Lecture 4a -- Transmission Line Equations

This video introduces the topic of transmission lines, derives the transmission line equations, telegrapher equations, and wave equations on transmission lines. It then goes on to solve the wave equations and express the voltage and current signals on a transmission line.

[@arbimoradian]

finally found someone that can focus on the material versus deciphering the accent of the lecturer. Bless you

[@empossible1577]

Happy to help!

[@alfredoespinoza2968]

Sir, you have explained this topic in a very easy way to follow, something that most of EMs textbooks can't do. Thanks for these lectures, they are very good.

[@empossible1577]

Thank you!!!

[@aaronbraun841]

Love the video, thanks.

[@riveredge3347]

This video clearly explains the topic that was confusing me 4 decades ago(partly because of my mediocre professor). I am a retired engineer and teach my kids math and physics. Thanks.

[@empossible1577]

Thank you!

[@ceasarhurtado5366]

I'm doing Magnetic Field Transmission in quarantine, your lectures did a better job at explaining the material than my prof. Thank you.

[@empossible1577]

Ha ha. Thank you!!

[@BentHestad]

Great Channel! Thank you, Sir! Greetings from Trondheim, Norway!

[@empossible1577]

Greetings Norway from El Paso, Texas USA!! I am glad the channel is helping you! You may want to also checkout the course websites where you can download the notes, gets links to the latest videos, and other learning resources. empossible.net/academics/

[@michaellove7912]

super helpful! thank you!

[@senishkhadka4685]

Finally understood this, thank you very much 🙏🙏

[@empossible1577]

Happy to help!!

[@santiagoolmos2423]

Thanks this was really useful

[@AbdulBasit-ex9pw]

Bravo believe me you are much much much better than my university teacher. Thanks man , thank you so much for your excellent efforts ♥️

[@empossible1577]

Thank you! Glad to hear the videos are helping you!

[@khaledalhorani7965]

Thank you so much! Your channel content is very interesting and I cannot keep myself from watching your courses one after the other. Your way of teaching and presenting ideas is plane, simple and thrilled. I really appreciate the golden opportunity for making these courses available for us. By the way, I want to ask if you recommend any book for understanding Microwave Engineering other than the David M. Pozar book. Thanks once again.

[@empossible1577]

Pozar certainly has the classic microwave book. Of all the newer textbooks I have look at, I don't like them. They read too simplistic like they were written in a single week. The best microwave books I have are extremely old ones that cover niche topics. Try searching amazon for more niche topic books like microstrip circuits, directional couplers, microwave filters, etc. I think you will find more that you like.

[@khaledalhorani7965]

@@empossible1577 That's exactly what I have been struggling with. Many thanks ...

[@bhaminibhujun8210]

Great explanation

[@klg1401]

hands-down best lecture. Way better than my prof

[@empossible1577]

Thank you!! I am very happy to see they helped you!

[@dobromirkostov9023]

Certainly a great video explaining the Telegrapher's equations intuitively and relating them to Maxwell curl equations!! Excellent stuff!! I have question at 17:20, is this really the Fourier Transform of those equations or they were simply rewritten in complex form?

[@empossible1577]

The "complex form" and the Fourier transform are the same thing. I think you are so used to mentally converting between time-domain and frequency-domain that you have lost site that it is actually a Fourier transform that is happening.

[@BorisGrishenco]

Thanks for content! It helps a lot!

[@empossible1577]

BorisGrishenco Happy to hear it is helping you!

[@johnmelvincostan9752]

well explained sir. thank you!

[@empossible1577]

Thank you!

Thank you so much for your useful lecture I have a question: At the load, in the matched impedance case, how power in the dielectric convert to the load? because no reflection, it's mean power was absorbed by load, right ?

[@empossible1577]

The power in the transmission line is just passing through. The line itself is not absorbing power. Therefore, at the load only one of two things can happen. First, power can reflect in which case is travels backward down the load toward to the source. Second, the power can transmit to the load from the cable. The load will have to be composed of lossy material that will absorb the energy.

[@alejandromoreira9896]

Wonderful. Easy to understand. Thank you.

[@empossible1577]

Thank you!

[@alfredoesp5270]

Hello Sir, very well explained as always! Just some quick questions regarding on min 17:00 to solve some doubts that I have. 1. Per my understanding, when we convert an harmonic/sinusoidal EM wave written in time-domain form to the phasor/complex form, we are esentially doing a Fourier Transform, since on complex/phasor form the equation is on frequency domain, right? 2. When Fourier-transforming the time-domain equations with (z,t) variables to frequency-domain (z, w) on min 17:00, the angular frequency variable "w" is not written on the Telegrapher Equations because we are asumming that the frequency is not going to change during the analysis (fixed value), correct? So that, we only focus on the varying behavior with respect to the space position "z" on the transmision line and this written form also matches with the phasor/complex form? Could you confirm those two questions, please. Thanks a lot!

