Angle Modulaion (Phase & Frequency Modulaion) EE442 Lecure 8 Spring 2017 1
Ampliude, Frequency and Phase Modulaion Wih ew excepions, Phase Modulaion (PM) is used primarily in digial communicaion 2
Why Use a Carrier Signal? Carrier signals are used or wo reasons: (1) To reduce he wavelengh or eicien ransmission and recepion (he opimum anenna size is ¼ o a wavelengh). A ypical audio requency o 3000 Hz has a wavelengh o 100 km and would need an eecive anenna lengh o 25 km! By comparison, a ypical FM carrier is 100 MHz, wih a wavelengh o 3 meers, and would have an 80 cm long anenna (ha is 31.5 inches long). (2) To allow simulaneous use o he same channel, called muliplexing. Each unique message signal has a dieren assigned carrier requency (e.g., radio saions) and share he same channel. The elephone company invened modulaion o allow phone conversaions o be ransmied over common phone lines. Mandaed by he FCC. 3
Illusraing AM, PM and FM Signals Carrier Wave Modulaing Signal m() Carrier signal m() AM [Chaper 4] Lahi & Ding; Page 252-292 AM Modulaed Signal PM PM Modulaed Signal [Chaper 5] FM FM Modulaed Signal ime 4
Phase-Frequency Relaionship When Frequency is Consan ( ) Acos( ( )) () is generalized angle ( ) Acos( ) C 0 () C 0 Slope: ( ) i d () d i C 0 ime 5
Concep o Insananeous Frequency Angle Modulaion ( ) Acos( ( )) () is generalized angle ( ) Acos( ) C 0 () () C 0 0 Slope: ( ) i d () d i Figure 5.1 rom Lahi & Ding; Page 253 C i ime 6
Angle Modulaion Gives PM and FM d () i( ) and ( ) i( ) d d i Angle Modulaion Phase Modulaion Frequency Modulaion Frequency modulaion and phase modulaion are closely relaed! 7
Comparing Frequency Modulaion o Phase Modulaion # Frequency Modulaion (FM) Phase Modulaion (PM) 1 Frequency deviaion is proporional o modulaing signal m() 2 Noise immuniy is superior o PM (and o course AM) 3 Signal-o-noise raio (SNR) is beer han in PM 4 FM is widely used or commercial broadcas radio (88 MHz o 108 MHz) 5 Modulaion index is proporional o modulaing signal m() as well as modulaing requency m Phase deviaion is proporional o modulaing signal m() Noise immuniy beer han AM bu no FM Signal-o-noise raio (SNR) is no as good as in FM PM is primarily or some mobile radio services Modulaion index is proporional o modulaing signal m() 8
Phase Modulaion (PM) ( ) k m( ) Generally we le 0. C 0 p 0 Le 0 0 ( ) Acos( k m( )) PM C p Equaion (5.3b) Lahi & Ding; Page 254 The insananeous angular requency (in radians/second) is d ( ) m( ) i( ) C kp C kpm( ) d d In phase modulaion (PM) he insananeous angular requency i varies linearly wih he derivaive o he message signal m(). (denoed here by m()). k p is phase-deviaion (sensiiviy) consan. Unis: radians/vol [Acually in radians/uni o he parameer m().]. 9
Frequency Modulaion (FM) Bu in requency modulaion he insananeous angular requency i varies linearly wih he modulaing signal m(), k m() i C ( ) ( k m( )) d k m( ) d C C k is requency-deviaion (sensiiviy) consan. Unis: radians/vol-sec. Then FM( ) Acos C k m( ) d Equaion (5.5) Lahi & Ding; Page 254 FM and PM are very much relaed o each oher. In PM he angle is direcly proporional o m(). In FM he angle is direcly proporional o he inegral o m(), i.e., () m d 10
