Oral-History:Harold A. Wheeler (1985)
About Harold A. Wheeler
Harold Wheeler, design engineer and inventor, is perhaps best known for his Neutrodyne invention and his development of Automatic Volume Control. In Ronald Kline's interview with Wheeler, the two men use Wheeler's laboratory notebooks to frame a discussion of the process of invention. Referring to Wheeler's notes from the mid-1920s, the interview begins with Wheeler's early work at the Bureau of Standards and his notebook entries on neutralized circuits and automatic volume control. In his comments on the process of invention, he repeatedly stresses his intellectual commitment to searching for simple solutions. He offers his development of AVC as an example of an inventor's willingness to violate existing rules and challenge existing inhibitions, in this case, against using diodes rather than triode circuits.
The interview continues with a discussion of his work at Hazeltine, including the development of measuring equipment and the design of RF amplifiers. He offers his thoughts on the relationship between physics and engineering and provides a lengthy discussion of theoretical versus practical work in the context of his published papers. The interview goes on to cover his use of curve matching to derive empirical formulas, and the relationship of this approach to the developing distinction between synthetic and analytic formulas. The interview concludes with a detailed discussion of two of his papers — "Inductance Formulas for Circular and Square Coils," and "Inductance Chart for Solenoid Coil" — as examples of his ability to present formulas in both orders — that is for both synthesis and analysis.
See Also: Harold Wheeler Oral History (1991)
About the Interview
Harold A. Wheeler: An Interview Conducted by Ronald R. Kline, IEEE History Center, August 28, 1985
Interview # 048 for the IEEE History Center, The Institute of Electrical and Electronics Engineers, Inc.
Copyright Statement
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It is recommended that this oral history be cited as follows:
Harold A. Wheeler, an oral history conducted in 1985 by Ronald R. Kline, IEEE History Center, New Brunswick, NJ, USA.
Interview
Interview: Harold A. Wheeler
Interviewer: Ronald R. Kline
Place: Hazeltine Date: August 28, 1985
Laboratory Notebooks
Kline:
This is a recording with Harold Wheeler. We’re looking at some laboratory notebooks in his office at Hazeltine. This is notebook number six, dated July 3, 1925 to July 1, 1926. In this notebook, Harold, did you use the same type of procedure or habits that you used in your Washington basement notebook?
Wheeler:
The Washington notebook was initiated as a log of receiving signals along with trying different circuits. The later notebook, number six, was a laboratory notebook, which was intended to write down the developments I was working on for the company. In this case, it started in the summer of 1925.
Kline:
Now, in the Washington laboratory notebook, you did write down some developmental work. The Neutrodyne invention was definitely development; you were writing down circuits, which you were going to experiment with. So, in that case, would there be some parallel between this work and the company notebook?
Wheeler:
Yes, in the earlier notebook I just wrote down everything. That is notebook number one in this series.
Neutrodyne
Kline:
OK. Now, for someone to use the notebook to get a fuller understanding of the Neutrodyne invention — your invention of neutralization — what does this circuit represent? On page ninety-six?
Wheeler:
That was the first neutralized circuit that I used, which had a reversed transformer with a balancing capacitor C.
Kline:
Was this circuit the one you actually built to test neutralization?
Wheeler:
Yes.
Kline:
And then this phrase, "New circuit tested," was the one that actually worked?
Wheeler:
Yes.
Kline:
OK. We were talking earlier, Harold, about the process of invention. Why don’t I stop here, and we can continue later?
Wheeler:
While we’re on page ninety-six: the following day at work, I described this to Dr. Lewis Paul, who was one of the recent Ph.D. workers at the Bureau of Standards Radio Laboratory.
Kline:
Did you take the laboratory notebook from your basement laboratory into the Bureau of Standards to describe it to him?
Wheeler:
Probably not.
Kline:
So you explained the circuit to him there. The circuit looks nice and neat. Someone coming across the circuit later would say, well this must have been the circuit that you had drawn out on paper and transferred to notebook. What was the case on that?
Wheeler:
The notebook was the first writing. It was one in a series of circuits that had some similarity, so there wasn’t anything unusual about the symbolism.
Kline:
So the notebook was your scratch pad; it was where you thought out your ideas for the invention?
Wheeler:
Yes.
Kline:
Did you carry that process later on in life, throughout all the notebooks?
Wheeler:
Pretty much. The next one we’re looking at, number 6, was my direct entries in whatever I was thinking about at the time.
Automatic Volume Control
Kline:
The diagrams are very neatly drawn, but it definitely looks like a working notebook. Is this the entry for the invention of the AVC?
Wheeler:
Page fourteen is my first note on that subject.
Kline:
This is notebook number six. It’s a loudspeaker volume control. June 30, 1925. Can you tell us why this date is crossed out here?
Wheeler:
That’s the date that I mentioned to one of my associates, John Dryer, and notes were being made on July 9.
Kline:
I see. Do you want to describe how you came to this invention on automatic volume control?
Wheeler:
It is detailed in the book. Let’s see if there’s anything more to say —
Process of Invention and Approach to Problems
Kline:
Well, for example, does the book describe the process of invention that’s shown here in the laboratory notebook? Does the book go into all the detail, the different methods of deriving automatic volume control?
