Civil Engineering Reference
In-Depth Information
3.5.4
Moment scaling and moment shifting
Since typical time constants in integrated circuits are of the order of picoseconds
to nanoseconds‚ consecutive moments can differ by many orders of magnitude.
Typically‚ the ratio of consecutive moments is of the order of the dominant
time constant of the system. This may lead to numerical errors due to the
limited precision afforded by computing machines. This is effectively addressed
by the use of
moment scaling.
If all capacitors and inductors are scaled by a
multiplicative factor‚ this is equivalent to multiplying the frequency variable‚
and hence the time variable‚ by a factor of For instance‚ if is set to
then the only difference after scaling is that the units of time are altered from
seconds to nanoseconds; the numerical errors in the computation are‚ however‚
greatly reduced.
The idea of
moment shifting
is to compute moments about a point other
than say about since this may be able to better capture the
effects of nondominant poles. It is easy to show that such a shift is equivalent
to adding a conductance of in parallel with a capacitor of value
C‚
and a
resistance of in series with an inductor of value
L
; for a detailed discussion‚
the reader is referred to [CPO02].
