Engineering and math

I should clarify that I have been working in the real world for about

3.5 years. You're right, I've never used any of this high-level stuff on the job. I'm just frustrated at my Master's class!

That's Teflon insulation... me, the klutz, can't burn it with an iron ;-)

...Jim Thompson

-- | James E.Thompson, P.E. | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona Voice:(480)460-2350 | | | E-mail Address at Website Fax:(480)460-2142 | Brass Rat | |

| 1962 | I love to cook with wine. Sometimes I even put it in the food.

Jim is designing ICs, and he can't breadboard in any meaningful way.

In fact, I rarely breadboard, and then only very small snippets, just to see how a part behaves. I'd never breadboard a full product... it's better to go straight to the final multilayer board, and let the people in production build the first one for me. I don't simulate much, either, and again that would be just a snippet of the entire product.

Jim has to simulate because the cost of spinning a wafer design is too high; he can't kluge, either!

John

I have "blue-wired" some chips... it's called ion milling... but it's VERY expensive, yet a quick way to see if a patch is going to work.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC\'s and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

...Jim Thompson

Nice to hear it from a real engineer. The method has nothing to do with MIT though. It is an old Prussian style education method, where a number of subjects are taught at the same time in sync (say surface integrals are introduced just before Maxwell eq's are discussed). Works great: you see the same topic in (usually several) different classes one after another. Now back to reality: very few schools other than MIT can afford this. I teach math at an engineering college (don't laugh or get angry with me now). All we hear is: keep students happy at all costs. That means: let them pick what they take and when they do that. Hard to pull that MIT trick here. I do spice my lectures with a bunch of examples from, say circuits, or mechanical engineering (gear tooth profiles, for example, or quantum chemistry stuff and telegraphy equation when I teach PDEs) but most of the time students do not understand applications themselves (it is hard to get them excited about transmission lines and microstrips when I only get blank stares from seniors when I say `transmission line'---they are all digital design majors nowadays). You can tell, I love engineering (and I work with a lot of `academic engineers') and I do try to get students excited about math but my usual approach (which finally relates to the topic of this thread) is rather subdued:

1) Analysing stuff in your head IS math or at least very akin to it. 2) Engineers rarely SEE what they are dealing with so for the most part they, too are dealing in abstractions.

As someone in this thread has put it, `You just need a basic feel for Fourier transforms, and frequency domain stuff'. And where exactly would you get that `feel' without studying math?

Alex

PS. Those who rely on SPICE simulations too much, just what do you guys do when the sim does not converge? I am not trying to pull Bob Pease on you or aything

This is easy: if you have two solutions satisfying homogeneous BC's their sum still satisfies the same BC's (also called the superposition property). Not true for nonhomogeneous BC's.

Why is superposition needed? Well, how do you solve the equation? By pieces (called elementary solutions) that are then ADDED together in a Fourier series. If addition destroyed the solution one would not get very far.

A rotten mathematician such as myself would have said that the solutions of a HBC problem form a space and linearize the problem.

Alex

Of course. I even _dream_ circuits ;-) I think I've been at this stuff so long I can _simulate_ circuits directly in my head and quickly find the faults.

I must admit to have an inability for certain abstractions... atomic physics gave me great heartburn ;-)

And lots of practice. I was fortunate enough to grow up in the "backward" state of West Virginia, where basics was ALL that was taught; and a wonderful Algebra teacher named Truchovesky who _forced_ me to think, and kept me loaded up with book after book, where I worked _every_ problem in them. Then likewise with Geometry and Trigonometry.

More and more, my consulting includes looking over the shoulder of young bucks, trying to teach. Unfortunately most can't "think" anywhere but in front of the tube... no hands-on experience whatsoever :-(

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC\'s and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

One way is to pick something interesting and use it as a learning tool. For example, you could build a radar detector test tool with a stripline, or maybe you could show them how to pull in off air sports broadcasts which are blacked out locally with a really good amplifier and antenna.

See

for a great way to teach logic to kids.

If it's a simple linear system, Bode plots. I can explain closed-loop stabilization to any reasonably intelligent person in 20 minutes, and design most stable loops in a couple of minutes with a pencil and a piece of graph paper.

If it's a nonlinear system, start with a Bode-based solution that sort of works somewhere, then simulate and tweak it.