Wheeler:
See what you think after that paragraph on page 198.
Kline:
I see from comparing the material in the book and the notebook that what you’ve actually done in the book — and I think this is valuable information — is to describe the notebook entries. It looks like you had the notebook out when you were writing the book. You described the notebook entries and what you were doing. So why don’t I move on to some other questions I have? One of them was about the process of invention. This morning, you said that when you were at the National Bureau of Standards, on the Neutrodyne invention, you didn’t understand why other people didn’t see what you saw. And that you did see it. Can you reconstruct those comments again for me?
Wheeler:
I’ve often wondered about things like that, and that was one specific example. I don’t have any logical deduction from it, but things that one can observe. First, I was coming in fresh with a very sparse amount of information in the field, and you might say I had no inhibitions. The men I was working with were more experienced, more educated — they were doing more difficult things, and I saw something easy. I might mention that I’ve sometimes said that was the secret of my success — that I perceived that some things were easy and had solutions, and worked on them. This would fit into that pattern, but I didn’t have any pattern by then. Now, central to invention are dissatisfaction and the refusal to take a defeatist attitude. I mean, you don’t accept what you see; you experience dissatisfaction and aim to do something about it. As you might imagine, most of the time it’s not easy! This is one case where my open mind saw something that the educated minds around me didn’t seem to see.
Kline:
You and they were both on the same track in some regards, as I understand it. You both perceived a problem with receivers having oscillations, and you both knew about the Miller effect, but they were working on solving the problem in a much different manner than you were. Is that characterization correct?
Wheeler:
The way I would describe it, they weren’t solving the problem, and I did! They were working on makeshifts, which were very mediocre, because they didn’t solve the problem. I saw a solution to the problem and drove right through to a useful result.
Kline:
Could I ask about the concepts you had then? Were they visual concepts, or were they expressed more in mathematics when you made the connection, say, between the Miller effect and what you had to neutralize?
Wheeler:
The math was very simple — Miller’s math wasn’t, but my solution and my solution’s math were very simple. So it was more just a concept of a relationship that could use one capacitor to cancel out the coupling of another. That’s all the math I had to have.
Kline:
When you built the circuits, how did you determine the values of the capacitors, the sizes of the coils, and so forth?
Wheeler:
There wasn’t anything difficult. Having set out to do that, I knew how to make coils for a tune. In this case I added another coil just alike except going in the opposite direction, and that was the reversing transformer. The external capacitor was equivalent to the internal capacitance of the tube. There wasn’t any problem making that. We had little capacitors which were called trimming condensers, so I connected one. To adjust it to the right value, I used the method described in the book, for which Hazeltine later gave me credit, to turn off the tube so it wouldn’t get any coupling through it. I adjusted the extra capacitors to meet that criterion.
Kline:
You’d still been amazed that you saw this solution. What were you, a freshman in college? These were much more experienced people with much more knowledge in the field. And you saw the fact that you needed to make the outside capacitance equal to the internal capacitance of the tube, and you needed to fashion the coil in the manner that you did. I mean, you saw the solution at once. Is that what you’re saying?
Wheeler:
Yes. Those were easy relationships once I had the concept.
Kline:
Do you remember how the concept came?
Wheeler:
I had a few days previously made a neutralizing circuit by connecting some reverse conductive coupling to cancel the internal coupling of the tube, and I knew that that was operative only at one frequency. I saw that if we did it a different way it would operate at all frequencies. There wasn’t any work involved; I just saw it.
Kline:
As you probably know, these sociologists and historians have been trying to figure out how inventors see these things and it still seems to be quite a bit of mystery.
Wheeler:
One advantage I had was an uncluttered mind.
Kline:
Would you say the same thing existed with the process of invention with your automatic volume control, or were the circumstances different there? About having an uncluttered mind in approach to it?
Wheeler:
Very little correlation. I’ll review also what went on there, which is also presented rather fully in the book. But it wasn’t the same. In the [case of the] automatic volume control, I had to violate the rules. It’s willingness to abandon the existing inhibitions — that’s what it was. That was a major part of it.
Kline:
You mean the inhibition against using a diode?
Wheeler:
A triode was an expensive bottle. To waste it by using it just as a diode was something no one in his right mind would do in those days.
Kline:
Especially radio experimentalists, right? Why did you think to use the diode rather than the triode?
Wheeler:
I tried some triode circuits, and they didn’t work very well, so I capitulated to the simplest thing I could see. I had one or two diode circuits in my notebook by that time, but it was definitely capitulation to retreat to the use of a whole triode just as a diode.
Kline:
In other words, the diode concept to do the rectification was there, obviously, but you looked at it really as a step backward, when you were coming up with the invention?
Wheeler:
Until I began to appreciate that with the diode I was getting the function of detection along with the function of rectifying the carrier to get a control bias. What I didn’t appreciate at that moment was that the diode had the potential of linear detection, which was hardly heard of at that time.
Kline:
How did you find that out?
Wheeler:
First we should go back to what other detectors were doing. Typically, the detector was a low-level operator, and low-level detection is always square law, with the result that high-quality broadcast stations had to hold down to about fifty percent modulation to avoid too much distortion. When I went to the diode it turned out that the diode worked on a higher signal and wasn’t square law. The DC rectified voltage from the diode was almost equal to the modulator carrier voltage, and that made it linear.
