Anybody good with Distributed Circuit models & Electromagnetics?

[polarmystery]

Greetings ATOT,

I'm having a lot of difficulty with one of my grad school courses and I could use some help with some of the material. If you are, please feel free to shoot me a PM. Thanks in advance.

P.S. Professor is unwilling to help, as he's a bit of a d*ck.

Here is the problem:

I think I got the first part down alright, but I'm having trouble with the Transfer functions for Vo for 2 & 3, and I'm a little less than clueless about the 4th one. The notes we were given to solve this problem are a little lacking (I think anyway).

Edit: I forgot to include Zo, which equals 75 Ohms.

Here are the models also:

 

[gophins72]

You could try posting it here but the quality of your responses will vary

 

[TecHNooB]

post it here!

 

[polarmystery]

if anyone can help, I'd appreciate it! (financially?)

 

[artikk]

I've taken basic transmission line theory but I'm not familiar with models referenced in 2 and 3. It's a bit weird Zo isn't included. For 1, however, if they want you to convert the trans. line model into lumped circuit equivalent, the signal has to be at specific frequency which translates into about 1/10 to 1/100 of wavelength of signal to qualify(borderline between circuits that can be solved with lumped models vs distributed models).
Also, you might get better help posting this in Highly Technical.

 

[polarmystery]

I've taken basic transmission line theory but I'm not familiar with models referenced in 2 and 3. It's a bit weird Zo isn't included. For 1, however, if they want you to convert the trans. line model into lumped circuit equivalent, the signal has to be at specific frequency which translates into about 1/10 to 1/100 of wavelength of signal to qualify(borderline between circuits that can be solved with lumped models vs distributed models).
Also, you might get better help posting this in Highly Technical.

Alright, will do. I also forgot to include Zo in this problem, which is 75 ohms. (as noted above)

 

[William Gaatjes]

I do not know if i fully understand what you ask. But when looking at that schematic, i will try. I might be wrong though.

I would like to try to help, but i do not understand this : "single segment circuit model".

It is obvious that the signal travels at a certain speed(a 1/x * c). This speed will give the signal a latency even at a distance of 10 cm.
The impedance of the signal source is 75 Ohm.
That wire will also exhibit a characteristic impedance.
I am sorry. I would have to look it up as well.

Your schematic reminds me of the time domain reflectometer.
Perhaps this can help you visualize.
http://en.wikipedia.org/wiki/Time-domain_reflectometer.

http://en.wikipedia.org/wiki/Transmission_line

 

[Sunny129]

the quality of responses will be much better here at Physics Forums. there is an "electrical engineering" sub-forum in the engineering section, as well as a "homework and coursework questions" sub-forum in the science education section.

 

[William Gaatjes]

the quality of responses will be much better here at Physics Forums. there is an "electrical engineering" sub-forum in the engineering section, as well as a "homework and coursework questions" sub-forum in the science education section.

I really have to divert some forum time from anandtech forum to that physics forum. Most interesting subjects they have.

 

[artikk]

For part 4 of assignment, try reading this pdf- http://ece.wpi.edu/analog/resources/transmissionline.pdf
Consider case 3: Rs=Zo, Rt(ZL)!=Zo, page 6 and especially 7.

 

[polarmystery]

the quality of responses will be much better here at Physics Forums. there is an "electrical engineering" sub-forum in the engineering section, as well as a "homework and coursework questions" sub-forum in the science education section.

I do have a post there with the same information . I'm getting some help, but the community seems to be just as confused as I am. I figure I'd ask my AT brethren.

 

[TecHNooB]

are you given R and G? or are you supposed to assume ideal t-line?

here's something I wrote in matlab that might be useful:

clc, clear all, close all

% T-line problem
s = tf('s');
v = 1.5e8;
Rs = 75;
Z0 = 75;
R = 1e-3;
G = 10e6;
C = 1/(Z0*v);
L = Z0^2*C;
Zload = 75;

% Quick approx for max risetime.
length = 1e-2;
minwavelength = length * 100; % Segment is 1/100th of the min wavelength.
minfreq = v / minwavelength; % Min frequency component given min wavelength.
risetime = 4 / minfreq; % Rough estimate of max risetime given min frequency.

