ELEC 350 Communiations Theory and Systems: I Analog Signal Transmission and Reeption ELEC 350 Fall 2007 1
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Analog Modulation A large number o signals are analog speeh musi video These signals an be used to modulate a arrier or transmission AM and FM radio Television ELEC 350 Fall 2007 3
Objetives o Modulation Convert a lowpass signal to bandpass Aommodate the simultaneous transmission o signals rom several soures Expand the signal bandwidth to inrease noise immunity ELEC 350 Fall 2007 4
Amplitude Modulation Double-sideband suppressed arrier (DSB-SC Conventional AM Single-sideband (SSB AM Vestigal-sideband (VSB AM ELEC 350 Fall 2007 5
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Phase-Loked Loop ELEC 350 Fall 2007 11
Conventional AM ELEC 350 Fall 2007 12
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Envelope Detetor ELEC 350 Fall 2007 15
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Assignment 2 Due Ot. 10, 2007 P&S 3.2 P&S 3.4 P&S 3.7, problems 1 and 2 only P&S 3.14 P&S 3.16 P&S 3.18 ELEC 350 Fall 2007 24
Nonlinear Devie ELEC 350 Fall 2007 25
Suppose that the nonlinear devie is approximated by a seond order polynomial v o ( t 2 n1 a n v n i ( t ELEC 350 Fall 2007 26
Input to the nonlinear devie Output o the nonlinear devie A band pass ilter with bandwidth 2W entered at yields where by design os(2 ( ( t A m t t v i os(2 ( 2 1 (2 os ( ( os(2 ( os(2 ( ( 1 2 1 2 2 2 2 2 1 2 2 1 t m t a a A a t A a t m a a m t t A m t a t A m t a t v o os(2 ( 2 1 ( 1 2 1 t m t a a A a t u 1 / ( 2 1 2 a m t a ELEC 350 Fall 2007 27
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Assume that Let The diode will turn on i and will turn o i The output aross the load resistor is Sine s(t is a periodi retangular untion, the Fourier series is A m(t 0 ( t 0 ( t os(2 ( t A t ( ] os(2 ( [ ( ( 0 ( 0 0 ( ( 0 ( t s t A m t t s t v t t t v t v i i 1 1 1 (2 2 os 1 2 1 ( 2 2 1 ( n n n t n t s ELEC 350 Fall 2007 29
Hene Passing through a bandpass ilter, we have other terms os(2 ( 4 1 2 ( ] os(2 ( [ 0 ( t m t A A t s t A m t t v os(2 ( 4 1 2 ( t m t A A t u ( v 0 t ELEC 350 Fall 2007 30
Balaned Modulator ELEC 350 Fall 2007 31
Ring modulator or DSB-SC AM 1 m(t 2 3 v o (t C(t 4 I (t > 0, 1, 4 on, and 2, 3 o, I (t < 0, 1,4 o, and 2,3 on, v o v o ( t m( t ( t m( t ELEC 350 Fall 2007 32
Thereore, we have v o ( t m( t ( t Sine (t is a periodi untion, the Fourier series an be expressed as ( t 4 n1 ( 1 2n 1 n1 os 2 (2n 1 t The desired DSB-SC AM signal is obtained by passing v 0 ( t through a bandpass ilter with enter requeny and bandwidth 2W. u( t 4 m( tos2 t ELEC 350 Fall 2007 33
AM Radio Broadasting Commerial AM-radio broadasting utilizes the requeny band 535-1605 khz or the transmission o voie and musi. Carrier spaing is 10 khz. The baseband message signal m(t is limited to 5 khz. Conventional AM is used rom an eonomi standpoint. The major objetive is to redue the ost o implementing the reeiver. A Superheterodyne reeiver is used in most AM radios. Intermediate requeny Image requeny IF 2 IF 455 khz ELEC 350 Fall 2007 34
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Rejetion o the radio signal at the image requeny ' Assume there are two reeived signals r ( t A [1 m ( t]os(2 t r 1 2 ( t The mixer output onsists o the two signals y y 1 2 ( t ( t LO The RF ampliier bandwidth is designed to be suiiently narrow so that the image requeny signal is rejeted BRF 2 IF The IF ampliier has bandwidth o 10kHz to rejet signal rom adjaent hannels. 1 A [1 m 2 A [1 m 1 A [1 m 2 IF ( t]os(2 ( t]os(2 ( t]os(2 ' IF t IF t t Desired signal Intererene rom image hannel