Kline:
But you found it through actually building it and testing it and seeing that it was linear.
Wheeler:
Well, from thinking about it. We didn’t have much testing in those days. You listened to it, but I came to realize what was going on and it wasn't long afterward that I realized that we also had something here that was also a great improvement in detection. The order of improvement you can realize when you consider that high-quality broadcast stations were shortly able to go to 100% modulation instead of fifty, which was the equivalent to four times the power.
Kline:
You mention the fact that you realized that by thinking about it; and I notice from your notebooks too, that you seem to do your thinking in drawing the circuits and don’t necessarily have to build the circuits? Is that true? Would that be another characteristic of your invention process?
Wheeler:
My aim was to write down in the notebook the things that were occurring to me. But usually it was just cryptic notes or diagrams, which were only a hint as to what I was thinking about.
Kline:
So in the notebooks, you would indicate whether you had tested the circuit or not, and sometimes perhaps you could draw the circuit out and say, "No, this won’t work".
Wheeler:
If it didn’t work, I might not even draw it.
Invention of AVC
Kline:
On the AVC again, as I understand it, there are two basic ideas. One is to feedback a signal from the detected signal to reduce the gain of the RF status. The other concept is how to do that, with what mechanism. Now, can you tell us how those two ideas came to you?
Wheeler:
All I remember is that as soon as I decided to try the diode, I immediately wrote down in my notebook how the diode could perform both functions. It was the mere connection of resistors and capacitors that took the rectified carrier to control the gain of a previous amplifier and use the rectified modulation to drive the audio amplifier from the same diode. The circuit for doing that was straightforward, in terms of my knowledge at that time. [break in tape] Some of my notes [this is notebook six] detail those functions, and the way I accomplished them all. That’s the process by which I decided how to use it.
Kline:
Page ninety-four isn’t the first time you’d been thinking about AVC. Correct?
Wheeler:
No. I thought about a lot of ways of doing it, some of them very complicated, some very refined. But when I came to using the diode, I saw that the diode could perform all those functions if I analyzed it and connected it up.
Kline:
What length of time do we have between your first entry on volume control and this one, which is dated January 2nd, 1926?
Wheeler:
The first entry is on July 9.
Kline:
And what page is that?
Wheeler:
Fourteen.
Kline:
So there’s eighty pages there, not all of them on automatic volume control.
Wheeler:
No. In fact, my time was divided among a lot of topics, and I was returning to the fall term of school at Johns Hopkins, so actually there are very few pages of entries on automatic volume control.
Kline:
Do you think any of the other work you were doing at the time was any influence on your idea of using the diode for both functions?
Wheeler:
No,
Kline:
What type of methods had you tried previously for automatic volume control? You said some were elegant.
Wheeler:
Words would fail. There weren’t very many, but there were a number of circuits in between.
Kline:
They all used triodes?
Wheeler:
There were one or two that used a diode in a little different context. I was trying like anyone would’ve to use the amplifying powers of a triode detector and then in some way to connect that and control the gain. It’s interesting that that’s the approach that Bell Telephone Laboratories took around that time.
Kline:
Isn’t that the approach that most other people used, to have some sort of automatic volume control, a triode and the feedback? Now when you first used the diode — not the one that you patented — but when you first used the diode, do you remember why did you have occasion to go to it?
Wheeler:
I’m looking for the page where I had just jotted it down in the notebook.
Kline:
You had the idea to perhaps go back to a diode?
Wheeler:
Yes. Seventeen, page 89, may have been my only previous thinking about using a diode.
Kline:
Now, when you’re thinking about it, Harold, did you make notes about the diode, or did you also draw a circuit for it? I don’t see a circuit.
Wheeler:
When you see a grid and plate, tie it together —
Kline:
Oh, yes, I see it, definitely so. So you did draw a circuit for it, a separate rectifier tube, for control, complete cutoff of amplifier obtained, about ten volts. Now what was unsatisfactory about this circuit?
Wheeler:
Unsatisfactory isn’t the right word; the diode was not used also as a detector. It was used only as a supplemental rectifier to develop a DC bias.
Kline:
So you had a triode use it as a detector?
Wheeler:
See, here we have the diode connected in here with the bias coupled back, and then we had a parallel connection to a triode detector.
Kline:
So it was the combination of the triode for the detector and the diode for the rectification and the detector for the gain control.
Wheeler:
Yes.
Kline:
And when you finished this, did you feel that this was a good solution to the problem?
Wheeler:
"Finished" just means I stopped drawing and went to bed.
Kline:
I understand. What I’m trying to get at, did you feel this was a workable solution?
Wheeler:
I knew it had some good features.
Kline:
But you mentioned earlier that one of the main elements in your inventive career has been the element of dissatisfaction. There must have been a little dissatisfaction with this or you would not have perhaps carried on.
Wheeler:
Right. The fact that it had a separate detector meant that it wouldn’t have had the combination of features that made diode AVC and linear detection the package of the future.
Kline:
Were you thinking in those terms then, Harold, of an invention that would have applicability for a long period of time? If I may ask so personal a question?
Wheeler:
That didn’t worry me. I was just interested in making something that would work.
