Functia de transfer

Functia de transfer

Se considera o linie de transmisie bifilara de lungime 2 Km avand urmatorii parametrii :

C=50 nF/km

L=635,119 mH/km

R=279,173 W/km

Ri=50 MW/km

Se cere sa se determine functia de transfer pentru tronsonul de linie considerata si corelatia intre intrare si iesire.

Z₁   Z₁

I_in I₁ I _out

I₂ I₃

U₁ U₃

U_in U₂ Z₂ Z₂ Z₀U_out

1 km 1 kmsarcina

Calcularea functiei de transfer:

H(s) = functia de transfer.

Functia de transfer se calculeaza cu ajutorul unui program in Matlab.

Impedanta caracteristica si viteza de propagare sunt :

Programul pentru calculul functiei de transfer:

R=279.173;

r=1e+7;

L=635.119*1e-3;

C=5*1e-8;

Z=3.564*1e+3;

B=r^2*Z;

S3=C*L^2*r+C^2*L*R*r^2;

S2=3*Z*L*r^2+2*C*L*R*Z*r^2+C^2*r^2*R*Z+L^2*r+2*C*L*R*r;

S1=3*r^2*Z*R*C+5*L*Z*r+2*L*r^2+2*C*r*R*Z+C*R^2*r^2+R*L;

TL=3*r*R*Z+3*r^2*R+Z*R+r^2*Z;

In urma rularii acestui program s-a determinat urmatoarea functie de transfer:

Programul pentru aflarea corelatiei intre intrarea (u) si iesirea (y) este:

t=0:0.0001:0.09;

u=cos(100*t); %intrare armonica.

num=[0.8096];

den=[10.11e-017 1.54 0.32e-003 1];

y=lsim(num,den,u,t);

% afisarea corelatiei intre intrare si iesire

[c1,lags] = xcorr(u,y);

c1 = mat2str(c1,2), lags

subplot(211);

plot(t,u);

grid;

subplot(212);

plot(t,y);

grid;

Se va afisa:

c1 =

[0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.00089 0.00099 0.0011 0.0012 0.0013 0.0014 0.0015 0.0016 0.0017 0.0018 0.0019 0.0019 0.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.0029 0.003 0.0031 0.0032 0.0033 0.0034 0.0035 0.0035 0.0036 0.0037 0.0038 0.0039 0.0039 0.004 0.0041 0.0042 0.0042 0.0043 0.0044 0.0045 0.0045 0.0046 0.0047 0.0048 0.0048 0.0049 0.005 0.005 0.0051 0.0052 0.0052 0.0053 0.0053 0.0054 0.0055 0.0055 0.0056 0.0056 0.0057 0.0057 0.0058 0.0058 ……………………………………………]

lags =

Columns 1 through 23

-900 -899 -898 -897 -896 -895 -894 -893 -892 -891 -890 -889 -888 -887 -886 -885 -884 -883 -882 -881 -880 -879 -878

Columns 24 through 46

-877 -876 -875 -874 -873 -872 -871 -870 -869 -868 -867 -866 -865 -864 -863 -862 -861 -860 -859 -858 -857 -856 -855

Columns 47 through 69

-854 -853 -852 -851 -850 -849 -848 -847 -846 -845 -844 -843 -842 -841 -840 -839 -838 -837 -836 -835 -834 -833 -832

Columns 70 through 92

-831 -830 -829 -828 -827 -826 -825 -824 -823 -822 -821 -820 -819 -818 -817 -816 -815 -814 -813 -812 -811 -810 -809……………………………………………………………………