A coaxial cable of characteristic impedance Z_0 and length l is connected to the

Question

A coaxial cable of characteristic impedance Z_0 and length l is connected to the input of an oscilloscope. The input impedance of the scope can be represented by the parallel combination of a resistor, R, and a capacitance, C. The transmission line is driven by a time harmonic source having angular frequency omega =2 pi f where f is the frequency in Hz and V_s is the phasor amplitude. In order to determine when the transmission line appears to be "just a pair of wires," plot |V(0)/V_s| vs. f for f = 1 Hz to f = 1 GHz. Use a log scale for both the abscissa and ordinate axes. Assume R = 1 MQ, C = 30 pf, Z_0 = 50 Ohm and l = 1.0 meter. The velocity of the waves on the transmission is 2/3 the speed of light, c_0, where c_0 = 3 times 10^8 m/sec. Do the calculation and graphing in Matlab.

Explanation / Answer

% program
% (coaxial cable ).
%
% This program plots the Transfer Function of coaxial Cable at
% various forms. Change the parameter 'rate' to alter the frequency
% upto which the graphs are plotted.

clear;

%------------------------ List of Parameters ------------------------------
Samples=2^11;
rate=8e6;                           % rate = Sampling Rate = Fs

L=1000;                 % Length of coaxial cable(meter).|
b=21.3e-3;              % Outer Dia (meter)              |
                        %                                |
a=6e-3;                 % Inner Dia (meter)              |
                        %                                |
Ur=1;                   % Permeability                   |
Er=2.3;                 % Permittivity                   | Coax Related
cond=1e-16;             % Conductivity of Dielectric     | Parameters
var_coax=2.5e-13;       % Arbitrary noise power          |
T0=310;                 % Noise Temperature (Kelvin)     |
Zr=50.08;               % Load impedance. Must equal to the characteristic
                        % impedance
                      
considerBita = 1;       % Whether the phase angle of the cable is to be
                        % calculated. 0 = 'No', 1 = 'Yes'
%-------------------------------------------------------------------------

Fsa=rate/Samples;
f=rate/2 - (Samples:-1:1)*Fsa;
f=f';                               % Freq for calculation of H(f).
H = coaxTF(f,Zr,L,b,a,Ur,Er,cond,considerBita);

figure();subplot(211)
plot(f,real(H))
title('Real Part of Transfer Function')
xlabel('Frequency')
ylabel('Real Part')

subplot(212),plot(f,imag(H))
title('Imaginary Part of Transfer Function')
xlabel('Frequency')
ylabel('Imaginary Part')

figure();subplot(211)
plot(f,abs(H))
title('Magnitude of Transfer Function')
xlabel('Frequency')
ylabel('Magnitude')

subplot(212),plot(f,angle(H))
title('Phase Angle of Transfer Function')
xlabel('Frequency')
ylabel('Phase Angle')

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.