Summary Deiniion: Insananeous requency is () i d () d Phase Modulaion Frequency Modulaion Angle Frequency ( ) C kpm( ) ( ) C k m( ) d dm() i C k () p i C k m d In phase modulaion m() drives he variaion o phase. In requency modulaion m() drives he variaion o requency. 11
A Picorial Way o View he Generaion o FM and PM m () H(j) = 1/j m( ) d Phase Modulaor () FM Frequency Modulaor m () H(j) = j d d. m () Frequency Modulaor () PM Phase Modulaor We require ha H(j) be a reversible (or inverible) operaion so ha m() is recoverable. 12
Equaions or FM Wave wih Single Tone Modulaion Carrier signal A cos( ) Carrier requency 2 Modulaing wave m( ) A cos( ) A single one requency Modulaing requency 2 (radians/sec) Deviaion sensiiviy Frequency deviaion k A Modulaion Index k C C m m m m C C m m k m m 22 Insananeous requency k A cos( ) cos( ) Remember FM( ) AC cos C k m( ) d, generally max min i C m m C m ka Modulaed wave FM( ) AC cosc m or FM( ) AC cos C sin( m) m sin( m) Handou 13
Generalized Angle Modulaion The irs block can be any linear ime-invarian (LTI) operaor i need only be inverible so ha we can recover m(). In general, we have Noe: h() is he uni impulse response GAM( ) Acos C m( ) h d Phase Modulaion: h( ) k ( ), Frequency Modulaion: h( ) k u( ) p We shall ocus more on Frequency Modulaion in his course and less on Phase Modulaion. 14
Average Power o a FM or PM Wave The ampliude A is consan in a phase modulaed or a requency modulaed signal. RF power does no depend upon he requency or he phase o he waveorm. FM or PM ( ) Acos ( k, m( )) C Average Power A 2 2 (always) This is a resul o FM and PM signals being consan ampliude. 15
Comparison o FM (or PM) o AM # Frequency Modulaion (FM) Ampliude Modulaion (AM) 1 FM receivers have beer noise immuniy 2 Noise immuniy can be improved by increasing he requency deviaion 3 Bandwidh requiremen is greaer and depends upon modulaion index 4 FM (or PM) ransmiers and receivers are more complex han or AM 5 All ransmied power is useul so FM is very eicien AM receivers are very suscepible o noise No such opion exiss in AM Bandwidh is less han FM or PM and doesn depend upon a modulaion index AM ransmiers and receivers are less complex han or FM (or PM) Power is wased in ransmiing he carrier and double sidebands in DSB (bu DSB-SC addresses his) 16
Phasor Inerpreaion o AM DSB wih Carrier C roaes aser han m us cos( C ) C ls cos( m ) m = us = ls Specrum: DSB AM C - m C C + m lower sideband upper sideband 17
Phasor Inerpreaion o AM DSB wih Carrier (coninued) 18
Example 5.1 in Lahi and Ding (pp. 256-257) Skech FM and PM waveorms or he modulaing signal m(). The consans k and k p are 2 10 5 and 10, respecively. Carrier requency c = 100 MHz.. m() FM PM k i C m m 2 m 1 and m 1 min i i min max 8 5 ( ) 1 10 1 10 ( ); max 8 5 10 10 ( 1) 99.9 MHz, 8 5 10 10 ( 1) 100.1 MHz kp 8 i C m( ) 110 5 m( ); 2.. m 20,000 and m 20,000 min i i min max max 8 10 5( 20, 000) 99.9 MHz, 8 10 5( 20, 000) 100.1 MHz. 19
Example 5.2 in Lahi and Ding (pp. 257-259) Skech FM and PM waveorms or he modulaing signal m(). The consans k and k p are 2 10 5 and /2, respecively. Carrier requency c = 100 MHz. FM k i C m m 2 8 5 ( ) 1 10 1 10 ( ) Since m() swiches rom +1 o -1 and vice versa, he FM wave Frequency swiches beween 99.9 MHz and 100.1 MHz. This is called Frequency Shi Keying (FSK) and is a digial orma. 20
