Contrary to conventional wisdom, it is interesting that one can find the Thevenin voltage using superposition. It is often argued one cannot use superposition in circuits where dependent sources are included.

I don't know that I've seen this claim as the conventional wisdom or even an actual claim (that you can't use superposition in circuits with dependent sources). Every text I have ever seen that covers superposition explicitly covers how to deal with dependent sources.

But I've certainly seen lots and lots of people do it wrong. The most common mistake is to try to "turn off" the dependent sources while the analysis is done for the others and then do one analysis for each dependent source in which that source is the only one that is "turned on". Even worse, they try to find the equivalent resistance by turning off all the sources, including the dependent ones, failing to realize that the dependent sources will respond to external stimuli if that stimulus produces a non-zero control signal.

 

Every text I have ever seen that covers superposition explicitly covers how to deal with dependent sources.

It's interesting that you say this. It's completely contrary to what Leach says (third paragraph) "After encountering so many challenges by students, the author researched circuits books in the library at his school and at a store of a large bookstore chain. None of the books said that superposition can be used with controlled sources. Indeed, the majority stated clearly that it could not."

His paper: http://users.ece.gatech.edu/mleach/papers/superpos.pdf

Your experience is that "Every text I have ever seen that covers superposition explicitly covers how to deal with dependent sources." whereas Leach says "None of the books said that superposition can be used with controlled sources."

It should give pause to each of us. We think our own experience is typical.

I will see a pronouncement on some forums about how things are in the world such as "Most DMMs don't measure true RMS". Or perhaps the exact opposite, "Most DMMs nowadays measure true RMS". I can't help but wonder, how does that person know that? Has he examined the specifications of "most" DMMs? Does he think that his experience is representative of the true state of affairs? Most people do it seems (how do I know this, you ask. )

 

Isc can be determined by inspection. If the terminals a-b are shorted, then Vab is zero and ix is zero. The 3ix dependent current source puts out no current. The 15ix voltage source puts out zero volts and is therefore equivalent to a short circuit. There is a path from the 30A source, through the 15ix (which is now a short) to the a-b terminals. The 30A feeds the a-b terminals.

 

But I've certainly seen lots and lots of people do it wrong. The most common mistake is to try to "turn off" the dependent sources while the analysis is done for the others and then do one analysis for each dependent source in which that source is the only one that is "turned on".

Perhaps fortune favors the stupid. I did exactly what you said I shouldn't and obtained the correct answer.

Mind you - Leach points out the only caution one must exercise in the case of dependent sources is ...

"...superposition of dependent sources is valid providing the controlling variable is not set to zero when the source is deactivated."

- A caution which I duly heeded.

 

Here's a quick survey of the five textbooks I have that were quickly accessible. I have several others, but they are on a bookshelf that is currently blocked by a couple tables stacked with papers I am sorting.

Hambley, "Electrical Engineering -- Principles and Practices", 3rd Ed., Prentice Hall, 2005.

This is a book I have never even opened. I picked it up basically for free a few years ago.

On p95 they introduce the superposition principle and the very first circuit they use to illustrate the principle has a current controlled current source.

Higgins, "Electronics with Digital and Analog Integrated Circuits", 1st Ed., Prentice Hall, 1983.

This is a book I have always hated, but I think that is because I encountered it's use in a course that was not a good match for it. I think this book assumes a prior course in circuit analysis, which if I were to read the preface might or might not be confirmed. The discussion of the superposition principle is limited to one short paragraph on p7 which starts out, "In a network with several independent sources, the resulting current is the sum of the currents caused by each source acting independently. This follows only for linear networks." Note that it does not say anything about in a network containing ONLY independent sources. If the network contains dependent sources then that is fine, as long as they are linear. But the analysis is done for each independent source.

Cogdell, "An Introduction to Circuits and Electronics", 1st Ed., Prentice Hall, 1986.

This book is the one I had in my Circuits I course and I found it to be frustratingly terse. In only 350 pages it "covered" circuit analysis, AC power, transformers, op-amps, digital logic, frequency domain concepts.

It's section on superposition is actually silent on the specifics of controlled sources, though it clearly states that the principle is valid for all linear circuits. If it were not valid for controlled sources, then this would not be a true statement.

Del Toro, "Electrical Engineering Fundamentals", 2nd Ed, Prentice Hall, 1986.

This book, to my surprise, actually doesn't seem to include dependent sources at all anywhere in it. Looking closely at the introductory material you find that it does define both independent and dependent sources, but explicitly states that the attention of the text is confined to independent sources. I consider that a pretty severe restriction.

Even so, in the section on superposition it explicitly states, "The sole requirement is that cause and effect bear a linear relationship to one another."

