SIGNAL SPECTRA EXPERIMENT AMPLITUDE MODULATION

NATIONAL COLLEGE OF SCIENCE AND TECHNOLOGY
Amafel Building, Aguinaldo Highway Dasmariñas City, Cavite

Experiment No. 5
AMPLITUDE MODULATION

Cauan, Sarah Krystelle P. August 09. 2011
Signal Spectra and Signal Processing/BSECE 41A1 Score:

Engr. Grace Ramones
Instructor

OBJECTIVES
1. Demonstrate an amplitude-modulated carrier in the time domain for different modulation
indexes and modulating frequencies.
2. Determine the modulation index and percent modulation of an amplitude-modulated carrier
from the time domain curve plot.
3. Demonstrate an amplitude-modulated carrier in the frequency domain for different modulation
indexes and modulating frequencies.
4. Compare the side-frequency voltage levels to the carrier voltage level in an amplitude-modulated
carrier for different modulation indexes.
5. Determine the signal bandwidth of an amplitude-modulated carrier for different modulating
signal frequencies.
6. Demonstrate how a complex modulating signal generates many side frequencies to form the
upper and lower sidebands.

SAMPLE COMPUTATIONS

Step 3 (Expected Modulating index)

Step 4 (Measured Modulating index)

Step 7 Question (Modulating Frequency)

Step 8 (Calculated Bandwidth)

Step 9 (Measured Bandwidth)

Step 9 Question (Percent Difference)

Step 10 (Voltage Amplitude of Side Frequencies)



Step 13 (Calculated Modulating index)


Step 16 (Calculated Bandwidth)

Step 17 (Voltage Amplitude of Side Frequencies)




Step 26 (Bandwidth)

Step 28 (Bandwidth)



DATA SHEET
Materials
Two function generators
One dual-trace oscilloscope
One spectrum analyzer
One 1N4001 diode
One dc voltage supply
One 2.35 nF capacitor
One 1 mH inductor
Resistors: 100 Ω, 2 kΩ, 10 kΩ, 20 kΩ

Theory:
The primary purpose of a communications system is to transmit and receive information such as
audio, video, or binary data over a communications medium or channel. The basic components in a
communications system are the transmitter communications medium or channel, and the receiver.
Possible communications media are wire cable, fiber optic cable, and free space. Before the
information can be transmitted, it must be converted into an electrical signal compatible with the
communications medium, this is the purpose of the transmitter while the purpose of the receiver is
to receive the transmitted signal from the channel and convert it into its original information signal
form. Is the original electrical information signal is transmitted directly over the communications
channel, it is called baseband transmission. An example of a communications system that uses
baseband transmission is the telephone system.
Noise is defined as undesirable electrical energy that enters the communications system and
interferes with the transmitted message. All communication systems are subject to noise in both the
communication channel and the receiver. Channel noise comes from the atmosphere (lightning),
outer space (radiation emitted by the sun and stars), and electrical equipment (electric motors and
fluorescent lights). Receiver noise comes from electronic components such as resistors and
transistors, which generate noise due to thermal agitation of the atoms during electrical current flow.
In some cases obliterates the message and in other cases it results in only partial interference.
Although noise cannot be completely eliminated, it can be reduced considerably.
Often the original electrical information (baseband) signal is not compatible with the
communications medium. In that case, this baseband signal is used to modulate a higher-frequency
sine wave signal that is in a frequency spectrum that is compatible with the communications
medium. This higher-frequency sine wave signal is called a carrier. When the carrier frequency is in
the electromagnetic spectrum it is called a radio frequency (RF) wave, and it radiates into space
more efficiently and propagates a longer distance than a baseband signal. When information is
transmitted over a fiber optic cable, the carrier frequency is in the optical spectrum. The process of
using a baseband signal to modulate a carrier is called broadband transmission.
There are basically three ways to make a baseband signal modulate a sine wave carrier: amplitude
modulation (AM), frequency modulation (FM), and phase modulation (PM). In amplitude modulation
(AM), the baseband information signal varies the amplitude of the higher-frequency carrier. In
frequency modulation (FM), the baseband information signal varies the frequency of the higher-
frequency carrier and the carrier amplitude remains constant. In phase modulation (PM), the
baseband information signal varies the phase of the high-frequency carrier. Phase modulation (PM)
is different fork of frequency modulation and the carrier is similar in appearance to a frequency-
modulated signal carrier. Therefore, both FM and PM are often referred to as an angle modulation. In
this experiment, you will examine the characteristics of amplitude modulation (AM).

