structural:scholar_edition, linguistic:translation, structural:expansion, stylistic:style_transfer
Frequency of oscillation - the Barkhausen criterion

To determine the frequency(s) ω 0 = 2 π f 0 {\displaystyle \omega _{0}\;=\;2\pi f_{0}} 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 v i (t) = V i e j ω t {\displaystyle v_{i}(t)=V_{i}e^{j\omega t}} and the amplitude and phase of the sine wave after going through the loop v o = V o e j (ω t + ϕ) {\displaystyle v_{o}=V_{o}e^{j(\omega t+\phi)}} is calculated