COMPUTER FORMULATION OF MIXED-MODE SWITCHING CIRCUITS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 20

linear voltage-controlled voltage sources in phase is shown in Fig.2.6.
The behavior of the controlled source is completely characterized by the
following relations called constitutive equations
and
Eqs.(2.7) and (2.8) can be written in a matrix format, leading to the
matrix stamps of the nonlinear controlled source, as shown in Fig.2.6.
The missing entries of the added rows and columns are zeros. Note that
nonlinear terms are purposely placed in the vector on the right hand
side of the equations such that the matrices and vectors on the left hand
side of the equation are all linear. The matrix stamps of other nonlinear
controlled sources can also be derived in a similar manner and they are
shown in Fig.2.6. The matrix stamps of linear controlled sources can be
obtained from that of the corresponding nonlinear controlled sources by
simply setting the nonlinear coefficients to zero.
2.5.2 Ideal Switches
As shown in Fig.2.7, there are only two distinct states associated
with the operation of an ideal switch connected to nodes and : the
ON state and the OFF state. Ideal switches are characterized by the
following constitutive equations:
The ON state is characterized by
The OFF state is characterized by
These characteristics can be mapped to the equations given in Fig.2.7.
The matrices for the ON and OFF states can also be combined by in-
troducing the switching variable