In amplitude modulation, the carrier frequency remains constant, but the instantaneous value of the
carrier amplitude varies in accordance with the amplitude variations of the modulating signal. An
imaginary line joining the peaks of the modulated carrier waveform, called the envelope, is the same
shape as the modulating signal with the zero reference line coinciding with the peak value of the
unmodulated carrier. The relationship between the peak voltage of the modulating signal (V m) and
the peak voltage of the unmodulated carrier (Vc) is the modulation index (m), therefore,

Multiplying the modulation index (m) by 100 gives the percent modulation. When the peak voltage of
the modulating signal is equal to the peak voltage of the unmodulated carrier, the percent
modulation is 100%. An unmodulated carrier has a percent modulation of 0%. When the peak
voltage of the modulating signal (Vm) exceeds the peak voltage of the unmodulated carrier (Vc)
overmodulation will occur, resulting in distortion of the modulating (baseband) signal when it is
recovered from the modulated carrier. Therefore, if it is important that the peak voltage of the
modulating signal be equal to or less than the peak voltage of the unmodulated signal carrier (equal
to or less than 100% modulation) with amplitude modulation.
Often the percent modulation must be measured from the modulated carrier displayed on an
oscilloscope. When the AM signal is displayed on an oscilloscope, the modulation index can be
computed from

where Vmax is the maximum peak-to-peak voltage of the modulated carrier and Vmin is the minimum
peak-to-peak voltage of the modulated carrier. Notice that when Vmax = 0, the modulation index (m)
is equal to 1 (100% modulation), and when Vmin = Vmax, the modulation index is equal to 0 (0%
modulation).
when a single-frequency sine wave amplitude modulates a carrier, the modulating process causes
two side frequencies to be generated above and below the carrier frequency be an amount equal to
the modulating frequency (fm). The upper side frequency (fuse) and the lower side frequency (fluff) can
be determine from

A complex modulating signal, such as a square wave, consists of a fundamental sine wave frequency
and many harmonics, causing many side frequencies to be generated. The highest upper side
frequency and the lowest lower side frequency are determined be the highest harmonic frequency
(fm (max), and the highest lower side frequency and the lower upper side frequency are determined by
the lowest harmonic frequency (fm (min)). The band of frequencies between (fC + fm (min)) and (fC + fm
(max)) is called the upper sideband. The band of frequencies between (f C – fm (min)) and (fC – fm (max)) is
called the lowers sideband. The difference between the highest upper side frequency (fC + fm (max))
and the lowest lower side frequency (fC – fm (max)) is called the bandwidth occupied by the modulated
carrier. Therefore, the bandwidth (BW) can be calculated from

This bandwidth occupied by the modulated carrier is the reason a modulated carrier is referred to as
broadband transmission.
The higher the modulating signal frequencies (meaning more information is being transmitted) the
wider the modulated carrier bandwidth. This is the reason a video signal occupies more bandwidth

than an audio signal. Because signals transmitted on the same frequency interfere with one another,
this carrier bandwidth places a limit on the number of modulated carriers that can occupy a given
communications channel. Also, when a carrier is overmodulated, the resulting distorted waveshape
generates a harmonic that generate additional side frequencies. This causes the transmitted
bandwidth to increase and interfere with other signals. This harmonic-generated sideband
interference is called splatter.
When an AM signal on an oscilloscope, it is observed in the time domain (voltage as a function time).
The time domain display gives no indication of sidebands. In order to observe the sidebands
generated by the modulated carrier, the frequency spectrum of the modulated carrier must be
displayed in the frequency domain (sine wave voltage levels as a function of frequency) on a
spectrum analyzer.
A sine wave modulated AM signal is a composite of a carrier and two side frequencies, and each of
these signals transmits power. The total power transmitted (PT) is the sum of each carrier power
((PC) and the power in the two side frequencies (PUSF and PUSB). Therefore,

