Millers Theorem

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)

bjt27

If Z is the impedance connected between two nodes, node 1 and node 2, it can be replaced by the two impedances Z1 and Z; Where Z1 is connected between node 1 and ground and Zis 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 Vi to the current I which flows from the input to the output.

bjt28

Z1 = V1 / I

I = ( Vi – V0 ) / Z = V(1 – Vo / Vi) / Z
I = Vi (1 – Av ) / Z
Z1 = Z / (1 – k)
bjt29
Z2 = Vo / I
I = ( Vo – Vi ) / Z = V(1 – Vi / Vo) / Z
I = Vo (1 – 1/Av ) / Z
Z2 = Z / (1 – 1/k)
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