text: Theory of feedback oscillators A feedback oscillator circuit consists of two parts connected in a feedback loop; an amplifier  and an electronic filter .  The filter's purpose is to limit the frequencies that can pass through the loop so the circuit only oscillates at the desired frequency.  Since the filter and wires in the circuit have resistance they consume energy and the amplitude of the signal drops as it passes through the filter.  The amplifier is needed to increase the amplitude of the signal to compensate for the energy lost in the other parts of the circuit, so the loop will oscillate, as well as supply energy to the load attached to the output.
  Frequency of oscillation - the Barkhausen criterion
  To determine the frequency(s)  at which a feedback oscillator circuit will oscillate, the feedback loop is thought of as broken at some point (see diagrams) to give an input and output port. A sine wave is applied to the input  and the amplitude and phase of the sine wave after going through the loop  is calculated
  and            so
  Since in the complete circuit  is connected to , for oscillations to exist
  The ratio of output to input of the loop, , is called the loop gain. So the condition for oscillation is that the loop gain must be one
  Since  is a complex number with two parts, a magnitude and an angle, the above equation actually consists of two conditions:
  The magnitude of the gain (amplification) around the loop at ω0 must be unity