AMPLITUDE MODULATION(AM)

ObjectivesTo describe the principles of AMTo define and analyze the modulation index To analyze the spectral analysis and

bandwidth calculationTo analyze the power distribution of AM

Lecture overviewPrinciples of amplitude modulation (AM)Modulation indexSpectral analysis and bandwidth calculationPower analysis of AM

Principles of AMDefinitions:

The process of changing the amplitude of a relatively high frequency carrier signal in proportion with the instantaneous value of modulating signal (information)

A process of translating information signal from low band frequency to high bandfrequency.

Cont’d…Information signal cannot travel far. It needs

carrier signal of higher frequency for long distance destination.

Inexpensive, low quality form of modulation

Cont’d…Amplitude of the carrier signal varies with

the information signal. The modulated signal consist of carrier

signal, upper sideband and lower sideband signals

The modulated AM signal (figure 1 & figure 2) needs to go through demodulation process to get back the information signal.

Cont’d…

The AM EnvelopeAM double-sideband full carrier (AM DSBFC)

is the most commonly used and the oldest and simplest form of AM modulation.

Sometimes called conventional AM or simply AM.

The outline of the positive and negative peaks of the carrier frequency re-create the exact shape of the modulating signal known as envelope.

Note that the repetition rate of the envelope is equal to the frequency of the modulating signal.

The Generation of AM Envelope

AM Frequency Spectrum and BandwidthAn AM modulator is a non-linear device.Nonlinear mixing results in a complex output

envelope consists of the carrier frequency and the sum (fc + fm) and difference (fc – fm) frequencies (called cross-products).

The cross-products are displaced from the carrier frequency by fm on both sides of it.

AM modulated wave contains no frequency component of fm.

Frequency spectrum of an AM DSBFC Wave

Bandwidth (BW)The BW of an AM DSBFC wave is equal to the

difference between the highest upper side frequency and lowest lower side frequency:

BW = [fc + fm(max)] – [fc – fm(max)]

= 2fm(max)

For efficiency transmission the carrier and sidebands must be high enough to be propagated thru earth’s atmosphere.

Example 1 For a conventional AM modulator with a

carrier freq of fc = 100 kHz and the maximum modulating signal frequency of fm(max = 5 kHz, determine:

a) Freq limits for the upper and lower sidebands.

b) Bandwidth.c) Upper and lower side frequencies produced

when the modulating signal is a single-freq 3-kHz tone.

d) Draw the output freq spectrum.

Modulation Index and Percent of ModulationUsed to describe the amount of amplitude

change (modulation) present in an AM waveform.

Percentage modulation (%m) is simply the modulation index (m) stated as a percentage.

More specifically percent modulation gives the percentage change in the amplitude of the output wave when the carrier is acted on by a modulating signal.

Cont’d…Mathematically, the modulation index is

And the percentage of modulation index is

c

m

E

Em

m = modulation index

Em = peak change in the amplitude output waveform (sum of voltages from upper and lower side frequencies)

Ec = peak amplitude of the unmodulated carrier

%100% xE

Em

c

m

Determining modulation index from Vmax and Vmin

Cont’d…If the modulating signal is a pure, single-

freq sine wave and the process is symmetrical then the modulation index can be derived as follows:

Therefore,

)(2

1

)(2

1

minmax

minmax

VVE

VVE

c

m

)(

)(

)(2

1

)(2

1

minmax

minmax

minmax

minmax

VV

VV

VV

VVm

Cont’d…Since the peak change of modulated

output wave Em is the sum of the usf and lsf voltages hence,

Then

lsfusflsfusfmEEwhereEEE

)(4

12

)(21

2

minmax

minmax

VV

VVEEE m

lsfusf

Eusf = peak amplitude of the upperside frequency (volts)

Elsf = peak amplitude of the lower side frequency (volts)

Cont’d…From the modulated wave displayed in the

previous slide, the maximum and minimum values of the envelope occurs at

+Vmax = Ec + Eusb + Elsb

+Vmin = Ec – Eusb – Elsb

-Vmax = -Ec - Eusb - Elsb

-Vmin = -Ec + Eusb + Elsb

Modulation Index for trapezoidal patternsModulation index, m can be calculated

using the equation: m = Emax – Emin/ Emax + Emin = Em / Ec = (A - B) / (A + B)

Cont’d…

% modulation of AM DSBFC envelope

Cont’d…For proper AM operation, Ec > Em means that

0≤ m ≤ 1.If Ec < Em means that m > 1 leads to severe

distortion of the modulate wave.If Vc = Vm the percentage of modulation index

goes to 100%, means the maximum information signal is transmitted. In this case, Vmax = 2Vc and Vmin = 0.

Example 2Suppose that Vmax value read from the

graticule on an oscilloscope screen is 4.6 divisions and Vmin is 0.7 divisions. Calculate the modulation index and percentage of modulation.

Example 3 For the AM waveform shown in Figure

below, determinea) Peak amplitude of the upper and lower side

frequencies.b) Peak amplitude of the unmodulated carrier.c) Peak change in the amplitude of the

envelope.d) Modulation index.e) Percent modulation.

AM Envelope for Example 3

The Mathematical Representation and Analysis of AM

Representing both the modulating signal Vm(t) and the carrier signal Vc(t) in trigonometric functions.