Visual Images and Simple Concepts
Kline:
So may I ask another question, related to the earlier one, about visual images? Do they play a role in any of this invention here?
Wheeler:
You can consider almost any concept in terms of a visual image. I suppose I could make a diagram of some speeches. Visual image is essential to creative thinking, and whether the visual image is in the form of mathematical functions, graphs, equations or the way something will sound when it comes out of the loudspeaker, the visual image is in there at some stage. That’s the reason we deal with diagrams in the book.
Kline:
Earlier you had talked about being able to see the neutralization process when no one else could; and here, with the diode, apparently you were able to at least try something that for some reason no one else wanted to try. They were inhibited in trying it. Would you say there was any relationship between those two events, those two achievements?
Wheeler:
Yes, but hard to describe. The fact that I used a diode for one function one week and then the following week used it for both functions gives you a hint of my mental processes in between times, subconscious if you wish.
Kline:
The ability to carry it out after you had the idea and put it into practice —
Wheeler:
Yes. That required what I would rate as just educated common sense, at that stage, because the actual circuit was extremely simple. As I say, with many of my developments, the contribution was a simple concept that from there was easy to carry out. So years later the Supreme Court said it wasn’t invention.
Kline:
And that’s a matter that would require more tape than I have here, I believe. Before I move on to the next topic, is there anything else you want to say on this whole topic of your process of invention? You were trained in physics, and usually physicists aren’t known as inventors in modern history. Is there anything else you want to say about this whole process of invention for you?
Wheeler:
Well, I don’t think you should generalize about physicists; but I think there is something fundamental in people either being educated or analyzing things in terms of simple concepts. The things that appeal to me, in all the work that I’ve done, are simple in concept and usually simple in execution. It’s the very simplicity of it that seems to have escaped the highly qualified, highly theoretical workers in the same field. A striking example of that is the piston attenuation. It’s been a common experience in my work that, after making an invention, I sit back and look at it, and say, "That’s too easy. Maybe it isn’t patentable!"
Kline:
I know the feeling of, "Why didn’t I think of that before?" Is that the type of feeling that you’re describing?
Wheeler:
That, I’m sure, is the reaction of some people in seeing work that I have done. It’s a fair reaction, and I’ve had the same reactions seeing some work done by others.
Hazeltine
Kline:
When you came to work full-time with Hazeltine, were you in a position where you could continue this type of activity? How were you able to inculcate that type of inventive activity in other people on the staff?
Wheeler:
During this whole period, the 1920s and 1930s, I had an excellent opportunity in terms of freedom and where I needed laboratory support. I don’t think anyone called me in and said, "Your assignment is to make inventions." They didn’t have to. What they had to do was keep me from spending all my time making inventions and not making anything work. So I was encouraged, definitely, to exercise innovation and make inventions. I had enough freedom to do it, and I had enough compensation, so I had very little worry about money, which is an unusual opportunity. As for assignments, McDonald, or later Arnett, gave me very thoughtful charters to work in some fields, which I did. One major activity was measuring equipment in the days when we did not have measuring equipment. We could buy it from a catalog, or if we did it was not particularly well suited to our purpose. So much of my inventive work went into making measuring equipment, and quite a few of them, I don’t doubt, were patentable. Our patent attorneys didn’t actually favor patenting measuring equipment but it didn’t bother me.
Kline:
What was the reason they did not favor patenting those?
Wheeler:
Because it would be sold in small quantities. It wouldn’t be worth telling someone not to make it.
Kline:
You said that McDonald would give you a charter to work in certain areas. Did you have your own separate space, like a small part of the laboratory?
Wheeler:
It wasn’t separated. In the 1920s at the Hoboken laboratory, our laboratory was three rooms and very few people, two or three engineers and McDonald and a machinist.
Kline:
Sounds very similar to the Edisonian type of invention — the early Edison.
Wheeler:
Yes. McDonald would lay out things that they wanted done, and maybe give me a line of measuring equipment and somebody to work with me to actually make it. Another line of innovation was in the design of RF amplifiers, the so-called uniform gain. It’s in my book. At one time my two assignments, so to speak, were in making a signals generator to measure receivers and making improvements in uniform gain amplifiers. And both of those were real opportunities.
Kline:
So these laboratory notebooks that start with the ones when you worked for Hazeltine show that type of activity. I was trying to get an idea of how long the AVC work took, but there was quite a bit of other activity in there. Is this the type of activity you’re talking about?
Wheeler:
Yes. I didn’t just concentrate on AVC during the six months between the time I got the idea and the time I made a working set. It actually occupied very little of my time — I was working on improvements in uniform gain and planning measuring equipment. In 1957, there was a list of things that I had been working on and we were considering filing patent applications. Automatic volume control was one of five.
Kline:
And what date is that?
Wheeler:
That’s August 18, late in the summer of 1957.
Kline:
I see. So who is L.A.H.?
Wheeler:
Hazeltine.
Kline:
One tube Neutrodyne.
Wheeler:
He had invented a very unusual one tube complete receiver using neutralization, among other things. My first assignment when I went to work for him was to make one and make it work, and that I did.
Kline:
So the next item here is, "Wheeler or Hazeltine? Neutralization of grid filament capacity."
Wheeler:
I think those topics would each be a long subject, but they were other projects that I was working on and which interested me.
