Department of Electrical and Computer Engineering,
LAB 3: AM Modulation and Demodulation
1. Objective
Students will build and test a different type of amplitude modulation (AM) transmitter. The
modulation will be accomplished by exploiting the nonlinear characteristics of a diode. The
system will be tested by transmitting a signal to a commercial AM radio. Students will design,
build and test the bandpass filter subsystem and the radio frequency (RF) amplifier stage.
Students will also design, build and test an envelope detector for AM demodulation.
2. Background
2.1 Modulation using diode nonlinearity
Amplitude modulation can be accomplished using a nonlinear element such as a forward biased
diode near the turn-on voltage. The overall system to be implemented is shown in block diagram
form in Figure 1. It is composed of a summer (Figure 2), a nonlinear circuit (Figure 3), a radio
frequency (RF) amplifier, and a bandpass filter. The heart of the system is the nonlinear circuit
shown in Figure 3. This circuit has an input-output function like that shown in Figure 4. This
curve is governed by the voltage-current characteristic curve of the diode. Note that when the
input voltage is in the 0.3V-0.5V range, the curve appears quadratic. We will exploit this to
create a double-sideband large-carrier (DSB-LC) AM signal.
The input to the nonlinear circuit is the sum of a message signal, the carrier, and a DC bias
voltage. Specifically this is given by
v1(t) 􀀠 m(t) 􀀎 c(t) 􀀎 B . (1)
The nonlinear circuit can be modeled with a polynomial as follows
2 3
2 11 2 1 3 1 v (t) 􀀠 c v (t) 􀀎 c v (t) 􀀎 c v (t) 􀀎… (2)
Limiting this to a second order polynomial yields
􀀋 􀀌 􀀋 􀀌2
2 1 2 v (t) 􀀠 c m(t) 􀀎 c(t) 􀀎 B 􀀎 c m(t) 􀀎 c(t) 􀀎 B . (3)
This model seems reasonable, based on inspection of the input-output curve in Figure 4.
Multiplying out the terms in (3) yields
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University of Dayton
Figure 1: AM modulator using nonlinear element
􀀋 􀀌
􀀋 􀀌
2 2 2 1
2 1
2 1 2
( ) 2 ( ) ( ) 2 ( ) (DSB-LC)
2 ( ) ( ) (baseband)
( )
v t cmt c t c B c c t
c B c B
c B c m t c m t
c c t
􀀠 􀀎 􀀎
􀀎 􀀎
􀀎 􀀎 􀀎
􀀎 (harmonic & DC)
. (4)
Note that we get some DC terms, baseband terms, a harmonic term and the desired DSB-LC
signal. The DSB-LC signal can be extracted by putting the signal through a bandpass filter.
Assuming that the carrier is at a much higher frequency than the baseband signal, a bandpass
filter centered at the carrier frequency should be able to effectively eliminate the DC, baseband
and harmonic terms. Neglecting the gain constant from the RF amplifier, this leaves us with the
following signal
v3 (t) 􀀠 2c2m(t)c(t) 􀀎 􀀋2c2B 􀀎 c1 􀀌c(t) . (5)
Note that for a sinusoidal carrier this represents a DSB-LC signal. The modulation index is given
2 1
2 |min{ ( )}|
c mt
c B c
. (6)
Note that the modulation index is controlled in large part by the DC bias voltage and the message
amplitude. We generally have little control over the polynomial parameters 1c and 2 c .
