CHAPTER 2: AMPLITUDE MODULATION (AM)Chapter 2/AM 2A communication channel can be almost anything, a pair of conductors or an optical fiber.Sometimes a channel can carry information signal directly and it would not be possible to transmit more than one signal without interference. Such situation require the use of a carrier signal whose frequency will propagate through the channel.This carrier wave will be altered or modulated by the information signal.When a carrier is used, the information signal is also known as the modulating signal.In an amplitude modulation technique, the base band information which is to be conveyed is impressed on to the carrier by varying its instantaneous amplitude.INTRODUCTIONChapter 2/AM 3There are three types of AM: Full Amplitude Modulation ( AM ) Double Sideband Suppressed Carrier (DSBSC) Single Sideband ( SSB )Amplitude modulation is relatively inexpensive, low-quality form of modulation that is used for commercial broadcasting of both audio and video signal.Also used for two-way mobile radio communications such as citizens band (CB) radio.AM modulators are nonlinear devices with two inputs and one output.TYPES OF AMPLITUDE MODULATIONChapter 2/AM 4This type of modulation was the first one in use in the very early days of broadcasting in the 1920s and has developed several names in the course of time.It is often called just simply amplitude modulation (AM) but sometimes envelope modulation or even double sideband with carrier (DSBWC).Also the term full AM is often to mean maximum amplitude modulation (index modulation, m=1).It is obtained by taking a single frequency carrier and altering its amplitude instantaneously in proportion to the instantaneous magnitude of a baseband signal.FULL AMChapter 2/AM 5The carrier is almost always a sine wave and the modulating signal can be a sine wave but is more often arbitrary waveform, such as an audio signal. Amplitude modulation is created by using the instantaneous modulating signal voltage to vary the amplitude of the modulated signal.Thus,AM IN GENERALt E t vt E t vc c cm m mcos ) (: signal Carrier cos ) (: signal Baseband==t E Et v E vm m cm c c cos) ('+ =+ =Chapter 2/AM 6The modulation index for AM is often quoted as a percentage and it is given by:For full AM, and normallyTherefore, the modulated signal for AM is: AM: TIME DOMAIN1 0where, = mEEmcmm c m cf f >> >> and 1 = mt t m Et tEEEt t E Et v vc m cc mcmcc m m cc c AM cos ) cos 1 (cos ) cos 1 (cos ) cos (cos'+ =+ =+ ==Chapter 2/AM Prepared By: Pn.Norliza Mohamed 7AM WAVEFORMChapter 2/AM 8EXAMPLEA carrier wave with an rms voltage of 2V and a frequency of 1.5MHz is modulated by a sine wave with a frequency of 500Hz and amplitude of 1 Vrms. Write an equation for the resulting signal.Solution:V 10 x42 . 9 sin ) 10 x14 . 3 sin 41 . 1 83 . 2 (Thus,sin ) sin (know, Werad/s 10 x14 . 3 500 x2rad/s 10 x42 . 9 10 x5 . 1 x2V 41 . 1 1 x2V 83 . 2 2 x26 336 6t t vt t E E vEEAMc m m c AMmcmc+ =+ == == == == = x x Chapter 2/AM 9MODULATION INDEXThe amount by which the signal amplitude is changed in modulation depends on the ratio between the amplitudes of the modulating signal and the carrier and it is given by:Modulation can also be expressed as a percentage, with percent modulation found by multiplying m by 100. For example, m = 0.5 correspond to 50% modulation.m also can be measured directly from AM waveform by measuring the peak-to-peak voltages A and B as shown.1 0where, = mEEmcmChapter 2/AM 10MODULATION INDEXAM waveform with m factorB AB Am+

=Chapter 2/AM 11max+Emin

Emin+Emax

EcE +cE mEmEmEmE ) . J t m E Envelopem c cos 1+ =+ ) . J t m E Envelopem c cos 1+=

MODULATION INDEX CALCULATIONSChapter 2/AM 12If the modulating signal is pure, single-frequency sine wave and the modulation process is symmetrical. Then percent modulation can be derived as follows:% 100 x ) () ( , percentage In ) ( 2 1) ( 2 1

Therefore,andWhere,2and 2min maxmin maxmin maxmin maxmin maxmin max min maxE EE EmE EE EEEmE E E E E EE EEE EEcmm c m cc m+

=+

== = + =+=

=MODULATION INDEX CALCULATIONSChapter 2/AM 13MODULATION INDEXPercent modulation of AM envelope: (a) modulating signal (b) unmodulated carrier (c) 50% modulated wave (d) 100% modulated wave.Chapter 2/AM 14MODULATION INDEXThe peak change in the amplitude of the output wave, Em is the sum of the voltages from the upper and lower side frequencies.Therefore:4 2) ( 2 1

2

know, We2or2 2 Thus, since but min max min maxmin maxE E E EE EE EEEEEEE E E E E EE E E E Elsf usfmmusfmlsflsf lsf lsf lsf usf mlsf usf lsf usf m