The total power transmitted (PT) can also be determined from the modulation index (m) using the
equation

Therefore, the total power in the side frequencies (PSF) is

and the power in each side frequency is

Notice that the power in the side frequencies depends on the modulation index (percent modulation)
and the carrier power does not depend on the modulation index. When the percent modulation is
100% (m = 1), the total side-frequency power (PSF) is one-half of the carrier power (PC) and the
power in each side frequency (PUSF and PLSF) is one-quarter of the carrier power (PC). When the
percent modulation is 0%, the total side-frequency power (PSF) is zero because there are no side
frequencies in an unmodulated carrier. Based on these results, it is easy to calculate that an
amplitude-modulated carrier has all of the transmitted information in the sidebands and no
information in the carrier. For 100% modulation, one-third of the total power transmitted is in the
sidebands and two-thirds of the total power is wasted in the carrier, which contains no information.
When a carrier is modulated by a complex waveform, the combined modulation index of the
fundamental and all of the harmonics determines the power in the sidebands. In a later experiment,
you will see how we can remove and transmit the same amount of information with less power.

Because power is proportional to voltage squared, the voltage level of the frequencies is equal to the
square root of the side-frequency power. Therefore the side-frequency voltage can be calculated
from

This means that the voltage of each side frequency is equal to one-half the carrier voltage for 100%
modulation of a sine-wave modulated carrier. When a carrier is modulated by a complex waveform,
the voltage of each side frequency can calculated from the separate modulation indexes of the
fundamental and each harmonic.
A circuit that mathematically multiplies a carrier and modulating (baseband) signal, and then adds
the carrier to the result, will produce an amplitude-modulated carrier. Therefore, the circuit in Figure
6-1 will be used to demonstrate amplitude modulation. An oscilloscope has been attached to the
output to display the modulated carrier in the time domain. A spectrum analyzer has been attached
to the output to display the frequency spectrum of the amplitude-modulated carrier in the frequency
domain.

XSA1 XSC1
Modulating Signal
XFG1
Ext T rig
+
_
IN T A B
+ _ + _ 0
0 MULTIPLIER SUMMER
3
Y
C
X 2 A 1
1 V/V
4 1 V/V 0 V B 0V

Carrier
1 Vpk
100kHz
0 0°

Procedure
Step 1 Open circuit file Fig 6-1. This circuit will demonstrate how mathematical
multiplication of a carrier and a modulating (baseband) signal, and then adding the
carrier to the multiplication result, will produce an amplitude modulated carrier.
Bring down the function generator enlargement and make sure that the following
settings are selected: Sine Wave, Freq=5kHz, Ampl = 1V, Offset=0. Bring down the
oscilloscope enlargement and make sure that the following settings are selected:
Time base (Scale = 50 µs/Div, Xpos= 0, Y/T) Ch A (Scale = 1 V/Div, Ypos = 0, DC)
Trigger (Pos edge, Level = 0, Auto).
Step 2 Run the simulation to one full screen display, then pause the simulation. Notice that
you have displayed an amplitude-modulated carrier curve plot on the oscilloscope
screen. Draw the curve plot in the space provided and show the envelope on the
drawing.

Step 3 Based on the function generator amplitude (modulating sine wave voltage, Vm) and
the voltage of the carrier sine wave (Vc), calculate the expected modulation index (m)
and percent modulation.
m=1 or 100%
Step 4 Determine the modulation index (m) and percent modulation from the curve plot in
Step 2.
m=1 or 100%
Question: How did the value of the modulation index and percent modulation determined from the
curve plot compare with the expected value calculated in Step 3?
The modulation index measured from the curve plot and the expected value
calculated are equal. They do not have any difference.

Step 5 Bring down the spectrum analyzer enlargement and make sure that the following
settings are selected: Frequency (Center = 100 kHz, Span = 100 kHz), Amplitude
(Lin, Range = 0.2 V/Div) Resolution = 500 Hz.
Step 6 Run the simulation until the Resolution Frequency match, then pause the simulation.
You have displayed the frequency spectrum for a modulated carrier. Draw the
spectral plot in the space provided.

