Given a pair of parallel run traces on a board, FR4, like this,

https://www.dropbox.com/s/2lqnbulsusx3e80/Microstrip_C.jpg?raw=1

There are three capacitances per unit length.

Assume w = 6 mils and g = 6 mils and the upper dielectric is 10 mils
thick, traces to ground. What are the capacitances? I'm not concerned
with transmission line effects now.

The Saturn software says that one trace by itself is 1.8 pf per inch.
It will also calculate odd and even mode impedances for a differential
microstrip, but not these capacitances directly.

I can find academic papers on this, full of gigantic equations but no
numbers. I suppose I could write a program to evaluate the equations.

I was prowling the net for a calculator but couldn't find one.

C3 will be an unfortunate routing between a fast DAC and its opamp,
basically from the opamp output to its inverting input.

John, if you'd describe the pair of traces (I can't access dropbox.com directly)
I'll see if I can answer your question.

Hul

John Larkin <jlarkin@highland_atwork_technology.com> wrote:

> Given a pair of parallel run traces on a board, FR4, like this,

> https://www.dropbox.com/s/2lqnbulsusx3e80/Microstrip_C.jpg?raw=1

> There are three capacitances per unit length.

> Assume w = 6 mils and g = 6 mils and the upper dielectric is 10 mils
> thick, traces to ground. What are the capacitances? I'm not concerned
> with transmission line effects now.

> The Saturn software says that one trace by itself is 1.8 pf per inch.
> It will also calculate odd and even mode impedances for a differential
> microstrip, but not these capacitances directly.

> I can find academic papers on this, full of gigantic equations but no
> numbers. I suppose I could write a program to evaluate the equations.

> I was prowling the net for a calculator but couldn't find one.

> C3 will be an unfortunate routing between a fast DAC and its opamp,
> basically from the opamp output to its inverting input.

On Fri, 16 Dec 2022 20:57:52 -0000 (UTC), Hul Tytus <ht@panix.com>
wrote:

>John, if you'd describe the pair of traces (I can't access dropbox.com directly)
>I'll see if I can answer your question.
>
>Hul

Cool. Two parallel microstrip traces, each 6 mils wide, with a 6 mil
gap between. Ground plane below.

_______ C3 _______

C1 C2
___________________________________________

The dielectric is 10 mils thick FR4, between the traces and the ground
plane.

(mils, 0.001 inches!)

If you can do that easily, it would be interesting to increase the gap
to 12 mils. Eventually at large gap C3 goes away and each trace goes
to about 1.8 pF per inch.

Thanks

>
>John Larkin <jlarkin@highland_atwork_technology.com> wrote:
>
>> Given a pair of parallel run traces on a board, FR4, like this,
>
>> https://www.dropbox.com/s/2lqnbulsusx3e80/Microstrip_C.jpg?raw=1
>
>
>> There are three capacitances per unit length.
>
>> Assume w = 6 mils and g = 6 mils and the upper dielectric is 10 mils
>> thick, traces to ground. What are the capacitances? I'm not concerned
>> with transmission line effects now.
>
>> The Saturn software says that one trace by itself is 1.8 pf per inch.
>> It will also calculate odd and even mode impedances for a differential
>> microstrip, but not these capacitances directly.
>
>> I can find academic papers on this, full of gigantic equations but no
>> numbers. I suppose I could write a program to evaluate the equations.
>
>> I was prowling the net for a calculator but couldn't find one.
>
>> C3 will be an unfortunate routing between a fast DAC and its opamp,
>> basically from the opamp output to its inverting input.
>
>

John, maybe... the capacitence between two 6 mil traces 6 mil apart on the top of a pc board w/ dielectric const. of 4.8
is calculated at 7.155e-13 farads per inch. This calculation has not yet been verified so the result need be considered a ballpark
estimate.
The capacitance of a single 6 mil trace between 2 ground planes 20 mils apart comes to 2.698 pf/inch.
This sould be equivilent to the sum of 2 distant traces on the top of a board. That I'll check. The calculation came,
I think, from Analog Device's "Microstrip & Stripline Design", "MT-094 tutorial".
The sum of these 2 should approximate your answer.

Hul

John Larkin <jlarkin@highland_atwork_technology.com> wrote:
> On Fri, 16 Dec 2022 20:57:52 -0000 (UTC), Hul Tytus <ht@panix.com>
> wrote:

> >John, if you'd describe the pair of traces (I can't access dropbox.com directly)
> >I'll see if I can answer your question.
> >
> >Hul

> Cool. Two parallel microstrip traces, each 6 mils wide, with a 6 mil
> gap between. Ground plane below.

> _______ C3 _______
>
> C1 C2
> ___________________________________________

> The dielectric is 10 mils thick FR4, between the traces and the ground
> plane.

> (mils, 0.001 inches!)

> If you can do that easily, it would be interesting to increase the gap
> to 12 mils. Eventually at large gap C3 goes away and each trace goes
> to about 1.8 pF per inch.

