Asymmetric Stripline / Microstrip online calculators for impedance and velocity

After numerous failed searches I found:

I think the stripline would have to be pretty far off-center for the phase velocity to be much different than c/sqrt(Er); in pen-and-paper analysis to derive the relatively simple equations for characteristic impedance, the dominant propagation mode is considered to be TEM.

If the geometry is so screwy that it can't be well-approximated by TEM the characteristic impedance equation is wrong, also.

I don't know what "asymmetric microstrip" is..?

I would hope the calculators cope with standard Stripline and Microstrip.

I just needed details for Asymmetric Stripline and standard Microstrip.

In the asymmetric stripline calculator you posted the propagation delay is calculated from the relative permittivity of the substrate alone, just so you know it's not returning anything different for that than the standard one.

IOW the phase velocity of the TEM mode is taken as a given to develop the pen-and-paper equations for the capacitance, and and thereby the characteristic impedance of both the symmetric and asymmetric stripline.

It's not just the relative permittivity of the substrate, as part of the EM field is in air. In some designs this is small enough to ignore the air part, but this must be determined, not just assumed.

Joe

This is sort of nuts. Microstrip is on the surface of a printed circuit board. Half the field is located in the substrate and the other half in the air above the board. It's consequently dispersive - different frequency components propagate at different velocities.

Strip-line is buried inside a printed circuit board and propagates in what can be a uniform environment. It's non-dispersive. A thicker layer of the insulating substrate above the strip line than below it could make it asymmetric, but I've no idea if this would mess up the propagation velocity. A different insulating substrate above the strip-line than below it presumably could make it dispersive.

The model of stripline amenable to pen-and-paper calculation has a conductor floating between two ground planes on the z axis, and dielectric to infinity in the xy plane, there's no field in the air in that model.

The microstrip model has field in air and is only quasi-TEM but they're not the same thing. What the hell is a "asymmetric microstrip" anyway?!

Not sure what y'all think these online calculators are doing. They're just automating the kind of pen-and-paper derived equations you can find in the textbooks, which make a number of assumptions to make the problem tractable to closed-form analysis.

Ya as I've been trying to explain, the propagation velocity has to be taken as a given to make finding either the symmetric or asymmetric stripline capacitance (and therefore Z_0) tractable to closed-form analysis. The simple online calculators don't do s*it but take it as a constant for stripline, based on the relative permeability of the substrate, in either the symmetric or asymmetric case.

I didn't think this required a PhD to explain but maybe you or Dr. Hobbs or someone can explain it better than I can..

I can probe a microstrip on a PCB and clearly see the propagation of a clean fast edge as it moves down the board. Dispersion is not an issue on a reasonable-sized PCB with, say, 250 ps logic edges.

On some extreme gadgets, like skinny traces on gen5 PCIe or something, the signals at a receiver look like noisy hairballs, but adaptive equalizers in the receivers clean them all up.

Saturn has an extensive list of the sources and references that they use. And it warns you if your geometry is outside the range that it likes.

The simple equations, like from the Motorola ECL book, get stupid (as in claim negative impedances) for some cases.

It means that the shape of the stripline cross-section is not symmetric in the plane perpendicular to the stripline conductor plane, where the "fold" line is either parallel or perpendicular to the stripline conductor plane. It does not mean circular symmetry.

The online calculators are all over the place, and some programmers are better at the physics and math than others. Larkin pointed to one of the better choices.

Joe

The simple equations in the Motorola Data book give good approximations to the characteristic impedance in the 50R to 75R range.

Back around 1990, when I needed to cover a wider range of impedances, I ended up buying Peter C.L. Yip's "High Frequency Circuit Design and Measurements" ISBN 0-412-34160-3. It had only just been published back then, and I'd found it in Heffer's in Cambridge U.K. which stocked that kind of book for undergraduate and postgraduate students.

It offered slightly longer equations - including natural logarithm terms

- which were claimed to stay valid for a slightly wider range of characteristic impedances.

Development being what it is, the project got cancelled before the relevant printed circuit boards got made or loaded. The precursor boards had worked well enough, after we'd tinkered with them, but we'd clearly needed to do better.

The main limiting factor in the accuracy of evaluating stripline impedance in closed-form is not knowing the actual surface charge density of the strip, but the relative permittivity is what it is as there's no field outside the substrate. It's pretty straightforward to develop the equations for an offset strip just by changing limits of integration in e.g section 3.7 of Pozar.

Microstrip is less amenable to closed-form solutions since the field extends outside the substrate so you have to come up with an approximate effective permittivity depending on the particular geometry.

Pozar has equations that cover a full page, and then it turns out that some if the terms occupy another page.

Simulation often works better than equations.

Simulation is just a computer evaluating equations. It's certainly a lot easier to let the computer do it for you, but both approaches rely on essentially the same set of equations.

Sure, dumb programs just execute dumb equations. There's a lot of that online.

A proper em simulation doesn't do that. It does the basic physics. We do a real e/m simulation to handle cases that have no textbook equations, like impedance matching an edge-launch SMA on a 6-layer board. Pozar didn't do that one.

We use ATLC. Works great.

Has anyone used Comsol Multiphysics for e/m simulation?

John Larkin doesn't have a clue about basic physics, so he doesn't realise that it is just equations.

Simulation programs use numerical integration on differential equations which don't lend themselves to closed form integrals. I did exactly that in my Ph.D. work in chemical kinetics back around 1968.

The "real" simulations are just more equations.

Pozar's equations can be integrated, but John Larkin doesn't know enough to realise what's going on.

Even if the user doesn't know what it is doing.

I certainly haven't. Some graduate student somewhere is bound to have tried to, and perhaps one could have succeeded.