On the Realization of 2-Port Immittance Matrices Without Transformers

The realization of immittance matrices of passive, bilateral two-ports without transformers is discussed. It is shown that given any symmetric, positive real, immittance matrix, as for example the open-circuit impedance matrix with entries
z_{11}(s)
,
z_{12}(s)
, and
z_{22}(s)
, provided only that the driving functions have nonzero real parts when the variable
s
is imaginary, a RLC network
N
without coupled coils can always be found such that the parameters of
N
are
z_{11}(s), Kz_{12}(s)
, and
z_{22}(s)
where
K
is any positive number no greater than
K_{\max}
. The value
K_{\max}
is determined by the given parameters and may or may not exceed unity. A simple rule for determining
K_{max}
is given. The realization procedure makes use of available approximation techniques which give rise to nonunique solutions. All solutions, however, are in the form of general lattice networks.