> Thanks

> >
> >John Larkin <jlarkin@highland_atwork_technology.com> wrote:
> >
> >> Given a pair of parallel run traces on a board, FR4, like this,
> >
> >> https://www.dropbox.com/s/2lqnbulsusx3e80/Microstrip_C.jpg?raw=1
> >
> >
> >> There are three capacitances per unit length.
> >
> >> Assume w = 6 mils and g = 6 mils and the upper dielectric is 10 mils
> >> thick, traces to ground. What are the capacitances? I'm not concerned
> >> with transmission line effects now.
> >
> >> The Saturn software says that one trace by itself is 1.8 pf per inch.
> >> It will also calculate odd and even mode impedances for a differential
> >> microstrip, but not these capacitances directly.
> >
> >> I can find academic papers on this, full of gigantic equations but no
> >> numbers. I suppose I could write a program to evaluate the equations.
> >
> >> I was prowling the net for a calculator but couldn't find one.
> >
> >> C3 will be an unfortunate routing between a fast DAC and its opamp,
> >> basically from the opamp output to its inverting input.
> >
> >

On Sat, 17 Dec 2022 17:23:32 -0000 (UTC), Hul Tytus <ht@panix.com>
wrote:

>John, maybe... the capacitence between two 6 mil traces 6 mil apart on the top of a pc board w/ dielectric const. of 4.8
>is calculated at 7.155e-13 farads per inch. This calculation has not yet been verified so the result need be considered a ballpark
>estimate.

I was hiking up to my car, over the freeway after work, and WAG'd 0.6
pf/inch! I probably assumed a lower Er. That makes the minimum
feedback C of my 80 MHz opamp about 1 pF, which is probably OK. We'll
spread the traces a bit anyhow.

> The capacitance of a single 6 mil trace between 2 ground planes 20 mils apart comes to 2.698 pf/inch.

That's embedded stripline. Saturn does that, calculates 3.3 pF/in.

>This sould be equivilent to the sum of 2 distant traces on the top of a board. That I'll check. The calculation came,
>I think, from Analog Device's "Microstrip & Stripline Design", "MT-094 tutorial".
> The sum of these 2 should approximate your answer.
>
>Hul

Did you do the calc by hand? It would be good to have a little
program. I might do one.

Thanks for the help.

>
>
>John Larkin <jlarkin@highland_atwork_technology.com> wrote:
>> On Fri, 16 Dec 2022 20:57:52 -0000 (UTC), Hul Tytus <ht@panix.com>
>> wrote:
>
>> >John, if you'd describe the pair of traces (I can't access dropbox.com directly)
>> >I'll see if I can answer your question.
>> >
>> >Hul
>
>> Cool. Two parallel microstrip traces, each 6 mils wide, with a 6 mil
>> gap between. Ground plane below.
>
>
>> _______ C3 _______
>>
>> C1 C2
>> ___________________________________________
>
>
>> The dielectric is 10 mils thick FR4, between the traces and the ground
>> plane.
>
>> (mils, 0.001 inches!)
>
>> If you can do that easily, it would be interesting to increase the gap
>> to 12 mils. Eventually at large gap C3 goes away and each trace goes
>> to about 1.8 pF per inch.
>
>> Thanks
>
>
>
>
>
>
>
>> >
>> >John Larkin <jlarkin@highland_atwork_technology.com> wrote:
>> >
>> >> Given a pair of parallel run traces on a board, FR4, like this,
>> >
>> >> https://www.dropbox.com/s/2lqnbulsusx3e80/Microstrip_C.jpg?raw=1
>> >
>> >
>> >> There are three capacitances per unit length.
>> >
>> >> Assume w = 6 mils and g = 6 mils and the upper dielectric is 10 mils
>> >> thick, traces to ground. What are the capacitances? I'm not concerned
>> >> with transmission line effects now.
>> >
>> >> The Saturn software says that one trace by itself is 1.8 pf per inch.
>> >> It will also calculate odd and even mode impedances for a differential
>> >> microstrip, but not these capacitances directly.
>> >
>> >> I can find academic papers on this, full of gigantic equations but no
>> >> numbers. I suppose I could write a program to evaluate the equations.
>> >
>> >> I was prowling the net for a calculator but couldn't find one.
>> >
>> >> C3 will be an unfortunate routing between a fast DAC and its opamp,
>> >> basically from the opamp output to its inverting input.
>> >
>> >

John Larkin <jlarkin@highland_atwork_technology.com> wrote in
news:nb1npht2104rimmjq394c41vpn0p9k678h@4ax.com:

> Given a pair of parallel run traces on a board, FR4, like this,
>

I find it hard to believe that you do not have any magnetics software.
Or if you do, are unable to use it right.

How long you been doin' this?

You have analysis software? You must just be missing something in
trying to use it then.

Also, you could try the tried and true ARRL Handbook.

On Sun, 18 Dec 2022 15:41:12 -0000 (UTC),
DecadentLinuxUserNumeroUno@decadence.org wrote:

>John Larkin <jlarkin@highland_atwork_technology.com> wrote in
>news:nb1npht2104rimmjq394c41vpn0p9k678h@4ax.com:
>
>> Given a pair of parallel run traces on a board, FR4, like this,
>>
>
>I find it hard to believe that you do not have any magnetics software.
>Or if you do, are unable to use it right.

Do you have software to solve this case? Please show us.

We've used ATLC to calculate impedances.

https://www.dropbox.com/s/adc5v715xrkusix/Edge_alone_3.jpg?raw=1

It is a mild nuisance to run. I'm not sure if it can do the
3-capacitor calculation.

>
> How long you been doin' this?
>
> You have analysis software? You must just be missing something in
>trying to use it then.
>
> Also, you could try the tried and true ARRL Handbook.

I suspect it wouldn't help here.

This 3-cap microstrip situation is discussed on the web a lot, in a
universally fuzzy hand-waving sort of way. I haven't found a
calculator or even a specific example with numbers.

Maybe I'll write a finite-element solver. I've always wanted to do
one.

Or just hack some cases and graph them and scale/interpolate.

John - putting such calculations into code for the first use takes twice as long
as doing it "by hand" but any further use pays nicely.