Because of the nature of the diode circuit, the voltage out of the nonlinear circuit is relatively
small (typically less than 0.7V). Thus, an RF amplifier stage can be used to boost the signal
prior to sending the signal to an antenna. As in the previous lab, we use a simple end-loaded wire
2.2 Demodulation using envelope detection
The envelope detector circuit is shown in Figure 5. It comprised of a diode followed by an RC
circuit. When the input voltage is positive, the capacitor charges (i.e., step response). When the
input goes negative, the diode becomes an open circuit and voltage on the capacitor exponentially
m(t ) 􀂦
RF AMP BPF 1v (t) 2v (t) 3v (t)
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decays (i.e., natural response) at a rate determined by the time constant (􀁗 􀀠 RC ). By choosing
an appropriate value for the time constant, the voltage will closely follow the envelope of the
modulated signal. The capacitor gets recharged by every peak but does not fall to zero between
peaks because the time constant limits the decay. Thus, choosing the time constant of the RC
circuit depends on the carrier frequency and message frequency. A rule of thumb is to use
≪ 𝜏 = 𝑅𝐶 < 1/𝐵, (7)
where cf is the carrier frequency in Hz and B is the bandwidth of the message signal in Hz as
well. A low-pass filter can be employed after the envelope detector to smooth out ripple in the
received signal.
Figure 2: Summing amplifier circuit.
Figure 3: Nonlinear circuit used for modulation.
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University of Dayton
Figure 4: Input/Output voltage relationship for nonlinear circuit (data from PSPICE with D1N4148
diode and 1.8k Ohm resistor with no additional load).
Figure 5: Envelope detector for simple demodulation of DSB-LC signals.
0.2 0.3 0.4 0.5 0.6 0.7 0.8
(t) (V)
(t) (V)
v1(t) (V)
2 v (t) (V)
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University of Dayton
3. Procedure
3.1 Nonlinear Circuit
Begin by constructing the nonlinear diode circuit shown in Figure 3. Let the input, v1(t) , be a
saw-tooth wave at 1kHz or higher. Set the peak-to-peak voltage to be 2V and set the DC offset
to +0.5V. Display the input on Channel 1 (X). Display the output, 2v (t) , on Channel 2 (Y). If
the output looks as you would expect, according to (2), set the oscilloscope for XY mode (use the
“Horiz” button and changing the ‘Time Mode’). Set the scales for approximately 500
mV/division on each input. Center the curve, which should look like that in Figure 4, and save a
screen capture. Identify and make note of the range of input voltages for which there is a nearly
quadratic response. What is the approximate center of this input voltage range and what is its
approximate extent?
3.2 Summing Amplifier Subsystem
To multiply two signals, we must add the two signals in question and apply the sum to the input
of the nonlinear circuit. Since one of our signals is an RF carrier, we must construct our summer
using a wide bandwidth operational amplifier (LF353, see datasheet attached). Construct the
inverting summing circuit shown in Figure 2. Let the message input, ()mt , be a 1kHz sinusoid
from the Agilent waveform generator, with a peak-to-peak voltage of approximately 0.2V. Using
the Agilent waveform generator, let the carrier be a 0.5V pp, 10kHz sinusoid, with a –0.4V DC
offset (note that this becomes +0.4V after the inverting summer). Apply the summed input to the
nonlinear circuit. Display the summed signal on Channel 1 and the output of the nonlinear circuit
on Channel 2. Use an external sync from the Agilent waveform generator so as to lock onto the
message signal. Adjust the amplitudes and offset as need to get the summed signal in the “sweet
spot” of the nonlinear circuit, identified in Section 3.1. If you are satisfied with the result, save a
screen capture and comment on what you observe. Try changing the message frequency and
shape (square, sawtooth, etc) and observe the output.
3.3 RF Amplifier
To boost the output of the nonlinear circuit, construct the non-inverting low-gain RF amplifier
that you designed in the pre-lab. This can be built using the second operational amplifier
contained on the LF353 chip. Connect the output of the nonlinear circuit to the input of the RF
amplifier and verify the operation of this circuit.
3.4 AM Broadcasting
Connect a length of wire to the output of the RF amplifier (i.e., an end-loaded wire antenna).
Increase the carrier to approximately 600kHz and let the message to be a sinusoid at
approximately 1kHz. Using the AM radio in the lab, tune in your signal by matching your
carrier frequency and the receiver. Try transmitting different message frequencies and
waveforms. Comment on what you hear. Demonstrate your successful system for the TA.
