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ECE 220 Lab 6 © revised April 2007 by R. N. Strickland
1
ECE 220 Lab 6
Frequency Response of AC Circuits
(Tone Control Ckt, Crossover Network, Tuning Ckt)
This lab examines the
steadystate frequency response
of ac circuits. Much of the necessary theory will be covered later
in the semester when we study Chapter 9 (Phasors & AC Circuit Analysis). Hence, this lab is a
preview
of the some of
the applications of that theory. Completing the prelab and lab will help you to understand the theory when we cover it
in class.
The
prelab
consists of PSpice simulations of the following circuits: 1. Lowpass (Butterworth) RC filter, 2. Tank (or
tuning) circuit, 3. Tone control circuit, 4. Loudspeaker crossover network. The main skill to be covered in the
experiments
is the measurement of gain and phaseshift at individual frequencies.
Measuring phaseshift involves
connecting two ac signals to the oscilloscope (set in XY Mode) to create Lissajous patterns. (See last page.)
Introduction
AC circuits are characterized by their steadystate response to sinusoidal inputs. In the figure, the input
(shown as V1) is the sinusoid:
+

TwoPort
Circuit
)
ft
2
cos(
V
)
t
(
v
i
in
π
=
where V
i
≥
0. The steadystate output sinusoid (i.e. after any
initial transient response has died out) is given by:
)
ft
2
cos(
V
)
t
(
v
o
o
θ
+
π
=
where V
o
≥
0, and
θ
(which may be positive or negative
1
) is
the phaseshift caused by the circuit, and the circuit’s gain is
given by the ratio V
o
/V
i
. When V
i
= 1V as shown in the figure,
the gain is simply equal to the amplitude of the output
sinusoid.
2
Both gain and phaseshift are frequencydependent. Plots of gain vs. frequency and phaseshift vs.
frequency constitute the
frequency response
of the circuit. (The individual plots are often called the
gain
response
and the
phase response
, respectively.) The main goal of this lab is to measure these responses and
understand what they mean.
One final point: gain response typically covers a very large range of values, so we use a special log scale
called the dB (decibel) scale, giving the dB gain response:
)
V
V
(
log
20
dB
i
o
10
=
. (In ECE 320 you will
study these gain curves in the form of
Bode plots.
)
Example
Shown are the sinewave input v
in
(t) and the resulting steadystate output v
o
(t) for some linear circuit. At the
frequency of the sinewave (1kHz or 6283 rads/s), the circuit has a dB gain of
.
The phaseshift at this frequency is given by the product:
time shift
×
radian frequency
, i.e. 0.1ms
×
6283
rads/s = 0.628 radians (36 degrees). The output is delayed relative to the input, so the phaseshift is actually
0.628 radians.
dB
02
.
6
)
0
.
1
/
5
.
0
(
log
20
10
−
=
v
o
(t)
v
in
(t)
T=1ms
1.0
0.5
0.1ms
Summary:
V
i
= 1.0 volts
V
o
= 0.5 volts
f = 1kHz,
ω
= 6283 rads/s
dB
gain = 6.02 dB
θ
= 0.628 rads
t
1
When
θ
> 0, the circuit is said to cause a
phase advance
, when
θ
< 0, the circuit creates a
phase delay
.
Because sinusoids are periodic, a phase advance of 160
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 Spring '08
 Strickland
 Frequency

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