Hul

John Larkin <jlarkin@highlandsnipmetechnology.com> wrote:
> On Sat, 17 Dec 2022 17:23:32 -0000 (UTC), Hul Tytus <ht@panix.com>
> wrote:

> >John, maybe... the capacitence between two 6 mil traces 6 mil apart on the top of a pc board w/ dielectric const. of 4.8
> >is calculated at 7.155e-13 farads per inch. This calculation has not yet been verified so the result need be considered a ballpark
> >estimate.

> I was hiking up to my car, over the freeway after work, and WAG'd 0.6
> pf/inch! I probably assumed a lower Er. That makes the minimum
> feedback C of my 80 MHz opamp about 1 pF, which is probably OK. We'll
> spread the traces a bit anyhow.

> > The capacitance of a single 6 mil trace between 2 ground planes 20 mils apart comes to 2.698 pf/inch.

> That's embedded stripline. Saturn does that, calculates 3.3 pF/in.

> >This sould be equivilent to the sum of 2 distant traces on the top of a board. That I'll check. The calculation came,
> >I think, from Analog Device's "Microstrip & Stripline Design", "MT-094 tutorial".
> > The sum of these 2 should approximate your answer.
> >
> >Hul

> Did you do the calc by hand? It would be good to have a little
> program. I might do one.

> Thanks for the help.

> >
> >
> >John Larkin <jlarkin@highland_atwork_technology.com> wrote:
> >> On Fri, 16 Dec 2022 20:57:52 -0000 (UTC), Hul Tytus <ht@panix.com>
> >> wrote:
> >
> >> >John, if you'd describe the pair of traces (I can't access dropbox.com directly)
> >> >I'll see if I can answer your question.
> >> >
> >> >Hul
> >
> >> Cool. Two parallel microstrip traces, each 6 mils wide, with a 6 mil
> >> gap between. Ground plane below.
> >
> >
> >> _______ C3 _______
> >>
> >> C1 C2
> >> ___________________________________________
> >
> >
> >> The dielectric is 10 mils thick FR4, between the traces and the ground
> >> plane.
> >
> >> (mils, 0.001 inches!)
> >
> >> If you can do that easily, it would be interesting to increase the gap
> >> to 12 mils. Eventually at large gap C3 goes away and each trace goes
> >> to about 1.8 pF per inch.
> >
> >> Thanks
> >
> >
> >
> >
> >
> >
> >
> >> >
> >> >John Larkin <jlarkin@highland_atwork_technology.com> wrote:
> >> >
> >> >> Given a pair of parallel run traces on a board, FR4, like this,
> >> >
> >> >> https://www.dropbox.com/s/2lqnbulsusx3e80/Microstrip_C.jpg?raw=1
> >> >
> >> >
> >> >> There are three capacitances per unit length.
> >> >
> >> >> Assume w = 6 mils and g = 6 mils and the upper dielectric is 10 mils
> >> >> thick, traces to ground. What are the capacitances? I'm not concerned
> >> >> with transmission line effects now.
> >> >
> >> >> The Saturn software says that one trace by itself is 1.8 pf per inch.
> >> >> It will also calculate odd and even mode impedances for a differential
> >> >> microstrip, but not these capacitances directly.
> >> >
> >> >> I can find academic papers on this, full of gigantic equations but no
> >> >> numbers. I suppose I could write a program to evaluate the equations.
> >> >
> >> >> I was prowling the net for a calculator but couldn't find one.
> >> >
> >> >> C3 will be an unfortunate routing between a fast DAC and its opamp,
> >> >> basically from the opamp output to its inverting input.
> >> >
> >> >

On Sun, 18 Dec 2022 08:26:12 -0800, John Larkin
<jlarkin@highlandSNIPMEtechnology.com> wrote:

>On Sun, 18 Dec 2022 15:41:12 -0000 (UTC),
>DecadentLinuxUserNumeroUno@decadence.org wrote:
>
>>John Larkin <jlarkin@highland_atwork_technology.com> wrote in
>>news:nb1npht2104rimmjq394c41vpn0p9k678h@4ax.com:
>>
>>> Given a pair of parallel run traces on a board, FR4, like this,
>>>
>>
>>I find it hard to believe that you do not have any magnetics software.
>>Or if you do, are unable to use it right.
>
>Do you have software to solve this case? Please show us.
>
>We've used ATLC to calculate impedances.
>
>https://www.dropbox.com/s/adc5v715xrkusix/Edge_alone_3.jpg?raw=1
>
>It is a mild nuisance to run. I'm not sure if it can do the
>3-capacitor calculation.
>
>
>>
>> How long you been doin' this?
>>
>> You have analysis software? You must just be missing something in
>>trying to use it then.
>>
>> Also, you could try the tried and true ARRL Handbook.
>
>I suspect it wouldn't help here.
>
>This 3-cap microstrip situation is discussed on the web a lot, in a
>universally fuzzy hand-waving sort of way. I haven't found a
>calculator or even a specific example with numbers.
>
>Maybe I'll write a finite-element solver. I've always wanted to do
>one.
>
>Or just hack some cases and graph them and scale/interpolate.

What kind of VNA are you using to tweak these boards?

On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:

> This 3-cap microstrip situation is discussed on the web a lot, in a
> universally fuzzy hand-waving sort of way. I haven't found a
> calculator or even a specific example with numbers.
>
> Maybe I'll write a finite-element solver. I've always wanted to do
> one.

For a stripline, you can just do a two-D solution; instead of Q = charge,
it's K = charge_per_inch, and the C_per_inch = d(K)/dV
with boundary condition being three conductors (two of 'em set
to ground?). That doesn't give three two-wire capacities, though: you have to
do something akin to the delta-wye inversion, I suppose.

