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AN826

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

Microchip Technology 

thicker and larger quartz wafers and range in a few

Henrys. High frequency crystals have thinner and

smaller quartz wafers and range in a few millihenrys.

R1 represents resistance measured in ohms. It repre-

sents the real resistive losses within the crystal. Values

of R1 range from 10 Ω for 20 MHz crystals to 200K Ω

for 1 kHz crystals.

C0 represents shunt capacitance measured in Far-

ads. It is the sum of capacitance due to the electrodes

on the crystal plate plus stray capacitances due to the

crystal holder and enclosure. Values of C0 range from

3 to 7 pF.

Example Crystal

Now that each of the equivalent components of a crys-

tal have been introduced, let’s look at an example crys-

tal’s electrical specifications that you would find in a

crystal data sheet or parts catalog. See Table 1.

TABLE 1: EXAMPLE CRYSTAL

SPECIFICATIONS

Parameter

Value

Frequency (fXTAL)

Load Capacitance (CL)

Mode of Operation

Shunt Capacitance (C0)

Equivalent Series

Resistance (ESR)

8.0 MHz

13 pF

Fundamental

7 pF (maximum)

100 Ω (maximum)

When purchasing a crystal, the designer specifies a

particular frequency along with load capacitance and

mode of operation. Notice that shunt capacitance C0 is

typically listed as a maximum value, not an absolute

value. Notice also that motional parameters C1, L1, and

R1 are not typically given in the crystal data sheet. You

must get them from the crystal manufacturer or mea-

sure them yourself. Equivalent Series Resistance

(ESR) should not be confused with R1.

For our example crystal the equivalent circuit values

are:

TABLE 2: EXAMPLE EQUIVALENT CIRCUIT

CRYSTAL VALUES

Equivalent Component

Value

C0

4.5 pF

C1

0.018 pF

L1

22 mH

R1

30 Ω

In Table 2 shunt capacitance is given as an absolute

value. Shunt capacitance can be measured with a

capacitance meter at a frequency much less than the

fundamental frequency.

© 2002 Microchip Technology Inc.

AN826

Crystal Resonant Frequencies

A crystal has two resonant frequencies characterized

by a zero phase shift. The first is the series resonant,

fs, frequency. The equation is:

fs

=

-----------1------------

2π L1C1

You may recognize this as the basic equation for the

resonant frequency of an inductor and capacitor in

series. Recall that series resonance is that particular

frequency which the inductive and capacitive reac-

tances are equal and cancel: XL1 = XC1. When the crys-

tal is operating at its series resonant frequency the

impedance will be at a minimum and current flow will be

at a maximum. The reactance of the shunt capacitance,

XC0, is in parallel with the resistance R1. At resonance,

the value of XC0 >> R1, thus the crystal appears resis-

tive in the circuit at a value very near R1.

Solving fs for our example crystal we find:

fs = 7,997,836.8 Hz

The second resonant frequency is the anti-resonant,

fa, frequency. The equation is:

fa = ---------------------1---------------------

2π

L1

×

----C----1---C----0----

C1 + C0

This equation combines the parallel capacitance of C0

and C1. When a crystal is operating at its anti-resonant

frequency the impedance will be at its maximum and

current flow will be at its minimum.

Solving fa for our example crystal we find:

fa = 8,013,816.5 Hz

Observe that fs is less than fa and that the specified

crystal frequency is between fs and fa such that

fs < fXTAL < fa

This area of frequencies between fs and fa is called the

“area of usual parallel resonance” or simply “parallel

resonance.”

Crystal Complex Impedances

The crystal has both resistance and reactance and

therefore impedance. Figure 8 has been redrawn in

Figure 9 to show the complex impedances of the equiv-

alent circuit.

DS00826A-page 5

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