1 ANALOGUE & DIGITAL COMMUNICATION Syed M. Zafi S. Shah & Uair Mujtaba Qureshi Lectures 5-6: Aplitude Modulation Part 1
Todays topics Recap of Advantages of Modulation Analog Modulation Defining Generation of AM Wavefor Modulation Index Envelop of AM Wavefor Frequency Spectru of the AM Wavefor Double Sideband Full Carrier (DSB-FC) Power distribution of AM wavefor Power distribution of AM Wavefor with 100% odulation Disadvantages of DSB-FC
Advantages of Modulation 3 Advantages of doing odulation are Easy of radiation Multiplexing Convenient Signal Processing Noise Norally the inforation to be transitted are Voice Video Data All these signals are baseband signals Baseband signals are not suitable for direct transission hence need to be odulated
How to odulate? 4 In order to ake our signal suitable for transission, we generate and alter carrier paraeters, such as Aplitude Frequency Phase All in accordance with our inforation signal Thus we coe across generally three kinds of odulation schees Aplitude Modulation Frequency Modulation Phase Modulation All these odulation schees lay under ubrella of Linear Modulation Schees
Aplitude Modulation 5 What is Aplitude Modulation? It is defined as a carrier signal whose aplitude is varied in proportion to the instantaneous aplitude of a odulating signal i-e our inforation signal Aplitude Modulation is the ost fundaental fors of odulation used in telecounications Faous exaple? AM Radio Broadcast!
Objective 6 Transit a low power signal over a large distance Modulate! Aplitude Modulation Change the aplitude of the carrier signal according to the inforation signal Superipose the inforation signal on the carrier signal
Achieving AM odulation -1 7 Suppose, we have a 1 Hz inforation signal which needs to be superiposed on a 10 Hz carrier signal These frequencies have been chosen for the sake of convenience Option1: Su up the two signals ( t) sin( 1t) c( t) sin( 10t) s( t) sin( 10t) sin( 1t) An op-ap based suing aplifier can be used for the purpose
Let s have a look at it 8 Envelop of AM Wavefor
Achieving AM odulation - 9 A suing op-ap used to add the inforation signal and the carrier signal does not result in an AM odulated signal
Achieving AM odulation -3 10 Siply suing up the two signals does not result in odulation The signals will overlap in tie-doain graphs which ight give the ipression of odulation Fro frequency-doain graphs, it becoes clear that the odulation never occurs
Aplitude (volts) Achieving AM odulation -4 11 15 10 5 0-5 -10-15 0 0.5 1 1.5.5 3 3.5 4 4.5 5 Tie (seconds)
Aplitude (volts) Achieving AM odulation -5 1 15 10 5 0-5 -10-15 0 0.5 1 1.5.5 3 3.5 4 4.5 5 Tie (seconds)
Aplitude (volts) Achieving AM odulation -6 13 15 10 5 0-5 -10-15 0 0.5 1 1.5.5 3 3.5 4 4.5 5 Tie (seconds)
Aplitude (volts) Aplitude (volts) Achieving AM odulation -6 14 15 15 10 10 5 5 0 0-5 -5-10 -10-15 0 0.5 1 1.5.5 3 3.5 4 4.5 5 Tie (seconds) -15 0 0.5 1 1.5.5 3 3.5 4 4.5 5 Tie (seconds)
Achieving AM odulation -7 15 In order to achieve Aplitude Modulation, we need a ultiplier not an adder The product of the carrier and odulating signal can be generated by applying both signals to a nonlinear coponent such as a diode. A square-law function is one that varies in proportion to the square of the input signals. A diode gives a good approxiation of a square-law response
Achieving AM odulation -8 16 The use of diode along with the resistor clip the negative half of the coposite signal (inforation + carrier signal). We get a pulsating DC with several higher order haronics (potentially infinite bandwidth?)
