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HR1 1. labor

Csatolt k辿tp坦lusp叩rt tartalmaz坦 line叩ris reziszt鱈v
     h叩l坦zatok, a MATLAB haszn叩lat叩nak
  lehets辿gei a HR feladatok megold叩s叩ban.


         A t辿nyleges labor anyaga
            let旦lthet a WEB-rl:
        http://psat.evt.bme.hu/hare1
1. feladat
Az al叩bbi h叩l坦zatra sz叩m鱈tsuk ki a csom坦-
ponti potenci叩lok 辿rt辿keit, felhaszn叩lva a
MATLAB adta lehets辿geket.


                  6立             8立
                            7立
             2立
                       3立

                                  4立
   10V                                 0.5A

                       5立
4
                                6立                                 8立
                                                              7立
                          2立    Ig12           Ig2                              3
                                          3立
                1+10
                               Ug1                    Ug2               4立
       10V                                                                                 0.5A
                                     1                   0
                                          5立
1. A csatolt k辿tp坦lus egyenletei               3. trendezve az egyenleteket
   Ug1=2-1= -3 Ig2                            1      2     3     4     kons.
                                                  3            -3
   Ug2=3-0 = 3 Ig1=3 (1+10-2)/2                                            -1       0          - 15
                                                  2            2
2. Csom坦ponti egyenletek                          1                         -1       1 1 1        10
                                                                   0                   + +
   4  4 3  4(  1+10 )                       6                         8        7 8 6         6
    +         +                =0
  7       8          6                                1            -1        1 1        -1
                                                                              +                   0.5
  3  3 4  1 2                                  3            3         4 8        8
    +         +         0 .5 = 0
  4       8       3                             1 1                                    -1          - 10
                                                 +                 0         0
 1         +10  2  1+10  4               5 6                                    6             6
     I g1+ 1        +            =0
  5             2             6
Feladat megval坦s鱈t叩sa MATLAB-bal.
                         1
A = kons.          = A kons.
珂艶乙看鉛糸叩壊
                                            4
             I6           6立                              8立
                                       U7
                                                     7立
                  2立        2                                  3
                                  3立
       1+10
                                                           4立
      P10V
10V                                                                  0.5A
                             1                  0
                                  5立


                  U7 =     4 = fi(4) = 5.1455 V
                   I6 =   [ 4 -( 1+10)]/6 = (fi(4)-(fi(1)+10))/6 = -0.441A
               P10V =     {[ 4 -( 1+10)]/6 + [ 2 -( 1+10)]/2}*10 =
                   = ((fi(4)-(fi(1)+10))/6+(fi(2)-(fi(1)+10))/2)*10 = -29.39 W
2. feladat
Hat叩rozzuk meg a h叩l坦zat Th辿venin
helyette- s鱈t kapcsol叩s叩nak param辿tereit ha
a./ us2=4V
b./ us2=6V !
                        1:3




                   5立         10立


                    2V        us2
iT1          iT2
                                          1:3
                                                                        Irz
                            uT1                       uT2
                                                                  U端j

                                    5立                  10立


                                         2V                 us2


1. A csatolt k辿tp坦lus egyenletei
 uT2 = 3 uT1                                          3. 珂艶乙看鉛糸叩壊hoz kapcsol坦d坦 egyenlet

 iT1 = -3 iT2                                           a./ U端j meghat叩roz叩sa eset辿n
2. Fesz端lts辿g 辿s 叩ram egyenletek                                              Irz = 0
 U端j = uT1 + 5 iT1 + 2
                                                        b./ Irz meghat叩roz叩sa eset辿n
 U端j = uT2 + 10 iT2 + us2
                                                                              U端j = 0
 iT1 + iT2 + Irz = 0
Feladat megval坦s鱈t叩sa MATLAB-bal.
 UT1     UT2      IT1      IT2      U端j      Irz   kon
  3       -1        0        0       0        0       0       uT2 = 3 uT1
  0        0        1        3       0        0       0        iT1 = -3 iT2
  1        0        5        0       -1       0       -2      U端j = uT1 + 5 iT1 + 2

  0        1        0       10       -1       0      -U s2    U端j = uT2 + 10 iT2 + us2

  0        0        1        1        0        1      0       iT1 + iT2 + Irz = 0
  0        0        0        0        0        1      0        a./ Irz = 0
  0        0        0        0        1        0      0        b./ U端j = 0