Kline:
Audio frequency amplifier, prevention of oscillations, automatic volume control, coil with neutralization.
Wheeler:
Now remember at that time the diode type had not appeared yet.
Kline:
The first mention you had of it was in July. So it did become a recognizable main research and development aim of the laboratory.
Wheeler:
And an opportunity for invention.
Working Relationship with McDonald
Kline:
Is that how McDonald would speak of those things?
Wheeler:
Pretty much.
Kline:
Now how would it work? I assume this was a give and take situation — you would mention things to him, and he would perceive some need also. The question is, what type of relation did you and he have as far as ideas for things to work on? Would it always be a one-way relation or would it be a two-way relationship?
Wheeler:
No, we communicated both ways. He had some inventions of his own that he was working on, and usually I didn’t. If I’d get new ideas I’d usually walk across the room and show him!
Kline:
So what was his position in the Hazeltine Company?
Wheeler:
It is well described in the book, but he was a chief engineer when there were only a few engineers in the company. We were only at most a room apart, and usually not that far.
Collaborative Work at Hazeltine
Kline:
I have another question relating to this. We were talking about you wanting to invent all the time, and that you already had that stimulus to do it. Could we talk about the origin of the stimulus a little bit?
Wheeler:
I think I got it from Professor Hazeltine. He filled his notebook with ideas of various kinds, and I liked that.
Kline:
Was there any influence from the image of the inventor in society then? Like Edison or Michael Houtine, or other inventors?
Wheeler:
No, but I didn’t need it. My notes describe a problem, and then maybe some analysis of it, and then I tried to make something that would work.
Kline:
Can you give an example on that?
Wheeler:
AVC.
Kline:
When you set out to describe the problem, you mean you would sit down and work out in general what the problem was?
Wheeler:
In the Bayside Laboratory, I organized educational meetings, classes, which were attended by all the engineers during working hours. Usually I gave a lecture, sometimes to other members of the staff, and it was in those meetings that I tried to introduce the staff to concepts and methods of approach that I had been using and found productive. I continued that even during the war, and I think that was a great help in utilizing the talents of our well-educated engineers, because that gave them different viewpoints and more ideas as to how the knowledge could be out to work.
Kline:
What types of methods of approach would you talk about?
Wheeler:
It wasn’t anything unusual. It was just teaching, except it was teaching the results of my experience in concepts and methods of solution. So it built on whatever they had in school.
Kline:
Would you use particular examples from their own work or your own work?
Wheeler:
Yes. There wasn’t anything outwardly unusual about it. We were talking about things that were advanced, but we could still talk about then in simple terms.
Theoretical and Practical Work
Kline:
This leads us into another topic, the relationship between theory and practice.
Wheeler:
And certainly it takes more than that you learn in physics class to make working machinery. It’s generally easier to write textbooks about principles. They don’t change very much, whereas to write textbooks about technology is much more difficult, and, as you have probably observed, is much more neglected. I haven’t seen any book about how to tie your shoe; technology is more elusive when it comes to describing it in words. But I think one of the first things you have to face is that there are laws of physics, and you’re trying to make use of them, not trying to beat them. I say that very seriously, because there have been some engineers who should know better who have wasted part of their careers trying to beat some laws of physics. In other words, they didn’t properly define the problem, and they didn’t properly define their search for a solution. I don’t know how to generalize there —
Kline:
Maybe we can approach it from some of the theoretical work that you’ve done. I’ve looked at the papers you wrote, and some of them have what I would call theoretical titles, like "Design Formulas for Dial Detectors," or "Formulas for Skin Effect," and "Design of RF [...] Coils." Now, what I’m trying to get at is —
Wheeler:
May I interrupt a moment? Those are not the titles that I would call theoretical. When I say that, do you get a hint of what I mean?
Kline:
Not quite.
Wheeler:
The design formulas you might say are cookbooks. Mine are usually derived theoretically, and sometimes the papers will give the derivation, and sometimes not. Now, the papers that I would call theoretical are "The Fundamental Limitations of Small Antennas," because they are much wider than immediate application. The "Grading [..] Series for Phase of Rays" of later years was a theoretical paper entirely; it was based on a very simple approach, in the way of derivation, and it was that simplicity that enabled me to arrive at it and enabled everybody today to utilize it. Now, that was not a cookbook approach; it was an approach of theoretical concepts and theoretical relations, which were far more far-reaching than any cookbook approach could be. Along that line, my first paper on ray antennas was very early, shortly after the war, and it was entitled, "Radiation Resistance of an Antenna in an Infinite Array." I perceived what no one else perhaps had put in an organized description by that time — that the behavior of an antenna in an infinite array was simpler than it was in an array 3 by 3., because there wasn’t any decision about how many elements. My work and the work of others around that time soon developed into a full theoretical approach, which we carried into testing and practical design based on the infinite array. As far as I’m aware, no one before that paper had ever said the words infinite array.
Kline:
So when you’re talking about theoretical work, you’re talking about work that you would classify as leaning towards contributions towards basic principles.
Wheeler:
Ways of expressing principles.
Kline:
If I can gather what you’ve been saying, you can work from that and derive practical results from those and then you also could derive cookbook type formulas based on this theoretical work. Is that the kind of hierarchy that you have been describing? When do you think that type of hierarchy developed in radio engineering?