John

Hear, hear.

SPICE (in it's various versions) is an excellent tool. BUT

-You need good models

-Even with good models it WILL lie to you

SPICE/Simulation is for after you have come up with a design, and need to verify it. It is to be used in conjunction with breadboarding. You don't design by writing a SPICE simulation and just varying component values

M Walter

Amen Alex.

This is where the engineers start to get separated from the boys.

M Walter, P.E.

That was me.

You get it by studying it and then applying it in real circuits until it becomes *qualitatively* intuitive. But after that, you seldom or never have to do the actual math. It's like division: I understand how the concept works and behaves, and can (not by choice!) code a binary fractional divide in assembly, but I never actually do division any more, not since the calculator was invented. I believe I've actually forgotten how to do long division.

Even concepts like mixing don't need hard math. I can show a person graphically what happens when you multiply two signals - the sideband shapes and such, folding through zero, like that - without writing equations.

I'll invert your point 2): what's most important is that you can *see* it. Being able to mechanically solve equations doesn't mean you understand what's going on. I've seen lots of people do spiffy math onto nonsense assumptions and insist that the collector voltage must be 3e7, because the math says so.

Just yesterday, I told one of my guys something like "we can tolerate a few degrees of phase shift without affecting the nuclear spins much, bacause a cosine is flat on top. But the Taylor series approximation of a cosine is mostly x-squared to start, so phase error piles up real fast if we get too much of it." That's sort of hearsay math, but he got the point. Now we can get *numerical* without solving for general solutions. Hell, we're just engineers: we don't have to understand it, we only have to make it work.

John

Nonsense. But GIGO applies. If you are a village idiot, or aspiring to be one, then stay away from simulators.

"writing a SPICE simulation and just varying component values" is not DESIGN. However you can design microchips without EVER breadboarding... I do at least four successful chip designs per year.

Keerect!

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC\'s and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

So true. I guess there is a subtle difference in perception here. What you mean by `doing math' is actually doing computations (symbolic or not). But what you are describing sounds perfectly `mathematical' to me: concepts are what matters. Everytime I botch a computation on the blackboard and say `I hate numbers', students get shocked: `Aren't you a mathematician?'. Well, yeah, but I mostly think in terms like `small', `large', or `this depends on that'...

Sure, or just by writing simple equations. SSB radio is a heck of a lot easier to understand just by playing with sines and cosines than by doing Hilbert transforms (for which it is even hard to show existance `for real' (trivial as a distribution though :) (sorry for so many nested parentheses))). I do have to point out though that the concept of a sideband IS rather abstract: it relies on Fourier transform. You could have learned it through experience and once it is `felt' it becomes part of your `inner voice'. I do not mean to imply that mathematicians own these abstractions in any way: heck, operational calculus was INVENTED by engineers!

Amen! What I meant was you cannot SEE, say flux through the core (it is kind of tricky to even measure) yet you can SEE what is happening in an inductor once the basics have been understood (my hat is off to engineers who actually do this kind of stuff).

One more thing I have to admit is that this perpetual agrument between engineers and `math people' is in large part due to mathematicians' lack of interest in engineering matters. Many times I have tried to talk to my colleagues about the beauty of real engineering and all I got back was `we know what they really need, so they should not tell us what to teach'. Some even add a bunch of nonsense about how art is closer to math than engineering. I found talking to engineers to be a lot easier. This is a pity since we can learn a lot from each other.

I have a somewhat trivial example of how misinterpretation of math can ruin a perfectly valid argument: I have a book on circuits (a bit old, from the seventies, see reference below if interested) that says (on p.

49) that to transfer maximal power to an 8Ohm speaker one should design an amp with 8Ohm ouput impedance. Such is the magic of math. Should not any engineer just FEEL how wrong this is? Now, if you have an ideal amp, WHY would putting a resistor in front of it make the power transfer any more efficient? And the formula is right there: p_L=v_t^2*R_L/(R_L+R_T)^2, so the smaller R_T the better. But no, derivatives rule, so wherever that p_L'=0 is where we wanna be. See, I admitted it, math can be overapplied, too :) (on the other hand, as a math person, I have to say that the problem is that this is a func of two variables so this is a Lagrange multipliers kind of problem, yeah, that is what they missed, ..., ok, I am just kidding).

