**Sum:** Back in the 60’s, I think, you wrote a book on differential amplifiers, any comments?

**RDM:** The book on Differential Amplifiers, this was not a textbook, it was a monograph, and it was a very narrow and specialized topic and it was really not even about differential amplifiers. A better title really was “Analysis of Unbalanced Symmetrical Circuits” because a differential amplifier is a symmetric circuit and there’s a well-known way of analyzing such a circuit, the half and half method, the common mode and the differential mode, and if you split the signals into those two components, each of them can be solved for with a half-circuit. The half-circuit is different for common mode and differential. That’s well-known, although you don’t see it much because it’s one of those old topics that’s been very thoroughly dealt with and of course forgotten. That’s the problem, like so many things, but anyway, that was the point where I picked it up because what I wanted to deal with was where those two symmetric halves were symmetric topologically but were imbalanced numerically, because there’s always unbalance with symmetric components, especially the betas of the transistors, but also there’s always a tolerance on the resistors or whatever. What I came up with was simply an analytic technique of how to incorporate quantitative unbalances yet still retain the simplicity of dealing with only half the circuit, and that’s all that monograph was about, so it was highly specialized. It was simply an analytic technique, but it was Low Entropy. I hadn’t thought of that word in those days and I hadn’t even formulated the idea, and yet in retrospect, that’s what the overall objective was to keep the simplicity in dealing with only half the circuit. That, in my present terminology, that’s looking for a Low Entropy answer.

**Sum:** Would you think that this is a good time to write a book on the subject?

**RDM:** My students at Caltech periodically press me to write a book because there is no text for that course, there never has been, and in fact, I’ve always said it’s my policy, if I ever do write a text for this course, I won’t give the course anymore, because one reason they don’t have any text, I don’t even give them notes, at Caltech they don’t even get the notes the outside people get, because I think it undermines the course if you have a text, especially if the text is written by the instructor. The students always say “well, I am busy and tired, I’ll skip the lecture and I can always read it in the book later” and I want to try to forestall that because 90% of the value, if any, of what I am trying to do is in the philosophy and the approach, not in the factual material. I tell the guys in class at Caltech at the very beginning of the course “if you are going to get anything out of this course, you have to come to the lectures, there is no other way. That’s where all the value is if there is any at all.” So that is why I don’t even give the Caltech people those notes.

**Sum:** What about putting it all on video tape? It is, of course, not as good as being at the lecture, but I think this is the closest thing to being in the lecture, what do you think?

**RDM:** But anyway that pressure to write a book has been there for a long time and then the people out in industry say the same thing “why don’t you put all this in a book, why don’t you videotape it?” and I keep saying “maybe I will some day” and then I say “well, I’ve written two books before and I don’t want that millstone around my neck again”, because to write a book, it has to be top priority because it takes a huge amount of time and a text is even more.

Text is very difficult to write because you have to have balanced subject material, you have to anticipate what a lot of different universities want to have in their course, and you have to be careful to have a balance, it’s a lot more work as well. So I have resisted doing that but finally I did videotape the whole course and then I began asking the class (this is the outside people), “would the videotape be useful?” Yeah. “How much would you pay for it?” Not much. And it’s clear that it would not be marketable as a standalone for anything like a reasonable price. There’s pros and cons on having the thing on a video tape, but it’s not a viable market place to replace the courses, so the videotape still sits there.

**Sum:** So, are we going to get a book or not?

**RDM:** So then I decided “well, I’m going to write a book, but it’s not going to be a text” and the least amount of work, which is the only way I can make the commitment to do it is it’s going to be the book of the course, so I had the videotape audio track transcribed and all I am going to do is do minimal editing of that transcription, put the pictures and equations in it, which is basically the course notes and it’s going to be called “Middlebrook’s Structured Analog Design Course: The Book”. It’s not going to pretend to be anything else. It’s the book of the course, as it is, so I don’t have to deal with any questions of balance and structure. It’s not a text for students. It may be a text for professors. At least that gets it down on paper, because the feedback I got from the people at the course was that the book is preferable to the videotape. A real book with words in it, they would like better than the videotape anyway.

**Sum:** You have mentioned about giving these magic techniques names, how are you going to do that?

**RDM:** Last year sometime, well, two years ago I guess, I came to that conclusion and so pretty soon, having reached that conclusion, I decided that the whole point about this approach is the philosophy of Design-Oriented Analysis in terms of Low Entropy expressions. The only analysis worth doing is analysis that can be worked backwards for design, otherwise what’s the point.

