Environmental Engineering Reference
In-Depth Information
Instantaneous charge (flux) distribution -
When the loop resistance
is neglected, the re-distribution of charge in ideal switched capacitor
networks, which are composed of a limited set of elements including
ideal switches, independent voltage sources, voltage-controlled volt-
age sources, and capacitors, takes place at switching instants only.
This unique characteristic of ideal switched capacitor networks en-
ables the analysis of these networks using simple algebraic equations
derived from the charge conservation of the networks at switching
instants.
Incomplete charge (flux) transfer -
When the loop resistance becomes
comparable to the duration of clock phases, the assumption that the
network variables reach their steady value of a clock phase before
reaching the end of the clock phase is violated. In this case, the
behavior of the circuits can not be depicted using algebraic equa-
tions that only take into account the value of the network variables
at discrete time instants, i.e. the clocking instants. Instead, differ-
ential equations that adequately depict the behavior of the circuits
continuously in the entire clock phase are needed. The value of the
network variables at the end of the clock phases must therefore be
determined by solving the differential equations using numerical in-
tegration. This not only increases the cost of simulation but also
complicates the analysis.
Inconsistent initial conditions -
Because practical switched capacitor
networks and switched current networks are designed in such a way
that the initial transient portion of the time domain response of these
networks in each clock phase is not important and the network vari-
ables reach their steady value of the clock phase before reaching the
end of the clock phase, i.e. the loop time constant is much small as
compared with the duration of the clock phases. In this case, it is
computationally advantageous to model switches as an ideal device,
leading to ideal switching. Ideal switching, however, may cause an
abrupt change in nodal voltages, as will be detailed in Chapter 5.
The abrupt change in the capacitor voltage gives rise to an impul-
sive capacitor current. Similarly, ideal switching may give rise to an
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