Example 5.2 in Lahi and Ding (pp. 257-259) coninued Skech FM and PM waveorms or he modulaing signal m(). The consans k and k p are 2 10 5 and /2, respecively. Carrier requency c = 100 MHz. PM kp. 8 1. i C m( ) 110 m( ) 2 4 This is carrier PM by a digial signal i is Phase Shi Keying (PSK) because digial daa is represened by phase o he carrier wave. PM( ) Acos C kpm( ) Acos C m( ) 2 ( ) Asin( ) when m( ) 1 PM PM C ( ) Asin( ) when m( ) 1 C Lahi & Ding; Page 258 21
Case I Narrowband FM (NBFM) There are wo approximaions or FM: Narrowband approximaion (NBFM) Wideband approximaion (WBFM) Lahi & Ding; Page 260 NBFM: FM( ) Acos C k m( ) d m B I k m( ) d 1, we have NBFM. Le k m( ) d k sin( ), m Then bandwidh B 2 FM m 1 = 0.2 NBPM requires << 1 radian (ypically less han 0.2 radian) ( C - m ) C ( C + m ) 22
Narrowband FM (NBFM) Equaion Sar wih design equaion or one requency : m A A A m m m A cos2 sin2 sin(2 ) NB ( ) cos 2 sin(2 ) NB ( ) cos 2 cos sin(2 ) sin 2 sin sin(2 ) Noe: cos sin(2 ) 1, and sin sin(2 ) sin(2 ) FM C C m FM C C m C C m NB FM () C C C m NB 1 FM( ) AC cos2 C AC cos2 ( C m) cos2 ( C m) 2 Resul rom AM modulaion wih one requency: 1 AM( ) AC cos2 C AC cos2 ( C m) cos2 ( C m) 2 The dierence is he sign (i.e., phase) o he dierence requency erm. Conclusion: Bandwidh: B 2 The NBFM bandwidh is comparable o ha o AM. T m m B NBFM AM 23
Case II Wideband FM (WBFM) WBPM requires >> 1 radian For wideband FM we have a nonlinear process, wih single one modulaion: WB FM ( ) Re A C exp j2 C j sin(2 m) We need o expand he exponenial ino a Fourier series so ha WB we can analyze ( ). FM WB FM C n C m n ( ) A J ( ) cos 2 ( n ) where he coeiciens J ( ) are Bessel uncions. n m B Specral analysis rom one modulaion o WBFM: Lahi & Ding; pp. 264-270 We will no cover his secion in ES 442 bu raher ocus upon a physical Inerpreaion o he specrum spread. 24
FM (or PM) Requires Much More bandwidh Than AM A A A Carrier Signal (requency c ) A C A Message Signal (requency m ) m A AM A Ampliude Modulaed Signal A WBFM Frequency Modulaed (FM) Signal 25
FM Specra as Funcion o Modulaion Index NBFM = 0.2 Number o Sidebands Bandwidh 0.1 2 2 m 0.3 4 4 m 0.5 4 4 m = 1.0 1.0 6 6 m 2.0 8 8 m 5.0 16 16 m 10.0 28 28 m = 5 Single one modulaion = 10 m BT or BW 26
Specra o an FM Signal Single-one modulaion A = 0.2 A m = 1.0 increasing, is consan, m is consan = 5 m is decreasing = 10 From A. Bruce Carlson, Communicaion Sysems, An Inroducion o Signals and Noise in Elecrical Communicaion, 2 nd ediion, 1975; Chaper 6, Figure 6.5, Page 229. 27
Measured Specra o an FM Radio Signal 200 khz Voice modulaion noise 28
Selecing an FM Saion Broadcas FM Radio covers rom 88 MHz o 108 MHz 100 saions 200 khz spacing beween FM saions 29
Speciicaions or Commercial FM Transmissions Service Type Commercial FM Radio Broadcas Television Sound (analog) Public saey Police, Fire, Ambulance, Taxi, Foresry, Uiliies, & Transporaion Amaeur, CE class A & Business band Radio Frequency Band 88.0 o 108.0 MHz 4.5 MHz above he picure carrier requency 50 MHz and 122 MHz o 174 MHz 216 MHz o 470 MHz Channel Bandwidh Maximum Deviaion Highes Audio 200 khz 75 khz 15 khz 100 khz 25 khz monaural & 50 khz sereo 15 khz 20 khz 5 khz 3 khz 15 khz 3 khz 3 khz Quesion: For FM broadcas wha is he modulaion index? 30
