LAB #45 Solution

Description

1) Read through these Lab #4#5 notes carefully. This prior review will save you a lot of time during the lab session, which will enable you to complete the lab in the time available.

2) Using the initial code given below, complete this MATLAB function that can be used to solve for the electric potential and electric field within an arbitrary rectangular coaxial cable. As you can see the input variables include the cable’s geometry (a, b, c, d, x0, and y0), and the boundary value (V0). At a minimum the output variables should include V, Ex, and Ey. Make sure that your code works by verifying the plots for the example rectangular coaxial cable as given above. Attending the MATLAB tutorial prior to your lab will be a great help.

function [V,Ex,Ey,C,We,We2,gridpointsx,gridpointsy,innerx,innery,outerx,outery]= bvprectangularcoax(a,b,c,d,xo,yo,er,Vo)
%
% This function used the finite difference method to solve the
% two-dimensional electrostatic boundary value problem related to a square
% coaxial cable.
% a = width of outer conductor
% b = height of outer conductor
% c = width of inner conductor
% d = height of inner conductor
% xo = the x-coordinate of the location of the bottom left corner of the inner conductor
% yo = the y-coordinate of the location of the bottom left corner of the inner conductor
% er = the relative permittivity of the dielectric which fills the space
% between the inner and outer conductor
% Vo = electric potential of the inner conductor (outer is grounded)

% Define the fundamental constant eo
eo=8.854e-12;

% Set number of nodes and node spacings Nx=201;

hx=a/(Nx-1) hy=hx; Ny=round(b/hy+1)

% Set the initial values of V to zero
V = zeros(Nx,Ny);

% Set the known potential values (or boundary values) V(1,1:Ny)=0; % Grounded left side

V(1:Nx,1)=0; % Grounded bottom side V(Nx,1:Ny)=0; % Grounded right side V(1:Nx,Ny)=0; % Grounded top side

innerstartx=round(xo/hx+1);

innerendx=round(innerstartx+c/hx);
innerstarty=round(yo/hy+1);
innerendy=round(innerstarty+d/hy);
V(innerstartx:innerendx,innerstarty:innerendy)=Vo; % Set potentials of inner conductor

% Determine the final voltage distributions (your code goes here…)

3) Using the approach discussed in the introduction above, write a few more lines of code which will enable you to estimate the capacitance per unit length of a general rectangular coaxial cable. You can assume that you have already determined the electric potential values at each node within the grid using your code from above.

University of Toronto 9 ECE Department