Us2=4

A=[3 -1 0 0 0 0;0 0 1 3 0 0;1 0 5 0 -1 0;0 1 0 10 -1 0;0 0 1 1 0 1;0 0 0 0 0 1]

kon=[0;0;-2;-Us2;0;0]
mo=Akon

B=[3 -1 0 0 0 0;0 0 1 3 0 0;1 0 5 0 -1 0;0 1 0 10 -1 0;0 0 1 1 0 1;0 0 0 0 1 0]
mo2=Bkon
Us2=6

kon=[0;0;-2;-Us2;0;0]

mo3=Akon

mo4=Bkon

                    mo         mo2             mo3   mo4
                 -1.0000    -1.4545   UT1      -2    -2
                 -3.0000    -4.3636   UT2      -6    -6
                  0         -0.1091    IT1      0     0
                  0          0.0364    IT2      0     0
                  1.0000     0        U端j       0     0
                  0         0.0727     Irz
                                                0     0

                              Mit jelent ez?

                        1/0.0727=
            1V          13.7551立
I1     K辿tkapuk                            I2 !!!!


                          U1                                                      U2


     tviteli t鱈pus炭 karakterisztik叩k (2 db)                      Hibrid t鱈pus炭 karakterisztik叩k (4 db)

          錚U 1 錚 錚U 2 錚                                           錚U 1 錚 錚I 1 錚         錚U 1 錚 錚I 1 錚
          錚 錚 = A錚 錚                      I2 !!!!                 錚 錚 = R錚 錚            錚 錚 = H錚 錚
          錚I 1 錚
          錚 錚    錚I 2 錚
                 錚 錚                                              錚U 2 錚
                                                                  錚 錚    錚I 2 錚
                                                                         錚 錚            錚I 2 錚
                                                                                        錚 錚    錚U 2 錚
                                                                                               錚 錚
          錚U 2 錚 錚U 1 錚                                           錚I 1 錚 錚U 1 錚         錚I 1 錚 錚U 1 錚
          錚 錚 = B錚 錚                                              錚 錚 = G錚 錚            錚 錚 = K錚 錚
          錚I 2 錚
          錚 錚    錚I 1 錚
                 錚 錚                                              錚I 2 錚
                                                                  錚 錚    錚U 2 錚
                                                                         錚 錚            錚U 2 錚
                                                                                        錚 錚    錚I 2 錚
                                                                                               錚 錚
              A =B 1                                                  R =G 1             H = K 1
     I1                      I2                              I3

U1            A1                  U2       A2                     U3

            錚U 1 錚   錚U 2 錚 錚U 2 錚 錚U 3 錚 錚U 1 錚    錚U 3 錚
            錚 錚 = A1 錚 錚 錚 錚 = A 2 錚 錚 錚 錚 = A1 A 2 錚 錚
            錚I 1 錚
            錚 錚      錚I 2 錚 錚I 2 錚
                     錚 錚 錚 錚       錚I 3 錚 錚I 1 錚
                                   錚 錚 錚 錚          錚I 3 錚
                                                    錚 錚
3. feladat
Hat叩rozzuk meg az al叩bbi k辿tkapu
lehets辿ges karakterisztik叩it, felhaszn叩lva a
MATLAB adta lehets辿geket.


                   6立             8立

         I1                  7立         I2
              2立
                        3立

    U1                             4立        U2


                        5立
3
                                   6立                                     8立
                                                                     7立
                I1           2立    Ig12               Ig2                              U2 I2
                                             3立
                     1+U1
          U1                      Ug1                        Ug2               4立               U2


                                        1                       0
                                             5立
1. A csatolt k辿tp坦lus egyenletei               3. trendezve az egyenleteket
               7 ismeretlen (U1, U2, I1, I2, 1, 2, 3) 5 egyenlet kell 5 egyenlet kell
   Ug1=2-1= -3 Ig2                         U U I I   
                                                   1         2       1    2         1    2      3

   Ug2=U2-0 = 3 Ig1=3 (1+U1-2)/2                3
                                                         -1          0    0
                                                                                3        -3
                                                                                                 0
2. Csom坦ponti egyenletek                          2                             2        2
    3  3 U 2  3(  1+ U1 )                   1     -1                     -1            1 1 1
                                                                     0     0             0     + +
        +         +                  =0            6     8                      6             7 8 6
    7        8              6                           1 1                     1        -1    -1
       U 2 U 2  3  1 2                       0      +           0    -1
          +            +         I 2 = 0               4 8                     3        3     8
       4        8           3                  1
             1          2 1 U1                          0       1     0
                                                                             1 1
                                                                              