On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whit3rd@gmail.com>
wrote:

>On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
>
>> This 3-cap microstrip situation is discussed on the web a lot, in a
>> universally fuzzy hand-waving sort of way. I haven't found a
>> calculator or even a specific example with numbers.
>>
>> Maybe I'll write a finite-element solver. I've always wanted to do
>> one.
>
>For a stripline, you can just do a two-D solution; instead of Q = charge,
>it's K = charge_per_inch, and the C_per_inch = d(K)/dV
>with boundary condition being three conductors (two of 'em set
>to ground?). That doesn't give three two-wire capacities, though: you have to
>do something akin to the delta-wye inversion, I suppose.

One could define a 2d matrix, where each element is the voltage on a
node.

Then define the conductors, with initial voltages. Force ground in a
box around the space. Iterate and see what voltages you get. ATLC does
that but computes txline impedances.

On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
> wrote:
> >On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
> >
> >> This 3-cap microstrip situation is discussed on the web a lot, in a
> >> universally fuzzy hand-waving sort of way. I haven't found a
> >> calculator or even a specific example with numbers.
> >>
> >> Maybe I'll write a finite-element solver. I've always wanted to do
> >> one.
> >
> >For a stripline, you can just do a two-D solution; instead of Q = charge,
> >it's K = charge_per_inch, and the C_per_inch = d(K)/dV
> >with boundary condition being three conductors (two of 'em set
> >to ground?). That doesn't give three two-wire capacities, though: you have to
> >do something akin to the delta-wye inversion, I suppose.
> One could define a 2d matrix, where each element is the voltage on a
> node.
>
> Then define the conductors, with initial voltages. Force ground in a
> box around the space. Iterate and see what voltages you get. ATLC does
> that but computes txline impedances.

Maybe this will do what you want?
https://quickfield.com/advanced/elec2.htm
Unfortunately, they don't make it easy to work out how much it would cost
for a commercial license.
This one is free, but it might take a bit more effort to define the problem.
https://freefem.org/
There are lots of other free finite element modelling packages around that
might also be suitable.

John

On Mon, 19 Dec 2022 15:13:51 -0800 (PST), John Walliker
<jrwalliker@gmail.com> wrote:

>On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
>> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
>> wrote:
>> >On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
>> >
>> >> This 3-cap microstrip situation is discussed on the web a lot, in a
>> >> universally fuzzy hand-waving sort of way. I haven't found a
>> >> calculator or even a specific example with numbers.
>> >>
>> >> Maybe I'll write a finite-element solver. I've always wanted to do
>> >> one.
>> >
>> >For a stripline, you can just do a two-D solution; instead of Q = charge,
>> >it's K = charge_per_inch, and the C_per_inch = d(K)/dV
>> >with boundary condition being three conductors (two of 'em set
>> >to ground?). That doesn't give three two-wire capacities, though: you have to
>> >do something akin to the delta-wye inversion, I suppose.
>> One could define a 2d matrix, where each element is the voltage on a
>> node.
>>
>> Then define the conductors, with initial voltages. Force ground in a
>> box around the space. Iterate and see what voltages you get. ATLC does
>> that but computes txline impedances.
>
>Maybe this will do what you want?
>https://quickfield.com/advanced/elec2.htm
>Unfortunately, they don't make it easy to work out how much it would cost
>for a commercial license.

Their example is almost my exact problem. I might try the limited
student edition, maybe buy the real thing if it looks OK.

The real thing costs 1K to 8K BP's.

>This one is free, but it might take a bit more effort to define the problem.
>https://freefem.org/
>There are lots of other free finite element modelling packages around that
>might also be suitable.
>
>John

On Monday, December 19, 2022 at 4:34:06 PM UTC-8, John Larkin wrote:
> On Mon, 19 Dec 2022 15:13:51 -0800 (PST), John Walliker
> <jrwal...@gmail.com> wrote:
>
> >On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
> >> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
> >> wrote:
> >> >On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
> >> >
> >> >> This 3-cap microstrip situation is discussed on the web a lot, in a
> >> >> universally fuzzy hand-waving sort of way. I haven't found a
> >> >> calculator or even a specific example with numbers.
> >> >>
> >> >> Maybe I'll write a finite-element solver. I've always wanted to do
> >> >> one.
> >> >
> >> >For a stripline, you can just do a two-D solution; instead of Q = charge,
> >> >it's K = charge_per_inch, and the C_per_inch = d(K)/dV
> >> >with boundary condition being three conductors (two of 'em set
> >> >to ground?). That doesn't give three two-wire capacities, though: you have to
> >> >do something akin to the delta-wye inversion, I suppose.
> >> One could define a 2d matrix, where each element is the voltage on a
> >> node.
> >>
> >> Then define the conductors, with initial voltages. Force ground in a
> >> box around the space. Iterate and see what voltages you get. ATLC does
> >> that but computes txline impedances.
> >
> >Maybe this will do what you want?
> >https://quickfield.com/advanced/elec2.htm
> >Unfortunately, they don't make it easy to work out how much it would cost
> >for a commercial license.
> Their example is almost my exact problem. I might try the limited
> student edition, maybe buy the real thing if it looks OK.

You don't need the detailed voltage in space, that's easily approximated. All you
need is to know how much CHARGE is in the electrode to make that voltage, i.e.
you need to know the integral of the field divergence around the electrode. Yeah,
a two-d grid of points is good enough. I'd be surprised if PC epsilon was controlled to
better than 10%.

