A Limitation of the Series-Parallel Structure

This paper disproves Darlington's conjecture that every
RC
-grounded two-port is equivalent to a series-parallel two-port. The proof depends upon the construction of a counterexample. This counterexample is a six-node
RC
-grounded two-port, whose admittance functions
Y_{11} = N_{11}/D, -Y_{12} = N_{12}/D, Y_{22} = N_{22}/D,
written without common factors, have compact poles at the zeros of
D
and for which
N_{12}
has a negative coefficient. In accordance with properties of
RC
series-parallel networks derived in an earlier paper, the network of the counterexample cannot be equivalent to any
RC
series-parallel two-port.