Environmental Engineering Reference
In-Depth Information
Appendix
FREQUENCY ANALYSIS OF RC NETWORKS
In this topic we have studied numerous configurations whose small-signal
equivalent circuits are made up of only three components, namely resistors,
capacitors, and controlled sources. The evaluation of fundamental circuit
parameters such as voltage and current gain transfer functions, but also input
and output impedances, is then placed in the context of the study of
generalised RC networks.
A.1 TRANSFER FUNCTION OF A GENERIC RC NETWORK
Consider the RC network in Fig. A.1, which includes
n
independent
capacitors. The transfer function between two generic network ports, as a
function of the complex frequency
s,
can be expressed in the general form
where
m < n.
Transfer function
G
(
s
) can be determined by applying
Kirchhoff' s laws to the network. But when the order,
n,
is high, or in other
words, when there is a large number of reactive components, we have to
solve a system with a great number of equations. Because of this, it would be
more practical to have a systematic method by which coefficients and
could be directly determined. This approach would also have the advantage
of allowing an approximate transfer function of reduced order, defined by
the user, to be derived.