The AM DSBFC modulator must be able to produce mathematical multiplication of these two analog signals

)2(sin)( tfVtv mmm

)2(sin)( tfVtv ccc

)2(sin)]2(sin[)( tftfVVtv cmmcam

Cont’d…Substituting Vm = mVc gives:

)2(sin)]2(sin1[

)2(sin)]2(sin[)(

tfVtfm

tftfmVVtv

ccm

cmccam

Constant + mod. signal

Unmodulated carrier

Cont’d…The constant in the first term produces the

carrier freq while the sinusoidal component in the first term produces side bands frequencies

])(2[cos2

])(2[cos2

)2(sin

)]2([sin)]2(sin[)2(sin)(

tffVm

tffVm

tfV

tftfmVtfVtv

mc

c

mc

c

cc

cmcccam

Upper side frequency signal (volts)

Lower side frequency signal (volts)

Carrier frequency signal (volts)

Cont’d…From the equation it is obvious that the

amplitude of the carrier is unaffected by the modulation process.

The amplitude of the side frequencies depend on the both the carrier amplitude and modulation index.

At 100% modulation the amplitudes of side frequencies are each equal to one-half the amplitude of the carrier.

Generation of AM DSBFC envelope showing the time-domain of the modulated wave, carrier&sideband signals

Voltage spectrum for an AM DSBFC wave

Example 4 One input to a conventional AM modulator is a

500-kHz carrier with an amplitude of 20 Vp. The second input is a 10-kHz modulating signal that is of sufficient amplitude to cause a change in the output wave of ±7.5 Vp. Determine

a) Upper and lower side frequencies.b) Modulation index and percentage modulation.c) Peak amplitude of the modulated carrier and

the upper and lower side frequency voltages.d) Maximum and minimum amplitudes of the

envelope.e) Expression for the modulated wave.

AM Power DistributionIn any electrical circuit, the power

dissipated is equal to the voltage squared (rms) divided by the resistance.

Mathematically power in unmodulated carrier is R

V

R

VP ccc 2

)2/( 22

Pc = carrier power (watts)

Vc = peak carrier voltage (volts)

R = load resistance i.e antenna (ohms)

Cont’dThe upper and lower sideband

powers will be

Rearranging in terms of Pc,

R

Vm

R

mVPP cclsbbus 82

)2/( 222

cc

lsbbus Pm

R

VmPP

424

222

Cont’d…The total power in an AM wave is

Substituting the sidebands powers in terms of PC yields

Since carrier power in modulated wave is the same as unmodulated wave, obviously power of the carrier is unaffected by modulation process.

lsbusbct PPPP

]2

1[2

4422

22

mPP

mP

Pm

Pm

PP

ccc

ccct

Power spectrum for AM DSBFC wave with a single-frequency modulating signal

Cont’d…With 100% modulation the maximum

power in both sidebands equals to one-half the carrier power.

One of the most significant disadvantage of AM DSBFC is with m = 1, the efficiency of transmission is only 33.3% of the total transmitted signal. The less wasted in the carrier which brings no information signal.

The advantage of DSBFC is the use of relatively simple, inexpensive demodulator circuits in the receiver.

Example 5 For an AM DSCFC wave with a peak

unmodulated carrier voltage Vc = 10 Vp, a load resistor of RL = 10 and m = 1, determine

a) Powers of the carrier and the upper and lower sidebands.

b) Total sideband power.c) Total power of the modulated wave.d) Draw the power spectrum.

Transmitter Efficiency

Transmitter efficiency, average power from sideband/total = ּת

power absorbed. = m²/ ( 2+m² )

Modulation by a complex information signalPrevious examples are all using a single frequency

modulation signal. In practice, however, modulating signal is very often a complex waveform made up from many sine waves with different amplitudes and frequencies.

Example: if a modulating signal contains three frequencies(fm1, fm2, fm3), the modulated signal will contain the carrier and three sets of side frequencies, spaced symmetrically about the carrier:

])(2[cos2

])(2[cos2

])(2[cos2

])(2[cos2

])(2[cos2

])(2[cos2

)2(sin)(

332

211

tffVm

tffVm

tffVm

tffVm

tffVm

tffVm

tfVtv

mc

c

mc

c

mc

c

mc

c

mc

c

mc

c

ccam

Cont’d..frequency spectrum for complex information signal

fcFc-fm1Fc-fm2Fc-fm3 Fc+fm1Fc+fm2 Fc+fm3

Cont’d..modulation index for complex information signalWhen several frequencies simultaneously

amplitude modulate a carrier, the combined coefficient of modulation is defined as:

mt=total modulation index/coefficient of modulation

m1, m2, m3, mn= modulation index/coefficient of modulation for input 1, 2 ,3 , n

22

3

2

2

2

1t...

nmmmmm

Cont’d..Power calculation for complex information signalThe combined coefficient of modulation can

be used to determine the total sideband power and transmitted power, using:

21

2

4

2

2

2

t

ct

tc

sbt

tc

lsbtusbt

mPP

mPP

mPPP

Example 6 For an AM DSBFC transmitter with an unmodulated

carrier power, Pc= 100W that is modulated simultaneously by three modulating signals, with coefficients of modulation m1=0.2, m2= 0.4, m3=0.3, determine:

a) Total coefficient of modulationb) Upper and lower sideband powerc) Total transmitted power

Low Level AM Transmitter

High Level AM Transmitter

At the end of this chapter, you should be able

To describe the principles of AMTo define and analyze the modulation

index To analyze the spectral analysis and

bandwidth calculationTo analyze the power distribution of AM