Environmental Engineering Reference
In-Depth Information
where is the Dirac impulse function. Now, consider a linear capacitor
in phase of a periodically clocked linear circuit. Let the voltage of the
capacitor at be Note that
is the
initial
condition of the capacitor in phase
Making use of
(2.11), we arrive at
The time interleaved operation of externally clocked circuits, as detailed
in Fig.2.5, requires that be zero outside phase To ensure that
is zero for the input to the sub-circuit of phase must be
removed. Also, the charge of the capacitor at the end of the clock phase,
i.e.
must be extracted completely. This is accomplished
by subtracting
from
In MNA, the above equation can be written in a matrix format, as shown
in Fig.2.8.
Most nonlinear capacitors encountered in integrated mixed-mode switch-
ing circuits are pn-junction induced. The small-signal behavior of a non-
linear capacitor is often characterized using its charge-voltage relation,
usually up to the order of three [2]
where and are the AC components of the charge stored in
the capacitor and the voltage across the capacitor, respectively.
and are constants and are functions of the DC operation point of the
capacitor. To exemplify the procedures of how (2.14) is derived, consider
the junction capacitance of an abrupt pn-junction
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