Quick Access to Circuit Transfer Functions via NAM Determinant/Cofactors Using UaL Technique

Determinants and cofactors play an important role in getting the circuit responses. Given the Nodal Admittance Matrix (NAM) of a linear circuit, its determinant and cofactors provide all the circuit responses, including the transfer functions, and the poles and zeros. This presentation shows how a matrix determinant and its cofactors are simply obtained through a UaL decomposition of a NAM and any other nonsingular matrix. The UaL decomposition procedure is an alternative to LU factorization but is shown to be simpler, computationally more efficient, and exact within the data size. In fact, the determinant, partial-determinants, and the cofactors are simply constructed during the UaL decomposition process with no extra effort needed. There is no division involved in the UaL process, as there is no division involved in finding determinants. A circuit example is worked out that demonstrates the application of UaL decomposition in finding the circuit transfer functions and responses.