Lab 2 Transmission Lines TA by gTkyE37m

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```									                                             ECE 3300 TA Documentation
Lab 2

MISSING INFORMATION ON THIS REFERENCE GUIDE
Questions from lab 2 pre-lab not answered:
2.1) Explain the concept of “step function response” of a system. See your circuits book if you do
not remember.
2.2) Explain how the bounce diagrams and their related voltage vs. time plots relate to the step
function response

There is NOT TA aid, nor sample measurements or calculations for the LAB 2 procedure.

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UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
ECE 3300 TA Documentation
Lab 2

Transmission Lines
Overview: This is the procedure to follow before and during lab 2.

Equipment Needed: See “Parts Needed” WORD or PDF document for TA.

For help: Contact Bryan Stenquist (560 8761, bstenqui@ece.utah.edu, MEB1222) or class
instructor. See website: http://www.ece.utah.edu/~ece3300

Prelab Discussion: Discuss with the class types of transmission lines. What is a transmission
line? What are RLCG parameters? What is Z0?

Help the students with the lab answering questions. Make sure you thoroughly understand the lab
before it starts.

Objectives:
 Learn about different types of transmission lines including coaxial cable, two wire lines,
and microstrip.
 Measure the effect of external materials on capacitance and therefore impedance of a line.
 Understand the meaning of characteristic impedance Z0 and how it differs from
impedance Z(z).
 Understand step function voltage transients on transmission lines.

Background:
Students should understand before the lab:
 Lumped element (RLGC) model for transmission lines (TL) and how to calculate the
RLGC parameters for a variety of transmission lines.
 How to make bounce diagrams and calculate the voltage at a point on the line as a
function of time.

References: (THE T.A. IS REQUIRE TO KNOW THIS MATERIAL)
 Textbook Chapter 2
 Prelab: Read Sections 2.1, 2.2, 2.4, 2.5.1 in the text
 Agilent Application Note 1304-2 on TDR Theory (available on the lab website)
 Step function response – see your basic circuits book.

Pre-lab :

1. RLGC Model of Transmission Lines:
Write a MatlabTM code that will calculate the values of R,L,G,C, α , β , velocity of propagation,
and Zo for a coaxial transmission line, two wire line, and parallel plate transmission line.

Matlab® code from TA Spencer (use this or your own code as a reference):

NOTE: This code creates an output file NOT required for the students, but it’s a complete
example of how to calculate the values of # 1 above.

2
UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
ECE 3300 TA Documentation
Lab 2

% Name: Spencer Streeter              Course: ECE 3300 Lab              Date: September 15, 2006
% Lab: Prelab 2                       File(s): data_in.m, RLGC.m, data_out.m

% This is the main data file that takes the data from a text file ('data_in.m') and enters there values
% into an array. 3 variables f, sg, and er are used to obtain a, b, vp, and ld for each element in
% their respective arrays.

% Begin           - ---------- - ---------- - ---------- -
clear all;
clc;
% Variable Glossary - ---------- - ---------- - ---------- -
% mat = materials                                              % e0 = epsilon_0
% f = frequency                                                % mu = mu
% alpha = alpha                                                % mr = mu_r
% alpha = beta                                                 % m0 = mu_0
% omega = omega                                                % sg = sigma
% ep = epsilon_prime                                           % ld = lambda
% epp = epsilon_prime prime                                    % p0 = power_0
% er = epsilon_r                                               % sg_c = conductor (sigma_c)

% Read data from file - ---------- - ---------- -length_1 and length_2 file format specifications
% coaxial line a and b of the inner and outer radius respectively.
% parallel-plate line it is thickness and width respectively.

% line_type        frequency length_1 length_2 conductor epsilon_r sigma
num_data=length(f);            % Since all values will have a frequency this is the logical array
% to find out how many cells are in all the arrays, though, in theory
% we could have chosen any of them.
for ii=1:1:num_data
m0=pi*4e-7;
mr=1;                               % assumed mu_r=1 which also assumes materials will
% not be magnetic such as ferrite materials
mu=mr*m0;
e0=8.854e-12;
omega(ii)=2*pi.*f(ii);             % omega(ii)=2.*pi.*f(ii);
ep(ii)=er(ii).*e0;                 % ep(ii)=e_p(ii).*e0;
epp(ii)=sg(ii)./omega(ii);         % epp(ii)=e_pp(ii).*e0;
e=er(ii).*e0;                      % unless we assume lossless model which is e=ep(ii) or
e=er(ii)*e0;ep(ii)+i.*epp(ii);
nbr= strcmp(ltyp(ii),ltypcmp)      % compare cell string value to char i.e. 'coaxial' for a match
[val,idx]=max(nbr);
mc=m0;                             % Assuming mc=m0 like in book problem 2.2
if idx==1                              % if #01
type='coaxial'
a=L1(ii);                          % a is inner radius of the wire
b=L2(ii);                          % b is the outer radius of the cable
Rs=sqrt(pi*f(ii).*mc./sg_c(ii));
Rp(ii)=Rs./(2*pi)*(1/a+1/b);
Lp(ii)=mu/(2*pi)*log(b/a);
Gp(ii)=2*pi.*sg(ii)./log(b/a);
3
UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
ECE 3300 TA Documentation
Lab 2
Cp(ii)=2*pi*e/log(b/a);
else if idx==2                       % if #02
type='parallel-plate'
a=L1(ii);                         % a is gauge or thickness of wire
d=L2(ii);                         % d is span or space between the wires
Rs=sqrt(pi*f(ii)*mc/sg_c(ii));
Rp(ii)=Rs/(pi*a);
Lp(ii)=mu./pi.*log(d/(2*a)+sqrt((d/(2*a))^2-1));
Gp(ii)=pi.*sg(ii)/log(d/(2*a)+sqrt((d/(2*a))^2-1));
Cp(ii)=pi.*e./log(d/(2*a)+sqrt((d/(2*a))^2-1));
else if idx==3                       % if #03
d=L1(ii);                         % d is the depth or thickness of the dielectric spacing
w=L2(ii);                         % w is the width of the parallel-plate line
Rs=sqrt(pi*f(ii)*mc/sg_c(ii));
Rp(ii)=2*Rs/w;
Lp(ii)=mu*d/w;
Gp(ii)=sg(ii)*w/d;
Cp(ii)=e*w/d;
else
type='undefined'
end;                                 % end if #03
end;                                 % end if #02
end;                                 % end if #01