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AM Modulation Summary Modulation Power Eiieny Spetral Eiieny (xw Modulation Complexity Demodulation Conventional AM low 2 low simple DSB-SC high 2 low omplex SSB high 1 high omplex VSB high 1-2 medium omplex ELEC 350 Fall 2007 38
Angle Modulation ELEC 350 Fall 2007 39
Angle Modulation Angle modulation Frequeny modulation (FM: Frequeny is hanged by the message m(t. Phase modulation (PM: Phase is hanged by the message m(t. Angle modulated signals have a high degree o noise immunity, but require larger bandwidth than AM signals. They are widely used in high-idelity musi broadasting. They have a onstant envelope, whih is beneiial when using nonlinear ampliiers. ELEC 350 Fall 2007 40
FM and PM Signals An angle-modulated signal u( t A os( ( t (t : the phase o the signal Instantaneous requeny i (t is given by 1 d i ( t ( t 2 dt Sine u(t is a bandpass signal, it an be represented as u( t A os(2 t ( t i 1 d ( t ( t 2 dt ELEC 350 Fall 2007 41
I m(t is the message signal, then in a PM system we have In an FM system i ( t k m( t 1 d ( t k m( t ( t 2 dt From the above relationships we have p ( t 2k k p t m( t m( d PM FM On the other hand d ( t dt d k p m( t dt 2k m( t PM FM ELEC 350 Fall 2007 42
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Maximum phase deviation in a PM system max k p max Maximum requeny deviation in an FM system max k max m( t m( t ELEC 350 Fall 2007 46
The message signal m( t a os(2 mt is used with either FM or PM or the arrier A os( 2 t. Find the modulated signal in eah ase. we have Solution: PM FM t k a ( t k pm( t k pa os(2 mt ( t 2k m( d sin(2 mt A u( t A os(2 t os(2 os(2 t sin(2 p m m t t PM FM p k k p m a a / m Modulation index or a general m(t p k k p max max m( t max m( t / W / W max Modulation index ELEC 350 Fall 2007 47
Narrowband Angle Modulation: I or all t, we have then we an use the approximation u( t A os(2 t ( t A os(2 tos( ( t A sin(2 tsin( ( t A os(2 t A ( tsin(2 t The modulation is very similar to onventional AM ( t 1 ELEC 350 Fall 2007 48
m( t a os(2 t m u( t A os(2 t 2 k a os(2 d u( t A 1 m( t os(2 t m A os(2 t os( sin(2 t A sin(2 t sin( sin(2 t A A os(2 t sin(2 mt sin(2 t 2 A A os(2 t os(2 ( m t os(2 ( 2 A os(2 t a os(2 t os(2 t m t m m A A os(2 t aos(2 ( m t os(2 ( m t 2 m t ELEC 350 Fall 2007 49
Conventional AM vs Narrowband FM ELEC 350 Fall 2007 50
Spetral Charateristis o Angle-Modulated Signals Assume that the message is a sinusoidal signal u( t A Re os(2 t sin(2 A e j 2 t e j sin(2 m t m t The signal sin( 2 m t is periodi with period T m 1/ The same is true or the omplex exponential signal sin( 2 t e j m Fourier series representation with oeiients n m u2 m t 0 1 m e j sin(2 m t e jn 2 m t dt 1 2 j( sin unu e du J Bessel untion o n ( the irst kind o 0 order n 2 ELEC 350 Fall 2007 51 m
Thereore, we have Finally we obtain The atual bandwidth o the modulated signal is ininite. However, the amplitude o the sinusoidal omponents o requenies or large n is very small. Property: n t n j n t j m m e J e 2 sin(2 ( n m n t j n t n j n t n A J e e J A t u m ( os(2 ( ( Re ( 2 2 n m odd ( even ( ( n J n J J n n n ELEC 350 Fall 2007 52
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Varator Diode Angle Modulator ELEC 350 Fall 2007 61
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A nonlinear devie ollowed by a bandpass ilter tuned to the desired enter requeny an be used as a requeny multiplier. For example, assume a nonlinear devie o the orm y t u t The output signal will be 2 ( n ( y t A t t 2 2 ( os (2 ( 2 A 1 2 A os(2 (2 t 2 ( t 2 2 The requeny is multiplied by a ator o 2.