                                                                                         1
                                                                                                0
                 + I1 +               =0       2                             5 2         2
              5              2                1 1                            1 1         -1     -1
         + U   + U                        +            0       -1    0  +
  I1 + 1 1 2 + 1 1 3 = 0                     2 6                            2 6         2      6
             2               6
珂艶乙看鉛糸叩壊 MATLAB-bal
U1=[3/2;-1/6;0;-1/2;1/2+1/6]
                                                      U1   U2     I1    I2   1   2   3
U2=[-1;-1/8;1/4+1/8;0;0]                              3                      3    -3
                                                           -1     0    0                0
I1=[0;0;0;1;-1]                                       2                      2    2
                                                      1    -1               -1        1 1 1
                                                                  0     0         0     + +
I2=[0;0;-1;0;0]                                        6    8                6         7 8 6
                                                           1 1                1   -1    -1
Fi1=[3/2;-1/6;1/3;1/5-1/2;1/2+1/6]                    0      +    0    -1
                                                           4 8                3   3     8
Fi2=[-3/2;0;-1/3;1/2;-1/2]                        1                         1 1 1
                                                            0     1     0              0
                                                   2                         5 2 2
Fi3=[0;1/7+1/8+1/6;-1/8;0;-1/6]                   1 1                         1 1 -1    -1
                                                    +       0     -1       0    +

  A ism = 0
                                                  2 6                         2 6 2     6


                                         M is1 = N is2                     ahol is1-ben van a
                                                                           karakterisztika bal
7x5     1x7         1x5
                                                                           oldala 辿s -k, is2-
                                         5x5    1x5             2x5    1x2 ben a jobb oldal
                        -1
 is1 = M N is2                                 M-1N 
                                                                              a karakterisztika
  1x5             5x5        2x5   1x2          2x5
MR=[U1 U2 Fi1 Fi2 Fi3]        NR=[ I1 I2]
MG=[I1 I2 Fi1 Fi2 Fi3]        NG=[ U1 U2]
MH=[U1 I2 Fi1 Fi2 Fi3]        NH=[ I1 U2]
MK=[I1 U2 Fi1 Fi2 Fi3]        NR=[ U1 I2]
MA=[U1 I1 Fi1 Fi2 Fi3]        NA=[ U2 I2]
MB=[U2 I2 Fi1 Fi2 Fi3]       NB=[ U1 I1]!!!!!!
                N辿zz端k az impedancia karakterisztik叩t!
MR=                                                         NR=
  1.5000 -1.0000 1.5000 -1.5000      0                         0   0
 -0.1667 -0.1250 -0.1667      0 0.4345                         0   0
       0 0.3750 0.3333 -0.3333 -0.1250                         0   1
 -0.5000       0 -0.3000 0.5000       0                       -1   0
  0.6667       0 0.6667 -0.5000 -0.1667                        1   0

     MR-1*NR=                                  MH-1*NH=
                                A hibrid karakterisztika pedig
R=     3.7489 -2.0426     立              H=     14.7333 立     -4.4444
       2.4715 0.4596                             -5.3778       2.1759 S
      -0.8809 0.7660                             -5.0000       1.6667
       1.2204 -1.5830                             9.7333      -3.4444
       1.8111 -0.3574                             3.7333      -0.7778

