John said:

Do you use Maxwell's equations to calculate microstrip impedance?

Maxwell's equations are needed to derive the formaulas to determine the

incremental (per unit length) R', G', C', and L' for a particular

geometry. Once those formulas are in hand, then Maxwell's equations

aren't needed anymore, unless you encounter a new geometry (which

wouldn't be called microstrip of course, which is just one particular

geometry.)

The values of the incremental parameters plug into the characteristic

impedance formula for a TEM transmission line to give the impedance.

That formula can be derived from circuit theory applied to an

incremental length of transmission line, which leads to the pair of PDEs

that are the wave equations. Solution of the wave equations leads to

the characteristic impedance relation.

In practice, one needs only the formulas. But I consider all formulas

suspect unless I work through the derivations myself. Also, if you are

the sort of person that gets deep satisfaction out of the way

mathematics so precisely and eloquently desribes physical phenomena,

then the experience of going through the math is very fulfilling.

The last time I used calculus was in estimating a mosfet's switching

power dissipation, maybe 5 years ago. It came out close to a quickie

graphical estimate, so wasn't actually necessary at all.

That is often the case, for this sort of thing.

I did take a year's worth of field theory in college, and we finally

got up to the full expression of Maxwell's equations (divergences,

gradients, curls, all that nasty vector field stuff.) I remembered it

just long enough to struggle through the final exam.

John

What really impressed me was the transmission line theory and the plane

wave propagation theory. I wish I had the time and patience to continue

on with the plane wave stuff, because we stopped just before getting

into the derivations of the Fresnel equations, and other optical issues

which are of great interest to my laser work. Ultimately, I'd like to

be able to understand plane waves in anisotropic media, which would

reveal the inner workings of frequency doubling crystals and optical

parametric oscillator crystals, and other non-linear optical and

electro-optical stuff. But I don't know if one can get that far without

tensors.

I had to learn the vector calc. on the fly as I took the course, because

I didn't have a formal class in it. But it wasn't difficult.

Trouble with all this stuff is you do indeed loose fluency in the

subject quickly without practice. But the overall impression and the

fundamental understandings remain, and are far deeper than anything I

could have gotten without the math treatment.

Good day!

--

_______________________________________________________________________

Christopher R. Carlen

Principal Laser/Optical Technologist

Sandia National Laboratories CA USA

[email protected] -- NOTE: Remove "BOGUS" from email address to reply.