How is the closed loop transfer function defined for an oscillator?

Question

an electronic oscillator is a device which can generate some signals without input signals. It is an unstable system realized with positive feedback, as shown in the following scheme:

Now I have two questions:

• How is the closed loop transfer function of this device defined? The input signal does not exist.

• How can we implement negative or positive feedback, if the input signal does not exist? I know that in negative feedback the feedback signal is added to the input signal, in positive feedback is subtracted. So in the first situation we use and adder circuit, in the second one a subtractor circuit. But what do we do in this case?

Answer 1

Just regard it as an amplifier with feedback where the real input is set to a value of zero: -

in negative feedback the feedback signal is added to the input signal, in positive feedback is subtracted. So in the first situation we use and adder circuit, in the second one a subtractor circuit.

Feedback +/- input is the same as feedback +/- 0 when the input is zero.

Answer 2

In feedback systems the feedback signal is fed back to the input of the amplifier. This definition does not require that it is added or substracted from an external input signal.

In oscillating systems there is no input node - however, if you want you can create an input node and you can use it - for test resp. calculation purposes - to connect an external input signal (without disturbing the loop gain).

Example: For each real oscillator, there are always some parts which are connected to ground (R or C). Instead of ground (0 volts) you can connect a test signal to this point. When the oscillation condition is fulfilled, the gain of this closed-loop system will be infinite.

Such an external input could be used also for injecting a short start impuls to the oscillatory system.