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Labor11

  • 1. HR1 1. labor Csatolt k辿tp坦lusp叩rt tartalmaz坦 line叩ris reziszt鱈v h叩l坦zatok, a MATLAB haszn叩lat叩nak lehets辿gei a HR feladatok megold叩s叩ban. A t辿nyleges labor anyaga let旦lthet a WEB-rl: http://psat.evt.bme.hu/hare1
  • 2. 1. feladat Az al叩bbi h叩l坦zatra sz叩m鱈tsuk ki a csom坦- ponti potenci叩lok 辿rt辿keit, felhaszn叩lva a MATLAB adta lehets辿geket. 6立 8立 7立 2立 3立 4立 10V 0.5A 5立
  • 3. 4 6立 8立 7立 2立 Ig12 Ig2 3 3立 1+10 Ug1 Ug2 4立 10V 0.5A 1 0 5立 1. A csatolt k辿tp坦lus egyenletei 3. trendezve az egyenleteket Ug1=2-1= -3 Ig2 1 2 3 4 kons. 3 -3 Ug2=3-0 = 3 Ig1=3 (1+10-2)/2 -1 0 - 15 2 2 2. Csom坦ponti egyenletek 1 -1 1 1 1 10 0 + + 4 4 3 4( 1+10 ) 6 8 7 8 6 6 + + =0 7 8 6 1 -1 1 1 -1 + 0.5 3 3 4 1 2 3 3 4 8 8 + + 0 .5 = 0 4 8 3 1 1 -1 - 10 + 0 0 1 +10 2 1+10 4 5 6 6 6 I g1+ 1 + =0 5 2 6
  • 5. 珂艶乙看鉛糸叩壊 4 I6 6立 8立 U7 7立 2立 2 3 3立 1+10 4立 P10V 10V 0.5A 1 0 5立 U7 = 4 = fi(4) = 5.1455 V I6 = [ 4 -( 1+10)]/6 = (fi(4)-(fi(1)+10))/6 = -0.441A P10V = {[ 4 -( 1+10)]/6 + [ 2 -( 1+10)]/2}*10 = = ((fi(4)-(fi(1)+10))/6+(fi(2)-(fi(1)+10))/2)*10 = -29.39 W
  • 6. 2. feladat Hat叩rozzuk meg a h叩l坦zat Th辿venin helyette- s鱈t kapcsol叩s叩nak param辿tereit ha a./ us2=4V b./ us2=6V ! 1:3 5立 10立 2V us2
  • 7. iT1 iT2 1:3 Irz uT1 uT2 U端j 5立 10立 2V us2 1. A csatolt k辿tp坦lus egyenletei uT2 = 3 uT1 3. 珂艶乙看鉛糸叩壊hoz kapcsol坦d坦 egyenlet iT1 = -3 iT2 a./ U端j meghat叩roz叩sa eset辿n 2. Fesz端lts辿g 辿s 叩ram egyenletek Irz = 0 U端j = uT1 + 5 iT1 + 2 b./ Irz meghat叩roz叩sa eset辿n U端j = uT2 + 10 iT2 + us2 U端j = 0 iT1 + iT2 + Irz = 0
  • 8. Feladat megval坦s鱈t叩sa MATLAB-bal. UT1 UT2 IT1 IT2 U端j Irz kon 3 -1 0 0 0 0 0 uT2 = 3 uT1 0 0 1 3 0 0 0 iT1 = -3 iT2 1 0 5 0 -1 0 -2 U端j = uT1 + 5 iT1 + 2 0 1 0 10 -1 0 -U s2 U端j = uT2 + 10 iT2 + us2 0 0 1 1 0 1 0 iT1 + iT2 + Irz = 0 0 0 0 0 0 1 0 a./ Irz = 0 0 0 0 0 1 0 0 b./ U端j = 0 Us2=4 A=[3 -1 0 0 0 0;0 0 1 3 0 0;1 0 5 0 -1 0;0 1 0 10 -1 0;0 0 1 1 0 1;0 0 0 0 0 1] kon=[0;0;-2;-Us2;0;0] mo=Akon B=[3 -1 0 0 0 0;0 0 1 3 0 0;1 0 5 0 -1 0;0 1 0 10 -1 0;0 0 1 1 0 1;0 0 0 0 1 0] mo2=Bkon
  • 9. Us2=6 kon=[0;0;-2;-Us2;0;0] mo3=Akon mo4=Bkon mo mo2 mo3 mo4 -1.0000 -1.4545 UT1 -2 -2 -3.0000 -4.3636 UT2 -6 -6 0 -0.1091 IT1 0 0 0 0.0364 IT2 0 0 1.0000 0 U端j 0 0 0 0.0727 Irz 0 0 Mit jelent ez? 1/0.0727= 1V 13.7551立
