Description
In this laboratory, we will develop several simple functions to understand the behaviour of harmonic wave voltage v(z,t) and current i(z,t) along a lossless transmission line versus position z and time t.
1. Instantaneous forward and backward waves along a lossless transmission line
Write two MATLAB functions that give the instantaneous voltage and current for a forward wave and a backward wave on a lossless transmission line,
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vf if ]= forward_wave(v0,omega,phi,Z0,vp,z,t)
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vb ib ]= backward_wave(v0,omega,phi,Z0,vp,z,t)
using the following equations for instantaneous voltage and current on a lossless transmission line,
-
-
( , ) =
cos
−
+
( , ) =
cos
−
+
( , ) =
cos
+
+
( , ) = −
cos
+
+
-
where v0 is the voltage amplitude, ω is the angular frequency, ϕ is the phase, Z0 is the characteristic impedance of the lossless line, vp is the phase velocity of the lossless line, z is the position on the line, and t is the time.
2. Movie of a forward wave and a backward wave
Consider the case of v0 = 1 V, ω = 2 π x 109 Hz, ϕ = 0 rad, Z0 = 50 Ω and vp = 2 x 10 8 m/s. Confine your numerical studies to a segment of transmission line 0 ≤ z ≤ 0.40 m over a duration of time 0 ≤ t ≤ 5 ns.
Using your functions above, write a MATLAB script that creates a movie for the forward going voltage wave and backward going voltage wave. To do this, create a vector z of distance values, a vector t of time values, a matrix vf of forward voltage wave values and a matrix vb of backward voltage wave values. Your variables should be defined such that vf(m,n) corresponds to the forward voltage at position z(m) and time t(n). Be sure that you have sufficiently many points of distance and time to capture the wave propagation accurately in your movie. The script segment below can be used to create a movie from your values of z, t, vf and vb .
for k=1:length(t)
plot(z, vf(k,:),’b’); hold on;
plot(z, vb(k,:),’r’); hold off;
xlabel(‘z [m]’);
ylabel(‘v(z,t)[V]’);
title(‘instantaneous voltage on a lossless line’); legend(‘v_f(z,t)’,’ v_b(z,t)’); axis([0 4 -1 1]);
M(k)=getframe;
end;
ECSE 354 – Electromagnetic Waves
ECSE 354 – Electromagnetic Waves
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