Wheeler:
Probably all along, just at different levels of apparent simplicity and apparent depth of thinking required to get them.
Kline:
So then earlier, when I’d asked about the relationship between physics and engineering, we were really talking about this hierarchy between theoretical work, which is very close to physics, and the cookbook —
Wheeler:
Sort of.
Kline:
What would be sort of different about that?
Wheeler:
I guess I don’t understand you.
Curve Matching
Kline:
Earlier we were talking about the relationship between physics and engineering within radio, and I said we were having a difficult time because there was too much knowledge separating the two. If you had physics on one end, which is real close to the theoretical work or basic principles you’re talking about, and then you have some practical applications and you also have some cookbook formulas from that, that’s sort of a hierarchy between the two.
Wheeler:
Well, it’s very amorphous, and there are some areas that get an opportunity for design of formulas. Here it’s interesting to note that what I call design formulas might now be described as slide rule computations as distinguished from more exotic computer methods of today. So I may set out on a computation that people have worked on with very involved, difficult mathematics, and one of my games is to convert it to a simple slide rule type formula that will get the right answer! That is sometimes called curve matching. So I’ve done a lot of that.
Kline:
By that you mean, you develop a formula, which fits the observed results, an empirically based formula?
Wheeler:
An empirical formula based on theoretical derivations but ending up with a simple formula. I have in mind one formula for a coil that was derived by some Japanese scientist around the turn of the century that had about thirty terms in it. Knowing the behavior toward either extreme, let’s say a short coil or a long coil, I made some formulas for interpolating the behavior between, which was essentially a curve match and putting in some ingenuity as to functions that would give that kind of a curve.
Kline:
So these are functions rather than something like coefficients. The hallmark, obviously, of empirically based formulas is coefficients. You’re describing something that I am not familiar with.
Wheeler:
A curve matching has two processes. One, finding a type of curve that tracks the relationship you’re working with. Two, finding the right coefficients to match it. One of the things that I’ve carried much further than most people bother to is finding the type of function that would follow a curve and then putting coefficients in to match it. One of my first papers was on that subject... inductance formula in 1928.
Kline:
So how did this type of work enter your design engineering work?
Wheeler:
One of my hobbies was getting formulas by which you could easily get answers. Professor Hazeltine had that hobby at times, too. I carried it much further as the years went on.
Kline:
Did you use it in your work in designing circuits?
Wheeler:
Yes. In the days of the slide rule, particularly, it was very important to have simple functions that would track what you’re trying to compute.
Kline:
When we were in the library earlier, I was looking up this book and there was this equation and I said, this equation looks like it was derived from first principles. You laughed and said, "Yeah, but it probably doesn’t describe the circuit." Is what you’re talking about related to equations that do describe the operations of the circuit?
Wheeler:
I’m not quite sure what I had in mind at that moment. Typically, in scientific books, there are many formulas that are idealized to the point where they’re of doubtful utility, and I’ve made a game of finding which ones were useful and putting them to use.
Kline:
Ohm’s law I think would be a useful equation.
Wheeler:
Yes, that was useful from the beginning.
Kline:
How about equations which one derives for describing the voltage of an amplifier?
Wheeler:
Incidentally, before Ohm’s law, they didn’t know it was going to come out that way. They just had an idea that the harder you pushed the more the current, and it was Ohm who reduced that to a quantitative basis.
Methods of Deriving Equations
Kline:
So when you were doing your early design work at Hazeltine, with equations you derived, how did you derive those equations?
Wheeler:
Every one different.
Kline:
You mean some from first principles and some empirically?
Wheeler:
Yes. There isn’t any general rule.
Kline:
If one were interested in how you did the work, would you find it in the notebooks? How you derived the equations?
Wheeler:
No.
Kline:
How would one find that?
Wheeler:
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You might find the process by which I arrived at an answer once I had the idea. Ideas are the things that make progress, and I think if we were bright enough we could observe children at an early age, like between two and four, and we might be able to select those who were going to thrive on ideas. They can distinguish from things you can see, from things you can do, and it’s not easy to describe what I’m talking about. What I’m hinting is that there’s no doubt individuals approach things differently, and evaluate various types of thinking differently, all the way from the one who can’t be bothered with the facts, and sometimes gets elected president, to the kind who aren’t satisfied with anything unless they delve deeply into it, and at least ask questions about how it happens. I imagine I was that type; I don’t pretend to remember, and I don’t know how much my parents would remember if they were still with me. I can’t remember particularly about our own children, but there’s no question in my mind that I got a large push from my association with Professor Hazeltine.
And even earlier, since my college physics professors didn’t ever hesitate to put me in classes that were beyond my over qualifications. While we’re talking about the areas where I’ve excelled, I look at other people, some of my acquaintances, some not, who have done things that I rate far beyond anything I’ve done. Whether it’s justified or not, I imagine that people in Cal Tech during the days when it was still small, were highly selected and given a tremendous opportunity that maybe nobody else was in those days. I’m talking about the days before and after the War. Now, whether Cal Tech is the right example, I think I may be correct in reviewing it as the highest quality technology institution in the world at a certain period when it was still small. I don’t have any documentation for that, but I mention it because there are people from Cal Tech whom I have seen spring ahead in their careers, in ways that I don’t find in mine. I’ve had a rather easy-going time, and I haven’t initiated satellites or atomic reactions or things like that, that to me seem to be beyond my sphere of imagination. Usually I’ve done things that were just one step ahead. So I take off my hat to the next echelon who explored in worlds that were unthinkable. That all correlates with my concept that I have found simple problems that had simple solutions. Now, of course, someone who first talked about a satellite in orbit might say the same thing, but it was much further beyond the current technology.
