Engineering and math

[snip]

I can't "talk about the mental operations of the design process itself" when you don't understand how my own mind is working ;-)

...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.

John Larkin wrote: (snip)

My guess is that the introspection, necessary to have anything meaningful to say on the subject, is rare.

I would say Bode plots and Fourier transforms are almost the same things.

Was it not for Fourier analysis nobody would ever plot anything in the frequency domain.

But your teachers teachers professor must have heard somthing about it!

Nonlinear theory is awful. In such cases I prefer to simulate!

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

I'll emphasize this with an easy example from history. The concept of density is dead easy for us to conceive and apply, today. It is a simple ratio between mass and volume, after all. Children learn the idea easily.

Take a look at the history behind it. There were a lot of people with a great deal of practical interest, yet it took rare people to disover what our senses do not directly inform us about. Once someone does discover the idea and explain it, it's child's play. But beforehand?

This doesn't address the "difficult math" you mention above, as density isn't difficult math. But the discovery of Euler's e^i*w = cos(w)+i*sin(w), or the discovery of rigorous application of infinitesimals in differential variables or .... Well, we can all apply these because we stand on the shoulders of those who discovered the ideas and put them on rigorous footings.

Analysis using density is often child's play. But look how long it took to discover as a useful principle. Natural philosophers were debating the ideas of sharp and blunt as a principle for floating and sinking, even in Galileo's day, for gosh sake. If someone told me "density is obvious," and imagine that they are as creative, imaginative, and smart as those who actually had to discover the idea, I'd just smile and walk away shaking my head.

Jon

To stay ahead of the game, so to speak. And the company is paying for it. I'm not sure how much it'll really help me other than to pad my resume. I do know that add'l education never hurts, though.

A distance learning program through my employer at Purdue.

Yuck. I know math is great stuff, but some of it is too far out there for me.

Not that I would have ever figured out calculus, but when I was 4, I remember looking at the edge of a razor blade and trying to tell my brother that it was not "so thin that it did not have width." We argued about it for a few minutes until finally I said, "What if you made some green Jello(R), and you took the razor blade and kept slicing it over and over, a 500 times? All the little slices would have to add up. The edges of the Jello would flop and spread out, right?" I figured it would spread out eventually, but I wasn't sure.

He got frustrated and told my mother that I was talking about slicing Jello(R) with razor blades and I got a spanking for playing with my Dad's tools.

-Le Chaud Lapin-

Good imagination, eh? That's important.

Jon

You're not confusing the procedure of plotting a curve with the math which underlies the analysis which gives the validity of the result, are you?

The math which gives (1 - exp(-t/tau)) as the step response for the system which has the frequency response 1 / (1 + s tau) *is* the Fourier transform. (Well, I would call it the Laplace transform, because that is the general method, but the Fourier transform is the name given to the analysis which gives the response to inputs which are (composed of) constant-amplitude sinewaves, i.e. described in the s (or Laplace) domain as being on the imaginary axis - the frequency axis above.)

Quite complicated answers ensue if you keep asking "why" past the point of - say

- "Kirchoff's current and voltage laws describe a circuit and all you have to do is solve them."

Hah!

of course not, try some thing like

if you're curious about this.

(For linear time invariant systems I'd be curious to see a method other than Laplace transform used to derive the frequency behaviour of the system in question.)

(I'll agree with that, actually.)

Well. Are you then content to switch integration methods in Spice when you simulate an ideal oscillator without knowing why? The answer might very well be "yes," for you, but I find it pretty comforting to know why some analysis methods will not give the true result for some problems. (I'm alluding to the "method=gear" and "method=trap" options in classic Spice, not the newfangled ones which "just work" :-) )

Dunno, I'm more of a linear system kind of person myself. How would you demonstrate the stability of such a design?

Best Regards

Jens

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Buy 'Modern Engineering Mathematics' and you'll have a practical guide to solve mathematical problems. It goes from really simple things like Pythagoras to Fourier and Laplace. 'Advanced Modern Engineering Math.' is still on my 'must buy asap' list because the first book doesn't cover all I need.

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I was using hypergeometric functions in grad school. Havn't seen one since.

Al

When I do a Bode plot anaysis of a closed-loop system, I have nothing to do with time-domain waveforms, step responses, or any of that. I plot gain as a function of frequency, and stay purely in the frequency domain. No "transform" is performed. Plotting amplitude versus frequency was no doubt done long before Fourier was born; probably any good piano tuner had the concept already.

Fourier invented an algorithm to map a (basically) time-domain function into the frequency domain. He didn't invent graphing, and his transform is not executed when I do a Bode plot. And the Fourier transform doesn't "validate" graphing gain versus frequency; the physics of resistors and capacitors does.

John

[....]

which

the

If you say so. I thought that Fourier was the first to show the output of a linear system to an input consisting of a combination of periodic signals.

Maybe I'm entirely wrong...

So, what ties the graphing of gain versus frequency to the physics of resistors and capacitors?

Best Regards

Jens

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    Key ID 0x09723C12, jensting@tingleff.org
        Analogue filtering / 5GHz RLAN / Mdk Linux / odds and ends
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         "Never drive a car when you\'re dead!" Tom Waits

which

I

the

to

Not worth arguing; but I swear I don't perform Fourier transforms to do Bode plots, and that I don't sum or superimpose sinewaves of different frequencies.

The simple expressions of the behavior of resistors and capacitors: e = i*r and i = C * dv/dt. I doubt that Fourier was aware of these, and his transform doesn't describe either phenom.

John

It was similar but different for me, I enjoyed algebra, less so geometry, and when i got to Calculus it drove me nuts; when i finally wrapped my mind around differential equations (about halfway through the second semester) my world changed. Suddenly i could see differential equations everywhere and in everything. Probably have a hell of a time trying to do the math now, but the worldview change persists.

--
 JosephKK
 Gegen dummheit kampfen die Gotter Selbst, vergebens.  
  --Schiller

You'd be amazed at th elevel of matrhs and logistics required for those cathedral or any large buildings from antiquity.

G

By not starting in the time domain at all. No domain crossing, no transform executed.

John

The Professors analyzing them now use all kinds of fancy math. They could not keep their jobs if they did not. The architects that created them barley used anything better than lame algebra, if that. Algebra did not really exist in the 11th through 15th centuries, yet they still built cathedrals still standing today.

--
 JosephKK
 Gegen dummheit kampfen die Gotter Selbst, vergebens.  
  --Schiller