I will quote this to my students TOMORROW.

Alex

PS. By the way, the book is Basic linear networks for elec. and electronics eng. by B. Leon and P. Wintz. It is not a bad book overall.

Just curious, but why are you going for a Master's degree now?

John

I have great respect for those really smart people who can do general, symbolic math and have it mean something. People like Maxwell and Heaviside and Shannon gave us the tools we need to build stuff.

But circuit design is the conception of functionality and the invention of topologies, ways to connect parts, and that's not math at all, or not in any sense I've heard of. One (usually) needs mathematical instincts while pushing the parts around, to separate the usable circuits from the infinity of bad ones, but real math, numerical or symbolic, comes in analysis, *after* the circuit exists. That can often be ignored, or done in Spice, or delegated to a scutt bunny (oops, sorry, intern) or even breadboarded, with a little care.

As someone else noted, I haven't taken an integral in a decade or so, to compute a fet dynamic power dissipation, and it confirmed a value derived from a simple graphical approximation. If I was designing the GPS system or a filter from scratch or something like that I'd need serious math, but I'm a circuit designer.

John

The Bode plot method is based on Fourier Analysis. Frequency on the x-axis, right? But it is not necessary to have complete knowledge in Sturm-Liouville theory to use Bode plots, as it is not necessary to know the details of the Otto or the Atkinson cycles to drive a car.

--
Sven Wilhelmsson
http://home.swipnet.se/swi

-------------------------------------------------------

I just have to reply to this. My research area is topology (pretty close to what you've described: connecting things together), and it is an integral area of mathematics. By the way, in my reasearch I have NEVER done a single computation and never even used a number. I have also observed that a lot of people (including my students) use the term `real math' or `difficult math' to mean `tedious long-winded computations'. Well, there is nothing difficult about pushing Fourier (Laplace, Walsh, Heaviside, Hilbert, take your pick) around for a couple of hours while taking integrals like mad---we KNOW how to do this, there is no reason to THINK here. Thinking about WHY a Fourier transform would work IS difficult, same way as thinking about how to circumvent, say, the Miller effect IS difficult. Sure, in any field there are shortcuts (Fourier? Why, it is an isometry on a Hilbert space. Miller effect? But that is what differential pairs are for ...) and sometimes they work just fine (most of the time, that is why they are shortcuts afterall). To put it bluntly, the difficult math was done by Steinmetz, Heaviside, Shannon, etc., the guys who came up with this. They gave us the certainty that the methods work, and they had the insight to use the right tools. Analysis using these methods is usually routine, i.e. easy (albeit time consuming sometimes). What you guys do while designing cicuits is difficult because it requires insight. I know, this is not a proof of anything but open any serious mathematical paper (or even not so serious one) and see what people refer to as `obvious'. Just one of these facts would need a couple of semesters to explain. But they do not require thinking (usually not too much) when you have done it a few times. Same way, when I read research papers in engineering, I sometimes struggle with what engineers say is `easy to see'. I do have some engineering experience but it still takes getting used to. One important thing about math though is that it collides with reality in engineering and I like saying in my classes: you learn mathematics and engineering for essentially the same purpose: to know when matematicians are lying to you. And when they are not, thing are easy: just use it.

I think another problem that a lot of people are unnknowingly struggling with is the FEAR of math instilled in them since high-school. I like to think of it as a chain reaction: bad uncaring teachers went to teach high-school and produced poor students some of which became bad, uncaring teachers themselves (what it the half life of the body of good teachers here?). Sure, math can be difficult but the math taught in college is realatively trivial compared to the real life applications engineers face. It is all the same after all: juggling parameters, trying to make things fit. Wouldn't you agree, that if one can master engineering, one should be able to master engineering math (it is mostly 18 century stuff after all) even if one would never apply it directly? The original question in this thread was: is lack of understanding of math an impedimant to becoming a designer? I guess the answer is: not directly but problems with understanding math might mean something else is wrong. Maybe the guy who is teaching it is a condescending jerk. Maybe one just cannot get motivated enough.

Alex

It is not. A plot of gain and phase vs frequency does not involve any of the math that is associated with the Fourier transform.

Is "Frequency on the x-axis" the definition of "Fourier analysis"?

It's not necessary to have *any* knowledge if it!

ditto

How do you design stable nonlinear control systems?

John