Armstrong Modulator The Armstrong modulator annot produe muh deviation, so a ombination o multipliers and mixers is used to raise the arrier requeny and the deviation. The multipliers are used to multiply the arrier and the deviation. The mixers are used to derease the arrier, while keeping the deviation onstant so that additional multiplier stages an be used to obtain more deviation. Example: An FM station is authorized to operate at 90.9 MHz, with maximum deviation o 75 KHz. The FM signal is generated with an Armstrong modulator whose output is 500 KHz with a deviation o 15.432 Hz. The modulator output is applied to 4 triplers and a doubler to obtain a requeny o 81 MHz and a deviation o 2.5 KHz. The 81 MHz signal is mixed with a 77.97 MHz signal to produe a 3.03 MHz signal whose deviation is still 2.5 KHz. This signal is ed through a doubler, tripler and quintupler to multiply the arrier to 90.9 MHz and the deviation to 75 KHz. ELEC 350 Fall 2007 64
Broadast FM Generation ELEC 350 Fall 2007 65
Generate an AM signal rom u(t Use an AM demodulator to reover m(t Pass the FM signal through a ilter with response I the input to the system is the output is This is an AM signal! 2 or ( ( 0 B k V H t d m k t A t u ( 2 2 os ( FM Demodulation t d m k t m t kk V A t v ( 2 2 os ( ( 0 ( 0
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Phase-Loked Loop FM Demodulator ELEC 350 Fall 2007 71
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Costas Loop Detetor ELEC 350 Fall 2007 73
Assignment 3 Due Ot. 26, 2007 P&S 3.24 P&S 3.26 P&S 3.27 P&S 3.28 P&S 3.30 P&S 3.31 ELEC 350 Fall 2007 74
Edwin Howard Armstrong ELEC 350 Fall 2007 75
FM Radio Broadasting Transmission o voie and musi signals (bandwidth o m(t is 15 khz 87.8-108 MHz 200 khz arrier spaing Maximum requeny deviation 75 khz Superheterodyne reeiver with intermediate requeny IF 10.7 MHz
FM Stereo Broadasting Most FM stations transmit musi in stereo using the outputs o two mirophones. A pilot tone at a requeny o 19 khz is added to the signal or the purpose o demodulating the DSB-SC AM signal. A monophoni FM reeiver an reover the sum signal L+R by using a onventional FM demodulator. Hene, FM stereo broadasting is ompatible with onventional FM.
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FM Stereo ELEC 350 Fall 2007 80
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Sample RBDS Signal ELEC 350 Fall 2007 82
Television Broadasting Commerial TV broadasting began as blak-and-white piture transmission by BBC in 1936. The two dimensional image is onverted to a onedimensional eletrial signal by sequentially sanning the image. The sanning o the eletron beam in the CRT is ontrolled by two voltage applied aross the horizontal and vertial deletion plates. In ommerial TV broadasting, the bandwidth o the video signal is limited to W = 4.2 MHz. VSB modulation is employed, the video transmission bandwidth is about 5.5 MHz.
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Television Audio Signal The audio portion o the TV signal is limited to W= 10 khz. The maximum requeny deviation in the FM signal is 25 khz. The FM signal bandwidth is 70 khz.
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