AN2867 datasheet(14/41 Pages) STMICROELECTRONICS

14 / 41 page

Pierce oscillator design

AN2867

14/41

DocID15287 Rev 9

oscillator transconductance ranges from a few µA/V to a few dozens of µA/V

depending on the product.

gmcrit is defined as the minimal transconductance of an oscillator required to maintain a

stable oscillation when it is a part of the oscillation loop for which this parameter is

relevant. gmcrit is computed from oscillation-loop passive components parameters.

Assuming that CL1 equals CL2, and that the crystal sees the same CL on its pads as the

value given by the crystal manufacturer, gmcrit is expressed as follows:

where

ESR = equivalent series resistance

C0 is the crystal shunt capacitance.

CL is the crystal nominal load capacitance.

F is the crystal nominal oscillation frequency.

For example, to design the oscillation loop for the HSE oscillator embedded into an

STM32F1 microcontroller which a transconductance value (gm) equal to 25 mA/V, we

choose a quartz crystal (from Fox) with the following characteristics:

frequency = 8 MHz

C0 = 7 pF

CL = 10 pF

ESR = 80

Ω .

To check if this crystal will oscillate with an STM32F1 microcontroller, let us calculate gmcrit:

Calculating the gain margin gives:

The gain margin is sufficient to start the oscillation and the “gain margin greater than 5”

condition is reached. The oscillator is expected to reach a stable oscillation after a typical

delay specified by the microcontroller datasheet.

If an insufficient gain margin is found (gainmargin < 5), the oscillation might start up under

typical conditions (achieved in laboratory conditions) when designing and testing the final

application. However, this does not guarantee that the oscillation will start up in operating

conditions. As a result, it is highly recommended that the selected crystal has a gain margin

higher than or equal to 5. Try to select a crystal with a lower ESR or/and a lower CL.

Whatever the specified parameter, the oscillator transconductance (gm) or the oscillation

loop maximal critical gain (gm_crit_max), the conversion between these two parameters is

possible, if need be. The relation between these two parameters is given by the below

formula:

gmcrit

4 ESR

πF

()

C0 CL

()

gmcrit

480

×10

()

–

×10

–

×10

()

0,23 mA V

⁄

gainmin

arg

gmcrit

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

0,23

-----------

107

Gm_crit_max

-------

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