Franclim F. Ferreira, Pedro Guedes de Oliveira, Vítor G. Tavares

Miller's theorem

The Miller’s theorem establishes that in a linear circuit, if there exists a branch with impedance Z, connecting two nodes with nodal voltages ­V₁and V₂, we can replace this branch by two branches connecting the corresponding nodes to ground by impedances respectively Z / (1-K) and KZ / (K-1), where K = V₂ / V₁.

In fact, if we use the equivalent two-port network technique to replace the two-port represented on the right to its equivalent, it results successively:

and, according to the source absorption theorem, we get the following:

As all the linear circuit theorems, the Miller’s theorem also has a dual form:

Miller's dual theorem

If there is a branch in a circuit with impedance Z connecting a node, where two currents I₁ and I₂ converge, to ground, we can replace this branch by two conducting the referred currents, with impedances respectively equal to (1+ a) Z and (1+ a) Z / a, where a = I₂ / I₁.

In fact, replacing the two-port network by its equivalent, as in the figure,

it results the circuit on the left in the next figure and then, applying the source absorption theorem, the circuit on the right.