Lesson 30 –
RL
and
RC
Circuits (Exponential and Sinusoidal Transient Responses) (Section 74)
(CLO 72)
This lesson is somewhat mathematically challenging since we will be differentiating exponentials
and sinusoids.
However, the concepts are easy to understand.
Start with a firstorder circuit driven by an exponential.
This is mathematically easier to solve than
the sinusoidal driven circuit.
The basic equation is as derived earlier
The
u
(
t
) implies that the driving signal
v
T
(
t
) has a finite start
time arbitrarily selected as
t
= 0.
This implies that there is an
initial condition,
v
(0) =
V
0
, that will have to satisfy the basic
equation. As with the step response, we find the solution in two parts: natural response and forced
response.
The natural response of a stable firstorder circuit is of the form
The natural response of a firstorder circuit always has this form because it is a general solution
of the homogeneous equation with the input set to zero.
The form of the natural response
depends on the physical characteristics of the circuit and is independent of the input. Be sure the
students understand this.
The forced response
v
F
(
t
), depends on both the circuit and the nature of the forcing
function (the input).
The forced response is a particular solution of the equation
0
)
(
)
(
)
(
T
F
F
T
≥
=
+
t
t
v
t
v
dt
t
dv
C
R
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 Spring '08
 MAURICIODEOLIVERIA
 Trigraph, The Circuit, RC circuit

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