Environmental Engineering Reference
In-Depth Information
The time domain sensitivity of the response of a periodically switched
linear circuit with respect to a circuit parameter
is defined as
The normalized sensitivity defined as
removes the impact of the value of the parameter to which sensitivity
is calculated on the sensitivity. The sensitivity to parasitic parameters
whose value is usually extremely small can also be computed from
To obtain the time-domain sensitivity of the response of periodically
switched linear circuits to a circuit parameter
we differentiate (6.1)
with respect to
Comparing the circuit depicted by (6.1) and that delineated by the above
expression one can see that both circuits are linear and have the same
topology but distinct inputs. The unknown of the circuit depicted by
the above equation is sensitivity and the circuit is hence called sensitiv-
ity network of For each circuit parameter, there is a corresponding
sensitivity network. The sensitivity networks have the identical topol-
ogy but distinct inputs. Also, these sensitivity networks are periodically
switched linear circuits with the same clock frequency as that of the
original circuit.
The time domain response of the sensitivity network is obtained by
differentiating (6.11) with respect to
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