So I said to myself “there’s one thing that I’m going to do before writing that book and that is I’ve got to get those two key phrases into the archival literature, so there’s a reference, because what I am trying to do all follows from those two phrases, so I said well first what I’ll do is I’ll submit a paper, I’ll join the IEEE Education Society, which I’ve never been associated with before. I did that and then I submitted a paper to one of their conferences called “Frontiers in Education”, and I gave one with those two key phrases in the title and to my surprise they accepted it, and I went and gave the paper at Purdue University in November 1991.

The time came for the session and I got up with considerable trepidation because this is the first time I’ve talked to an academic audience. All the stuff I talk about is either to my own class at Caltech, or to outside working engineers. This was the first time that I talked about this topic to academic people because here’s the whole audience of professors and instructors, and so I made sure there was a wide path to the exit in that meeting room, because here am I someone unknown to them getting up and saying “you’re doing it all wrong and here’s the way to do it”. To my relief and surprise it went over very well. So well in fact that one of them got up at the end and said “I was a working engineer for 11 years and now I am teaching at an academic place and I can really see the value of this and I am going to try to adopt this in my own course.”

As Val, said afterward to some people, we didn’t plant him in the audience, but he was a perfect shill. Anyway it went over very well, but of course lot of things go over well, but that’s the last you hear of them, but anyway I dropped those phrases into the archival literature but I was already interested in a new development.

**Sum:** What is the nature of the analog course you are teaching in Caltech now?

**RDM:** My course at Caltech is a second level course and so is the outside one for industry, and it’s really a course in “technical therapy” because I have to take the guys through a Freudian regression, back to high school, because that’s where the quadratic equation comes in. That’s the lowest level material. A lot of the other stuff was in electronics college courses, but you have to take them back through all of that to the point that they recognize and accept the fact that a lot of the stuff that we were told is not useful. It’s not wrong of course, but it’s not in the best form, not in the most useful form, in other words, it is not Low Entropy.

I gave a couple more papers at these education-type conferences. In fact, I went to the same conference again last year, Frontiers in Education, the location was Nashville this time. They move around, the same conference was in November 1992.

The second paper I gave was called “The Quadratic Equation Revisited” and that went over well too. But of course vanished, I mean, it’s in the proceedings but no one will ever notice. The quadratic is the first formula we learn and it’s ingrained in our minds. We’ll never forget that and what I tried to show in that paper is there’s a lot better formats, depending on the purpose, that is you can get more useful information out of it than is apparent.

**Sum:** What are some of the problems you find in the quadratic equation?

**RDM:** It has two defects: it’s High Entropy because you can’t interpret the meaning of the a ,b, c in that combination. You might as well not write that formula in terms of circuit elements, you might as well put numbers in right away because that’s all you can do after you put symbols in the formula, is put numbers in.

The second defect is the computational inaccuracy, in the case of real roots, and so what I refer to as the preferred version of that function overcomes both of those disadvantages. In other words, you stand back and you get a much broader perspective of what that equation is telling you, therefore on what you can do with it. The rest of the techniques are not as low a level as that, they are college level, but similar.

**Sum:** Perhaps you could enlighten us on the impracticality of the old methods.

**RDM:** We were taught loop and node analysis. We were taught how to find input and output impedances and it’s OK, it’s not wrong, but it’s very hard to do anything with the answers that you get that way. We’re taught to get the equation as a huge numerator divided by a huge denominator. But what if you don’t like the number that comes out as the answer? What if it doesn’t meet the specifications? Now what do you do? Well, that’s where I pick up the story and try to show putting it in Low Entropy form enables you to work back, and the second thing is, how do you get it to come out in Low Entropy form in the first place? And that’s where all those other techniques come in, doing the algebra on the circuit diagram, get rid of loops and nodes by Thevenin reduction .

We all learn Thevenin and Norton, we all do umpteen examples of it and get A’s in the course, but how often do you use it since? Hardly ever, because no one ever told us why it was useful and the reason it’s useful is every time you use one of those theorems, you get rid of one loop or one node, so you can gradually reduce the complicated network into a single loop and write the answer in one line. That’s why they’re useful, but we don’t get told that. It’s simply one of these theorems that we have to learn. It’s not going to be any use in the real world. Well, my whole philosophy is all of those things are useful if you go about it the right way. That’s what the whole approach is about; that’s why I referred to these courses as second level.

**References**

K. Kit Sum, “Power Factor and Its Effect on Power Quality”, presented at the PCIM/Power Quality Conference, Hotel Queen Mary, Long Beach, California, October 16-19, 1989.

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