gamma(ii)=sqrt((Rp(ii)+j*omega(ii)*Lp(ii))*(Gp(ii)+j*omega(ii)*Cp(ii)));
alpha(ii)=real(gamma(ii));
beta(ii)=imag(gamma(ii));
Z0(ii)=(Rp(ii)+j*omega(ii)*Lp(ii))/gamma(ii);
vp(ii)=omega(ii)/beta(ii);
% the units of the velocity of propagation-vp(m/s)
end;

%Write data to file - ---------- - ---------- - ---------- -
fid=fopen('data_out.m','wt');
fprintf(fid,'%s\t%s\t%s\t%s\t%s\t%s\t%s\t%s\t%s\t%s\t\n',...
'line_type',...
'frequency(GHz)',...
'alpha(Np/m)',...
'velocity_of_propagation)E8(m/s)',...
'Rp',...
'Lp',...
'Gp',...
'Cp',...
'Z0');
for kk=1:1:num_data
fprintf(fid,'%s\t',char(ltyp(kk,:)));
fprintf(fid,'%g\t',f(kk)/1e9);
fprintf(fid,'%s\t',mat2str(alpha(kk)));
fprintf(fid,'%s\t',mat2str(beta(kk)));
fprintf(fid,'%s\t',mat2str(vp(kk)/1e8));
fprintf(fid,'%s\t',mat2str(Rp(kk)));
4
UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
ECE 3300 TA Documentation
Lab 2
fprintf(fid,'%s\t',mat2str(Lp(kk)));
fprintf(fid,'%s\t',mat2str(Gp(kk)));
fprintf(fid,'%s\t',mat2str(Cp(kk)));
fprintf(fid,'%s\n',mat2str(Z0(kk)));        % for conversion back use str2double(Z0)
end
fclose(fid);

% Note, might be able to use this for percentage error
% All TEM Lines share the following useful relations
% L'*C'=mu*epsilon;
% G'/C'=sigma/epsilon;
% L'G'=mu*sigma; (made up one relation ship thru multiplication)

%%%%%%%%                   END OF MATLAB FILE                 %%%%%%%%%%%

Compare the values below to the Lab 1 given values.

Output file from the Matlab® code above:

f                 up
Line type                                                   R’         L’            G’            C’        Z0
2.76E-                       9.08E-    55.0758
coaxial      1       0.0461     31.437       1.999     3.695                 0.00045602
07                           11     -i*0.0368
parallel-                                                         7.05E-                       3.55E-    140.924
1       0.0219     31.437       1.999     2.626                0.000178221
plate                                                            07                           11     +i*0.0145
4.19E-                       5.98E-     83.719
Twin-lead       1       0.0290     31.437       1.999     2.750                    0.0003
07                           11     -i*0.0103

2. Voltage Step Function Response:
Sketch Voltage Reflection Diagrams (Bounce Diagrams) for a 50 Ω RG58 coaxial line…

for reference.

Questions from lab 2 pre-lab:
2.1) Explain the concept of “step function response” of a system. See your circuits book if you
do not remember.
2.2) Explain how the bounce diagrams and their related voltage vs. time plots relate to the step
function response.

Lab Material
Equipment List: See TA equipment list for this lab.

I.           Transmission Lines
1. Using the capacitance meter, measure the capacitance of the RG58 coax and two wire…
2. Plot the capacitance versus distance of the coaxial and two wire transmission lines on a
single graph…
3. Measure the capacitance of the two-wire line buried in sand
4. Measure the resistance R of the longest RG58 coaxial cable…

5
UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
ECE 3300 TA Documentation
Lab 2

Measurements values should be similar to those values calculated using the Matlab® code.

II.      Time Domain Reflectometry

1. Understanding the AEA 20/20 TDR

See the ‘Lab 2 procedure’ document to see how to set up and use the TDR with the
‘TDR PC Vision’ software.

3. Results

Use the TDR to measure and record the results from the following loads:

NOTE: The TDR has an impedance of 79 ohms!!!! Connect an RG59 (75 ohm) cable to the TDR,
shown to plug in resistors and the short circuit. Use pre-built capacitors and inductors.

Use the Spencer TA Lab 2 excel documents as reference for the results that should be
obtained by students.

Discussion and Conclusions:
Answer any questions students might have about the Discussion and other questions