Sinusoidal Oscillator Circuits Reexamined

Singular network condition is proposed to study oscillators. It states that a circuit is a potential oscillator if and only if the rank of the network matrix of size n X n is (n -1) at the frequency of oscillations. The dual (if it exists) and adjoint circuit of an oscillator are also oscillators. Limitations of Barkhausen’s approach are pointed out. It is explained that there are many ways to generate oscillations other than Barkhausen’s positive feedback configuration. The new approach emphasizes that appropriate D C inputs / initial conditions are important.