Re: Asymmetric Stripline / Microstrip online calculators for impedance and velocity

On 5/20/2025 5:39 PM, john larkin wrote:

On Tue, 20 May 2025 14:09:46 -0400, bitrex <user@example.net> wrote:
 

On 5/20/2025 1:59 PM, Bill Sloman wrote:

On 20/05/2025 11:53 pm, Mike Perkins wrote:

>
I can find numerous calculators that provide impedance for the above
structures, but are there any that give propagation velocity too?

>
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.

 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.
 

>
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.
>

>
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 shit 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..

 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.
 

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.