=

= =

== = = + = + == + =Chapter 2/AM 15EXAMPLEFrom the AM waveform shown, determine:(a) Peak amplitude of the lower and upper side frequencies(b) Peak amplitude of the unmodulated carrier(c )Peak change in the amplitude of the envelope (d) Index of modulation (e) Percent modulationAnswer:(a) 4V(b) 10V(c) 8V(d) 0.8(e) 80%Chapter 2/AM 16EFFECT OF MODULATION INDEXc mE E m where, 1c mE E m > > where, 1c mE E m = = where, 1Chapter 2/AM 17OVERMODULATIONWhen the modulation index is greater than 1, overmodulation is said to be present.It creates distortion in demodulated signal and may result in the signal occupyinga larger bandwidth than normal.Since spectrum space is tightly controlled by law, overmodulation of an AMtransmitter is actually illegal, so it must be prevented.180ophase changeChapter 2/AM 18From the general expression of the modulated signal for AM, we can expand it by using a trigonometric rules. Thus,Hence, three different frequencies can be obtained.tmEtmEt Et t mE t Et t m E vm ccm ccc cc m c c cc m c AM) cos(2) cos(2coscos cos coscos ) cos 1 ( + ++ =+ =+ =x x x2frequency, sideband Upper 2frequency, sideband Lower 2frequency, carrierOriginalm cm c USBm cm c LSBccf f ff f ff+= + =

===FREQUENCY DOMAINChapter 2/AM 19AM FREQUENCY SPECTRUMChapter 2/AM 20EXAMPLE1. Calculate the modulation index for the Emax= 150mV and Emin = 70mV2. a) A 1 MHz carrier with an amplitude of 1V peak is modulated by a 1 kHz signal with m = 0.5. Sketch the voltage spectrumb) If an additional 2 kHz signal modulates the carrier with m = 0.2.Sketch the voltage spectrum3. CB radio channels are 10 kHz apart. What is the maximum modulation frequency that can be used if a signal is to remain entirely within its assigned channel?Answer:(a) 0.364(c) 10kHzChapter 2/AM 21AM BANDWIDTHThe bandwidth needed to transmit a full AM signal can be seen from the spectrum.In general, a narrow bandwidth is desirable.In any situation where spectrum space is limited, a narrow bandwidth allows more signals to be transmitted simultaneously than does a wider bandwidth, beside give less noise thereby increasing signal-to-noise ratio.The bandwidth calculation consists of the signals extends from thelower side frequency to the upper side frequency. The difference between these is simply twice the modulation frequency.Therefore, the bandwidth for AM is simply: mm c m c LSB USB AMff f f f f f BW2) ( ) (=+ ==Chapter 2/AM 22POWER IN AMIn any electrical circuit, the power dissipated in a load by an unmodulated carrier is equal to the rms carrier voltage squared divided by the load resistance as follow:It is not a total signal power but only that portion that is used to transmit information.Since the carrier in an AM signal remains unchanged with modulation, it contains no information.Its only function is to aid in demodulating the signal at the receiver.This makes AM inherently wasteful of power.RPrms2) (V=Chapter 2/AM 23POWER IN AMPower in an unmodulated carrier is given by:Since the two sideband frequencies have the same amplitude so the power in both sidebands are equal. Therefore,) ( resistance load (V) ltage carrier vo peak(W) carrierthe of powerWhere,2707 022; ==== =REPRER) E . (Pccc ccUSB LSBcUSB LSBP PmEE E= = =2Chapter 2/AM 24POWER IN AMPower in each sideband can be found by:ccUSB LSBcccccUSB LSBPmRE mP PREPRE mRE mRmEP P4 2 42 since ) 2 )( 4 (1x 241x 222222 2 2222='+

'

= = = =='+

'

= =Chapter 2/AM 25The total sideband power is given by:The total power in AM is:ccc cUSB LSB SBPmPmPmPmP P P2424 4222 2==+ =+ =cc cUSB LSB cSB c TPmPmPP P PP P P'+

'