John Larkin wrote:
> On Mon, 19 Dec 2022 15:13:51 -0800 (PST), John Walliker
> <jrwalliker@gmail.com> wrote:
>
>> On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
>>> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
>>> wrote:
>>>> On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
>>>>
>>>>> This 3-cap microstrip situation is discussed on the web a lot, in a
>>>>> universally fuzzy hand-waving sort of way. I haven't found a
>>>>> calculator or even a specific example with numbers.
>>>>>
>>>>> Maybe I'll write a finite-element solver. I've always wanted to do
>>>>> one.
>>>>
>>>> For a stripline, you can just do a two-D solution; instead of Q = charge,
>>>> it's K = charge_per_inch, and the C_per_inch = d(K)/dV
>>>> with boundary condition being three conductors (two of 'em set
>>>> to ground?). That doesn't give three two-wire capacities, though: you have to
>>>> do something akin to the delta-wye inversion, I suppose.
>>> One could define a 2d matrix, where each element is the voltage on a
>>> node.
>>>
>>> Then define the conductors, with initial voltages. Force ground in a
>>> box around the space. Iterate and see what voltages you get. ATLC does
>>> that but computes txline impedances.
>>
>> Maybe this will do what you want?
>> https://quickfield.com/advanced/elec2.htm
>> Unfortunately, they don't make it easy to work out how much it would cost
>> for a commercial license.
>
> Their example is almost my exact problem. I might try the limited
> student edition, maybe buy the real thing if it looks OK.
>
> The real thing costs 1K to 8K BP's.
>
>
>> This one is free, but it might take a bit more effort to define the problem.
>> https://freefem.org/
>> There are lots of other free finite element modelling packages around that
>> might also be suitable.
>>
>> John
>
>
>

Seems to me that you can work it out from the even and odd mode
impedances and velocities. Works fine for isolated traces.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

On Mon, 19 Dec 2022 16:33:54 -0800, John Larkin
<jlarkin@highland_atwork_technology.com> wrote:

>On Mon, 19 Dec 2022 15:13:51 -0800 (PST), John Walliker
><jrwalliker@gmail.com> wrote:
>
>>On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
>>> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
>>> wrote:
>>> >On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
>>> >
>>> >> This 3-cap microstrip situation is discussed on the web a lot, in a
>>> >> universally fuzzy hand-waving sort of way. I haven't found a
>>> >> calculator or even a specific example with numbers.
>>> >>
>>> >> Maybe I'll write a finite-element solver. I've always wanted to do
>>> >> one.
>>> >
>>> >For a stripline, you can just do a two-D solution; instead of Q = charge,
>>> >it's K = charge_per_inch, and the C_per_inch = d(K)/dV
>>> >with boundary condition being three conductors (two of 'em set
>>> >to ground?). That doesn't give three two-wire capacities, though: you have to
>>> >do something akin to the delta-wye inversion, I suppose.
>>> One could define a 2d matrix, where each element is the voltage on a
>>> node.
>>>
>>> Then define the conductors, with initial voltages. Force ground in a
>>> box around the space. Iterate and see what voltages you get. ATLC does
>>> that but computes txline impedances.
>>
>>Maybe this will do what you want?
>>https://quickfield.com/advanced/elec2.htm
>>Unfortunately, they don't make it easy to work out how much it would cost
>>for a commercial license.
>
>Their example is almost my exact problem. I might try the limited
>student edition, maybe buy the real thing if it looks OK.
>
>The real thing costs 1K to 8K BP's.
>
>
>>This one is free, but it might take a bit more effort to define the problem.
>>https://freefem.org/
>>There are lots of other free finite element modelling packages around that
>>might also be suitable.
>>
>>John
>
>

Quickfield quoted me over $13,000 for the single-seat Electro module.

I assume it would require the usual FlexLM sort of horror to run.

I might lay out a proto board with a few cases, measure, and graph.
Good enough.

On Tue, 20 Dec 2022 10:22:55 -0500, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

>John Larkin wrote:
>> On Mon, 19 Dec 2022 15:13:51 -0800 (PST), John Walliker
>> <jrwalliker@gmail.com> wrote:
>>
>>> On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
>>>> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
>>>> wrote:
>>>>> On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
>>>>>
>>>>>> This 3-cap microstrip situation is discussed on the web a lot, in a
>>>>>> universally fuzzy hand-waving sort of way. I haven't found a
>>>>>> calculator or even a specific example with numbers.
>>>>>>
>>>>>> Maybe I'll write a finite-element solver. I've always wanted to do
>>>>>> one.
>>>>>
>>>>> For a stripline, you can just do a two-D solution; instead of Q = charge,
>>>>> it's K = charge_per_inch, and the C_per_inch = d(K)/dV
>>>>> with boundary condition being three conductors (two of 'em set
>>>>> to ground?). That doesn't give three two-wire capacities, though: you have to
>>>>> do something akin to the delta-wye inversion, I suppose.
>>>> One could define a 2d matrix, where each element is the voltage on a
>>>> node.
>>>>
>>>> Then define the conductors, with initial voltages. Force ground in a
>>>> box around the space. Iterate and see what voltages you get. ATLC does
>>>> that but computes txline impedances.
>>>
>>> Maybe this will do what you want?
>>> https://quickfield.com/advanced/elec2.htm
>>> Unfortunately, they don't make it easy to work out how much it would cost
>>> for a commercial license.
>>
>> Their example is almost my exact problem. I might try the limited
>> student edition, maybe buy the real thing if it looks OK.
>>
>> The real thing costs 1K to 8K BP's.
>>
>>
>>> This one is free, but it might take a bit more effort to define the problem.
>>> https://freefem.org/
>>> There are lots of other free finite element modelling packages around that
>>> might also be suitable.
>>>
>>> John
>>
>>
>>
>
>Seems to me that you can work it out from the even and odd mode
>impedances and velocities. Works fine for isolated traces.
>
>Cheers
>
>Phil Hobbs

I have a little Basic program for single traces, but one input is
effective Er.

Saturn gives c and l for single microstrips.

I have never seen a calculator for my three-capacitor case.