FM Bandwidh and he Modulaion Index Lahi & Ding Chaper 5 see pages 261 o 263 Narrowband FM (NBFM) << 1 radian B 2B where B is he bandwidh o m( ) NB FM Wideband FM (WBFM) >> 1 radian WB B 2( B) 2 B( 1) Carson's Rule FM or B 2( ) T m Peak requency deviaion is = k A m Modulaion index m B 31
Phasor Consrucion o an FM Signal C We are consrained by consan ampliude or boh FM and PM signals. This is NBFM. The nex slide shows an animaion o his in operaion. C 32
Sidebands Consruced From Phasors in FM Modulaion Animaion showing how phase modulaion works in he phasor picure -- phase modulaion wih a sinusoidal modulaion waveorm and a modulaion deph o π/4 radians. The blue line segmens represen he phasors a he carrier and he harmonics o he modulaion requency. 33
Direc Generaion o FM Signal Using a VCO V DD m() LC Tank Circui Volage Conrol m() NB FM() Varacor diodes osc 1 LC 1 eq 34
Indirec Generaion o an FM Signal Using Muliplicaion In his mehod, a narrowband requency-modulaed signal is irs generaed and hen a requency muliplier is used o increase he modulaion index. The concep is shown below: m () NBFM NB () FM WB FM () Frequency Muliplier A requency muliplier is used o increase boh he carrier requency and he modulaion index by ineger N. 35
C 1 WB () FM Armsrong Indirec FM Transmier Example NB FM() C 4 4 200 khz 1 25Hz 91.2 MHz 76.8 khz PA Lahi & Ding; pp. 275-277 NBFM generaion X48 Muliplier C NB () FM C 3 3 LO X64 Muliplier 1.9 MHz 1.6 khz BPF 10.9 MHz C 2 12.8 MHz 2 1.6 khz The mixer does no change Noe: These numbers are relaed o an FM broadcas radio saion. Crysal Oscillaor 36
Generaion o Narrowband Frequency Modulaion (NBFM) m () FM( ) Acos C k m( ) d NBFM requires << 1 radian DSB-SC modulaor k NBFM Lahi & Ding; Figure 5.10 Page 276 Asin( c ) -/2 Acos( c ) Carrier 37
Generaion o Narrowband Phase Modulaion (NBPM) ( ) Acos( k m( )) PM C p m () k p NBPM Asin( c ) -/2 Acos( c ) 38
Advanages o FM Advanages o requency modulaion 1. Resilien o noise: The main advanage o requency modulaion is a reducion in noise. As mos noise is ampliude based, his can be removed by running he received signal hrough a limier so ha only requency variaions remain. 2. Resilien o signal srengh variaions: In he same way ha ampliude noise can be removed, so oo can signal variaions due o channel degradaion because i does no suer rom ampliude variaions as he signal level varies. This makes FM ideal or use in mobile applicaions where signal levels consanly vary. 3. Does no require linear ampliiers in he ransmier: As only requency changes conain he inormaion carried, ampliiers in he ransmier need no be linear. 4. Enables greaer eiciency : The use o non-linear ampliiers (e.g., class C and class D/E ampliiers) means ha ransmier eiciency levels can be higher. This resuls rom linear ampliiers being inherenly ineicien. 39
Disadvanages o FM Disadvanages o requency modulaion 1. Requires more complicaed demodulaor: One o he disadvanages is ha he demodulaor is a more complicaed, and hence more expensive han he very simple diode deecors used in AM. 2. Sidebands exend o ininiy eiher side: The sidebands or an FM ransmission heoreically exend ou o ininiy. To limi he bandwidh o he ransmission, ilers are used, and hese inroduce some disorion o he signal. 40
Pracical Frequency Demodulaors Frequency discriminaors can be buil using various ways: FM slope deecor Balanced discriminaor Quadraure demodulaors Phase locked loops (superior echnique) Zero crossing deecor 41
