EFI - uloha 01 simulace

EFI - uloha 01 - simulace řešení podle katalogu

K simulaci byl pouzit program SADYS. Jeho vystup je dale uveden v upravenem tvaru.

Vstupni data
Prenosova funkce NDP
Prenosova funkce kmitoctove odnormovane DP
"Graf" kmitoctove charakteristiky NDP a DP
"Graf" - detail propustneho a nepropustneho pasma filtru
Tabulka hodnot prenosu pro vybrane kmitocty NDP

 *;
 *: dp - antialising - c20625
 om0=1;
 e  1; r1 1-2=1;
 l1 2-3=1.296492/om0; l2 3-4=0.209957/om0;
 c1 4  =1.129925/om0;
 l3 3-5=1.89632/om0; l4 5-6=0.404908/om0;
 c2 6  =1.032803/om0;
 l5 5-7=1.900117/om0;
 c3 7  =0.89303/om0;
 r2 7  =1.667;
 *pz;

Byla vybrana struktura T se seriovymi LC obvody v pricnych vetvich. Pro ilustraci jedne z moznosti programu je v zadani pouzita konstanta om0, kterou je provedeno kmitoctove odnormovani.

Prenosova funkce NDP

 tran p2=V.7/e coef;run;

 POLES     REAL PART             IMAG PART
   1  -3.7944183874133D-01   3.2343910461171D-01
   2  -3.7944183874133D-01  -3.2343910461171D-01
   3  -6.7056526674369D-02   1.0202367518124D+00
   4  -6.7056526674369D-02  -1.0202367518124D+00
   5  -2.2530444944768D-01   8.0927013400436D-01
   6  -2.2530444944768D-01  -8.0927013400436D-01

 ZEROS     REAL PART             IMAG PART
   1   0.0000000000000D+00   1.5463687901582D+00
   2   0.0000000000000D+00  -1.5463687901582D+00
   3   0.0000000000000D+00   2.0530995690366D+00
   4   0.0000000000000D+00  -2.0530995690366D+00

 GAIN CONSTANT =  1.13718267783044D-02

Prenosova funkce kmitoctove odnormovane DP

 modify om0=50265.481;tran p1=V.7/e coef;run; :om0=2pi*8000

 POLES     REAL PART             IMAG PART
   1  -1.9072826535857D+04   1.6257822167517D+04
   2  -1.9072826535857D+04  -1.6257822167517D+04
   3  -3.3706285674765D+03   5.1282691063726D+04
   4  -3.3706285674765D+03  -5.1282691063726D+04
   5  -1.1325036522928D+04   4.0678352544663D+04
   6  -1.1325036522928D+04  -4.0678352544663D+04

 ZEROS     REAL PART             IMAG PART
   1   0.0000000000000D+00   7.7728971040690D+04
   2   0.0000000000000D+00  -7.7728971040690D+04
   3   0.0000000000000D+00   1.0320003737852D+05
   4   0.0000000000000D+00  -1.0320003737852D+05

 GAIN CONSTANT =  2.87322688284403D+07

Poznamka: Vsimnete si tvaru zadani zmeny hodnoty konstanty om0 (modify om0=nova_hodnota). Tato zmena je trvala, t.j. plati az do dalsi pripadne zmeny hodnoty om0.
Na zmene je hodnot polu a nul prenosove funkce je zrejmy dopad kmitoctoveho normovani. Overte si, k jake zmene doslo a porovnejte s odvozenim normovani.

"Graf" kmitoctove charakteristiky NDP a DP

"Graf" je uveden predevsim opet pro porovnani vlivu kmitoctoveho normovani na prubeh charakteristiky. Je zrejme, ze jde pouze o posun na kmitoctove ose. Meritko na kmitoctove ose je logaritmicke!
V grafu je doprava vynasen prenos v dB, dolu roste kmitocet (v Hz, proto mezi propustneho pasma NDP neodpovida 1, ale hodnota 0.159...). Na hornim okraji grafu je uveden v zavorce rozdil hodnot prenosu pro dve sousedni sloupcove pozice v grafu a pak hodnoty prenosu pro jednotlive linky rastru.

 *fre;
 nplot(41) db.p1,db.p2;run;

