AN2867 datasheet(18/41 Pages) STMICROELECTRONICS

18 / 41 page

Pierce oscillator design

AN2867

18/41

DocID15287 Rev 9

± 5% of their nominal value. From crystal point of view, the two load capacitors are mounted

in series which means that their contribution to the CL is (CL1 = CL2)/2. As CL1 equals CL2,

the tolerance on their contribution to CL remains the same and is equal to ± 5%. Now if we

consider that all the remaining contributors to the CL are maintained to their nominal values

at design stage (to assess the frequency shift magnitude induced only by load capacitor

tolerances), then the load capacitance seen by the crystal (CL) will either decrease by

0.175 pF or increase by the same value. This will induce an oscillation shift of:

The above example shows that the lower the pullability, the lower the impact of small load

capacitance deviation on the frequency shifting. Crystal pullability is an important factor

when defining the final application PPM budget.

Where

Cm is the crystal motional capacitance

C0 is the crystal shunt capacitance

CL is the crystal nominal load capacitance

Next sections give a more detailed description on how to calibrate the oscillation frequency

and how to estimate the final accuracy uncertainty (PPM) budget.

3.8

Safety factor

3.8.1

Definition

Resonators (such as crystal resonators) are well known to undergo aging effects. They

manifest themselves over time in a deviation of resonator parameters from their initial

values defined by the resonator specifications. Among the affected parameters there is the

resonator ESR which value depends on the surrounding environmental conditions such as

moisture and temperature.

The oscillator transconductance also depends on the microcontroller power supply voltage

and on the temperature.

The safety factor parameter allows to qualify the oscillator safe operation under the

operating conditions and during the application life. It measures the ability of the oscillator

not to fail under operating conditions.

The safety factor is defined as the ratio between the oscillator negative resistance and the

resonator ESR. It is given by the below formula:

0.175 pF 45 PPM/pF

~7.8 PPM (~0.7 s/day for a time-keeping function such as RTC)

Pullability PPM pF

⁄

()

×10

2C0 CL

()

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

Oscillator negative resistance

Crystal ESR

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

RADD Crystal ESR

Crystal ESR

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

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