I see a lot of formulas online for trace-trace capacitance, but they
assume that the facing edges of the traces are simple parallel-plate
capacitors in a uniform dielectric. That doesn't feel right to me.

On Tuesday, December 20, 2022 at 6:16:37 PM UTC, John Larkin wrote:
> On Tue, 20 Dec 2022 10:22:55 -0500, Phil Hobbs
> <pcdhSpamM...@electrooptical.net> wrote:
>
> >John Larkin wrote:
> >> On Mon, 19 Dec 2022 15:13:51 -0800 (PST), John Walliker
> >> <jrwal...@gmail.com> wrote:
> >>
> >>> On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
> >>>> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
> >>>> wrote:
> >>>>> On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
> >>>>>
> >>>>>> This 3-cap microstrip situation is discussed on the web a lot, in a
> >>>>>> universally fuzzy hand-waving sort of way. I haven't found a
> >>>>>> calculator or even a specific example with numbers.
> >>>>>>
> >>>>>> Maybe I'll write a finite-element solver. I've always wanted to do
> >>>>>> one.
> >>>>>
> >>>>> For a stripline, you can just do a two-D solution; instead of Q = charge,
> >>>>> it's K = charge_per_inch, and the C_per_inch = d(K)/dV
> >>>>> with boundary condition being three conductors (two of 'em set
> >>>>> to ground?). That doesn't give three two-wire capacities, though: you have to
> >>>>> do something akin to the delta-wye inversion, I suppose.
> >>>> One could define a 2d matrix, where each element is the voltage on a
> >>>> node.
> >>>>
> >>>> Then define the conductors, with initial voltages. Force ground in a
> >>>> box around the space. Iterate and see what voltages you get. ATLC does
> >>>> that but computes txline impedances.
> >>>
> >>> Maybe this will do what you want?
> >>> https://quickfield.com/advanced/elec2.htm
> >>> Unfortunately, they don't make it easy to work out how much it would cost
> >>> for a commercial license.
> >>
> >> Their example is almost my exact problem. I might try the limited
> >> student edition, maybe buy the real thing if it looks OK.
> >>
> >> The real thing costs 1K to 8K BP's.
> >>
> >>
> >>> This one is free, but it might take a bit more effort to define the problem.
> >>> https://freefem.org/
> >>> There are lots of other free finite element modelling packages around that
> >>> might also be suitable.
> >>>
> >>> John
> >>
> >>
> >>
> >
> >Seems to me that you can work it out from the even and odd mode
> >impedances and velocities. Works fine for isolated traces.
> >
> >Cheers
> >
> >Phil Hobbs
> I have a little Basic program for single traces, but one input is
> effective Er.
>
> Saturn gives c and l for single microstrips.
>
> I have never seen a calculator for my three-capacitor case.
>
> I see a lot of formulas online for trace-trace capacitance, but they
> assume that the facing edges of the traces are simple parallel-plate
> capacitors in a uniform dielectric. That doesn't feel right to me.

I believe Clayton Paul's book Analysis of Multiconductor Transmission Lines describes several methods of calculating these capacitances. IIRC Fortran code was provided. I don't have my copy to hand but no doubt it'll be available for download somewhere.

John Larkin wrote:
> On Tue, 20 Dec 2022 10:22:55 -0500, Phil Hobbs
> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>
>> John Larkin wrote:
>>> On Mon, 19 Dec 2022 15:13:51 -0800 (PST), John Walliker
>>> <jrwalliker@gmail.com> wrote:
>>>
>>>> On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
>>>>> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
>>>>> wrote:
>>>>>> On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
>>>>>>
>>>>>>> This 3-cap microstrip situation is discussed on the web a lot, in a
>>>>>>> universally fuzzy hand-waving sort of way. I haven't found a
>>>>>>> calculator or even a specific example with numbers.
>>>>>>>
>>>>>>> Maybe I'll write a finite-element solver. I've always wanted to do
>>>>>>> one.
>>>>>>
>>>>>> For a stripline, you can just do a two-D solution; instead of Q = charge,
>>>>>> it's K = charge_per_inch, and the C_per_inch = d(K)/dV
>>>>>> with boundary condition being three conductors (two of 'em set
>>>>>> to ground?). That doesn't give three two-wire capacities, though: you have to
>>>>>> do something akin to the delta-wye inversion, I suppose.
>>>>> One could define a 2d matrix, where each element is the voltage on a
>>>>> node.
>>>>>
>>>>> Then define the conductors, with initial voltages. Force ground in a
>>>>> box around the space. Iterate and see what voltages you get. ATLC does
>>>>> that but computes txline impedances.
>>>>
>>>> Maybe this will do what you want?
>>>> https://quickfield.com/advanced/elec2.htm
>>>> Unfortunately, they don't make it easy to work out how much it would cost
>>>> for a commercial license.
>>>
>>> Their example is almost my exact problem. I might try the limited
>>> student edition, maybe buy the real thing if it looks OK.
>>>
>>> The real thing costs 1K to 8K BP's.
>>>
>>>
>>>> This one is free, but it might take a bit more effort to define the problem.
>>>> https://freefem.org/
>>>> There are lots of other free finite element modelling packages around that
>>>> might also be suitable.
>>>>
>>>> John
>>>
>>>
>>>
>>
>> Seems to me that you can work it out from the even and odd mode
>> impedances and velocities. Works fine for isolated traces.
>>
>> Cheers
>>
>> Phil Hobbs
>
> I have a little Basic program for single traces, but one input is
> effective Er.
>
> Saturn gives c and l for single microstrips.
>
> I have never seen a calculator for my three-capacitor case.
>
> I see a lot of formulas online for trace-trace capacitance, but they
> assume that the facing edges of the traces are simple parallel-plate
> capacitors in a uniform dielectric. That doesn't feel right to me.
>

It's a 2-D Laplace problem, which you can code up pretty fast--set up a
uniform rectangular grid, draw equipotentials, and sweep through the
array setting the potential at each cell to be the average of its
nearest neighbors. With N conductors, I expect that it would needs
N*(N-1)/2 runs with different boundary conditions to get all the mutual
capacitances, but in complicated situations you could probably prune
that some, based on the configuration.

