How Do Textbooks Bridge Circuit Theory and Electromagnetic Theory?

[thegreenlaser]

I'm in EE and I've taken a fair bit of both circuit theory and EM theory, but I've always struggled a little bit with connecting the two. I think my main issue is that textbooks are usually very clear about how they've defined resistance, capacitance and inductance, but then they're not so clear about justifying those definitions, except in very simple cases. In particular, it seems that they're justified separately from one another (e.g., the definition of capacitance is justified only when there aren't any resistive or inductive effects present) but then we use them all simultaneously.

I end up feeling like we calculate a bunch of values by dividing integrals by other integrals, and we call those things "inductance" or "capacitance" or "resistance," and then plug them into a circuit accordingly, but I've never really seen a clear justification that the network of resistors, capacitors, and inductors I end up with is actually a good approximation of the full field/source analysis. Are there any books that go through a thorough analysis of this sort of thing? Something that really "bridges the gap" between Maxwell's equations and the circuits that we use to approximate them?

Thanks.

 

[mishima]

Chapter 11 of Kraus' Electromagnetics 4th edition is titled "The relation between field and circuit theory" and deals with exactly what you are talking about.

I am from a physics background and do not know what is considered standard in engineering treatments of the subject, but this book in general had tremendous insights into field theory for me. For example how to solve laplace's equation by drawing pictures instead of using math, and interpreting capacitance and inductance in terms of the permittivity/permeability of "field cells".

Overall the book is quite nicely written, id say sophomore level for US. Every chapter has topics meant to be interesting which makes for a good read. Some chapters are completely devoted to application. I have heard the latest edition however chops out a bunch of good stuff.

 

[lurflurf]

I don't know much about circuit analysis but it is a series of approximations. There is lumped matter discipline more accurate is distributed element model. The idea is electromagnetics can be simplified by a low-frequency approximation as well as an assumption that effects are concentrated (ie current is restricted to idealized wires). Then we get Kirchhoff's circuit laws from continuity (conserved charge) and Maxwell-Faraday law of induction. It is also interesting that other subject like mass, momentum, and heat transfer are similarly simplified producing an analogous circuit theory (for example the electronic–hydraulic analogy). Also older books on circuit theory have more topological flavor even though at the time topology was primitive, now that topology is well developed electrical engineers seem largely uninterested in it.

 

[thegreenlaser]

Chapter 11 of Kraus' Electromagnetics 4th edition is titled "The relation between field and circuit theory" and deals with exactly what you are talking about.

I am from a physics background and do not know what is considered standard in engineering treatments of the subject, but this book in general had tremendous insights into field theory for me. For example how to solve laplace's equation by drawing pictures instead of using math, and interpreting capacitance and inductance in terms of the permittivity/permeability of "field cells".

Overall the book is quite nicely written, id say sophomore level for US. Every chapter has topics meant to be interesting which makes for a good read. Some chapters are completely devoted to application. I have heard the latest edition however chops out a bunch of good stuff.

My library only has the first edition, so hopefully that chapter is still there.

I don't know much about circuit analysis but it is a series of approximations. There is lumped matter discipline more accurate is distributed element model. The idea is electromagnetics can be simplified by a low-frequency approximation as well as an assumption that effects are concentrated (ie current is restricted to idealized wires). Then we get Kirchhoff's circuit laws from continuity (conserved charge) and Maxwell-Faraday law of induction. It is also interesting that other subject like mass, momentum, and heat transfer are similarly simplified producing an analogous circuit theory (for example the electronic–hydraulic analogy). Also older books on circuit theory have more topological flavor even though at the time topology was primitive, now that topology is well developed electrical engineers seem largely uninterested in it.

I'm aware of this argument, I'm just looking for a more in-depth rigorous version of it. The lumped matter discipline thing seems to mostly just deal with resistances. The assumption that flux is constant with respect to time means that this argument doesn't work for all the cases where we calculate the inductance of a structure, doesn't it?

 

[jasonRF]

Chapter 4 of "fields and waves in communication electronics" by ramo, whinnery and van duzer addresses this to some degree as well (at least in 2nd edition that I learned from). I have not spent any time with Kraus' book so I don't know which is better, but most university libraries should have some edition of Ramo and Kraus, as they are well known classics.

jason

edit: just thought I would give an example from ramo: they compute the impedance of round wires and you do indeed find both a resistive and an inductive part, as you would expect. My copy of the book is at work right now so I cannot think of other examples.

