MATLAB/SIMULINK TECHNOLOGY OF THE SYGNAL MODULATION

Transcription

1 J Modern Technology & Engineering Vol2, No1, 217, pp76-81 MATLAB/SIMULINK TECHNOLOGY OF THE SYGNAL MODULATION GA Rusamov 1*, RJ Gasimov 1, VG Farhadov 1 1 Azerbaijan Technical Universiy, Baku, Azerbaijan Absrac The paper discusses he feaures of modeling and sudy of he basic modulaion echniques on Malab/Simulink The mehods of analog modeling, as well as ampliude, frequency, phase, and oher modulaions are given This allows one o ge acquained wih he possibiliies of modern compuer echnology in he field of signal modulaion Keywords: analogue modulaion, ampliue and frequency modulaon, modeling in Malab/Simulink Corresponding Auhor: Gazanfar Rusamov, Azerbaijan Technical Universiy, H Javid ave 25, AZ173, Baku, Azerbaijan, gazanfarrusamov@gmailcom Manuscrip received: 14 February Inroducion In he firs par of he paper various modulaion mehods and heir Malab funcions have been given Here we consider he modelling echniques in Malab/Simulink for he main modulaion ypes The maer of he problem is no given in deail by he modelling way in he exisence lieraure [1, 2] 2 Single one ampliude modulaion - AM [3, 4] Suppose ha he modulaed signal is xm ( ) AM cos( ) and he supporing signal is given as, (1) where, are modulaed and supporing frequencies, correspondingly While realizing he AM modulaion o ge correc (single polar) resul usually wopolar x M sygnal is replaced in he posiive side along he abcissa axis (2) Noe ha single polar signal is echnically easily realizable I is known ha in AM modulaion ampliude A of he supporing signal varies proprionally o he modulaing signal So puing he expression (2) ino (1) insead of A we ge he modilaed signal or (3) 76

2 GA RUSTAMOV e al: MATLAB/SIMULINK TECHNOLOGY OF THE Here The raio of he ampliudes of he modulaing and modulaed signals is call a modulaion coefficien or modulaion deph In he case m>1 we observe he absolue modulaion If one can measure he values A min and A max of he modulaing signals pracically (by he help for insance oscillograph), hen he modulaion deph may be compued by he following simple expression 3 Frequency modulaion-fm Following given above definiion in his case he frequency of he modulaed signal x AP varies linearly wih respec o he modulaing signal x M (4) Addion of he consan ω serves for he raising he frequaency The whole phase is found by he ingeraing of he expression (4) as follows Here is an iniial condiion So, he carrier signal be in he form, hen FM- Modulaed signal will be in he form Then in his case he frequency of he modulaed signal x AP varies proporionally o he modulaing signal x M 4 Modelling in MATLAB Firs consider he AM modulaion Example 1 Le he passing useful signal be To ge single polar (same sign) infomaive signal we add here according o (2) he consan parameer A Suppose ha A 4 Le he carrier signal be Here f is he frequences of he carrier vibraions In he ampliude modulaion A( ) xmm ( ) Firs we solve AM-modulaion problem in MATLAB In Fig1 corresponging MATLAB program and and resuls of he modulaion are given 77

3 J MODERN TECHNOLOGY & ENGINEERING, V2, N1, 217 Figure 1 As we see obained single polar signal x MM differs from he iniial informaive wopoalr signal x M by he consan A 4 This difference can be annulaed during demodulaion (deeciraion) Example 2 Now le s consider AM modulaion problem (single one) aking ino accoun m Suppose ha In his case due o relaion (3) he modulaed signal will be In Fig 2 for he values A =1, Ф=φ =, and m=[, 5, 1] ([%,5%, 1%]) he MATLAB program and corresponding graphs are given 78

4 GA RUSTAMOV e al: MATLAB/SIMULINK TECHNOLOGY OF THE Figure 2 As we see in he case m he modulaion was no arised This is shown by xmap xap cos( 1) By increasing of he values of m he ampliude of he modulaed signal x MAP increases, ha may couse he super modulaion a m>1 5 Modelling in Simulink package Here we model he AM modulaion problem considered in Example 1 in Simulink pachage Here he modulaiong signal is The slidding signal is The carrier signal is In Fig 3 corresponding Simulink scheme and modulaed x MAP signal is given cos(2*pi *1 *u) Xap Clock Fcn Produc 3*cos(2*pi *u)-sin(6*pi *u) Xm Xmm Scope Fcn1 A To Workspace 4 Consan Clock1 To Workspace1 a) b) Figure 3 79

5 J MODERN TECHNOLOGY & ENGINEERING, V2, N1, 217 As one can see he resul is he same wih in Example 1 Bu here he ime vaies in he inerval 2 Configuraion parameers are: Type-Fixed-sep, size- 1, Solver-ode 3 6 Angle modulaion Le he carrier signal be Here ω is an angle frequency in rad/sec, φ is an iniial phase in rad Expression (5) may be wrien in he form (5) Here is an angle depenging on rad and is called a whole phase The angle of he carrier signal may also be modulaed as is ampliude A This is called an angle modulaion The angle modulaion may be realized by wo ways 1 PM-modulaion In his case he phase ( ) varies propoionally o he modulaing signal x M 2 FM- modulaion In his case he frequency ( ) varies propoionally o he modulaing signal x M 51 PM-modulaion As is known in PM modulaion depending on he modulaing signal x M he phase of he signal x AP varies PM and FM modulaions indeed are clousely relaed Acually, changing of he phase influences o he frequency and vice versa To demonsrae his fac suppose he phase varies by he low In Fig4 he corresponding Simulink scheme and modulaed x MAP signal is given Clock u1 Xm 2*cos(5*u(1)+u(2)) Fcn1 1 *sin(2*u(1)) u2 Scope Fcn2 To Workspace Clock1 To Workspace1 a) b) Figure 4 As one can see from his fugure boh he frequaency and phase of he modulaed x MAP vary 8

6 GA RUSTAMOV e al: MATLAB/SIMULINK TECHNOLOGY OF THE Now we consider he square impulse sequence as a modulaing x M signal corresponding o he digial code Since in his case he phase is consan ( or 1) he frequence does no vary and one can see obviously he variaion of he phase of he modulaed signal The carries and supporing signals are: In Fig 5 he corresponding Similink scheme and modulaed x MAP signal is given Clock 4 u1 u2 Xm 2*cos(5*u(1)+u(2)) Fcn1 Pulse Generaor Gain Scope To Workspace a) b) Figure 5 As we see from he figure he phase changes arise of he modulaed signal in he impulse jumping poins This is observed by he breaking of he fuzziness frequency of he vibraions 7 Conclusion Clock1 The aricle discusses he feaures of modeling and sudy of he basic modulaion echniques on Malab/Simulink Mehods of analog modeling, in paricular ampliude, frequency, phase, and oher modulaions are given I makes possible o evaluae he modulaion capabiliies in he field of modern compuer echnology and offer more consrucive schemaic soluions References To Workspace1 1 Sergienko AB, (27) Digial Signal Processing, Texbook for high schools, 2nd ediion, Pier, 751 p 2 Solonina AI, Arbuzov SM, Digial Signal Processing, Modeling in Malab, Tex book, SPb 3 Rusamov GA, (212) Auomaic Regulaion Theory, Modeling in Malab-Simulink, Texbook, Azerbaijan Technical Universiy, Baku, 75 p 4 Rusamov GA, (216) Digial Signal Processing The review lecures, Azerbaijan Technical Universiy, Baku, 32 p 81