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AN826

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

Microchip Technology 

AN826

FIGURE 9:

CRYSTAL EQUIVALENT

CIRCUIT COMPLEX

IMPEDANCES

The complex impedances [5] are defined as:

Z0 = 2----π--–--f-j-C----0-

Z1 = R1 + j2πfL1 – 2----π---1-f--C----1-

Combining Z0 and Z1 in parallel yields:

Zp

=

----Z---0---Z----1---

Z0 + Z1

We plug in the values of Table 2 in a spreadsheet pro-

gram and solve Zp over frequency. We observe the

reactance verses frequency plot in Figure 10.

FIGURE 10:

300000

200000

REACTANCE VERSES

FREQUENCY

fa

fs

100000

0

-100000

-200000

-300000

-400000

7,975,70,09078,75,09082,70,09085,75,09089,70,09092,75,09096,70,09099,85,00003,80,00006,85,00010,80,00013,85,00017,80,00020,85,00024,80,00027,85,00031,80,00034,85,00038,80,00041,85,00045,80,00048,500

Frequency (Hz)

This plot shows where the crystal is inductive or capac-

itive in the circuit. Recall that positive reactances are

inductive and negative reactances are capacitive. We

see that between the frequencies fs and fa the imped-

ance of the crystal is inductive. At frequencies less than

fs and frequencies greater than fa the crystal is capaci-

tive.

As mentioned earlier, the equivalent circuit shown in

Figure 8 (B) is a simplified model that represents one

Oscillation mode. For this example that is the Funda-

mental mode. The plot in Figure 10 does not show

Overtone modes and spurious responses. Therefore,

the crystal can appear inductive to the circuit at these

Overtone modes and spurious responses. Care must

be taken in the selection of oscillator components, both

internal and external, to ensure the oscillator does not

oscillate at these points.

Drive Level

Drive level refers to the power dissipated in the crystal.

Crystal data sheets specify the maximum drive level

the crystal can sustain. Overdriving the crystal can

cause excessive aging, frequency shift, and/or quartz

fracture and eventual failure. The designer should

ensure that the maximum rated drive level of the crystal

is not exceeded. Drive level should be maintained at

the minimum levels necessary for oscillator start-up

and maintain steady-state operation.

Power dissipation of the crystal can be computed by

P = ER-----21

where E is the rms voltage across the crystal exactly at

series resonance [3][6]. However, for the crystal oscil-

lators discussed in this Application Note, the crystal

operates slightly off series resonance in the area of

usual parallel resonance (this will be explained in the

section on Crystal Oscillators). Therefore, current will

need to be measured by using an oscilloscope current

probe. Connect the probe on one leg of the crystal, if

space permits, or in the oscillator loop. Finally calculate

power by

P = I2R1

Crystal Quality Factor (Q)

Due to the piezoelectric effect of the crystal, a physical

displacement occurs when an electric field is applied.

The reverse effect happens when the crystal is

deformed: electrical energy is produced across the

crystal electrodes. A mechanically resonating crystal is

seen from its electrodes as an electrical resonance.

Therefore the crystal behaves like a tuned circuit and

like a tuned circuit the crystal can store energy. We can

quantify the amount of stored energy by stating the

quality factor (Q) of the crystal. Crystal Q is defined as

[5]:

Q = -X-R---L-1--1 = -X----C--1-1---R----1

Where XL1 (or XC1) is the reactance of L1 (or C1) at the

operating frequency of the crystal. Do not confuse the

operating frequency with fa or fs. The operating fre-

quency can be anywhere between fa or fs in the area of

usual parallel resonance.

DS00826A-page 6

© 2002 Microchip Technology Inc.

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