[@empossible1577]

1. Correct. 2. If frequency w is changed, the differential equation would have to be solved again for I(z) and V(z). I suppose in this sense I(z) and V(z) are functions of frequency w. However, writing them as V(z,w) and I(z,w) might be misleading that you can simply plug a different value of omega into I and V and get a correct answer.

[@alfredoesp5270]

@@empossible1577 Thank you so much for your quick answer!

[@nareshkumarsaini713]

Thank you so much sir

[@bijoytarafder7164]

For me, the KCL is wrong (15:25), why "Gdz*v(z+dz,t)" instead of v(z+dz,t)/Gdz? For capacitance as well?? Sir, Please explain.

[@empossible1577]

Ohms law is V = I R. However, Ohms law in terms of conductance is V = I / G. G is conductance, not resistance, therefore the current through an element is I = G V. There really is not trick to the capacitance term. The current through a capacitor is I = C dV/dt.

[@cglaspirantlife1551]

Y u r changing only one side of equation in case of both kvl and kcl? Plz explain

[@empossible1577]

Are you saying that is bothers you that I write both equations as sum=0? For KCL, for example, you could write that is incoming current = outgoing current Instead, I write it as Incoming current - outgoing current = 0 It is a similar thing for KVL. Does this answer your question? I am afraid maybe I do not understand what you are asking.

[@lambdaprime2487]

thank you for your exellentte videos. However, I do not understand how the current which is a flux of electrons which move with a very small velocity (drift speed) can travel at celirity of light on transmission line (telegraph's equation) ?

[@empossible1577]

I am uncertain about the specific drift velocity of electrons. In fact, for an AC signal, the average drift velocity is zero. When talking about an electromagnetic wave, the velocity of the electrons is oscillating. The speed of the wave is how quickly the oscillation travels, not the electrons themselves. Does this make sense?

[@lambdaprime2487]

@@empossible1577 : Ya little bit, but I can't relate I = dq / dt to the current equation in the form of a wave equation. If i measure the current with an ammeter on the power line, what will it be? electrons flux or electrons oscillations?

[@selvakumare7433]

Awesome video,very thank you and tomorrow is my exam

[@empossible1577]

Good luck on the exam! I hope you do well!

[@user-tj3re5tm2u]

Very valuable content. Could we get the ppt?

[@empossible1577]

Glad the materials are helping you! The electronic notes and other resources are available on the course website. Here is the link... emlab.utep.edu/ee4347appliedem.htm

[@DRACOBUCIO]

LGRC model, Is the only model? Are there other models?, where can I find it and why do we use LGRC model instead of the others?

[@empossible1577]

There are other models for sure. They tend to be used for specialized lines. The model I use here is the classic one used in the textbooks. It is simple, intuitive, and explains all of the the transmission line phenomena for standard lines just fine.

[@DRACOBUCIO]

@@empossible1577 Ok, thanks for asking. Do you know where can I find other kinds of models? I mean, like a book or something, I just wanna see it with my own eyes, please. BTW, now, I'm a suscriber. Excelent videos!

[@empossible1577]

@@DRACOBUCIO Right now my wings are clipped. My university got hacked and we have been without e-mail, access to our storage drives, and other IT things for over three weeks. Even worse, we are not getting any straight answers about when that may return. I cannot dig through any of my materials any time soon. Try searching for "alternative transmission line models" in Google. Let me know what you find. Very sorry!!!

[@BasitAli07]

Can you tell me from where i get the notes of this topic?

[@empossible1577]

Happy to help. This particular video is now Lecture 8a in the Electromagnetic Field Theory Course. Here is a link to the course website: empossible.net/academics/emp3302/ I recommend using the course website as your main portal. You can download the notes, get links to the latest versions of the notes and videos, and get other learning resources. Hope this helps!!

[@BasitAli07]

@@empossible1577 Thanks Alot

[@relaxwithme4695]

why the bottom wire has no resistance

[@empossible1577]

This is such a great question, I added some slides to the lecture to clarify this. Unfortunately, the new slides are not in the video until I can rerecord. You can get the revised PDF from the course website at the following link. It is Lecture 8a. empossible.net/emp3302/ In the PDF, see slides 8-12 that I just added. The short story is that there certainly is resistance and inductance associated with both wires. It is just that these are in series so they are combined and then written on the top conductor only because we had to choose one and it seems to be the more standard way to draw a circuit. Hope this helps!!

[@jmckendry84]

An excellent video, but with one minor (intended to be constructive) criticism - I think it would be better to either show how the final solutions for V(z) and I(z) are arrived at, or at least refer to somewhere where the viewer can look it up, as opposed to "A mathematician did it!" approach shown here. IMO it's always better to give some explanation rather than simply presenting the solution and asking the student to simply accept that it *is* the solution.

[@empossible1577]

I always struggle with things like this. Too much detail and I cannot get through all of hte information that I want to cover. Skip some things and sharp folks like yourself are frustrated. Maybe I need to start including appendices or something. That would let me skip other large derivations that do not provide much insight.