ECE 405 - ANALOG COMMUNICATIONS - INVESTIGATION 7 INTRODUCTION TO AMPLITUDE MODULATION - PART II FALL 2005 A.P. FELZER To do "well" on his invesigaion you mus no only ge he righ answers bu mus also do nea, complee and concise wrieups ha make obvious wha each problem is, how you're solving he problem and wha your answer is. You also need o include drawings o all circuis as well as appropriae graphs and ables. From he las Invesigaion we know ha ampliude modulaed signals s( like he ollowing s( are generaed as ollows m( Ac cos(2π c ka s( = A c [ 1 k a m( ]cos( 2π c wih 1 m( 1; 0 <ka 1; c >> bandwidh o m(. The main objecives o his Invesigaions are o show how muliple AM saions can ransmi a he same ime wihou inerering wih each oher and o show how a receiver can deec and hen demodulae he saion we wan o lisen o. 1. From he las Invesigaion we know ha one o he main reasons or modulaing signals is ha anennas are pracical only a he higher requencies o he carriers. The oher big advanage o modulaion is ha i allows us o ransmi many dieren signals a he same ime by using dieren cener requencies c as indicaed in he ollowing diagram [ ] [ ] [ ] [ ] C1 C2 C3 C4 We call his requency division muliplexing (FDM). Memorize his erm. Then ind how many AM radio saions can be ransmied in he requency range 1MHz o 1.1MHz i each saion is alloed 10KHz o specrum. 2. From he las problem we see ha o recover he baseband signal o a given radio saion we irs have o separae i rom all he ohers. One way o do his is o build a bandpass iler as ollows 1
G(j) c wih an adjusable cener requency c. Bu his is hard o do. A more pracical circui is a superheerodyne - or superhe as ollows All Saions Superhe Modulaed Signal O Desired Saion consising o a local oscillaor wih an adjusable requency LO ogeher wih a ixed bandpass iler as ollows v( w( cos( 2π LO Bandpass Filer c = 455 KHz s IF ( The basic operaion o a superhe is as ollows (1) The signal v( rom he anenna is irs muliplied by a sinusoid o requency LO rom he local oscillaor LO. The value o LO is conrolled by he user as he or she urns a knob or pushes a buon on he radio (2) The resuling produc w( is hen passed hrough a ixed bandpass iler wih a cener requency o 455 KHz as ollows G IF (j) 455 KHz wih a passband ha is wide enough or only one radio saion. Noe ha we reer o c = I = 455 KHz as he inermediae requency (IF) and he passband iler as he IF Filer. Noe ha he "carrier requency" o he radio saion ha makes i hrough he bandpass iler has been shied o c = 455 KHz From his we see ha or a user o une a paricular saion he or she needs o adjus he local oscillaor o a requency ha pus he desired saion in he passband o he IF iler. Memorize his resul. Now suppose he sum o signals v( received by he anenna is as ollows v( = v 1 ( v 2 ( = 2cos(2π9x10 5 2cos(2π1.045x10 6 2
and ha LO =1.5 MHz a. Skech he specral plo o v( b. Find and skech he specral plo o w(. Hin - make use o he ac ha c. Find and skech he specral plo o s( d. Which saion is he radio uned o e. Wha is LO when we're lisening o v 1 ( cos(x)cos(y) = 0.5cos(x y) 0.5cos(x y) 3. Suppose he signal v( being received by he anenna o he AM radio in Problem (2) is equal o he sum o wo radio saions. And ha is specrum V( ) is as ollows V() C2 C1 C1 C2 wih C1 = 600 KHz and C 2 = 700 KHz and ha LO =1.155 MHz a. Skech he specrum o w( in he circui o Problem (2) b. Skech he specrum o s( in he circui o Problem (2). Which saion is being uned in 4. Once we have separaed ou a desired AM signal s( like he ollowing s( rom all hose being received by he anenna we need o demodulae i - recover he baseband signal m(. One relaively simple way o do his is wih an envelope deecor as ollows s( R C y( m( a. Describe and draw equivalen circuis o wha's going on when s( > y( b. Describe and draw equivalen circuis o wha's going on when s( < y( c. Describe in words he consrains on he RC ime consan = RC required or he circui o work properly d. Make use o your resuls in pars (a) and (b) o skech he circui's response y( o he signal above 3
e. Why do we call such circuis envelope deecors 5. Demodulaion schemes like hose in Problem (4) are examples o wha we reer o as noncoheren deecion because he receiver does no require is own copy o he carrier cos( 2π c. Coheren deecors on he oher hand make use o he carrier. Memorize hese erms. And hen skech he specrums o illusrae he operaion o he ollowing coheren AM deecor s( r( A c cos( 2π c Low Pass Filer m( Local Oscillaor or s( wih he ollowing specrum S() C C 6. The objecive o his and he res o he problems o his Invesigaion is o inroduce some variaions on ampliude modulaion ha reduce he power and bandwidh o he modulaed signal a he expense o circui complexiy. The irs is Double Side Band Suppressed Carrier modulaion which is reerred o as DSB-SC. DSB-SC is jus like AM excep ha he carrier sinusoid is no ransmied as indicaed in he ollowing specrum o a DSB-SC signal S() C In paricular s( or an AM signal is given by s( = A c [ 1 k a m( ]cos( 2π c while or a DSB-SC signal we have simply ( ) s( = A c m(cos 2π c C a. Skech he specrum o he DSB-SC signal wih m( = cos(2π1000 and carrier requency c =1 MHz b. How much power does a DSB-SC signal s( = A c m(cos 2π c signal when A c = 5, k a = 0.8 and m( = cos(2π1000 c. Veriy ha he ollowing coheren deecor ( ) save over an AM 4
s( r( Low Pass Filer m( A c cos( 2π c Local Oscillaor wih a local oscillaor generaing a carrier requency a he same phase as he ransmier will demodulae he DSB-SC signal wih he ollowing specrum S() C C by inding and skeching he specrums R( ) and M( ) as s( passes hrough he demodulaor 7. Single-Sideband (SSB) modulaion is jus like DSB-SC excep ha only one o he sidebands is ransmied insead o boh. Suppose in paricular ha he specrum o a given message signal m( is as ollows M() a. Skech he specrum o he corresponding DSB-SC signal b. Skech he specrum o he lower sideband c. Skech he requency response o a iler or obaining SSB rom DSB-SC d. Wha are advanages o single-sideband over DSB-SC 5