SAMPLED-DATA SIMULATION OF PERIODICALLY SWITCHED NONLINEAR CIRCUITS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 139

truncated Taylor series expansion of these nonlinear elements at their
DC operating points [45]. Elements of such a characteristic are said
to be weakly nonlinear. To illustrate this, consider a nonlinear voltage-
controlled voltage source in a periodically switched nonlinear circuit with
the input

where and are the controlling and controlled voltages of the
voltage-controlled voltage source in phase respectively, as shown in
Fig.7.1, and are constants. In phase the circuit is nonlinear
time-invariant. The network variable of the circuit can be represented
in their Volterra series to the order of 3

where is the Volterra series expansion of Rep-
resenting the voltages of both the controlling branch and that of the
controlled branch of the voltage-controlled voltage source in Volterra se-
ries of the input using (3.17) of the order of three, where is a

nonzero constant, and substituting the results into (7.1) give

Note that the second subscript in (7.3) specifies the order of Volterra
series expansion. Eq.(7.3) is a power series in Since a power series
equals to zero if and only if all the coefficients of the power series are
identically zero, we obtain