 

[lurflurf]

What do you want more depth in?
-The exact assumptions
-When the assumptions are plausible
-How much error we introduce
-What to do when the assumption fails

Yes we have in our low frequency limit an explicit magneto static assumption that clearly fails for inductors. As you know circuit books tend to ignore this completely or just state it is unimportant. One thing that can be done (other than ignoring the problem) is throwing terms (displacement currents, batteries and what have you) into compensate, but I think that is confusing. He is something about it

http://ocw.mit.edu/courses/physics/...etism-spring-2002/lecture-notes/lecsup315.pdf
http://ocw.mit.edu/courses/physics/...netism-spring-2002/lecture-notes/lecsup41.pdf

 

[thegreenlaser]

Chapter 4 of "fields and waves in communication electronics" by ramo, whinnery and van duzer addresses this to some degree as well (at least in 2nd edition that I learned from). I have not spent any time with Kraus' book so I don't know which is better, but most university libraries should have some edition of Ramo and Kraus, as they are well known classics.

jason

edit: just thought I would give an example from ramo: they compute the impedance of round wires and you do indeed find both a resistive and an inductive part, as you would expect. My copy of the book is at work right now so I cannot think of other examples.

I have a hold on this one (1st ed.) and the Kraus 1st edition, so we'll see what happens when they get in.

What do you want more depth in?
-The exact assumptions
-When the assumptions are plausible
-How much error we introduce
-What to do when the assumption fails

Yes we have in our low frequency limit an explicit magneto static assumption that clearly fails for inductors. As you know circuit books tend to ignore this completely or just state it is unimportant. One thing that can be done (other than ignoring the problem) is throwing terms (displacement currents, batteries and what have you) into compensate, but I think that is confusing. He is something about it

http://ocw.mit.edu/courses/physics/...etism-spring-2002/lecture-notes/lecsup315.pdf
http://ocw.mit.edu/courses/physics/...netism-spring-2002/lecture-notes/lecsup41.pdf

I guess the first two points are really what I want more info on. Some quantification of the error would also be nice to see. What to do when the assumptions fail isn't really a concern for me right now, as long as the assumptions still cover the "calculate resistance, capacitance, and inductance of this structure" problems that you would typically see in an undergrad E&M book for EE. For example, the assumptions in lumped matter discipline are clear and well laid out, but they're pretty restrictive and don't cover a lot of the cases where this theory is used (e.g. transmission lines).

 

[Lavabug]

Something that really "bridges the gap" between Maxwell's equations and the circuits that we use to approximate them?

This resonated with me, because my EM course notes had a chapter dedicated to this specifically. I think it was mostly based off the book by Reitz (Foundations of EM Theory, similar to Griffiths but much older), since the book focuses a lot on the microscopic fundamentals of EM theory.

A good exercise I remember seeing is to derive KCL and KVL from Maxwell's equations and charge conservation for a circuit with slowly varying currents (or similarly, a transmission line long enough that the period of the signal is << the travel time), I don't remember the details right now but the derivations were very simple and intuitive.

 

[thegreenlaser]

Chapter 4 of "fields and waves in communication electronics" by ramo, whinnery and van duzer addresses this to some degree as well (at least in 2nd edition that I learned from). I have not spent any time with Kraus' book so I don't know which is better, but most university libraries should have some edition of Ramo and Kraus, as they are well known classics.

jason

edit: just thought I would give an example from ramo: they compute the impedance of round wires and you do indeed find both a resistive and an inductive part, as you would expect. My copy of the book is at work right now so I cannot think of other examples.

I just got my hands on the first edition from my school's library, and it's been very helpful! Depending on how I like the rest of the material, I might actually pick up a copy of this one.

 

[jasonRF]

If you do decide to pick up a copy, I do not recommend spending the extra money it will cost for the 3rd edition. I compared it to my 2nd edition copy, and there are maybe 20 pages of extra stuff. "Very good" condition used copies of the 2nd edition can be found on amazon for $10 + shipping. I've used my copy so much over the past 20 years that it is getting pretty worn out - at some point I will have to pick up another copy!

jason