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3.5 Band Pass Filter
While not necessary for operation during the tests above, a bandpass filter would be required in
any commercial AM transmitter to limit each station to approximately 10kHz (center frequencies
ranging from 540kHz to 1600kHz). Construct the bandpass filter you designed in the pre-lab (do
not incorporate into transmitter yet) and test it by applying a sinusoidal input and sweeping the
frequency for a range centered about the center frequency. Once you are satisfied with its
operation, incorporate the filter into your system. If you wish to test transmission with the BPF in
place, you need to move your antenna connection to the output of the BPF. Note that the passive
BPF will cause some attenuation, even in the passband, negatively impacting transmission power.
Change the frequency of your message to a 10KHz sinusoidal signal. Display the output of the
RF amplifier (input to BPF) on Channel 1 and the output of the BPF on Channel 2. Save a screen
capture showing these signals. Try different message signals and frequencies and observe the
output. How does the time-domain output differ before and after the BPF? Explain the
differences you observe. It may be helpful to refer to Equations (4) & (5).
Use the FFT function to display the frequency spectrum of the signal before the BPF. Set the
FFT for 2MSa/sec with a center frequency of 600kHz and a span of 500kHz. Try changing the
message frequency, carrier frequency, message waveform, and observe the corresponding spectra.
Try to understand what you observe. Save a screen capture and explain the source of the major
peaks in the spectrum that you capture. Be sure to capture the peak at the fundamental frequency
of the carrier and the peaks from the message (the sideband power). Next, observe the FFT of the
signal after the BPF. Save a screen capture and explain what you observe.
3.6 Demodulation
Construct the envelope detector in Figure 5 using the design values from the pre-lab. Test your
detector with an AM signal from a laboratory signal generator. Initially use a 600kHz, 5V peakto-
peak, sinusoidal carrier and 1kHz sinusoidal message (refer to Lab 1 if necessary). Observe
the input AM signal on Channel 1 and your detector output on Channel 2. Use the external sync
from the message signal generator. Save a screen capture illustrating the successful demodulation
of an AM signal. Vary the modulation level and modulation waveform and observe the results.
What happens when you over-modulate the carrier (modulation index > 1)? Vary the carrier
frequency and observe the results? For what range of carrier frequencies does you detector
appear to adequately demodulate a 1kHz sinusoidal message? What range of message
frequencies does your detector adequately demodulate with a fixed 600kHz carrier?
4. Computer Aided Analysis
Implement and simulate/verify the lab-experiment (summing inverting unity gain
amplifier, followed by a non-linear circuit cascaded with an RF low-gain non-inverting
amplifier/booster and a BPF filter) using NI Multisim. You may use a 0.2V peak-to-peak
1 KHz sinusoidal signal as the input message signal. Provide screen capture(s) of your
circuit schematic and corresponding input/output waveforms for the relevant stages by
making use of an Agilent Scope. Make sure to annotate the names of all your teammates
on the circuit design schematic (MultiSim: Go to Place -> Text). Note that PowerPoint
slides will be available to guide you through the complete simulation process of the labexperiment.
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University of Dayton
Calculate the frequency response of your BPF by hand and plot the magnitude and phase
frequency response with MATLAB. Use units of dB for the gain (magnitude frequency
response), and let the horizontal axis be frequency in Hz plotted on a log axis (i.e., use
semilogx(.)). Using the equation editor in Word, include a few steps and the final result of your
frequency response analysis in your report. What is the theoretical attenuation in dB at the
carrier? What is the theoretical attenuation in dB 10kHz from the carrier?
5. Lab Group report write-up
Create a Word document organized according the numbered procedure sections (Sections 3 and
4). Provide screen captures with detailed descriptions and answers to the questions posed in the
lab next to the appropriate procedure section.
1. One member of your team is required to upload an electronic copy of the group
report on isidore.
2. As a team you are also required to submit one hardcopy of the group report.
Bonus Question: In the 1700’s a major scientific problem of the day was how to determine the
longitude of a vessel at sea. Latitude, you see, can be determined by measuring the angle of the
sun to the horizon at it highest point in the day. Longitude was not so simple in those days. Who
is credited with solving this problem and how was it solved?