Abstract
Electrical networks consisting of inductances, resistances, an. d capacitances form
a group with the impedance function as an absolute invariant. That is, to a given
impedance function there corresponds an infinite number of networks, any one of
which can be obtained from any other by a special linear transformation of the in-
stantaneous mesh currents and charges of the network. In this manner one may
arrive at the complete infinite set of networks equivalent to a given network of any
number of meshes. This is done by writing down the three fundamental quadratic
forms of the network. Then a linear affine transformation of the instantaneous mesh
currents and charges of the network results in the formation of new quadratic forms,
the matrices of the coefficients of which represent a member of the group, i.e. , an
equivalent network. Instead of performing the substitutions, the three matrix multi-
plications C A C are used, one for each quadratic form, where A represents the original
matrix, C the transformation matrix, and C' its conjugate. It may be possible to ex-
tend this theory to include continuous systems where the quadratic forms become
integrals or infinite series and one deals with infinite matrices and infinite transfor-
mations.
Users
Please
log in to take part in the discussion (add own reviews or comments).