Creative Cookbook Formulas and Coils
Kline:
So you would characterize your ideas of the relationship between physics and engineering in your work also as a very mixed, amorphous thing. You just used whatever was available at the time and did what was necessary, and as you said it was usually a step improvement. But when I read the book here, I see that these step improvements come to quite a substantial thing.
Wheeler:
There are many steps; is that what you’re saying?
Kline:
I guess so! When I was an engineer they would say "cookbook" with a little bit of disdain, although we would all use those formulas. Could I ask what was the stimulus and impetus to publish and derive those type of formulas?
Wheeler:
Some cookbook formulas are imaginative, and some are not. I say mine are imaginative!
Kline:
And how do you mean they’re imaginative?
Wheeler:
There is nothing like an example. The inductance of a coil involves some erratic functions that aren’t on the cycle. Need I say more? And there are simple functions for a short coil, and simple for a long coil. The general formulas, you look at a table of coefficients, and that’s what I reject. I hate to look at tables on something I can turn out on a slide rule. Incidentally, many tables are obsolete today, as you know.
Kline:
I notice this is very short paper, too. Is that another trademark of you, Harold?
Wheeler:
I aim at it. Let’s say this is one they didn’t tell me to cut in half.
Kline:
You did not like looking up coefficients in tables, so how did you get around that?
Wheeler:
Well, first, as you may realize, an inductance formula doesn’t tell you how big you can make the coil to get the inductance. It just tells you that if you have a coil you can figure its inductance. And those were the only kind of formulas in my early days — what we now dignify with the name analytical as distinguished from synthetic, analysis as distinguished from synthesis. Well, formulas for synthesis are very few in the literature, and presenting my formulas in both orders is one of the unusual things that my papers do in the last twenty years. Formulas for synthesis as well as analysis. For example, a coil. One ways of making the two interchangeable is to make a graph, and you can read it either way — to plot a graph of the inductance against size. Then if you want a certain inductance look at the size. In an ordinary [helical?] coil, you add certain dimensions, diameter, turns per inch, and inductance. By making a certain chart, I was able to make one with which you could start with anything you wanted and get anything else you wanted.
Kline:
In other words you could start with a size and figure out the inductance.
Wheeler:
So I made this chart, I might say rather laboriously. Making the chart, once I had the concept, was not difficult, because for a size, number of turns, we could figure the inductance. By shaping this bunch of lines I had a conversion between sizes, turns per inch, and inductance, and the concept was that you couldn’t make a chart like that. The table that I was talking about determined these curves.
Kline:
So you turned the table into the curves. So rather than looking it up on the table you look it up on the curves.
Wheeler:
And the table only required only a few points to draw a smooth curve.
Kline:
What are these formulas here?
Wheeler:
They are second order relationships, so they are not involved in the principal formula I’m talking about. I use that every day, so to speak, for estimating purposes, because the graphical picture when you’re estimating is worth more than any formula.
Kline:
Now I see. What you’re saying is that this is an imaginative cookbook.
Wheeler:
And that a picture in your mind is what is needed. When I say no one else ever made a chart like that, that’s a kind of a sterile comment; but no one else ever made a chart that would do this, and that is a significant comment. I sent this in to the IRE Proceedings; they sent it to a reviewer. He rejected it and, said there was nothing new in it, that we’ve had that formula for years. Well, now I read between the lines that he never had to design a coil. And in reading between the lines, I’m casting aspersion upon typical reviewers who are college professors usually, and have never had to design a coil. So he didn’t realize that not only was this a new approach to design synthesis, but also that there wasn’t anything in the literature that would take its place.
Kline:
Perhaps he did not realize the value of having the information in this form.
Wheeler:
As they say in business, he never had to meet a payroll.
Kline:
Right. Are you saying that one cannot use the formula to design a coil?
Wheeler:
You can’t work the table backwards. This is a four-dimensional problem; there isn’t any way that you can just plot four dimensions in a useful way. You need a family of curves or something like that. This is a family of curves, but I don’t have to interpolate any more than between these close lines, because to use this you can take any three dimensions you want and find the last. You take this and this and this, and the lines get to this point and you read the fourth. And any two you can start with and nobody had ever done that. It was impossible with the elliptic functions and everything to write the thing backward.
Kline:
I’ve never designed a coil. If I see a formula for a coil, and I see that that one relates the inductance to the parameters describing the size to the coil —
Wheeler:
Those aren’t quite my words. It gives the inductance if you know all the others.
Kline:
Right. Inductance in terms of the parameters, the physical dimensions of the coil. So I have that formula; I have a table that shows all of those parameters and the inductance, and I have this. Are you saying that all three give the same information, basically?
Wheeler:
But not in the same order. See, for the inductance formulas you have to know everything except the inductance. You haven’t made the coil yet! You don’t know what the size is going to be! All you know is that you have to have one parameter.
