In general, the miller theorem is used for converting any circuit having configuration of figure 2.48 (a) to another configuration shown in figure 2.48 (b)

If Z is the impedance connected between two nodes, node 1 and node 2, it can be replaced by the two impedances Z_{1} and Z_{2 }; Where Z_{1} is connected between node 1 and ground and Z_{2 }is connected between node 2 and ground.

**Proof Of Miller’s Theorem**

Miller’s theorem states that, the effect of resistance Z on the input circuit is a ratio of input voltage V_{i} to the current I which flows from the input to the output.

Z_{1} = V_{1} / I

I = ( V

_{i}– V_{0}) / Z = V_{i }(1 – V_{o}/ V_{i}) / ZI = V

_{i}(1 – A_{v}) / Z**Z**

_{1}= Z / (1 – k)Z

_{2}= V_{o}/ II = ( V

_{o}– V_{i}) / Z = V_{o }(1 – V_{i}/ V_{o}) / ZI = V

_{o}(1 – 1/A_{v}) / Z**Z**

_{2}= Z / (1 – 1/k)
Advertisements