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AN826

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

Microchip Technology 

FIGURE 4: SHUNT-C COUPLED LC SERIES

RESONATOR

Quality Factor

Q (quality factor) is the ratio of stored energy in a reac-

tive component such as a capacitor or inductor to the

sum total of all energy losses. An ideal tuned circuit

constructed of an inductor and capacitor will store

energy by swapping current from one component to the

next. In an actual tuned circuit, energy is lost through

real resistance. The equation for a tuned circuit Q is

reactance divided by resistance:

Q = X---

R

We are concerned about circuit Q because it defines

the bandwidth that a tuned circuit will operate. Band-

width is defined as the frequency spread between the

two frequencies at which the current amplitude

decreases to 0.707 (1 divided by the square root of 2)

times the maximum value. Since the power consumed

by the real resistance, R, is proportionally to the square

of the current, the power at these points is half of the

maximum power at resonance [2]. These are called the

half-power (-3dB) points.

For Q values of 10 or greater, the bandwidth can be cal-

culated:

BW = --f-

Q

Where f is the resonant frequency of interest. Relatively

speaking, a high-Q circuit has a much narrower band-

width than a low-Q circuit. For oscillator operation, we

are interested in the highest Q that can be obtained in

the tuned circuit. However, there are external influ-

ences that effect circuit Q.

The Q of a tuned circuit is effected by external loads.

Therefore we differentiate between unloaded and

loaded Q. Unloaded Q defines a circuit that is not influ-

enced by an external load. Loaded Q is a circuit influ-

enced by load.

OSCILLATOR CIRCUITS

There are limitless circuit combinations that make up

oscillators. Many of them take on the name of their

inventors: Butler, Clapp, Colpitts, Hartley, Meacham,

Miller, Seiler, and Pierce, just to name a few. Many of

these circuits are derivatives of one another. The

reader should not worry about a particular oscillator’s

nomenclature, but should focus on operating principles

© 2002 Microchip Technology Inc.

AN826

[4]. No one circuit is universally suitable for all applica-

tions [5]. The choice of oscillator circuit depends on

device requirements.

Now let’s add circuitry to the simplified oscillator block

diagram of Figure 2. Figure 5 shows a simplified oscil-

lator circuit drawn with only the RF components, no

biasing resistors, and no ground connection [3]. The

inverting amplifier is implemented with a single transis-

tor. The feedback mechanism depends upon which

ground reference is chosen. Of the numerous oscillator

types, there are three common ones: Pierce, Colpitts,

and Clapp. Each consists of the same circuit except

that the RF ground points are at different locations.

FIGURE 5: SIMPLIFIED OSCILLATOR

CIRCUIT WITHOUT RF GROUND

The type of oscillator that appears on the PICmicro®

microcontroller is the Pierce and the type implemented

on the rfPIC12C509AG/509AF transmitter is the Col-

pitts.

Pierce Oscillator

The Pierce oscillator (Figure 6) is a series resonant

tuned circuit. Capacitors C2 and C3 are used to stabi-

lize the amount of feedback preventing overdrive to the

transistor amplifier.

The Pierce oscillator has many desirable characteris-

tics. It will operate over a large range of frequencies

and has very good short-term stability [6].

FIGURE 6: PIERCE OSCILLATOR

Colpitts Oscillator

The Colpitts oscillator (Figure 7) uses a parallel reso-

nant tuned circuit. The amplifier is an emitter-follower.

Feedback is provided via a tapped capacitor voltage

divider (C2 and C3). Capacitors C2 and C3 form a

capacitive voltage divider that couples some of the

energy from the emitter to the base.

DS00826A-page 3

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