It converges reasonably fast, especially on modern hardware. You can do
a fair bit better by using successive over-relaxation (SOR). For a
small 2D problem it's hardly worth it.

Cheers

Phil Hobbs

(Who had to code something like this for a second-year undergraduate
lab, using an original Data General Nova.)

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

On Tue, 20 Dec 2022 10:11:00 -0800, John Larkin
<jlarkin@highland_atwork_technology.com> wrote:

>On Mon, 19 Dec 2022 16:33:54 -0800, John Larkin
><jlarkin@highland_atwork_technology.com> wrote:
>
>>On Mon, 19 Dec 2022 15:13:51 -0800 (PST), John Walliker
>><jrwalliker@gmail.com> wrote:
>>
>>>On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
>>>> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
>>>> wrote:
>>>> >On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
>>>> >
>>>> >> This 3-cap microstrip situation is discussed on the web a lot, in a
>>>> >> universally fuzzy hand-waving sort of way. I haven't found a
>>>> >> calculator or even a specific example with numbers.
>>>> >>
>>>> >> Maybe I'll write a finite-element solver. I've always wanted to do
>>>> >> one.
>>>> >
>>>> >For a stripline, you can just do a two-D solution; instead of Q = charge,
>>>> >it's K = charge_per_inch, and the C_per_inch = d(K)/dV
>>>> >with boundary condition being three conductors (two of 'em set
>>>> >to ground?). That doesn't give three two-wire capacities, though: you have to
>>>> >do something akin to the delta-wye inversion, I suppose.
>>>> One could define a 2d matrix, where each element is the voltage on a
>>>> node.
>>>>
>>>> Then define the conductors, with initial voltages. Force ground in a
>>>> box around the space. Iterate and see what voltages you get. ATLC does
>>>> that but computes txline impedances.
>>>
>>>Maybe this will do what you want?
>>>https://quickfield.com/advanced/elec2.htm
>>>Unfortunately, they don't make it easy to work out how much it would cost
>>>for a commercial license.
>>
>>Their example is almost my exact problem. I might try the limited
>>student edition, maybe buy the real thing if it looks OK.
>>
>>The real thing costs 1K to 8K BP's.
>>
>>
>>>This one is free, but it might take a bit more effort to define the problem.
>>>https://freefem.org/
>>>There are lots of other free finite element modelling packages around that
>>>might also be suitable.
>>>
>>>John
>>
>>
>
>Quickfield quoted me over $13,000 for the single-seat Electro module.
>
>I assume it would require the usual FlexLM sort of horror to run.
>
>I might lay out a proto board with a few cases, measure, and graph.
>Good enough.

You might try FEMM

https://www.femm.info/wiki/Download

Or make a simple PCB and measure the C ?

boB

On Tue, 20 Dec 2022 20:52:17 -0500, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

>John Larkin wrote:
>> On Tue, 20 Dec 2022 10:22:55 -0500, Phil Hobbs
>> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>>
>>> John Larkin wrote:
>>>> On Mon, 19 Dec 2022 15:13:51 -0800 (PST), John Walliker
>>>> <jrwalliker@gmail.com> wrote:
>>>>
>>>>> On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
>>>>>> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
>>>>>> wrote:
>>>>>>> On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
>>>>>>>
>>>>>>>> This 3-cap microstrip situation is discussed on the web a lot, in a
>>>>>>>> universally fuzzy hand-waving sort of way. I haven't found a
>>>>>>>> calculator or even a specific example with numbers.
>>>>>>>>
>>>>>>>> Maybe I'll write a finite-element solver. I've always wanted to do
>>>>>>>> one.
>>>>>>>
>>>>>>> For a stripline, you can just do a two-D solution; instead of Q = charge,
>>>>>>> it's K = charge_per_inch, and the C_per_inch = d(K)/dV
>>>>>>> with boundary condition being three conductors (two of 'em set
>>>>>>> to ground?). That doesn't give three two-wire capacities, though: you have to
>>>>>>> do something akin to the delta-wye inversion, I suppose.
>>>>>> One could define a 2d matrix, where each element is the voltage on a
>>>>>> node.
>>>>>>
>>>>>> Then define the conductors, with initial voltages. Force ground in a
>>>>>> box around the space. Iterate and see what voltages you get. ATLC does
>>>>>> that but computes txline impedances.
>>>>>
>>>>> Maybe this will do what you want?
>>>>> https://quickfield.com/advanced/elec2.htm
>>>>> Unfortunately, they don't make it easy to work out how much it would cost
>>>>> for a commercial license.
>>>>
>>>> Their example is almost my exact problem. I might try the limited
>>>> student edition, maybe buy the real thing if it looks OK.
>>>>
>>>> The real thing costs 1K to 8K BP's.
>>>>
>>>>
>>>>> This one is free, but it might take a bit more effort to define the problem.
>>>>> https://freefem.org/
>>>>> There are lots of other free finite element modelling packages around that
>>>>> might also be suitable.
>>>>>
>>>>> John
>>>>
>>>>
>>>>
>>>
>>> Seems to me that you can work it out from the even and odd mode
>>> impedances and velocities. Works fine for isolated traces.
>>>
>>> Cheers
>>>
>>> Phil Hobbs
>>
>> I have a little Basic program for single traces, but one input is
>> effective Er.
>>
>> Saturn gives c and l for single microstrips.
>>
>> I have never seen a calculator for my three-capacitor case.
>>
>> I see a lot of formulas online for trace-trace capacitance, but they
>> assume that the facing edges of the traces are simple parallel-plate
>> capacitors in a uniform dielectric. That doesn't feel right to me.
>>
>
>It's a 2-D Laplace problem, which you can code up pretty fast--set up a
>uniform rectangular grid, draw equipotentials, and sweep through the
>array setting the potential at each cell to be the average of its
>nearest neighbors. With N conductors, I expect that it would needs
>N*(N-1)/2 runs with different boundary conditions to get all the mutual
>capacitances, but in complicated situations you could probably prune
>that some, based on the configuration.
>
>It converges reasonably fast, especially on modern hardware. You can do
>a fair bit better by using successive over-relaxation (SOR). For a
>small 2D problem it's hardly worth it.
>
>Cheers
>
>Phil Hobbs