 DP - ANTIALISING - C20625                                  

  X ...     FREQ
  1 ... DB .P1      *** prubeh pro NDP ***
  2 ... DB .P2      *** prubeh pro kmitoctove odnormovanou DP ***
 AXIS Y=>
  1( 1.7E+00) -1.0000E+02     -6.6667E+01         -3.3333E+01    -3.8147E-06
  2( 5.0E+00) -3.0000E+02     -2.0000E+02         -1.0000E+02     0.0000E+00
               !                   !                   !                   !  
 AXIS X        0123456789012345678901234567890123456789012345678901234567890
  3.9676E-02   !-------------------!-------------------!-----------------12! 
  5.5780E-02   !                   !                   !                 12! 
  7.8421E-02   !                   !                   !                 12! 
  1.1025E-01   !                   !                   !                 12! 
  1.5500E-01   !                   !                   !                 12! 
  2.1791E-01   !                   !                   !          2      1 ! 
  3.0636E-01   !                   !                   !     2           1 ! 
  4.3071E-01   !                   !                   !      2          1 ! 
  6.0552E-01   !                   !                   !      2          1 ! 
  8.5130E-01   !                   !                   !     2           1 ! 
  1.1968E+00   !                   !                   !    2            1 ! 
  1.6826E+00   !                   !                   !   2             1 ! 
  2.3655E+00   !                   !                   !  2              1 ! 
  3.3257E+00   !                   !                   ! 2               1 ! 
  4.6755E+00   !-------------------!-------------------2-----------------1-! 
  6.5733E+00   !                   !                  2!                 1 ! 
  9.2413E+00   !                   !                 2 !                 1 ! 
  1.2992E+01   !                   !                2  !                 1 ! 
  1.8265E+01   !                   !               2   !                 1 ! 
  2.5679E+01   !                   !              2    !                 1 ! 
  3.6102E+01   !                   !            2      !                 1 ! 
  5.0755E+01   !                   !           2       !                 1 ! 
  7.1356E+01   !                   !          2        !                 1 ! 
  1.0032E+02   !                   !         2         !                 1 ! 
  1.4104E+02   !                   !        2          !                 1 ! 
  1.9828E+02   !                   !      2            !                 1 ! 
  2.7876E+02   !                   !     2             !                 1 ! 
  3.9191E+02   !                   !    2              !                 1 ! 
  5.5097E+02   !                   !   2               !                 1 ! 
  7.7461E+02   !-------------------!--2----------------!-----------------1-! 
  1.0890E+03   !                   ! 2                 !                 1 ! 
  1.5310E+03   !                   2                   !                 1 ! 
  2.1524E+03   !                  2!                   !                 1 ! 
  3.0261E+03   !                 2 !                   !                 1 ! 
  4.2543E+03   !                2  !                   !                 1 ! 
  5.9811E+03   !               2   !                   !                 1 ! 
  8.4087E+03   !             2     !                   !              1    ! 
  1.1822E+04   !            2      !    1              !                   ! 
  1.6620E+04   !      1    2       !                   !                   ! 
  2.3366E+04   !          2        !1                  !                   ! 
  3.2850E+04   !---------2---------1-------------------!-------------------! 
 AXIS X        0123456789012345678901234567890123456789012345678901234567890

"Graf" - detail propustneho a nepropustneho pasma filtru

Detail propustneho pasma ma linearni meritko na kmitoctove ose. Pro nej je lepe viditelne rovnomerne zvlneni v propustnem pasmu. U nepropustneho pasma je pouzito logaritmicke meritko.

 *fre;
 freq/lin 200 8000;  *** Propustne pasmo - linearni meritko kmitoctu ***
 nplot(41) db.p1;run;

  X ...     FREQ
  1 ... DB .P1      
 AXIS Y=>
  1( 5.0E-03) -4.1000E+00     -4.0000E+00         -3.9000E+00    -3.8000E+00
               !                   !                   !                   !  
 AXIS X        0123456789012345678901234567890123456789012345678901234567890
  2.0000E+02   !----1--------------!-------------------!-------------------! 
  3.9500E+02   !      1            !                   !                   ! 
  5.9000E+02   !           1       !                   !                   ! 
  7.8500E+02   !                1  !                   !                   ! 
  9.8000E+02   !                   !   1               !                   ! 
  1.1750E+03   !                   !          1        !                   ! 
  1.3700E+03   !                   !                 1 !                   ! 
  1.5650E+03   !                   !                   !    1              ! 
  1.7600E+03   !                   !                   !          1        ! 
  1.9550E+03   !                   !                   !               1   ! 
  2.1500E+03   !                   !                   !                  1! 
  2.3450E+03   !                   !                   !                   1 
  2.5400E+03   !                   !                   !                  1! 
  2.7350E+03   !                   !                   !              1    ! 
  2.9300E+03   !-------------------!-------------------!---------1---------! 
  3.1250E+03   !                   !                   !  1                ! 
  3.3200E+03   !                   !              1    !                   ! 
  3.5150E+03   !                   !      1            !                   ! 
  3.7100E+03   !                  1!                   !                   ! 
  3.9050E+03   !           1       !                   !                   ! 
  4.1000E+03   !      1            !                   !                   ! 
  4.2950E+03   !   1               !                   !                   ! 
  4.4900E+03   !   1               !                   !                   ! 
  4.6850E+03   !      1            !                   !                   ! 
  4.8800E+03   !            1      !                   !                   ! 
  5.0750E+03   !                   !1                  !                   ! 
  5.2700E+03   !                   !          1        !                   ! 
  5.4650E+03   !                   !                   ! 1                 ! 
  5.6600E+03   !                   !                   !          1        ! 
  5.8550E+03   !-------------------!-------------------!-----------------1-! 
  6.0500E+03   !                   !                   !                   1 
  6.2450E+03   !                   !                   !               1   ! 
  6.4400E+03   !                   !                   !     1             ! 
  6.6350E+03   !                   !           1       !                   ! 
  6.8300E+03   !                1  !                   !                   ! 
  7.0250E+03   !     1             !                   !                   ! 
  7.2200E+03   !    1              !                   !                   ! 
  7.4150E+03   !                 1 !                   !                   ! 
  7.6100E+03   !                   !                   !  1                ! 
  7.8050E+03   !                   !                   !                   1 
  8.0000E+03   !---1---------------!-------------------!-------------------! 
 AXIS X        0123456789012345678901234567890123456789012345678901234567890

