What impedance is being calculated? Top line against dotted one below?
It occurred to me that if I drive my top and bottom lines out of phase, which I will, there will be an equipotential plane midway through the board. So I could sneak a ground plane in there and nothing would change. With the ground plane, it becomes two microstrips, and there are lots of microstrip solvers.
There would still be some fringing errors, like in your fig 4.20, which doesn't assign a symbol to the board width.
Am 08.06.2025 um 23:58 schrieb john larkin:
Calculated is the impedanz of the symmetical line, above and dotted one beneath the FR4.
Yes, that is right. The solution is approximate; no one has yet integrated an exact one.
The problem is that the 2nd page is blurred in the first photo and cut off in the second photo. My schoolboy German is likely good enough to read it, especially with help from Google Translate.
Actually, an ordinary smart phone may suffice, if in sufficient light. If too little light, the camera shutter speed is too slow, and it's hard to hold it still enough, and the depth of focus is too shallow.
Joe
It's just a parallel plate waveguide.
For the TEM mode Z0 = 377*sqrt(ur/er)*(d/w).
ur/er - substrate permeability/permittivity (relative) d - dist between copper w - width copper strip
Formulas for the higher modes also exist.
But I'd have to look them up.
Your free space impedance is easier for me to comprehend than the one contained in Chemandy's calculator:
Danke,
That assumes that all the capacitance is confined to the rectangle between the plates. Actually, that's good enough for what I'm doing now, just making a txline transformer.
And that one assumes an infinite ground plane.
I suspect that all such formulas are wrong, except in a few rare cases like a coax. EM simulation is better.
It's good enough for typical impedances used in PCB's (120 ohm or less) where w/d > 1.
What Z0 do you need.
Get Cadence to come along and demonstrate Alllegro + Clarity to you.
The days of using formulas to calculate these things are long gone.
We have lots of programs and web sites that use the formulas!
I need to put a fast kilovolt pulse into a 50 ohm load. I can use a GaN fet and a transmission line step-up/isolation transformer.
I'd like to make the windings from PCBs with roughly 50 ohm differential impedances, but if the txline windings are short compared to rise time, it doesn't matter much.
I was just interested that this geometry is not included in any pcb impedance programs that I know of. The imaginary equipotential plane is a workaround.
Supposedly that's exactly _why_ this specific geometry is not explicitly included.
Jeroen Belleman
Am 11.06.2025 um 11:36 schrieb Jeroen Belleman:
The text in my book states that this line geometry is unstable. Other lines and geometries in the vicinity have a significant disruptive influence on Z.
Same as microstrip.
Embedded differential striplines have a similar equipotential plane, but lots of apps handle that one.
The edge-to-edge diff stripline, with a vertical equipotential plane, would be a nasty case. Imagine a stripline trace that is perpendictular to its ground plane. Imagine asking some board house to fab that.
That is true for any geometry that does not confine the fields.
Jeroen Belleman
So we lay coaxial cables and waveguides.
Sure, but what will you do on a PCB?
Jeroen Belleman
I usually do it with asymmetrical lines.
---------------------------------- line ////////////////////////////////// FR4
********************************** Ground plane
Well, maybe a little.
I could make my txline transformer with coax. We've done that before.
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