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EE43/EE100 — LAB #7
RC Filters Guide
I.
Introduction
In this lab you will determine the inputoutput characteristics of an RC filter, and then use PSpice to
simulate the RC filter behavior.
RC Filter Characteristics
Figure 1 below shows an RC filter connected to a sinusoidal voltage source.
This circuit is termed a
twoport circuit (Fig. 2) where the voltage source produces the input voltage V
in
and the output voltage
V
out
appears across resistor R.
+

V
out
V
in
+

R
C
v
in
v
out
Figure 1
:
An RC filter with a series capacitor and
output resistor R.
Figure 2
:
A twoport circuit.
Recall that we customarily represent an AC voltage as a periodic function of time, such as
V
(
t
) =
V
0
cos(
ω
t
) where
V
0
is the amplitude of the voltage,
t
is time, and
ω
is the angular frequency, whose
units are radians per second.
The angular frequency is related to frequency,
f
, measured in Hertz, by
ω
= 2
π
f.
For example, if the frequency,
f
, of the ordinary power line voltage in the U.S. is 60 Hz, then
the associated angular frequency,
ω
, is 377 radians/s (2
π×
60).
Transfer Function
A twoport circuit is characterized by its transfer function, whose magnitude is defined as 
V
out
/
V
in
,
where
V
out
and
V
in
are phasor voltages (as indicated by the boldface type).
The variation of the
transfer function with frequency characterizes the circuit, whether the circuit is an amplifier (does it
amplify high frequencies more than low frequencies?) or a filter (does the filter pass the low
frequencies or the high frequencies better?).
If you analyze the RC circuit of Fig. 1 using Kirchhoff’s voltage law, the phasor voltages
V
out
and
V
in
, the resistance R and the impedance of the capacitor
Z
C
= 1/j
ω
C, you can show that the magnitude
of the transfer function is
2
)
ω
RC
(
1
ω
RC
+
=
in
out
V
V
An approximate loglog plot of transfer function magnitude vs. frequency is shown in Figure 3.
The
filter characteristic has been simplified to appear as two lines that intersect at the angular frequency
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for which
ω
RC = 1, or
ωτ
= 1, where
τ
is the time constant RC for this circuit.
If plotted precisely,
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 Spring '09
 Gupta
 Alternating Current, Hertz, Logarithmic scale, RC circuit, Lowpass filter, Vin

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