LR Circuit

Contents

symbolic

clear
L1 = sym('L1');
R1 = sym('R1');
Vs = sym('Vs');
% vector of unknowns
V1 = sym('V1');
V2 = sym('V2');
Iv = sym('Iv');
IL = sym('IL');
y = sym([V1; V2; Iv; IL]);

Build system

Gm = nmAcc(2,0,1/R1,sym(zeros(4,4)));
Cm = sym(zeros(4,4));
Is = sym(zeros(4,1));
m = 3;
Gm = mnaVsrc(m,1,0,Gm);
Is(m) = Vs;
m = 4;
Gm = mnaVsrc(m,1,2,Gm);
Cm(m,m) = -L1;

% show results
disp('y (unknowns)');
pretty(y);
disp('Gm');
pretty(Gm);
disp('Cm');
pretty(Cm);
disp('Is (rhs)');
pretty(Is);

y (unknowns)

  +-    -+
  |  V1  |
  |      |
  |  V2  |
  |      |
  |  Iv  |
  |      |
  |  IL  |
  +-    -+
Gm

  +-              -+
  |  0,  0, 1,  1  |
  |                |
  |      1         |
  |  0, --, 0, -1  |
  |     R1         |
  |                |
  |  1,  0, 0,  0  |
  |                |
  |  1, -1, 0,  0  |
  +-              -+
Cm

  +-              -+
  |  0, 0, 0,  0   |
  |                |
  |  0, 0, 0,  0   |
  |                |
  |  0, 0, 0,  0   |
  |                |
  |  0, 0, 0, -L1  |
  +-              -+
Is (rhs)

  +-    -+
  |   0  |
  |      |
  |   0  |
  |      |
  |  Vs  |
  |      |
  |   0  |
  +-    -+

state equations

stateeq

x (state variable)

  IL
A

    R1
  - --
    L1
B

  Vs
  --
  L1
C

  +-    -+
  |   0  |
  |      |
  |  R1  |
  |      |
  |  -1  |
  |      |
  |   1  |
  +-    -+
D

  +-    -+
  |  Vs  |
  |      |
  |   0  |
  |      |
  |   0  |
  |      |
  |   0  |
  +-    -+
y

  +-    -+
  |  V1  |
  |      |
  |  V2  |
  |      |
  |  Iv  |
  |      |
  |  IL  |
  +-    -+
C*x+D

  +-       -+
  |    Vs   |
  |         |
  |  IL R1  |
  |         |
  |   -IL   |
  |         |
  |    IL   |
  +-       -+

Published with MATLAB® 7.7