Step 7 Measure the carrier frequency (fc), the upper side frequency (fUSF), the lowest side
frequency (fLSF), and the voltage amplitude of each spectral line and record the
answer on the spectral plot.
fc = 100 kHz Vc = 999.085 mV
fLSF = 95.041 kHz VLSF = 458.267 mV
fUSF = 104.959 kHz VUSF = 458.249 mV
Question: What was the frequency difference between the carrier frequency and each of the side
frequencies? How did this compare with the modulating signal frequency?
fc – fLSF = fm = 4.959 kHz fUSF – fc = fm = 4.959 kHz
The result above and the modulating signal frequency from the function generator
differs with 0.041 kHz or 0.82%
How did the frequency of the center spectral line compare with the carrier frequency?
Both the frequency of the center spectral line and the carrier frequency is 100 kHz.
There is no difference between the values of the two.
Step 8 Calculate the bandwidth (BW) of the modulated carrier based on the frequency of the
modulating sine wave.
BW = 10 kHz
Step 9 Determine the bandwidth (BW) of the modulated carrier from the frequency spectral
plot and record your answer on the spectral plot.
BW = 9.918 kHz
Question: How did the bandwidth of the modulated carrier from the frequency spectrum compare
with the calculated bandwidth in Step 8?
The measured and the calculated bandwidths differ with just 0.082 kHz or 0.82%.

Step 10 Calculate the expected voltage amplitude of each side frequency spectral line (VUSF
and VLSF) based on the modulation index (m) and the carrier voltage amplitude
VUSF = VLSF = 0.5 V
Questions: How did the calculated voltage values compare with the measured values in on the
spectral line?
There is only 0.0407 V difference between the calculated VUSF and the measured
values in on the spectral line. It is only 9.11% difference.
What was the relationship between the voltage levels of the side frequencies and the voltage level of
the carrier? Was this what you expected for this modulation index?
The voltage levels of the side is one-half of the carrier voltage. Yes, this is expected
for a sine-wave modulated carrier with 100% modulation.
Step 11 Change the modulating signal amplitude (function generator amplitude) to 0.5 V (500
mV). Bring down the oscilloscope enlargement and run the simulation to one full-
screen display, then pause the simulation. Notice that you have displayed an
amplitude-modulated carrier curve plot on the oscilloscope screen. Draw the curve
plot in the space provided and show the envelope on the drawing.

Step 12 Based on the voltage of the modulating (baseband) sine wave (Vm) and the voltage of
the carrier sine wave (Vc), calculate the expected modulation index (m) and the
percent modulation.
m = 0.5 = 50%
Step 13 Determine the modulation index (m) and the percent modulation from the curve plot
in Step 11.
m = 0.51 = 51%
Questions: How did the value of the modulation index and percent modulation determined from the
curve plot compare with the expected value calculated in Step 12?
The difference of the modulation indexes are only 0.01. The measured values is
2% different with the expected modulation index.
How did this percent modulation compare with the percent modulation in Step 3 and 4? Explain any
difference.

It is decreased by half. The percent modulation is directly proportional to the
modulating amplitude, that is why when the modulating amplitude reduced by
50% the percent modulation also decreased by half.

Step 14 Bring down the spectrum analyzer enlargement. Run the simulation until the
Resolution Frequency match, then pause the simulation. You have plotted the
frequency spectrum for a modulated carrier. Draw the spectral plot in the space
provided.

Step 15 Measure the carrier frequency (fC), the upper side frequency (fUSF), the lower side
frequency (fLSF), and the voltage amplitude of each spectral line and record the
answers on the spectral plot.
fc = 100 kHz Vc = 998.442 mV
fLSF = 95.041 kHz VLSF = 228.996 mV
fUSF = 104.959 kHz VUSF = 228.968 mV
BW = 9.918 kHz
Question: How did the bandwidth of the modulated carrier from this frequency spectrum compare
with the bandwidth on the spectral plot in Step 6? Explain.
The bandwidth of the modulated carrier from the frequency spectrum and the
bandwidth on the spectral plot in Step 6 have both the same values. The bandwidth
is not affected by the variation of the amplitude of the modulating signal but the
frequency of the modulating signal.
Step 17 Calculate the expected voltage amplitude of each side frequency spectral line (VUSF)
based on the modulation index (m) and the carrier voltage amplitude (VC).
VUSF = VLSF = 0.25 V
Questions: How did the calculated voltage values compare with the measured values in on the
spectral plot?

