Question

What does it mean to determine Ao for Vo = 0V?

So I have a graph of Vo vs Vin which are the gain characteristics. What doesn't make sense to me is that, wouldn't the gain Ao = 0 for Vo = 0v ?

Answer 1

Mathematically, gain is represented in the form of straight line,

or    

so the gain is actually a slope of a straight line whose value is given by

which is defined as the " rate of change output with respect to rate of change of input voltage"

so for above linear system with gain "A", A will remain constant through out unless the graphical representation is piecewise.

Suppose the equation of a system is given by   ;

in the above equation, If the input applied is 1V then the output is 0, which doesn't mean that the gain A is zero. If the gain for a system is zero then the output will always be zero. As if the gain lies between 0 and 1 the system acts as attenuator and not as an amplifier.

Furthermore, If 0 input is applied to an ideal linear system then the output must be zero. no matter what the gain A is