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switch or send a digital signal: in your computer, such abrupt changes occur
billions of
times
every second!
In response to the changed input voltage, the currents and voltages in the circuit will
change: gradually they will reach new steadystate conditions, but before then, some
transient changes will occur that exist only for a certain amount of time.
Transient responses occur in all circuits. Their parameters depend on resistances,
capacitances, and inductances; their features are described with differential equations.
Of course, the simplest
differential equations
are
of the first order:
they look like
dx
dt
+
k
"
x
=
0
or
dx
dt
+
k
"
x
=
f
(
t
)
The circuits, whose responses can be described (accurately enough) with such equations,
are called the
FirstOrder Circuits.
They include circuits with sources, resistors, and
one energystoring element – a capacitor or an inductor. We call them
RC and RL
circuits.
The timedependent
x
in the equations above can be a current or a voltage.
In this course, we consider the simplest case where
f
(
t
)
is a constant or a step function.
The solutions to these differential equations above have been known for at least 200
years. They are exponential:
x
(
t
)
=
A
"
e
#
k
"
t
+
B
=
A
"
e
#
t
$
+
B
, where
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 Spring '07
 Ganago
 Volt

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