AN2867 datasheet(7/41 Pages) STMICROELECTRONICS

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AN2867

Quartz crystal properties and model

Fs is the series resonant frequency when the impedance Z = 0. Its expression can be

deduced from equation (1) as follows:

(2)

Fa is the anti-resonant frequency when impedance Z tends to infinity. Using equation (1), it

is expressed as follows:

(3)

The region delimited by Fs and Fa is usually called the area of parallel resonance (shaded

area in Figure 2). In this region, the crystal operates in parallel resonance and behaves as

an inductance that adds an additional phase equal to 180 ° in the loop. Its frequency Fp (or

FL: load frequency) has the following expression:

(4)

From equation (4), it appears that the oscillation frequency of the crystal can be tuned by

varying CL load capacitance. This is why in their datasheets, crystal manufacturers indicate

the exact CL required to make the crystal oscillate at the nominal frequency.

Table 2 gives an example of equivalent crystal circuit component values to have a nominal

frequency of 8 MHz.

Using equations (2), (3) and (4) we can determine Fs, Fa and Fp of this crystal:

and

If the load capacitance CL at the crystal electrodes is equal to 10 pF, the crystal will oscillate

at the following frequency:

To have an oscillation frequency of exactly 8 MHz, CL should be equal to 4.02 pF.

Table 2. Example of equivalent circuit parameters

Equivalent component

Value

14.7 mH

0.027 pF

5.57 pF

π LmCm

------------------------------

Fa Fs 1

---------

Fp Fs 1

2C0 CL

()

------------------------------







7988768 Hz

8008102 Hz

7995695 Hz

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