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According to ST AN2867 Oscillator design guide for STM32, the oscillator circuit requires a Rext resistor

There are minimal boards with stm32f030f4p6 on ebay, aliexpress... It looks that rext is missing on the schematics. It only have a crystal and 2 capacitors Do you think the board can run on HSE anyway ?

Here is the schematics http://www.uctronics.com/download/U3808-1.jpg

Thanks

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It will run without \$R_{ext}\$, but the clock will be noisier (because you don't have a low pass filter anymore), which may or may not effect the application. You may experience anything from more jitter on the clock which will affect timing or worst case an occasional upset.

From the app note (app notes are good to read)

The role of this resistor is to limit the drive level of the crystal. With CL2, it forms a low-pass filter that forces the oscillator to start at the fundamental frequency and not at overtones (prevents the oscillator from vibrating at 3, 5, 7 etc. times the fundamental frequency). If the power dissipated in the crystal is higher than the value specified by the crystal manufacturer, the external resistor RExt becomes mandatory to avoid overdriving the crystal.

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