AM Modulation and Demodulation - University of Dayton : Homepages

1. Objective
ECE 401L COMMUNICATIONS LABORATORY
LAB 3: AM Modulation and Demodulation
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
The nonlinear circuit can be modeled with a polynomial as follows
v1( t) = mt () + ct () + B.
(1)
v () t = cv () t + cv () t + cv () t + ...
(2)
2 3
2 1 1 2 1 3 1
Limiting this to a second order polynomial yields
( ) ( ) 2
v () t = c mt () + ct () + B + c mt () + ct () + B . (3)
2 1 2
This model seems reasonable, based on inspection of the input-output curve in Figure 4.
Multiplying out the terms in (3) yields
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
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mt ()
ct ()
∑
B
1
RF AMP BPF
() v t 2 () v t 3 ()
1 v t
RF AMP BPF
() v t 2 () v t 3 () v t
Figure 1: AM modulator using nonlinear element
( )
( )
v () t = 2 cmtct ()() + 2 cB+ c ct () (DSB-LC)
2 2 2 1
+ cB + cB
2
2 1
+ + +
2
2 cB 2 c1 mt () cm 2 () t (baseband)
2
cc 2 t
(DC)
+ ()
(harmonic & DC)
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
. (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
( )
v () t = 2 cmtct ()() + 2 cB+ c ct () . (5)
3 2 2 1
Note that for a sinusoidal carrier this represents a DSB-LC signal. The modulation index is given
by
2 c2|min{ mt ()}|
m =
. (6)
2cB+
c
2 1
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 c 1 and c 2 .
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
antenna.
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
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decays (i.e., natural response) at a rate determined by the time constant ( τ = 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
1/ f ≪τ = RC ≪ 1/ B,
(7)
c
where f c is the carrier frequency in Hz and B is the bandwidth of the message signal. A lowpass
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.
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
3

v2() t
(V)
0.3
0.25
0.2
0.15
0.1
0.05
Figure 4: Input/Output voltage relationship for nonlinear circuit (data from PSPICE with D1N4148
diode and 1.8k Ohm resistor wi th no additional load).
3. Prelab Assignment
0
0.2 0.3 0.4 0.5 0.6 0.7 0.8
v1() t (V)
Figure 5: Envelope detector for simple demodulation of DSB-LC signals.
• Design a simple RLC bandpass filter centered at 600kHz with a 40kHz bandwidth (i.e.,
attenuation < -3dB in a 40kHz passband) using available component values. The lab has
10uH, 47uH, and 100uH inductors. The available resistor values are shown in Table 1
and the available capacitor values are shown in Table 2. Make sure you convert your
design frequencies to radians/sec before using standard filter formulas. Verify your
design with a PSPICE frequency sweep analysis.
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
4

• Design a low-gain RF amplifier using a LF353 op-amp for the output stage. Keep in
mind that the gain-bandwidth product for this op-amp is 4MHz. This is higher than the
741 but it still limits our gain considerably for RF applications. For example, with a gain
of 100, the op-amp circuit will only operate out to about 40kHz. Choose a suitable gain
for operation at approximately 600kHz and design a non-inverting amplifier with this
gain. Use available component values.
• Design the envelope detector where ( B f )
4. Procedure
Use available component values.
4.1 Nonlinear Circuit
τ = 1/ + 1/ /2,
B = 5 kHz and f = 600 kHz.
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, v2( t ) , on Channel 2 (Y). If
the output looks as you would expect, according to (2), set the oscilloscope for XY mode (use the
“Main/Delayed” button). Set the scales for approximately 200 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?
4.2 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, mt () , input be a 1kHz sinusoid
from the WaveTek, with a peak-to-peak voltage of approximately 0.2V. 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
WaveTek 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 4.1. 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.
4.3 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.
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
c
c
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4.4 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.
Build an inverting audio amplifier using a standard operational amplifier (i.e., dual LM1458 or
single 741). Connect the microphone. Verify the output of the amplifier on the scope and select
a gain (by changing the feedback resistor value) that yields roughly a 0.2V peak-to-peak output
voltage when speaking normally (you want the same voltage levels that the WaveTek is
producing). Connect the amplifier output in place of the WaveTek input and try transmitting your
voice. How does the transmitter perform compared to the chopper modulator transmitter? Does
it have more range, less range, or about the same?
4.5 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 past the designed 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.
Remove the microphone input from the summer and return to a 10kHz sinusoidal message signal
from the WaveTek. 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
Equation (4).
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.
4.6 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.
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
6

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?
4.7 Computer Aided Analysis
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?
Analyze the nonlinear diode circuit in Figure 3. Insert a DC voltage source in PSPICE and
perform a DC sweep analysis, plotting the output over the resistor. The resulting plot should look
like Figure 4. Use diode model D1N4148. Include the PSPICE plot and schematic in your writeup.
5. Lab Write-up
Create a Word document organized according the numbered procedure sections (Sections 4.1-
4.7). Provide screen captures with detailed descriptions and answers to the questions posed in the
lab next to the appropriate procedure section.
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?
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
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Table 1: Resistor values available in the lab
4.7 5.1 5.6 6.2 6.8 7.5 8.2 9.1
10 12 15 18 20 22 24 27
30 33 36 39 43 47 51 56
62 68 75 82 91 100 120 150
180 200 220 240 270 300 330 360
390 430 470 510 560 620 680 750
820 910 1k 1.2k 1.5k 1.8k 2k 2.2k
2.4k 2.7k 3k 3.3k 3.6k 3.9k 4.3k 4.7k
5.1k 6.2k 6.8k 7.5 8.2k 9.1k 10k 12k
15k 18k 20k 22k 24k 27k 30k 33k
36k 39k 43k 47k 51k 56k 62k 68k
75k 82k 91k 100k 120k 150k 180k 200k
220k 240k 270k 300k 330k 360k 390k 430k
470k 510k 560k 620k 680k 750k 820k 910k
1M 1.2M 1.5M 1.8M 2M 2.2M 2.4M 2.7M
Table 2: Capacitor values available in the lab.
10 pF 0.0022 uF 0.47 uF 470 uF
15 pF 0.0033 uF 0.68 uF 1000 uF
22 pF 0.0047 uF 1 uF 2200 uF
33 pF 0.0068 uF 2.2 uF
47 pF 0.01 uF 3.3 uF
68 pF 0.015 uF 4.7 uF
100 pF 0.1 uF 6.8 uF
150 pF 0.15 uF 10 uF
220 pF 0.047 uF 22 uF
330 pF 0.061 uF 33 uF
470 pF 0.022 uF 47 uF
680 pF 0.033 uF 100 uF
0.001 uF 0.22 uF 220 uF
0.0015 uF 0.33 uF
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
8