V = 1;
dVdt = V / risetime;
Vs = dVdt/s^2; % Laplace of dV/dv*t*u(t).
% 'r' model.
A = tf([G],[C*G, 1]); % G in parallel with 1/sC.
B = s*(L + imag(Zload)) + R + real(Zload); % Series R, sL, and Zload.
ApB = (1/A + 1/B)^-1; % A in parallel with B.
VoVi = (real(Zload) + imag(Zload)*s) / (R + s*L + real(Zload) + imag(Zload)*s)
ViVs = ApB / (Rs + ApB)
Vo = Vs*ViVs*VoVi; % Laplace of Vout.

% '7' model.
Y = (1/(real(Zload) + imag(Zload)*s) + 1/G + s*C)^-1;
X = s*L + R;
VoVi2 = Y / (X + Y);
ViVs2 = (X + Y) / (Rs + X + Y);

figure(1);
subplot(2,2,1);
bode(VoVi);
title('r Vin to Vout');
subplot(2,2,3);
bode(ViVs);
title('r Vs to Vin');
subplot(2,2,2);
bode(VoVi2);
title('7 Vin to Vout ');
subplot(2,2,4);
bode(ViVs2);
title('7 Vs to Vin');

figure(2);
subplot(2,1,1);
bode(Vs);
title('Vs');
subplot(2,1,2);
bode(Vo);
title('Vo');

The placement of L and C cause interesting differences between the freq response of 'r' and '7' models.

 

[polarmystery]

are you given R and G? or are you supposed to assume ideal t-line?

here's something I wrote in matlab that might be useful:

clc, clear all, close all

% T-line problem
s = tf('s');
v = 1.5e8;
Rs = 75;
Z0 = 75;
R = 1e-3;
G = 10e6;
C = 1/(Z0*v);
L = Z0^2*C;
Zload = 75;

% Quick approx for max risetime.
length = 1e-2;
minwavelength = length * 100; % Segment is 1/100th of the min wavelength.
minfreq = v / minwavelength; % Min frequency component given min wavelength.
risetime = 4 / minfreq; % Rough estimate of max risetime given min frequency.

V = 1;
dVdt = V / risetime;
Vs = dVdt/s^2; % Laplace of dV/dv*t*u(t).
% 'r' model.
A = tf([G],[C*G, 1]); % G in parallel with 1/sC.
B = s*(L + imag(Zload)) + R + real(Zload); % Series R, sL, and Zload.
ApB = (1/A + 1/B)^-1; % A in parallel with B.
VoVi = (real(Zload) + imag(Zload)*s) / (R + s*L + real(Zload) + imag(Zload)*s)
ViVs = ApB / (Rs + ApB)
Vo = Vs*ViVs*VoVi; % Laplace of Vout.

% '7' model.
Y = (1/(real(Zload) + imag(Zload)*s) + 1/G + s*C)^-1;
X = s*L + R;
VoVi2 = Y / (X + Y);
ViVs2 = (X + Y) / (Rs + X + Y);

figure(1);
subplot(2,2,1);
bode(VoVi);
title('r Vin to Vout');
subplot(2,2,3);
bode(ViVs);
title('r Vs to Vin');
subplot(2,2,2);
bode(VoVi2);
title('7 Vin to Vout ');
subplot(2,2,4);
bode(ViVs2);
title('7 Vs to Vin');

figure(2);
subplot(2,1,1);
bode(Vs);
title('Vs');
subplot(2,1,2);
bode(Vo);
title('Vo');

The placement of L and C cause interesting differences between the freq response of 'r' and '7' models.

It's an ideal t-line so there is no R and G. Yeah I think that helps me out. I gotta figure out how to plot Vo with respect to time though, as that's what I think our prof wants. (That post in the OT section is for some kind of operator that is in our notes that I think we need. I've just been playing around with MATLAB trying to get it to work, so that's why I didn't post it here).

 

[TecHNooB]

It's an ideal t-line so there is no R and G. Yeah I think that helps me out. I gotta figure out how to plot Vo with respect to time though, as that's what I think our prof wants. (That post in the OT section is for some kind of operator that is in our notes that I think we need. I've just been playing around with MATLAB trying to get it to work, so that's why I didn't post it here).

