jagomart
digital resources
picture1_Pulse Modulation Pdf 90383 | Pulse Item Download 2022-09-16 01-27-14


 207x       Filetype PDF       File size 0.06 MB       Source: www.pitt.edu


File: Pulse Modulation Pdf 90383 | Pulse Item Download 2022-09-16 01-27-14
tele 2060 pulse modulation what if the carrier signal were a pulse train instead of a sinusoid three approaches pulse amplitude modulation pam pulse width modulation pwm pulse position modulation ...

icon picture PDF Filetype PDF | Posted on 16 Sep 2022 | 3 years ago
Partial capture of text on file.
            Tele 2060
                                         Pulse Modulation
              • What if the Carrier Signal were a Pulse Train Instead of a
                 Sinusoid?
              • Three Approaches
                   Pulse Amplitude Modulation (PAM)
                   Pulse Width Modulation (PWM)
                   Pulse Position Modulation (PPM)
              • Each of these Approaches Uses a Discrete Signal to Carry an
                 Analog Signal
                                                                                Martin B.H. Weiss
            Pulse Modulation - 1                                             University of Pittsburgh
            Tele 2060
                                  Bandwidth of a Pulse Train
              •Vf Vττ[sin(ππfττ)/(ππfττ)]
                   () = 
              • ττ is the Duration of the Pulse
              •V is the Amplitude of the Pulse
                        th
              •The N Harmonic of a Pulse Train
                   Vn = (Vττ/T)[sin(nx)/(nx)] = (Vττ/T)sinc(ττ/T)
                   T is the Interval Between Pulses (i.e., the Period)
                   x = πτπτ/T
                                                                                Martin B.H. Weiss
            Pulse Modulation - 2                                             University of Pittsburgh
             Tele 2060
                                   Bandwidth of a Pulse Train
               • Find the “Zeros”
                                                    nx
                     We Need the Location of sin(       ) = 0
                                         nπτπτ T   ππ
                     This Occurs When          /  = 
                                    nT ττ
                     That is, When  / =1/  (By Substitution)
                    Let f =1/T, So Zeros Occurs at nf0 = 1/ττ
                          0
                                                 n                           f    ττ
                     The First Zero Occurs at  =1, or at the Frequency  =1/
               • Note The Following
                    Most of the Signal Energy (92%) is Contained in the
                                                  f     ττ
                     Frequency Between 0 and  =1/
                    Thus, we can Ignore the Higher Frequency Components
                                                                                 Martin B.H. Weiss
             Pulse Modulation - 3                                             University of Pittsburgh
             Tele 2060
                                               Example
               •V 
                    = 5V
               •T 
                   = 25µsec
                  ττ
               •  = 5µsec
               •Spectrum
                                st       f    ττ
                     Calculate 1  zero:  =1/ =1/5µsec=200KHz
                                           0
                    Calculate 2nd zero: f =2/ττ =400KHz
                                           1
                                                                                 Martin B.H. Weiss
             Pulse Modulation - 4                                             University of Pittsburgh
                  Tele 2060
                                          Pulse Amplitude Modulation (PAM)
                     • Modulate a Pulse Stream with a Signal
                            Used in Dimension PBX’s
                            Type of a AM system
                     • Categories
                            Natural PAM
                                 ‰ Top of Pulse Conforms to the Signal Shape
                                 ‰ Makes Mathematics Easy
                            Flat Top PAM
                                 ‰ More Practical
                                 ‰ Approaches Natural PAM for Narrow Pulses
                                                                                                                      Martin B.H. Weiss
                  Pulse Modulation - 5                                                                            University of Pittsburgh
                  Tele 2060
                                                          Bandwidth of PAM
                     •vt mtpt
                          () =  ( ) ( )
                            m t
                                 ( ) is the Modulating Waveform
                            p t
                                ( ) is the Pulse Train
                     • Fourier Equivalent of a Pulse Train
                            p t        Vττ T          Vττ T             x       ωωt              x           ωωt
                                ( ) =       /   + (2       /  )[sinc( )cos            + sinc(2 )cos(2             ) + . . .]
                                         x     πτπτ T
                              Where   =             /
                     •Thus,
                           v(t) = m(t)Vττ/T + m(t)(2Vττ/ΤΤ)[sinc(x)cosωωt + sinc(2x)cos(2ωωt) + . . .]
                            This is in the Same General Form of the AM Signal:
                                     ( )=   ( )  /   + [(2    / )sinc( )] ( )cos       + [(2    / )sinc(2 )] ( )cos(2       ) + . . .
                                 ‰ v t   mtV T             V           x m t         t       V             x m t           t
                                                ττ          ττ ΤΤ                  ωω         ττ ΤΤ                      ωω
                                      ( )=      ( ) +   [  (    )+ (       )] +   [  ( -2 )+     ( +2 )] + . . .
                                 ‰ X f c M f          c M f-f      Mf+f         c Mf f Mf f
                                      s     0          1       s          s      2         s           s
                                    Where   = 2          [sin(n     )/n     )] =     sinc(     )
                                             c      Vf ττ       ππ ττ   ππ ττ    f ττ      nf ττ
                                 ‰                               f       f
                                              n       s           s       s       s          s
                                                                                                                      Martin B.H. Weiss
                  Pulse Modulation - 6                                                                            University of Pittsburgh
            Tele 2060
                                             Example
              •V
                  =5V
              •T
                  =5µsec, or fs=200,000/sec
                 τ τ 
              • =1µsec
                             f    ττ     -6
              • First Zero,  0=1/ =1/10 =1MHz
              •fττ       f ττ
                 s = .2,   s  = .628
              •c
                   = (10)(.2)[sinc(0)]=2
                 0
              •c
                   = (10)(.2)[sin(.628)/.628]=2(.935)=1.87
                 1
              •c
                   = 2[sinc(.4)]=2(.757)=1.514
                 2
                                                                             Martin B.H. Weiss
            Pulse Modulation - 7                                           University of Pittsburgh
            Tele 2060
                                Form of the Harmonic Terms
              •Vmt nωωt
                  n ()cos(     s ), Where
                   ωω     ππ T
                      s = 2 / s, or the Angular Sampling Frequency
                       V VττT          nx nx x πτπτ T
                    and    =(   / )[sin(   )/(  )],  =  /
                          n
              • Observation:
                   m t
                      ( ) is Completely Contained in DC Component
                   Thus, Low Pass Filtering can be Used for Demodulation
                                                                             Martin B.H. Weiss
            Pulse Modulation - 8                                           University of Pittsburgh
The words contained in this file might help you see if this file matches what you are looking for:

...Tele pulse modulation what if the carrier signal were a train instead of sinusoid three approaches amplitude pam width pwm position ppm each these uses discrete to carry an analog martin b h weiss university pittsburgh bandwidth vf v is duration th n harmonic vn t sinc interval between pulses i e period x find zeros nx we need location sin this occurs when nt that by substitution let f so at nf first zero or frequency note following most energy contained in and thus can ignore higher components example sec spectrum st calculate khz nd modulate stream with used dimension pbx s type am system categories natural top conforms shape makes mathematics easy flat more practical for narrow vt mtpt m modulating waveform p fourier equivalent where same general form cos mtv c mf fs mhz terms vmt angular sampling observation completely dc component low pass filtering be demodulation...

no reviews yet
Please Login to review.