Electronic Devices and Circuits Engineering Sciences 154

### Partial Fraction Expansion

See Section 7.1 in Sedra and Smith
In general, any transmission or response function can be written

where the z's (zeroes) and p's (poles) are, respectively, the roots of the numerator and denominator of the function.

If there are no repeated poles, a partial fraction expansion is possible.  (This is not a significant limitation, but requires one more relatively trivial step.)

where

Each represents a characteristic solution - i.e.

For reference see table of Laplace transform pairs
RLC Example:

where

For subsequent computations it useful to note that

In this case

Revisiting Bode Plots (Diagrams)

An Example

A Discussion of Decibels