  • 10. I1 K辿tkapuk I2 !!!! U1 U2 tviteli t鱈pus炭 karakterisztik叩k (2 db) Hibrid t鱈pus炭 karakterisztik叩k (4 db) 錚U 1 錚 錚U 2 錚 錚U 1 錚 錚I 1 錚 錚U 1 錚 錚I 1 錚 錚 錚 = A錚 錚 I2 !!!! 錚 錚 = R錚 錚 錚 錚 = H錚 錚 錚I 1 錚 錚 錚 錚I 2 錚 錚 錚 錚U 2 錚 錚 錚 錚I 2 錚 錚 錚 錚I 2 錚 錚 錚 錚U 2 錚 錚 錚 錚U 2 錚 錚U 1 錚 錚I 1 錚 錚U 1 錚 錚I 1 錚 錚U 1 錚 錚 錚 = B錚 錚 錚 錚 = G錚 錚 錚 錚 = K錚 錚 錚I 2 錚 錚 錚 錚I 1 錚 錚 錚 錚I 2 錚 錚 錚 錚U 2 錚 錚 錚 錚U 2 錚 錚 錚 錚I 2 錚 錚 錚 A =B 1 R =G 1 H = K 1 I1 I2 I3 U1 A1 U2 A2 U3 錚U 1 錚 錚U 2 錚 錚U 2 錚 錚U 3 錚 錚U 1 錚 錚U 3 錚 錚 錚 = A1 錚 錚 錚 錚 = A 2 錚 錚 錚 錚 = A1 A 2 錚 錚 錚I 1 錚 錚 錚 錚I 2 錚 錚I 2 錚 錚 錚 錚 錚 錚I 3 錚 錚I 1 錚 錚 錚 錚 錚 錚I 3 錚 錚 錚
  • 11. 3. feladat Hat叩rozzuk meg az al叩bbi k辿tkapu lehets辿ges karakterisztik叩it, felhaszn叩lva a MATLAB adta lehets辿geket. 6立 8立 I1 7立 I2 2立 3立 U1 4立 U2 5立
  • 12. 3 6立 8立 7立 I1 2立 Ig12 Ig2 U2 I2 3立 1+U1 U1 Ug1 Ug2 4立 U2 1 0 5立 1. A csatolt k辿tp坦lus egyenletei 3. trendezve az egyenleteket 7 ismeretlen (U1, U2, I1, I2, 1, 2, 3) 5 egyenlet kell 5 egyenlet kell Ug1=2-1= -3 Ig2 U U I I 1 2 1 2 1 2 3 Ug2=U2-0 = 3 Ig1=3 (1+U1-2)/2 3 -1 0 0 3 -3 0 2. Csom坦ponti egyenletek 2 2 2 3 3 U 2 3( 1+ U1 ) 1 -1 -1 1 1 1 0 0 0 + + + + =0 6 8 6 7 8 6 7 8 6 1 1 1 -1 -1 U 2 U 2 3 1 2 0 + 0 -1 + + I 2 = 0 4 8 3 3 8 4 8 3 1 1 2 1 U1 0 1 0 1 1 1 0 + I1 + =0 2 5 2 2 5 2 1 1 1 1 -1 -1 + U + U + 0 -1 0 + I1 + 1 1 2 + 1 1 3 = 0 2 6 2 6 2 6 2 6
  • 13. 珂艶乙看鉛糸叩壊 MATLAB-bal U1=[3/2;-1/6;0;-1/2;1/2+1/6] U1 U2 I1 I2 1 2 3 U2=[-1;-1/8;1/4+1/8;0;0] 3 3 -3 -1 0 0 0 I1=[0;0;0;1;-1] 2 2 2 1 -1 -1 1 1 1 0 0 0 + + I2=[0;0;-1;0;0] 6 8 6 7 8 6 1 1 1 -1 -1 Fi1=[3/2;-1/6;1/3;1/5-1/2;1/2+1/6] 0 + 0 -1 4 8 3 3 8 Fi2=[-3/2;0;-1/3;1/2;-1/2] 1 1 1 1 0 1 0 0 2 5 2 2 Fi3=[0;1/7+1/8+1/6;-1/8;0;-1/6] 1 1 1 1 -1 -1 + 0 -1 0 + A ism = 0 2 6 2 6 2 6 M is1 = N is2 ahol is1-ben van a karakterisztika bal 7x5 1x7 1x5 oldala 辿s -k, is2- 5x5 1x5 2x5 1x2 ben a jobb oldal -1 is1 = M N is2 M-1N a karakterisztika 1x5 5x5 2x5 1x2 2x5
  • 14. MR=[U1 U2 Fi1 Fi2 Fi3] NR=[ I1 I2] MG=[I1 I2 Fi1 Fi2 Fi3] NG=[ U1 U2] MH=[U1 I2 Fi1 Fi2 Fi3] NH=[ I1 U2] MK=[I1 U2 Fi1 Fi2 Fi3] NR=[ U1 I2] MA=[U1 I1 Fi1 Fi2 Fi3] NA=[ U2 I2] MB=[U2 I2 Fi1 Fi2 Fi3] NB=[ U1 I1]!!!!!! N辿zz端k az impedancia karakterisztik叩t! MR= NR= 1.5000 -1.0000 1.5000 -1.5000 0 0 0 -0.1667 -0.1250 -0.1667 0 0.4345 0 0 0 0.3750 0.3333 -0.3333 -0.1250 0 1 -0.5000 0 -0.3000 0.5000 0 -1 0 0.6667 0 0.6667 -0.5000 -0.1667 1 0 MR-1*NR= MH-1*NH= A hibrid karakterisztika pedig R= 3.7489 -2.0426 立 H= 14.7333 立 -4.4444 2.4715 0.4596 -5.3778 2.1759 S -0.8809 0.7660 -5.0000 1.6667 1.2204 -1.5830 9.7333 -3.4444 1.8111 -0.3574 3.7333 -0.7778