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and respectively. These Volterra circuits have the same in-
cidence matrix but different inputs. This observation reveals that in
solving these circuits, the transit matrix for all Volterra circuits
are the same and need to be computed only once. The zero-state
vectors, however, differ and must be computed separately.
The input of the circuit characterized by (12.27) is obtained from the
solution of (12.26) whereas that of the circuit depicted by (12.28) is
from the solution of (12.26) and that of (12.27). Volterra circuits
must be solved in a sequential order with the lower-order Volterra
circuits solved first.
Although the topology of and are identical, the frequency
components of and differ from each other due to their
distinct inputs. As a result, LU-decomposition of
must
be performed separately.
3. Harmonic Distortion
In this section, the frequency response of a periodically switched non-
linear circuits to a sinusoidal input is obtained using the method pre-
sented in the preceding sections.
3.1 The First-Order Volterra Circuit
Let the input of a periodically switched nonlinear circuit be
The sinusoidal input contains two distinct frequency components at
and Using the principle of superposition, it can be shown that
the complete response of
denoted by
contains the frequency
components
and can be written as
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