Environmental Engineering Reference
In-Depth Information
Using the property of the orthogonality of exponential series, it can be
shown that the phasors of the voltage and current of the resistor are
related by
Substituting this relation into
(10.14) we obtain
where and are the phasors of the voltage and
current of the resistor in the adjoint network, respectively. In order to
have (10.17) hold for arbitrary
we set
Eq.(10.18) reveals that the resistor
R
in
N
maps to a resistor in
with
the same resistance.
3.3 Capacitors and Inductors
Following the similar procedures as those for resistors one can show that
the phasors of the voltage and current of a capacitor in periodically
switched linear circuits is related to each other by
where
C
is the capacitance. Substituting (10.19) into (10.14)
To validate (10.20) for arbitrary
we impose
Search WWH ::
Custom Search