FM Slope Deecor Perorms FM o AM Conversion Envelope Deecor FM() Slope ses requency o volage conversion acor 42
Balanced Discriminaor (Foser-Seeley Discriminaor) Tuned Circui Envelope Deecor Cenered around c FM() Transer Characerisics 43
Quadraure Demodulaor Block Diagram FM signal is convered ino PM signal PM signal is used o recover he message signal m() () FM Phase Shiing Circui Phase Comparaor Circui Low-Pass Filer m () Signal delay 0 imes carrier requency C = 90 degrees (or /2). Phase Deecor 44
Using XOR Gae or Phase Frequency Deecor XOR A B Oupu 0 0 0 0 1 1 1 0 1 1 1 0 45
Quadraure Demodulaor Implemenaion () FM m () () FM Phase shier (or delay ime) 46
Phase-Locked Loops A PLL consiss o hree basic componens: Phase deecor Loop iler Volage-conrolled oscillaor (VCO) PLL Diagram: A cos ( ) C i Hs () Oupu signal is phase Phase Deecor Low-Pass Filer Bias Generaor 2B cos ( ) C o Oscillaor (VCO) e () o 47
Zero-Crossing Deecors 48
Zero-Crossing Deecor Illusraion hps://www.slideshare.ne/avocado1111/angle-modulaion-35636989 49
Example FM 6 3 ( ) 10 cos 2 (10 ) 8sin(2 (10 ) ) FM() 50
Soluion o Example Sar wih he basic FM equaion: FM( ) AC cos 2 C sin(2 m) Compare his o (a) We see by inspecion ha c = 1,000,000 Hz and m = 1000 Hz. (b) The modulaion index is = 8. (c) The peak deviaion requency is (d) The bandwidh is FM 6 3 ( ) 10 cos 2 (10 ) 8sin(2 (10 ) ) m 8 1000 8,000 Hz B 2 ( 1) 2,000(8 1) 18,000 Hz FM m 51
Inererence Pre-Emphasis and De-Emphasis in FM FM Frequency PM FM wih Pre- and De-emphasis ilers Channel noise acs as inererence in FM and is uniorm over he enire BW. Voice and music have more energy a lower requencies, so we need o emphasize heir upper requencies by ilering. However, he HF emphasis mus be removed a he receiver using a de-emphasis iler. (Used commercially in recording indusry) m() Pre-emphasis Filer FM Transmier Channel FM Receiver De-emphasis Filer R 1 C R 2 AWG Noise R 1 C Filering improves SNR in FM ransmission. 52
Typical Pre-Emphasis and De-Emphasis Filers Transmier Pre-emphasis Filer R 1 C R 2 Receiver De-emphasis Filer R 1 C Lahi & Ding; Chaper 5, pp. 286-289 H( ) ( db) Vou 1 jr1c H( ) V 1 j R R C in 1 2 H( ) ( db) Vou H( ) V 1 in 1 jr C 1 +6 db/ocave -6 db/ocave 2.1 khz 33 khz 2.1 khz 1 RC 1 2 1 1 R R C log( ) 1 RC 1 log( ) 53
Analog and Digial FM Cellular Telephones 1G analog cellular elephone (1983) AMPS (Advanced Mobile Phone Service) Firs use o cellular concep Used 30 khz channel spacing (bu voice BW was B = 3 KHz) Peak requency deviaion = 12 khz, and B T = 2( + B) = 2(12 khz + 3 khz) = 30 khz Two channels (30 khz each); one or uplink and one or downlink Used FM or voice and FSK or daa communicaion No proecion rom eavesdroppers Successor o AMPS was GSM (Global Sysem or Mobile) in early 1990s GSM is 2G cellular elephone Sill used by nearly 50% o world s populaion GSM was a digial communicaion sysem Modulaing signal is a bi sream represening voice signal Used Gaussian Minimum Shi Keying (GMSK) laer in EE 442 Channel bandwidh is 200 khz (simulaneously shared by 32 users This is 4.8 imes improvemen over AMPS More o come on cellular... 54
Digial Carrier Modulaion ASK, FSK and PSK Ampliude Shi Keying Frequency Shi Keying Phase Shi Keying Digial Signals 55
Quesions? 56