Lab 4: Fourier Transform and AM Radio
ECE 210  Fall 2003
In Lab 4, you will finally connect all of your receiver components and tune an AM radio broadcast.
You will
follow the radio signal through the entire system, from antenna to loudspeaker, in the time domain and the frequency
domain.
I.
PRELAB
The Fourier transform is an important tool in the analysis of your AM radio receiver. Make sure you understand
the theory before you come to lab.
(a)
5
0
5
x 10
4
0
t
f(t)
2.5
2.5
1
(b)
0
0
t
f(t)
t = pi/6
1
Figure 1: rect and sinc functions for prelab.
1. Find the Fourier transforms of rect and sinc signals shown in Figures 1a and b. By definition,
F
(
ω
)
, the Fourier
transform of signal
f
(
t
)
is
F
(
ω
) =
∞
∞
f
(
t
)e

jωt
dt
. Do not just use the lookup tables for the first transform.
(a)
(b)
2. Read part II C of the lab instructions, AM Radio Receiver, on pages 46. This will save you time in lab.
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II.
LABORATORY EXERCISE
•
Equipment: Function generator, oscilloscope, protoboard, and wires.
•
Components: Threestage circuit from Lab 2, bandpass filter from Lab 3, RF amplifier, and mixer.
A.
Fourier Transform
It can be difficult to identify features in the oscilloscope’s display of the Fourier transform if you do not know
what to expect. In this section, you will learn to identify features in the Fourier transform by looking at the Fourier
transforms of some well known signals.
1. No circuit is used for this part of the laboratory. Connect the function generator’s output to Channel 1 of the
oscilloscope.
2. Set the function generator to create a 1 kHz square wave with amplitude 1 V peaktopeak. Turn on burst mode
by pressing “Shift” then “Burst”.
3. Set the oscilloscope to display the magnitude of the Fourier transform of a segment of the input signal:
•
Press “+/”
•
Turn on Function 2
•
Press “Menu”
•
Press “Operation” until FFT appears
•
Set the Operand to Channel 1
•
Set the time/div to 2 ms (you may need to adjust this later)
•
Press “FFT Menu”
•
Set the window to “Hanning”[1]
•
Set the units/div to 10 dB and the ref level to 0 dBV
•
Set the center frequency to 12.2 kHz, and set the frequency span to 24.4 kHz. To choose the center frequency
and frequency span, press the appropriate button and use the cursor knob to change the frequency. If the
oscilloscope tells you that the center frequency or frequency span is at a limit, increase or decrease the
time/div and try again.
•
The oscilloscope now displays

F
(
ω
)

in dB units, defined as
20 log

F
(
ω
)

, where
F
(
ω
)
is the Fourier
transform of windowed (see the footnote regarding Hanning window) segment of the oscilloscope input
f
(
t
)
.
Since
20 log

F
(
ω
)

= 10 log

F
(
ω
)

2
, the scope display is also related to the
energy spectrum

F
(
ω
)

2
of the segment of
f
(
t
)
. We will refer to the display as
frequency spectrum
of the input. Note
that the spectrum is only shown over positive frequencies
f
=
ω
2
π
within the frequency band specified in
the last step above.
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