If you don't need R and G, i'd rewrite the transfer functions so its not as cluttered. you can solve for Vout by just knowing the time it takes for the wave to go across the line (you have propagation speed and length). Then, given that you know Zload (hopefully its all real ), you can calculate the reflection coefficients at the two points where impedance mismatches can occur and just do some wave stacking. however, the number of terms may reach infinite, so the answer may have to be written as a summation of shifted and scaled versions of the input.

http://en.wikipedia.org/wiki/Reflection_coefficient

^ you'll need that equation.

btw, i goofed on the input function (ramp instead of step). :|

 

[polarmystery]

If you don't need R and G, i'd rewrite the transfer functions so its not as cluttered. you can solve for Vout by just knowing the time it takes for the wave to go across the line (you have propagation speed and length). Then, given that you know Zload (hopefully its all real ), you can calculate the reflection coefficients at the two points where impedance mismatches can occur and just do some wave stacking. however, the number of terms may reach infinite, so the answer may have to be written as a summation of shifted and scaled versions of the input.

http://en.wikipedia.org/wiki/Reflection_coefficient

^ you'll need that equation.

btw, i goofed on the input function (ramp instead of step). :|

Is it safe to assume that my transfer functions for the r model and 7 model are different? (The r-model would cause the inductor to be floating) The approach that me and a few classmates are taking in solving these problems is finding the transfer function, then taking the inverse laplace and plotting them in the time domain. In our slides, the instructor in a sample first takes a transfer function and calculates its unit-step response. He then proceeds to take the same function, but instead multiplies a ramp function and a what looks like time delay function. It ends up looking something like this:

H(s) = transfer function
R(s) = 1/s^2
D(s) = (1 - e^(-s* (Trise/0.8)) / (Trise/0.8))

Such that Vo = ilaplace of D(s)*R(s)*H(s) in that order. I have the same topic on the physics forum but I didn't understand them that well. See here for what I mean for above:

http://www.physicsforums.com/showthread.php?t=537956

 

[TecHNooB]

Is it safe to assume that my transfer functions for the r model and 7 model are different? (The r-model would cause the inductor to be floating) The approach that me and a few classmates are taking in solving these problems is finding the transfer function, then taking the inverse laplace and plotting them in the time domain. In our slides, the instructor in a sample first takes a transfer function and calculates its unit-step response. He then proceeds to take the same function, but instead multiplies a ramp function and a what looks like time delay function. It ends up looking something like this:

H(s) = transfer function
R(s) = 1/s^s
D(s) = (1 - e^(-s* (Trise/0.8)) / (Trise/0.8))

Such that Vo = ilaplace of D(s)*R(s)*D(s) in that order. I have the same topic on the physics forum but I didn't understand them that well. See here for what I mean for above:

http://www.physicsforums.com/showthread.php?t=537956

hes basically doing Vin(s)*H(s) = Vout(s).

Vin(t) = t*u(t) - (t - delay)*u(t - delay)
Vin(s) = 1/s^2 - e^(-delay*s)/s^2 = (1 - e^(-delay*s)) / s^2.

you could take the inverse laplace, tho it could get ugly fast

 

[polarmystery]

hes basically doing Vin(s)*H(s) = Vout(s).

Vin(t) = t*u(t) - (t - delay)*u(t - delay)
Vin(s) = 1/s^2 - e^(-delay*s)/s^2 = (1 - e^(-delay*s)) / s^2.

you could take the inverse laplace, tho it could get ugly fast

This is what i've been trying to do all day, but I went through about 10 sheets of paper! He managed to do it in our notes, but he converted R, L, and C to real values. I'm going to have to sleep on this stuff, because it's still pretty confusing to me. It's coincidence I have MATLAB to do these plots, because he assumes that we do all of these by hand :'(

 

[TecHNooB]