 *fre;
 freq 12000 50000; *** Nepropustne pasmo - logaritmicke meritko kmitoctu ***
 nplot(41) db.p1;run;

  X ...     FREQ
  1 ... DB .P1      
 AXIS Y=>
  1( 6.7E-01) -1.0000E+02     -8.6667E+01         -7.3333E+01    -6.0000E+01
               !                   !                   !                   !  
 AXIS X        0123456789012345678901234567890123456789012345678901234567890
  1.2000E+04   !-------------------!-------------------!--------------1----! 
  1.2436E+04   !                   !      1            !                   ! 
  1.2888E+04   !                   !                   !         1         ! 
  1.3356E+04   !                   !                   !            1      ! 
  1.3841E+04   !                   !                   !            1      ! 
  1.4343E+04   !                   !                   !          1        ! 
  1.4864E+04   !                   !                   !      1            ! 
  1.5404E+04   !                   !                   ! 1                 ! 
  1.5964E+04   !                   !          1        !                   ! 
  1.6544E+04   !           1       !                   !                   ! 
  1.7145E+04   !                   !              1    !                   ! 
  1.7767E+04   !                   !                   ! 1                 ! 
  1.8413E+04   !                   !                   !     1             ! 
  1.9082E+04   !                   !                   !       1           ! 
  1.9775E+04   !-------------------!-------------------!---------1---------! 
  2.0493E+04   !                   !                   !          1        ! 
  2.1237E+04   !                   !                   !           1       ! 
  2.2009E+04   !                   !                   !            1      ! 
  2.2808E+04   !                   !                   !            1      ! 
  2.3636E+04   !                   !                   !            1      ! 
  2.4495E+04   !                   !                   !            1      ! 
  2.5385E+04   !                   !                   !            1      ! 
  2.6307E+04   !                   !                   !            1      ! 
  2.7262E+04   !                   !                   !            1      ! 
  2.8252E+04   !                   !                   !           1       ! 
  2.9279E+04   !                   !                   !           1       ! 
  3.0342E+04   !                   !                   !           1       ! 
  3.1444E+04   !                   !                   !          1        ! 
  3.2586E+04   !                   !                   !          1        ! 
  3.3770E+04   !-------------------!-------------------!---------1---------! 
  3.4996E+04   !                   !                   !        1          ! 
  3.6267E+04   !                   !                   !        1          ! 
  3.7585E+04   !                   !                   !       1           ! 
  3.8950E+04   !                   !                   !      1            ! 
  4.0365E+04   !                   !                   !      1            ! 
  4.1831E+04   !                   !                   !     1             ! 
  4.3350E+04   !                   !                   !    1              ! 
  4.4925E+04   !                   !                   !   1               ! 
  4.6557E+04   !                   !                   !   1               ! 
  4.8248E+04   !                   !                   !  1                ! 
  5.0000E+04   !-------------------!-------------------!-1-----------------! 
 AXIS X        0123456789012345678901234567890123456789012345678901234567890

Tabulka hodnot prenosu pro vybrane kmitocty NDP:

Program SADYS umoznuje pocitat hodnoty prenosu ve vybranych kmitoctovych bodech. Ktere body byly vybrany je zrejme, pokud si uvedomite, ze vzhledem k charakteru programu je vystup v Hz, t.j. misto normovanych hodnot kmitoctu je pouzita jejich hodnota delena 2×PI.

 *fre;
 freq=0.0464563,0.1198734,0.1550104,0.1591549,0.2387324,
      0.2461123,0.3267612;
 print db.p2;run;

  X ...     FREQ
  1 ... DB .P2      *** T.j. prenos v dB NDP ****

    X              1
    4.64563D-02   -3.80124D+00
    1.19873D-01   -3.80124D+00
    1.55010D-01   -3.80124D+00
    1.59155D-01   -4.08134D+00
    2.38732D-01   -6.35313D+01
    2.46112D-01   -1.67539D+02
    3.26761D-01   -1.71144D+02