Achieving AM odulation -9 17 Diodes and transistors whose function is not a perfect square-law function produce higher-order haronics Called inter-odulation products Probles The resultant signal will have the inforation signal, the carrier signal, the AM signal sidebands and various haronics
Achieving AM odulation -10 18 Inter-odulation products are easy to filter out Tuned circuits Tuned circuits filter out the odulating signal and carrier haronics, leaving only carrier and sidebands The AM signal
Achieving AM odulation -1 19 If the tuned circuit filters out the unwanted signals leaving behind the carrier signal and the AM signal (sidebands)
0 Achieving AM odulation -14
Analyses of the AM wavefor -1 1 i (t) (t) Inforation signal Modulated signal c(t) Carrier signal
Analyses of the AM wavefor - ) ( ) ( ) ( t t c t s AM Hz f t f V t t V t 1 ) sin( ) ( ) 1 sin( ) ( Hz f t f t c t t c c c 10 ) sin( ) ( ) 10 sin( ) (
Analyses of the AM wavefor -3 3 s AM ( t) sin( f t) V sin( f t) c sin( ) sin( ) 1 cos cos s AM V ( t) cos c c f t f t cos f t f t
Aplitude (volts) Analyses of the AM wavefor -4 4 10 8 6 4 0 - -4-6 -8-10 0 0. 0.4 0.6 0.8 1 1. 1.4 1.6 1.8 Tie (seconds)
5 Analyses of the AM wavefor -5
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Points to ponder 7 Now on we ll refer all signals in ters of voltage signals Our inforation signal is expressed as Where v V v Peak value of V Sin( t) Carrier Signal can expressed as vc Vc Sin( ct) Instantaneous aplitude of f Where v V c c c f Frequency of Peak value of Frequency of odulating signal Instantaneous aplitude of c odulating signal odulating signal carrier signal carrier signal carrier signal
Points to ponder 8 Usually Inforation signal frequency f = 0Hz 0kHz AF range Correspondingly Carrier signal frequency fc = 300kHz 3MHz MF range The carrier frequency reains constant in entire odulation process Only the aplitude varies in accordance with the odulating signal Increase/decrease in the aplitude of the odulating signal causes the corresponding increase/decrease in both positive & negative peaks of the carrier aplitude What iffc f?
9 Let s look at Modulated signal
Envelope -1 30 Envelope: The iaginary line that connects the positive and negative peaks of the carrier wavefors It gives the exact shape of odulating inforation signal Modulating signal uses peak value of carrier signal rather than zero as its reference point Zero reference line of odulating signal coincides with the peak value of the carrier signal The envelop varies above & below the carrier aplitude In general, V < Vc but what if V > Vc?
Envelope - 31 e ve V c V sin( f t) e ve V c [ V V c V sin(f sin(f t) t)]
A atheatical treatent -3 3 How uch aplitude of the carrier are we changing with respect to the aplitude of the inforation signal? Modulation Index The ratio of the aplitude of the odulating signal to the aplitude of the carrier signal Several nae for the odulation index odulation factor and depth of odulation Percent odulation (percentage odulation)
A atheatical treatent -4 33 Matheatically, the odulation index (M) is given as, V M V Note that it is unit-less quantity Percent odulation is given as, V M % 100 Vc In tie doain, percent odulation is expressed in ters of peak or peak to peak values of a sine wave, so V ax V ax p p p p V V in in c p p p p Your Hoework!
