Feedback in electronic circuits

” The process of injecting some portion of output signal of a circuit back as input to the same circuit is known as feedback. “

Consider the following system which shows amplification of input voltage V_i by factor ‘A’.

Output Voltage = Amplification factor * Net Input Voltage &#x2509&#x2509 &#x2780

V_o = A*V_i

Note that amplification factor of the system is given by (Vo/Vi ).

connecting feedback to the above system gives,

Here, ‘β’ fraction of the output current V_o is feedback as input to the system, i.e V_f = βV_o &#x2509&#x2509 &#x2781

Also, in the case of oscillators, the feedback element provides 0^o or 360^o of total phase shift to the feedback signal.

So, the total input to the system becomes ( V_i + V_f )

From equation &#x2780 we get,

V_o = A * ( V_i + V_f )

V_o = AV_i + AV_f

V_o = AV_i + AβV_o (from eq &#x2781)

V_o ( 1 – Aβ) = AV_i

V_o/V_i = A/(1 – Aβ)

&#x21d2 Gain of a system with positive feedback is given by A/(1 – Aβ).

It can be clearly noted that whether the input signal in the system will be amplified or attenuated or will remain sustained depends on the value of ‘Aβ’.

Therefore 3 cases arise:

Note that ‘A’ represents the amplification of the signal without feedback and ‘β‘ represents the fraction of output voltage that will be fed back to the system.

Case 1) Aβ < 1 :

Here decaying oscillations are generated by the oscillator. Below is an example of decaying oscillations.

Case 2) Aβ > 1 :

Here, growing oscillations are generated. Below is an example of growing oscillations.

Case 3) Aβ = 1 :

Here, sustained oscillations are generated by the oscillator. Below is an example of sustained oscillations.

So, Sustained Oscillations are generated only when Aβ = 1.