Dorf (Editor), The Electrical Engineering Handbook, 1st Ed., CRC Press, 1993.

The section on superposition is a bit weak, particularly with regard to dependent sources. However, the entire section on network theorems is based on linearity and the only constraint regarding dependent sources is that, when finding the equivalent impedance of a Thevenin or Norton equivalent circuit that you can't just null the independent sources, but rather you either have to computer the open circuit voltage and short circuit current or you have to analyze the circuit with a test source places across the terminals.

I also happen to have the textbook that I learned transform methods from:

Harrison, "Transform Methods in Circuit Analysis", 1st Ed., Saunders, 1990.

This is what it has to say, "In a linear, bilateral network with multiple independent sources, the voltage at any node, or the current in any branch is the algebraic sum of the node voltage or branch current produced by each independent source acting alone. A linear, bilateral network is one which consists entirely of independent sources, linearly dependent sources, and linear, bilateral passive elements."

Now, I have to admit that I do have some texts that do not explicitly show how to use superposition with dependent sources, so either my memory is filling in gaps or I just haven't looked in those particular books specifically for this issue. I suspect it's a combination of both. But none of them come close to asserting that you can't use superposition with dependent sources. I suspect that some of those that don't address it explicitly where superposition is introduced do use superposition in the analysis of at least a few op-amp circuits and an opamp is nothing more than a voltage controlled voltage source.

While I would look less favorably on a text that neglects showing how to apply superposition to circuits having linearly dependent sources, I would flatly reject any text that asserts that superposition cannot be applied to such circuits; the author of such a text has no business writing a text on circuit analysis in the first place and it is a disservice to subject students to their flat wrong claims.

I wonder if Leach was seeing texts that described superposition by talking about circuits that contain multiple independent sources and incorrectly inferred that they were implying that the circuit can only contain indepedent sources. This is perhaps a pretty reasonable misinterpretation, but it IS a misinterpretation.

 

I wonder if Leach was seeing texts that described superposition by talking about circuits that contain multiple independent sources and incorrectly inferred that they were implying that the circuit can only contain indepedent sources. This is perhaps a pretty reasonable misinterpretation, but it IS a misinterpretation.

Have a look at what he says under the heading "II. Introduction". He says he examined 20 textbooks. Fourteen of them specifically discussed dependent sources, so I don't think he made that misinterpretation.

 

I've looked over the first page of Leach's paper and it is full of contradictions. He says he couldn't find a single book that covered the use of superposition in circuits with dependent sources, yet then he says he surveyed twenty texts and admits that the treatment of superposition in fourteen of them included the application to circuits with dependent sources and that three of the six that didn't included an example that included a dependent source. From this, he conclludes that circuit texts either state or imply that superposition of dependent sources is not allowed. Huh????

It's probably not surprising that his paper was rejected by two journals and that he had to resort to self-publishing it on the internet.

It appears to me that he is way overstating the claim that superposition can't be used when depedent sources are involved, but rather that he doesn't like the way that the analysis is presented. Okay. But just because you don't like the way a text covers a topic doesn't justify the claim that the text claims, implicitly or explicitly, that it can't be done.

It's admittedly difficult for me to wade through his work because of his utter disdain for proper use of units and, instead, practice of just tacking on whatever units he thinks he want to the final result. Sloppy, sloppy, sloppy.

I don't have any real problem with his method, but I don't see it as anything new or revolutionary.

 

This might also be of interest.

http://www.enggjournals.com/ijet/docs/IJET12-04-03-013.pdf

 

I doubt Leach is asserting authors don't treat dependent sources in superposition examples - rather they disallow the independent deactivation of said sources. A matter which the reference in my penultimate post takes up.

 

That seems to be little more than a repackaging of Leach's internet paper, though I haven't looked at it in detail. I tried to get a bit of information on the International Journal of Engineering and Technology and, other than their own site, have largely come up dry. Their ISSN appears to be 1793-8236 (1793-8244 for electronic). I can't find it in any of the journal rankings I looked at, but I'm not too good at tracking that kind of stuff down. I do see that it is "open access", which is not always a bad thing, but often it means, "You pay us, and we will publish it in our 'peer reviewed' journal." I have no idea if IJET is that way or not -- I can't find an acceptance rate on their website, but this is usally not a good sign.

 

I think your right, and I think that the second paper makes a much clearer statement of this.

 

Well I / we have well & truly hijacked the OP's thread.

Will they ever return? Perhaps they were (somewhat justifiably) frustrated or found their answer elsewhere or were successful by their own devices.

It's often very hit & miss - this helping "business" - I wonder sometimes about the value of responding to questions when the outcome often remains unsatisfactorily inconclusive.

To the many or few who are following this - let us know how it turns out for you if you ever ask for help.