Microcontroller oscillator circuit working

 Circuit consists of two parts: an inverting amplifier that supplies a voltage gain and 180° phase shift and a frequency selective feedback path. The crystal combined with Cx and Cy form a tuned PI network that tends to stabilize the frequency and supply 180° phase shift feedback path. In steady state, this circuit has an overall loop gain equal to one and an overall phase shift that is an integer multiple of 360°. Upon being energized, the loop gain must be greater than one while the voltage at XTAL grows over multiple cycles. The voltage increases until the NAND gate amplifier saturates. At first glance, the thought of using a digital NAND gate as an analog amplifier is not logical, but this is how an oscillator circuit functions.