On the Periodic Steady-State Problem by the Newton Method

The methods by which linear sensitivity circuits have been used to evaluate the sensitivity matrix,
{\partial}x(T)/{\partial}x(0)
, can be improved. The sensitivity matrix is used in the computation of the Jacobian of
f(x(0))=x(0)-x(T)=0
, (
T
being the period) in a periodic steady-state problem. It is shown here that the sensitivity matrix can be obtained from the solution of a linear homogeneous matrix equation which is simply derived by differentiating the state equations or a mixture of algebraicdifferential equations arising from any formulation. This simplification makes the method easier and more practical to implement in a general purpose CAD program. Examples are given.