+ =+ =+ + =+ =21222TOTAL POWER IN AMChapter 2/AM 26IMPORTANT INFORMATION OF AMThe total power in an AM signal increase with modulation, reaching a value 50%, greater than that of the unmodulated carrier for 100% modulation. The extra power with modulation goes into the sidebands; the carrier power does not change with modulation.The useful power,that is the power that carries information, is rather small reaching a maximum of one-third of the total signal power for 100% modulation and much less at lower modulation indices. For this reason, AM transmission is more efficient when the modulation index is as close to 1 as practicable.Chapter 2/AM 27DSBSCObviously that full AM is an efficient and wasteful method of communications.Two-third of the transmitted power appears in the carrier which conveys no information.One way to overcome this problem is simply to suppress the carrier where the resulting signal is only the upper and lower sidebands.Such a signal is referred to as a double-sideband suppressed carrier (DSBSC)signal.The benefit is that no power is wasted on the carrier and the power saved can be put into the sidebands for stronger signals over longer distances.DSB signal is rarely used because the signal is difficult to recover at the receiver.It can be obtained by multiplying the carrier and the baseband signal together in a balanced modulator.Chapter 2/AM 28DSBSC GENERATIONThus, the DSBSC expression can be shown as:t E t EtE EtE Et t E Et E t Et v t v vm c D m c Dm cc mm cc mc m c mc c m mc m DSBSC) cos( ) cos() cos(2) cos(2cos coscos cos) ( ) ( + +=+ +==- =- =t E t vm m m cos ) ( =t E t vc c c cos ) ( =DSBSCvChapter 2/AM 29DSBSC FREQUENCY SPECTRUMChapter 2/AM 30DSBSC BANDWIDTHFrom the frequency spectrum, the bandwidth of a DSBSC signal is exactly the same as that for a full AM which is:One familiar use of this method of modulation is in subcarrier modulation of the L-R signal in stereo VHF FM radio.DSBSC is not often found on its own as a modulation scheme. It is used as the basis for generating single-sideband suppressed-carrier(SSBSC).mm c m c LSB USB DSBSCff f f f f f BW2) ( ) (=+ ==Chapter 2/AM 31DSBSC vs. FULL AMBoth that full AM and the DSBSC signals are very similar in appearance but with two important differences: There are 180ophase change at the nodes for DSBSC and no phase change for full AM. Envelope lines actually cross for DSBSC but touch asymptotically for full AM.Chapter 2/AM 32DSBSC vs. FULL AMChapter 2/AM 33SSBFull AM or DSBSC generates two sets of sidebands, each containing the same information.The information is redundant therefore all the information can be conveyed in just one sideband.By eliminating one sideband produces a single-sideband (SSB)signal and can produce more efficient AM signal.SSB signal offers four major benefits: The spectrum space is less where it occupied only half of full AM and DSB signals. It allows more signals to be transmitted in the same frequency range less interference between signals. All the power previously devoted to the carrier and other sideband can be channeled into the single sideband. This produces a stronger signal and more reliably received at greater distances and greater efficiency.Chapter 2/AM 34SSBFour major benefits (cont.): There is less noise on the signal. Since SSB signal has less bandwidth than full AM or a DSB signal, thus there will be less noise on it. This is a major advantage in weak signal long-distance communications. Therefore, SNR can be improved. SSB signals experience less or no fading than an AM signal. Fading means that a signal alternately increases and decreases in strength as it picked up by the receiver. It occurs because the carrier and sidebands may reach the receiver shifted in time and phase with respect to one another.SSB is widely used in two-way radio communications such as in military, in Citizens Bands radio as well as in telephone system.Chapter 2/AM 35SSB GENERATIONThe simplest way to obtain an SSB signal is to take a DSBSC signal and removeone sideband by filtering.This leaves the other sideband only either the upper or lower sideband.After LPF only the lower sideband will remain:After HPF only the upper sideband will remain:t E t vm m m cos ) ( =t E t vc c c cos ) ( =SSBv LPF/HPFDSBSCvtE Evm cc mSSB) cos(2 =tE Evm cc mSSB) cos(2 + =Chapter 2/AM 36SSB FREQUENCY SPECTRUMIf only the lower sideband remain:Chapter 2/AM 37SSB FREQUENCY SPECTRUMIf only the upper sideband remain:Chapter 2/AM 38SSB BANDWIDTHThe two sidebands of an AM signal are mirror to each other, so it is not necessary to transmit both in order to communicate.Removing one sideband obviously reduces the bandwidth by at least a factor of two.mc m c SSBmm c c SSBff f f BWff f f BW= + ===) ( or ) (Chapter 2/AM 39AM WAVEFORMS AS COMPARISONSChapter 2/AM 40AM radio broadcastingTV picture (video)Two-way radio Air craft Amateur radio Citizens Band (CB) radio MilitaryDigital data transmissionComputer modemCOMMON AM APPLICATIONSAM ExampleQ1. Given that VAM(t) = 35 cos (2 x 106)t +15 cos (1.97 x 106)t+15 cos (2.03 x 106)t V. Calculate:a) Modulation index, mb) Peak modulating voltage, Emc) The frequencies of the modulating signals and carrier.d) Frequency spectrum and its amplitudee) Bandwidth of the AM signal.Q2) An AM signal in which the carrier is modulated by 90% contains 2.5 kW at the carrier frequency.a) Calculate the power content of the upper and lower sidebandsb) if the percent modulation drops to 50%, find the power at the carrier and the power content of each of the sidebands. Chapter 2/AM 41AM ExampleQ3. Given an AM signal as follows:VAM(t) = 10 cos (4x x 106)t + 4.75 cos (3.99x x 106)t + 4.75 cos(4.01x x 106)t V. By assuming that the load resistance, RL= 10 ;, calculate:a) the modulation index, mb) the carrier frequency, fcand the modulating frequency, fm.c) the AM bandwidth.d) the power of carrier that being transmitted, PC.e) the power content at lower sideband, PLSB and upper sideband, PUSB.f) the total power, PT.Chapter 2/AM 42