It would be fun, but the big lift is defining the geometry. ATLC uses
Paint and inputs a colored bitmap.

>
>(Who had to code something like this for a second-year undergraduate
>lab, using an original Data General Nova.)

John Larkin wrote:
> On Tue, 20 Dec 2022 20:52:17 -0500, Phil Hobbs
> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>
>> John Larkin wrote:
>>> On Tue, 20 Dec 2022 10:22:55 -0500, Phil Hobbs
>>> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>>>
>>>> John Larkin wrote:
>>>>> On Mon, 19 Dec 2022 15:13:51 -0800 (PST), John Walliker
>>>>> <jrwalliker@gmail.com> wrote:
>>>>>
>>>>>> On Monday, 19 December 2022 at 17:58:53 UTC, John Larkin wrote:
>>>>>>> On Sun, 18 Dec 2022 20:18:08 -0800 (PST), whit3rd <whi...@gmail.com>
>>>>>>> wrote:
>>>>>>>> On Sunday, December 18, 2022 at 8:26:22 AM UTC-8, John Larkin wrote:
>>>>>>>>
>>>>>>>>> This 3-cap microstrip situation is discussed on the web a lot, in a
>>>>>>>>> universally fuzzy hand-waving sort of way. I haven't found a
>>>>>>>>> calculator or even a specific example with numbers.
>>>>>>>>>
>>>>>>>>> Maybe I'll write a finite-element solver. I've always wanted to do
>>>>>>>>> one.
>>>>>>>>
>>>>>>>> For a stripline, you can just do a two-D solution; instead of Q = charge,
>>>>>>>> it's K = charge_per_inch, and the C_per_inch = d(K)/dV
>>>>>>>> with boundary condition being three conductors (two of 'em set
>>>>>>>> to ground?). That doesn't give three two-wire capacities, though: you have to
>>>>>>>> do something akin to the delta-wye inversion, I suppose.
>>>>>>> One could define a 2d matrix, where each element is the voltage on a
>>>>>>> node.
>>>>>>>
>>>>>>> Then define the conductors, with initial voltages. Force ground in a
>>>>>>> box around the space. Iterate and see what voltages you get. ATLC does
>>>>>>> that but computes txline impedances.
>>>>>>
>>>>>> Maybe this will do what you want?
>>>>>> https://quickfield.com/advanced/elec2.htm
>>>>>> Unfortunately, they don't make it easy to work out how much it would cost
>>>>>> for a commercial license.
>>>>>
>>>>> Their example is almost my exact problem. I might try the limited
>>>>> student edition, maybe buy the real thing if it looks OK.
>>>>>
>>>>> The real thing costs 1K to 8K BP's.
>>>>>
>>>>>
>>>>>> This one is free, but it might take a bit more effort to define the problem.
>>>>>> https://freefem.org/
>>>>>> There are lots of other free finite element modelling packages around that
>>>>>> might also be suitable.
>>>>>>
>>>>>> John
>>>>>
>>>>>
>>>>>
>>>>
>>>> Seems to me that you can work it out from the even and odd mode
>>>> impedances and velocities. Works fine for isolated traces.
>>>>
>>>> Cheers
>>>>
>>>> Phil Hobbs
>>>
>>> I have a little Basic program for single traces, but one input is
>>> effective Er.
>>>
>>> Saturn gives c and l for single microstrips.
>>>
>>> I have never seen a calculator for my three-capacitor case.
>>>
>>> I see a lot of formulas online for trace-trace capacitance, but they
>>> assume that the facing edges of the traces are simple parallel-plate
>>> capacitors in a uniform dielectric. That doesn't feel right to me.
>>>
>>
>> It's a 2-D Laplace problem, which you can code up pretty fast--set up a
>> uniform rectangular grid, draw equipotentials, and sweep through the
>> array setting the potential at each cell to be the average of its
>> nearest neighbors. With N conductors, I expect that it would needs
>> N*(N-1)/2 runs with different boundary conditions to get all the mutual
>> capacitances, but in complicated situations you could probably prune
>> that some, based on the configuration.
>>
>> It converges reasonably fast, especially on modern hardware. You can do
>> a fair bit better by using successive over-relaxation (SOR). For a
>> small 2D problem it's hardly worth it.

>
> It would be fun, but the big lift is defining the geometry. ATLC uses
> Paint and inputs a colored bitmap.

Bumpfiles are super simple, so that's not difficult to reproduce. One
of your Python brethren probably has a library that'll do that part
right off.

For programs that put out pictures, I always just generate bumpfiles and
then call 'convert' from ImageMagick to make whatever more complicated
file type I actually want.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

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