[Homer J Simpson]

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.

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 http://www.warrenrobinett.com/rockysboots/ for a great way to teach
logic to kids.

 

[John Larkin]

Sturm-Liouville_theory is the mathematical basis
for very much in modern physics including electronics.
Most of us know about Fourier Analysis.
How would we deal with e.g feedback in control systems without
Fourier Analysis or Laplace transforms?

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

 

[mark]

[email protected] wrote:

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

 

[mark]

Amen Alex.

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

M Walter, P.E.

 

[John Larkin]

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?

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

 

[Jim Thompson]

[email protected] wrote:

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

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

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

"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.

M Walter

Keerect!

...Jim Thompson

 

[[email protected]]

As someone in this thread has put it, `You just need a basic feel for

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.

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'...

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.

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!

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.

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'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.

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).

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

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.

 

[John Popelish]

John Popelish wrote:

nice. fancy sharing?

Sure.

LTspice allows you to replace the inductance value with a
flux function of x, where x represents the current through
the inductor.

The first example I attempted was just a fit of the general
conic quadratic to a data set for a 518 uHy that someone
posted to the Yahoo LTspice group.

flux=sgn(x)*(2.858458e-4*abs(x)+4.825486e-3-sqrt(6.407706e-8*x*x+(-2.332992e-6)*abs(x)+2.328531e-5))

But this can be generalized as:

flux=sgn(x)*(A1*abs(x)+A2-sqrt(A3*x*x+A4*abs(x)+A2*A2))
where
Linf=inductance at inflection point
Lmin=inductance at infinite current
L0=inductance at zero current
Iinf=current at inflection point

A1=Linf
A3=Lmin*Lmin-2*A1*Lmin+A1*A1
A4=2*A1*A3
A2=Iinf*A3/(L0-A1)

I hope I got that all right.

 

[John Larkin]

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!

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

John

 

[John Larkin]

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.

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

 

[Sven Wilhelmsson]

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.

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.

 

[[email protected]]

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.

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

 

[John Larkin]

The Bode plot method is based on Fourier Analysis.

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.

Frequency on the x-axis, right?

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

But it is not necessary to have complete knowledge in Sturm-Liouville theory
to use Bode plots,

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

as it is not necessary to know the details of the Otto or
the Atkinson cycles to drive a car.
ditto

How do you design stable nonlinear control systems?

John

 

[John Larkin]

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

This is interesting. Humans can be so different. The things you say
are hard - *why* a Fourier transform works, or how to avoid Miller
degeneration, are obvious to me in a flash, without really thinking.
Designing circuit topologies is pure instinct to me, and takes no
effort and sometimes no time, either. And when I'm working on a tricky
problem with one of my guys, it's uncanny that sometimes we will come
up with the same solution. Last week, Rob and I were agonizing over a
nasty tradeoff in the DDS synthesizer board we're doing. After a
couple of minutes of grunting and scratching, we said, literally
simultaneously "Dither the dac!" So he, younger and more energetic
(and probably smarter) than I am, went away and designed a cool FPGA
block that makes a 10-bit dac think it's a 16-bit dac.

But pages of math notation, and the prospect of closed-loop solutions
to partial differential equations is not "usually routine" to me, it
gives me the horrors. Really good, challenging designs happen when
people like me brainstorm with people like you. More engineering
schools should appreciate this difference and teach appropriately.
There's a good reason why they don't.

When I was in EE school, my profs weren't impressed with me because I
wasn't very good with the fancy theory, and I didn't tell them that I
was designing modems and pipeline control systems and Saturn IV and
C-5A flight hardware on the side.

Engineers like to talk about the technology they use, but seldom want
to talk about the mental operations of the design process itself.

John

 

[Jim Thompson]

On Thu, 12 Oct 2006 09:19:43 -0700, John Larkin

[snip]

Engineers like to talk about the technology they use, but seldom want
to talk about the mental operations of the design process itself.

John

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

 

[John Popelish]

John Larkin wrote:
(snip)

Engineers like to talk about the technology they use, but seldom want
to talk about the mental operations of the design process itself.

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

 

[Sven Wilhelmsson]

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.

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

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

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

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

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

How do you design stable nonlinear control systems?

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

 

[Jonathan Kirwan]

<snip>
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).
<snip>

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

 

[[email protected]]

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

John

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.

 

[[email protected]]

Say, where are you studying for your Master's?

A distance learning program through my employer at Purdue.

I suppose there's a reason why you're not pursuing a Master's in
Mathematics. (wicked grin)

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