ideas on how to understand this

If you're interested in a general overview of electromagnetic waves, take a look at the "Radio Amateur's Handbook".

If you're taking a course and expect to pass it, you need to LEARN the stuff that's gonna be on the test. There's no substitute for learning the math required by the course.

Stated another way, if you don't want to learn the material, don't take the class.

The book is currently called The ARRL Handbook.

As stated: if you want to pass the class, suck it up and learn the stuff. Or, at least, memorize it long enough to get a C.

E&M is classic theoretical physics: a few governing equations, and a whole lot of conclusions that can be drawn from them. E&M -- in a classroom setting -- is all about starting from those four little old equations by Maxwell, doing a s**tload of math, and finding out something about the world that you didn't know before.

On the bright side, I know plenty of working engineers that just barely scraped by E&M and went on to brilliant careers in industry -- while there are a few jobs that demand that you understand that stuff, most just require you to remember a few of the derived factoids.

Agree completely. There are obvious exceptions, but for many projects, lots of math is a sign that the engineer either doesn't understand the problem or technology or both, or is trying to use the wrong technology. Also will result in manufacturing issues. If it takes six digit precision to make it work, it's gonna be difficult to make them on a production line.

But you still gotta pass the class to get the degree that gets the job.

If going round and round in the same groove is okay with you, you can ignore the math. Otherwise not. Every new thing I've ever done, with one or two exceptions, took a bunch of math to get going. Even new classes of circuits--one reason that analogue folks are getting rarer is that you can't do good analogue design just by poking SPICE till something seems to work.

Cheers

Phil Hobbs

Many, perhaps, but not all -- much of my business involves doing projects that the folks that can't handle lots of math can't even start on.

But -- if I find myself needing six digits of precision to get things to work, then I do make a point to have a long conversation with the customer that mentions the words "feasibility", "practicality" and "cost" quite a few times.

One of my customers is an entirely self-taught circuit designer, and is doing brilliant things. Of course, he's good at identifying the bits where he's weak, and he shoots that stuff off to me to vet.

I find that (usually), once I understand something I don't need to flog a whole bunch of math to get it to all come together. But initially I most certainly do.

_Not_ being able to do the math, and just being a blind "SPICE jockey" is certainly a road to error -- but then, I've known some pretty good analog circuit designers who couldn't go from an op-amp circuit to a transfer function to save their lives, but knew _exactly_ how to simulate that circuit in SPICE so that they'd be sure it'd work in real life.

I applaud being a "blind 'SPICE jockey'"... it's good for business ;-) ...Jim Thompson

SPICE is a good and useful thing, but when you use it as a substitute for thought, it limits you and you eventually get in trouble. (Google for "one trick pony".) ;)

I have no doubt that a highly intelligent but nonmathematical person might be able to do everything in Horowitz & Hill, and then some. Win Hill himself is an example, if I'm not mistaken, and so was Jim Williams.

But if you re-read Jim's piece on his CCFL backlight work of 20 or so years ago, it's hard not to think, "Jim, you know, an afternoon's worth of analytic math would have saved you six months' pain."

Another example is the essential difference between heaters and Peltier coolers for temperature stabilization, which is not obvious without doing the math, at least in outline: heater-based systems are far more vulnerable to thermal forcing in general, because the heat leak has to equal the average heater power plus device dissipation, whereas a Peltier or phase-change (cryogenic) system can be as well insulated as you like.

And in my business, before trying something new, I always have to grind through a feasibility calculation, which is always analytical. Probably a quarter of my business is doing photon budgets for smart, well-educated folks who aren't confident enough to do it for themselves. Practice!

Cheers

Phil Hobbs

I messed around with something for a few hours in LTSpice - I then dragged out Routh-Hurwitz and found out in twenty minutes that what I was trying to do wasn't possible. Doh!

Douglas Adams called those things "recreational impossibilities". ;)

In my first engineering job, I spent a whole day trying to build a phase shifter whose phase vs. frequency slope was positive--in other words, as I later realized, a time machine. (I had to stabilize my fancy PLL the hard way.)

Cheers

Phil Hobbs

Are you an undergard? First or second year? E&M was one of my favorite courses. There's a few basic equations. And lot's of ways to apply them. For any course you've got to get the basic's done pat. You can't just memorize some derivations. Electro statics and Magneto 'statics' are built on pieces of Maxwells equations. The course is traditionally taught historically so you don't get to the full equations till the end of the course. If you're learning vector calculus at the same time you're learning E&M then the math can be a bit overwhelming... but in some ways getting the math down... curls and gradients and all, may be more useful.

George H.

ng

Hide quoted text -

I'm not sure Tim was saying you didn't need math?

My notebooks are cover in (roughly) equal parts, Math, drawings, and circuits... though lots of time the math becomes stapled in pages.

George H.

old

--

ects,

he

ob.

is

most

is

og

You just gotta use some math to calculate the size of the heat fin you need for the Peltier. :^)

It's amazing how many people won't try and calculate something. I often make mistakes... but then the measurement points out an error... and I learn something. If I'd just been poking around I'd learn nothing at all... except for that one instance.

George H.

t -

You probably do need scientific notation for that, it's true. ;)

Even when their livelihoods depend on it working, which is the really astounding thing.

Cheers

Phil Hobbs

quoted text -

I'm not saying you don't need any math. I'm saying that it's easy to try to use too much math in the initial stages. Math is only as useful as the equations you write and the numbers you plug in. Spice is a design verification tool, not a synthesis tool.

The gain of a common emitter transistor amplifier is Rc/Re. With that knowledge and an understanding of gain-bandwidth product, an ENGINEER can easily decide how many stages are needed and the appropriate devices to use. You then start tweaking that basic design to account for the more subtle aspects and for stability. THEN you plug it into spice to determine if you were correct, and possibly refine further.

Give the same problem to a SPICE JOCKEY and you're likely to get fewer stages with higher gains sitting on the edge of stability. Bean counters love the fewer parts. Manufacturing managers, not so much. The spice jockey is less likely to have those "leaps" that are the stuff of technical advancement and patents. They're less likely to recognize when the design requirements and acceptance criteria are incomplete. Hint, that's always. They're too busy tweaking the component values on the wrong spice model.

As a mentor, would you rather teach spice to an engineer or try to teach engineering to a spice jockey? I've never been very successful at the latter. If they made it thru college without the engineering mentality, they're probably not ever gonna get it. Real engineers are rare, and they're formed very early in life.

Math good...basic understanding much better.