Kline:
Can you think of any other cases of that?
Wheeler:
Lots. What else might you want to make?
Kline:
I could see for a capacitor it would be the same. How about calculating the size of a capacitor in a vacuum tube circuit? Would that be a different problem?
Wheeler:
Well, that is not so straightforward.
Kline:
Would a formula work for that, if you derived a formula?
Wheeler:
You can’t answer it without being more specific.
Kline:
You’re saying if I have a lot of parameters that are unknown, an approach like this works out well, but if I have a circuit where I know most of the other parameters but I need to calculate the value of a capacitor, I could solve for C.
Wheeler:
Yes. That’s generally what you find in the literature, and to get the value of C in some cases requires looking it up in tables, which is a messy way of doing it.
Kline:
Or doing some algebraic manipulation of an equation.
Wheeler:
We’re assuming that that’s been done, unless you mean solution by trial and error.
Kline:
What you’re then saying is that the designer doesn’t start with...
Wheeler:
A formula for inductance.
Kline:
— or with the value for inductance.
Wheeler:
He DOES start with the formula for inductance, but that doesn’t give him a quick answer. So here I’ve put them all together.
Kline:
That explains your comment that the reviewer never designed a coil.
Analytic and Synthetic Formulas
Wheeler:
He didn’t, and one might say, at this time in the literature, the distinction between analysis and synthesis was developing.
Kline:
Can you expand a little more on that?
Wheeler:
Well, the academic approach had been to compute the physical properties of a structure. Networks. You state the C and the L and compute the impedance. That is the viewpoint of analysis, and we’ve known for years what’s right and wrong. Then somebody, the engineer, had to plot some curves, families of curves, pick out points on the curve, in order to get the way to make it, and that’s been a typical engineering approach. That is a crude approach to synthesis, because if you have to plot the curve or do it by trial and error, you don’t have a formula. There's an example of putting complicated formulas into slide rule form, but it’s not with synthesis.
Kline:
Now, explain again what you mean by slide-rule form.
Wheeler:
Simple functions. See, a slide rule has functions up to exponential and hyperbolic, so the slide rule means you can get the curve by using those functions.
Kline:
Well, first let me record the two papers we’re talking about. The first one was called, "Inductance Chart for Solenoid Coil," and that was published in the IRE Proceedings in 1950.
Wheeler:
I’ll give you that because we hand it to every one of our new engineers.
Kline:
I can see why. The second one we were referring to was "Inductance Formulas for Circular and Square Coils" in Proceedings of the IEEE, 1982. The second one you gave me looks more like analysis.
Kline:
The first one was graphical, and the second was slide rule; the second was analysis. But here we have a more difficult problem. This I might say is probably one of my best-known papers for being highly useful and easily put on computers. Here we have what they call micro strip. It’s a misnomer, but we’ll call it that. Dialectic sheet, metalized on one side, and printed strips on the other side. Very common and very widely used. About ten years ago I found a way of computing what the dielectric would do when it isn’t full of dielectric, partially filled. Then gradually over the years I got more and more ambitious, and my early paper computed what the line impedance would be for different kinds of dielectric, and gave curves for design. The curves are still useful for understanding relations. Here, I found a functional form by which, if I specified the wave resistance, wave impedance, from the width, I could turn around and get the width from the wave impedance. That was mathematical invention of a high order. The giants of theory wouldn’t say that. They would say I was just puttering around — and I was. But I got a useful answer! They would say I was just puttering around, and I would say don’t knock it. So, here, you’ll find analytical formulas for the resistance.
Kline:
In terms of all the other parameters.
Wheeler:
But they are in a form that can be reversed, so here’s the formula for synthesis. It’s simple.
Kline:
When did this stuff start to appear in the engineering literature, in radio science?
Wheeler:
When I brought it down. This particular problem was regarded as insoluble.
Kline:
For this particular one? Do you think other engineers had used this kind of approach? They have the sizes rather than the —
Wheeler:
Now and then. You find cases where someone has had the motivation and the initiative to approach it that way, and it is not a motivation that doesn’t exist. Rather few people have done anything about it. Just ordinary run of the mill engineers every now and again get the idea, "Oh, you can do this."
Kline:
So do you think radio engineers, say in the 1930s and 1940s, worked from analytical formulas?
Wheeler:
That’s what they were taught. That’s what I’m saying.
Kline:
I see. But they couldn’t practically use that, though.
Wheeler:
They weren’t taught to do it the other way, so they had to do it by cut and try.
Kline:
So they had to do it by cut and try within the analytical formula?
Wheeler:
Yes. Plot a set of curves — that was the typical method. I might say I plotted a set of curves, but this is a quantum jump forward in the ease of utilizing these curves — different.
Kline:
This is the way it’s still taught! The analytical way.
Wheeler:
Yes, I think you would be hard pressed to find any real exception to that. I think there’s a simple principle there. If you have a structure you can by some method figure what the electric magnetic fields are going to do in that structure. But if you don’t have that structure, only a value of inductance, you don’t know what the field configuration will be, so you don’t know how to make it.
Kline:
Yes, that hit me when you were talking, that became clear! Well, I think earlier engineers had it too, but we won’t get into that.
