Environmental Engineering Reference
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denotes the vector of the network variables of mixed-mode switch-
ing circuits in the time domain. denotes the vector of the
network variables of mixed-mode switching circuits in the frequency
domain.
denotes the vector of the network variables of mixed-mode
switching circuits in phase denotes the vector of the
Fourier transform of the network variables of mixed-mode switching
circuits in phase
denotes the vector of the first-order time derivative of the
network variables of mixed-mode switching circuits in phase
denotes the vector of the network variables of mixed-
mode switching circuits at the time instant
It can also
be written as
where
denotes Dirac
impulse function.
2.4 Sub-Circuits
The topology of an externally clocked circuit changes from one clock
phase to another and remains unchanged during each clock phase. This
observation suggests that an externally clocked circuit with a total of
K
phases in a clock period can be considered as an assembly of
K time-
invariant
sub-circuits that are interconnected via the initial conditions
of elements with memory (capacitors and inductors), as depicted graph-
ically in Fig.2.5. These sub-circuits are operated in a time-interleaved
fashion such that
and
The time duration in which the input
is connected to the sub-circuit
is specified by the window function
defined as
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