This is what i've been trying to do all day, but I went through about 10 sheets of paper! He managed to do it in our notes, but he converted R, L, and C to real values. I'm going to have to sleep on this stuff, because it's still pretty confusing to me. It's coincidence I have MATLAB to do these plots, because he assumes that we do all of these by hand :'(

the transfer function concept should be no problem. however, if you don't have the wave point of view, this might help

http://www.youtube.com/watch?v=wbkyQw_B258

if you look back at that wiki page for reflection coefficient, youll see that for an open load, a voltage wave will bounce back with twice the amplitude. whats going to happen to that step is it's going to travel across the segment, "see" the open, reflect off of it entirely with a positive polarity, and stack up with the part of the wave that's still going forward. the reflection depends on the coefficient. in the simple case, where Z0 and Rs are the same, there's only 1 reflection. when there's multiple reflection points, its like pinball and you have a lot of wave stacking.

 

[William Gaatjes]

I do not know if it will help you.
But chapter six of this book explains what you need to do.

If you can get the e-book or the pdf it will explain a lot.
http://www.selexyz.nl/product/97800...cb-design-using-orcad-capture-and-pcb-editor/

If you want i can copy some pictures and text later on.


The lumped element model is discussed here. Perhaps single segment means single element as analogy.

 

[William Gaatjes]

Although i have not tried LTspice with transmission models, if i find the time i will try it later this day :

LTspice from linear technology is a free program to simulate electric behavior.
Primary use is to simulate designs with components from linear technology.
But you can also use it to simulate basic behavior of components. It will draw graphs and diagrams at your choosing. You can use a "probe" to measure different sections.
And also from transmission lines if you provide the model. A quick search on the internet might help to provide models.

http://www.linear.com/designtools/software/#LTspice


Texas instruments also provides simulation software for the interested but i find it more restricted then LTspice.

 

[polarmystery]

Although i have not tried LTspice with transmission models, if i find the time i will try it later this day :

LTspice from linear technology is a free program to simulate electric behavior.
Primary use is to simulate designs with components from linear technology.
But you can also use it to simulate basic behavior of components. It will draw graphs and diagrams at your choosing. You can use a "probe" to measure different sections.
And also from transmission lines if you provide the model. A quick search on the internet might help to provide models.

http://www.linear.com/designtools/software/#LTspice


Texas instruments also provides simulation software for the interested but i find it more restricted then LTspice.

For our next homework assignment, our professor has us using LTspice for T-line analysis. We turned in that assignment yesterday and I think I did okay as far as correctness was concerned. It was a bitch to complete.

 

[William Gaatjes]

For our next homework assignment, our professor has us using LTspice for T-line analysis. We turned in that assignment yesterday and I think I did okay as far as correctness was concerned. It was a bitch to complete.

To be honest, i also have to find out how to create a spice model. I used LTspice to explain some basic behavior or to test some opamp filters or just designs with LT components in them. I do think it is a wonderful program. But as any advanced toolset in software, it has a learning curve. If you never used and you have to work against the clock, it can indeed be stressing.

I just got home, i did not have the time to try anything but when reading your post, i see it is of no use either. Lucky me.

I just read the chapter six from the book i mentioned while traveling home today. The book i mentioned in the post above really explains a lot. Transmission lines are explained wonderfully.

 

[William Gaatjes]

If you or anyone is still interested, i copied the relevant pages(19 pages) of chapter 6 of the book i mentioned, to a pdf of about 506kB in size.
It is only a very small part(excerpt) of a book of 472 pages total. I think it is ok.

If anybody notifies me of a public share server where i can upload it to, i will.

 

[polarmystery]

If you or anyone is still interested, i copied the relevant pages(19 pages) of chapter 6 of the book i mentioned, to a pdf of about 506kB in size.
It is only a very small part(excerpt) of a book of 472 pages total. I think it is ok.

If anybody notifies me of a public share server where i can upload it to, i will.

I am, but I have no public share folder.

 

[William Gaatjes]

I am, but I have no public share folder.

You are in luck, i have created an account to share files.

I will leave available for the time being.


EDIT:

Link is removed to the 19 pages pdf because i do not want cause any copyright issues. Although it is only 19 pages out of a book of 472, i am not the author. If you want the pdf, post a message and i will place the link again or PM it to you. I will also rename the file thus caching of old web pages will only help for a while. I am sorry i can not leave the link as it is but i also have to respect in a reasonable way copyrights.