The difference between the calculated voltage and the measured values based on
the spectral plot is 9.17%.
What was the relationship between the voltage levels of the side frequencies and the voltage level of
the carrier? How did it compare with the results in Step 6?
The voltage levels of the side frequencies are one-fourth of the voltage level of the
carrier. Compare to Step 6, it decreases by half because of the reduction of the
modulation index to 50%

Step 18 Change the modulating amplitude (function generator amplitude) to 0 V (1 µV). Bring
down the oscilloscope enlargement and run the simulation to one full screen display,
then pause the simulation. Draw the curve plot in the space provided.

Step 19 Based on the voltage of the modulating (baseband) sine wave (Vm) and the voltage of
the carrier sine wave (Vc), calculate the expected modulation index (m) and percent
modulation.
m = 0.1 × 10-6
Step 18.
m=0
Questions: How did the value of the modulation index and the percent modulation determined from
the curve plot compare with the expected value calculated in Step 19?
The difference between the computed and the measured modulation indexes is
only a 0.1 × 10-6 difference. It is almost equal to zero.
How did this waveshape compare with the previous amplitude-modulated waveshapes? Explain any
difference.
The waveshape of is like the waveshape of the carrier. The reason for this is that
the modulating signal is almost zero, and appears like a carrier only.

Step 21 Bring down the spectrum analyzer. Run the Resolution Frequencies match, then
pause the simulation. You have plotted the frequency spectrum for an unmodulated
carrier. Draw the spectral plot in the space provided.

Step 22 Measure the frequency and voltage amplitude of the spectral line and record the
values on the spectral plot.
fc = 100 kHz Vc = 998.441 mV
Questions: How did the frequency of the spectral line compare with the carrier frequency?
The frequency of the spectral line and the carrier frequency are the same.
How did the voltage amplitude of the spectral line compare with the carrier amplitude?
The difference between the amplitude of the spectral line and the carrier amplitude
is 0.16%.
How did this frequency spectrum compare with the previous frequency spectrum?
Because of the absence of the modulating frequency, the frequency spectrum only
showed the carrier frequency. There is no side frequencies.
Step 23 Change the modulating frequency to 10 kHz and the amplitude back to 1 V on the
function generator. Bring down the oscilloscope and run the simulation to one full
screen display, then pause the simulation. Notice that you have displayed an
amplitude-modulated carrier curve plot on the oscilloscope screen. Draw the curve
plot in the space provided and show the envelope on the drawing.

Question: How did this waveshape differ from the waveshape for a 5 kHz modulating frequency in
Step 2?
In this waveshape, there is greater number of cycles per second. This is because the
frequency of the modulating signal increases.
Step 24 Bring down the spectrum analyzer enlargement. Run the simulation until the
Resolution Frequencies match, then pause the simulation. You have plotted the
frequency spectrum for a modulated carrier. Draw the spectral plot in the space
provided.

Step 25 Measure the carrier frequency (fC), the upper side frequency (fUSF), and the lower side
frequency (fLSF) of the spectral lines and record the answers on the spectral plot.
fc = 100 kHz
fLSF = 90.083 kHz
fUSF = 109.917 kHz
BW = 19.834 kHz
Question: How did the bandwidth of the modulated carrier for a 10 kHz modulating frequency
compare with the bandwidth for a 5 kHz modulating frequency in Step 6?
The bandwidth of the modulated carrier increased by 10 kHz.
Step 27 Measure the voltage amplitude of the side frequencies and record your answer on the
spectral plot in Step 24.
Vc = 998.436 mV
VLSF = 416.809 mV
VUSF = 416.585 mV
Question: Was there any difference between the amplitude of the side frequencies for the 10 kHz plot
in Step 24 and the 5 kHz in Step 6? Explain.
Yes there is a difference of 41.458 mV. Meaning, the frequency of the modulating
frequency affects the amplitude of the side frequency. It is inversely proportional to
the amplitude.
Step 28 Change the modulating frequency to 20 kHz on the function generator. Run the
simulation until the Resolution Frequencies match, the pause the simulation. Measure