34 Effects of degree of odulation on the odulated signal
Exaple 1 35 What is the depth of odulation for an AM signal if the odulation (t) and carrier c(t) signals are given as, ( t) 10sin( 1t) c( t) 0sin( 10t) Sketch the envelope of the AM signal
Frequency Spectru of AM Wavefor 36 The instantaneous value of either the top or the botto voltage envelop v1 is coputed with the values of the carrier signal & the odulating signal v1 Vc v Vc Vsint It is basically an addition of the odulating signal with the peak value of the carrier signal The instantaneous value of entire odulated AM wavefor v can calculated as v v1sinct
37 e e e e e AM AM AM AM AM Double Side Band Full Carrier By substituting the value of v1 v v v v v e AM v 1 ( V V c v sinct c sinct v1sin c sint)sinct t )sinct sint sinct 1 Vc sinct V{ [cos( C ) t cos( c ) t]} Vc Vc Vc sinct cos( C ) t cos( c ) t CARRIER Upper Side Band Lower Side Band f V c ( V V c v f c f This AM wavefor is also called as Double Side Full Carrier (DSBFC) sin Asin B (1/ )[cos( A f c f B) cos( A B)]
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Points to ponder 40 It is evident fro the expression that The central carrier frequency reains independent of the odulating signal It is the sidebands that change in proportion with the odulating voltage and the depth of odulation The LSB & USB created are the irror (inverted) iages Since the peak values ters of the two sidebands i-e LSB & USB are equal, we have V c V LSB V USB To be continued
41 ANALOGUE & DIGITAL COMMUNICATION Syed M. Zafi S. Shah & Uair Mujtaba Qureshi Lectures 7-8: Aplitude Modulation Part 1
Points to ponder 4 When all three frequency coponents are in phase, they add together linearly and for the axiu signal aplitude, Vax i-e V V V ax Since V ax V V V LSB V V c c LSB ax V V V V USB LSB, LSB USB V V USB is also equal to thesu of Fro above two equation we have V V USB V c& V
Proble 3.1 43 A carrier signal with a peak voltage of.0v is aplitude odulated with a10-khz sine wave. The odulation voltage has an effective value of 750V. Copute the following The percent odulation index The instantaneous voltage of the positive and negative envelop when sine wave copleted 68µs of its cycle. Sketch the AM wavefor in tie-doain and frequency-doain
Proble 3. 44 An AM broadcast station s peak carrier voltage of kv has been aplitude odulated to an index of 75% with a khz test tone. The station s broadcast frequency is 810kHz. Copute the following The lower and upper sideband frequencies The peak odulation voltage i-e V The peak lower and upper sideband voltages The axiu signal aplitude i- e Vax
Power distribution in AM Wavefor 45 Total effective (rs) power in AM Wavefor is P VCr..s VLSBr..s VUSBr..s PT R R R (0.7071VC) (0.7071VUSB) (0.7071VLSB) PT R R R VC VUSB VLSB PT R R R Since power in the upper and lower side bands are equal P Since the total Power in the carrier, P P T LSB LSB P C P P P USB USB LSB P USB V (0.7071 R V 8R C C ) P 4 V 8R C C C VC R, we have
Proble 3.3 46 A spectru analyzer with an input ipedance of 50Ωs is used to easure the power spectru of an AM signal at the output of a preaplifier circuit. The AM signal has been odulated with a sine wave. The effective carrier power, Pc is 750W, and each sideband PLSB and PUSB is 10W. Copute the following: The total effective power, PT The peak carrier voltage, Vc The odulation index and percent odulation index The odulation voltage, V The lower and upper sideband voltage, VLSB, VUSB
47 Power distribution in AM wave for 100% Modulation In order to analyse AM wavefor in ters of power efficiency, the condition iplies is =1 i-e 100% odulation is used which sets the axiu power utilization Therefore, P P T T P P C C P C 4 P C P C 4 1.5P C
Points to ponder 48 It is apparent that the total effective power in sideband of AM wavefor is one-half of the carrier frequency For 100% odulation, two-third of the total power is dissipated by the carrier frequency
Proble 3.4 49 An AM transitter has an effective carrier level of 50 kw. If the carrier is odulated with a sine wave, copute the following: The total effective transitter power for a percent odulation index of 50% The effective power in each sideband for odulation index of 50% The total effective transitter power for 100% odulation The effective power in each sideband for 100% odulation
Disadvantages of DSB-FC 50 /3 of power resides in the duy carrier signal who has no inforation Waste of power LSB & USB contain the sae inforation signal Waste of Bandwidth + Waste of power too! What ore?