartz crystal

near fundament resonance is shown in Figure 8 (B).

The equivalent circuit is an electrical representation of

the quartz crystal’s mechanical and electrical behavior.

It does not represent actual circuit components. The

crystal is, after all, a vibrating piece of quartz. The com-

ponents C1, L1, and R1 are called the motional arm and

represents the mechanical behavior of the crystal ele-

ment. C0 represents the electrical behavior of the crys-

tal element and holder.

FIGURE 8: CRYSTAL EQUIVALENT

CIRCUIT

The equivalent circuit in Figure 8 (B) represents one

Oscillation mode. For the types of crystal oscillators we

are interested in, we will focus on Fundamental mode

crystals. A more complex model can represent a crystal

through as many overtones as desired. For the sake of

simplicity this simple model is usually employed and

different values are used to model Fundamental or

Overtone modes. Spurious resonances occur at fre-

quencies near the desired resonance. In a high quality

crystal, the motional resistance of Spurious modes are

at least two or three times the primary resonance resis-

tance and the Spurious modes may be ignored [3].

C1 represents motional arm capacitance measured

in Farads. It represents the elasticity of the quartz, the

area of the electrodes on the face, thickness and shape

of the quartz wafer. Values of C1 range in femtofarads

(10-15 F or 10-3 pF).

L1 represents motional arm inductance measured in

Henrys. It represents the vibrating mechanical mass of

the quartz in motion. Low frequency crystals have

DS00826A-page 4

© 2002 Microchip Technology Inc.

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