the bandwidth (BW) of the modulated carrier on the spectrum analyzer and record
the value.
BW = 39.67 kHz
Question: How did the bandwidth compare with the bandwidth for the 10 kHz modulating
frequency? Explain.
The bandwidth increased by 20 kHz. The reason for this is that bandwidth is twice
the modulating frequency.
Step 29 Change the modulating signal frequency band to 5kHz and select square wave on the function
generator. Bring down the oscilloscope enlargement and run the simulation to one full screen
display, then pause the simulation. Notice that you have displayed a carrier modulated by a
square wave on the oscilloscope screen. Draw the curve plot in the space proved and show
the envelope on the drawing.

Question: How did this waveshape differ from the waveshape in step 2?
The waveshape is complex wave. The modulating signal is square wave.
Step 29.
m=1
Step 31 Bring down the spectrum analyzer enlargement. Run the simulation until the Resolution
Frequency match, the pause the simulation. You have plotted the frequency spectrum for a
square-wave modulated carrier. Draw the spectral plot in the space provided. Neglect any
side frequencies with amplitudes less than 10% of the carrier amplitude.

Step 32 Measure the frequency of the spectral lines and record the answers on the spectral plot.
Neglect any side frequencies with amplitudes less than 10% of the carrier amplitude.
fc = 100 kHz
fLSF1 = 95.041 kHz fLSF2 = 85.537 kHz
fUSF1 = 104.959 kHz fUSF2 = 114.876 kHz
Question: How did the frequency spectrum for the square-wave modulated carrier differ from the
spectrum for the sine wave modulated carrier in Step 6? Explain why there were different.
There are lot of side bands generated in this frequency domain. Because square
wave consists of a fundamental sine wave frequency and many harmonics, there
are lot of side frequencies generated.
plot and record your answer on the spectral plot. Neglect any side frequencies with
amplitudes less than 10% of the carrier amplitude.
9.506 kHz
Question: How did the bandwidth of the 5-kHz square-wave modulated carrier compare to the
bandwidth of the 5-kHz sine wave modulated carrier in Step 6? Explain any difference.
There is a 0.002 kHz difference between the waveshape. However, the bandwidth
of the fUSF1 and fLSF1 is equal to the answer in Step 6.
Step 34 Reduce the amplitude of the square wave to 0.5 V (500 mV) on the function generator. Bring
down the oscilloscope enlargement and run the simulation to one full screen display, then pause the
simulation. Draw the curve plot in the space provided.

Step 35 Determine the modulation index (m) and percent modulation from the curve plot in Step 34.
m = 0.5 = 50%

Question: What is the difference between this curve plot and the one in Step 29? Explain.
The minimum amplitude modulated signal is not at 0 V unlike with Step 29. This is
because the percent modulation is 50%.

CONCLUSION

From the word itself, in amplitude-modulated signal the instantaneous value of the carrier
amplitude varies while the carrier frequency is constant. When a circuit added a carrier to the
product of a carrier and modulating signal will produce an amplitude-modulated carrier.

The oscilloscope displays the time-domain which is the relationship of the time and the
amplitude voltage. The percent modulation is the ratio of the peak amplitude of modulating signal
and the peak amplitude of the carrier signal. It is directly proportional to the modulating signal and
inversely proportional to the carrier signal. It can also be determined through the maximum and the
minimum amplitude of the modulated signal. The amplitude variation of the carrier peaks has the
shape of the modulating signal and is referred to as envelope.

Moreover, the spectrum analyzer displays the frequency domain which is the relationship of
the amplitude voltage and the frequency. The carrier frequency is at the center and has the highest
voltage amplitude. The two side bands is generated by a sine wave modulating signal. The signals
generated by the modulation process are called sidebands and occur at frequencies above and below
the carrier frequency. The amplitude of the sidebands is half the modulation index and the carrier
voltage. So the amplitude of the sidebands is directly proportional to the modulation index and the
carrier voltage. The bandwidth is twice the frequency of the modulating frequency.

Lastly, a complex modulating signal generates lot of frequency. A square wave modulating
signal is an example of complex signal because of its a fundamental sine wave frequency and many
harmonics.

SIGNAL SPECTRA EXPERIMENT AMPLITUDE MODULATION

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