Estimating PC pad capacitance?

[Tom Bruhns]

Anyone have any favorite reasonably accurate applets or formulas or
the like for calculating the capacitance of a small rectangular
surface against an extensive ground plane? That is, for example, the
capacitance of the pad for a surface-mount part, where there's a
ground plane about 1.5mm behind the pad, through FR4 PC board
material, er about 4.5.

I have a clue that the fringing effects for small pads is significant,
in that I can use a simple-minded calculator that only uses the plate
area for a cap with two equal size plates, and doesn't consider
fringing effects, and get one value -- and then look at the pad as if
it were a short section of microstrip transmission line, calculate the
capacitance per unit length of that geometry line, and multiply by the
length of the pad to get an estimate of the pad capacitance. For one
example get about two times higher capacitance than the "dumb" plate
area/separation applet gives. Given that there is additional fringing
for the pad versus what's considered in the microstrip, I suppose the
actual capacitance is even higher.

I know there are full-blown geometry calculators, some available for
free, but I'm hoping for something simpler to use, along the lines of
typical microstrip applets where you enter length, width, dielectric
thickness, pad thickness, and dielectric relative permittivity, and an
answer with perhaps 10% accuracy pops out.

Cheers,
Tom

 

[John Larkin]

Anyone have any favorite reasonably accurate applets or formulas or
the like for calculating the capacitance of a small rectangular
surface against an extensive ground plane? That is, for example, the
capacitance of the pad for a surface-mount part, where there's a
ground plane about 1.5mm behind the pad, through FR4 PC board
material, er about 4.5.

I have a clue that the fringing effects for small pads is significant,
in that I can use a simple-minded calculator that only uses the plate
area for a cap with two equal size plates, and doesn't consider
fringing effects, and get one value -- and then look at the pad as if
it were a short section of microstrip transmission line, calculate the
capacitance per unit length of that geometry line, and multiply by the
length of the pad to get an estimate of the pad capacitance. For one
example get about two times higher capacitance than the "dumb" plate
area/separation applet gives. Given that there is additional fringing
for the pad versus what's considered in the microstrip, I suppose the
actual capacitance is even higher.

I know there are full-blown geometry calculators, some available for
free, but I'm hoping for something simpler to use, along the lines of
typical microstrip applets where you enter length, width, dielectric
thickness, pad thickness, and dielectric relative permittivity, and an
answer with perhaps 10% accuracy pops out.

Cheers,
Tom

It would be handy to have a graph of c versus size for, say, square
pads at a unit distance above a ground plane, namely a fringing graph.

If you google "fringing" it's usually preceded by the word
"neglecting."

John

 

[Tom Bruhns]

It would be handy to have a graph of c versus size for, say, square
pads at a unit distance above a ground plane, namely a fringing graph.

If you google "fringing" it's usually preceded by the word
"neglecting."

John

Yes, good idea, John. If I don't find the simple applet I'm looking
for, maybe I can make such a graph. I do have applications that can
do the calculation accurately, and if I fire one up to make one calc,
it should be fairly easy to just change the pad size and run it for a
range of sizes. I'd probably do it for not only square but for
perhaps 1.2:1, 1.5:1 and 1:2 ratio rectangles too.

Cheers,
Tom

 

[John Larkin]

Yes, good idea, John. If I don't find the simple applet I'm looking
for, maybe I can make such a graph. I do have applications that can
do the calculation accurately, and if I fire one up to make one calc,
it should be fairly easy to just change the pad size and run it for a
range of sizes. I'd probably do it for not only square but for
perhaps 1.2:1, 1.5:1 and 1:2 ratio rectangles too.

Cheers,
Tom

If you do that, I'd love to get a copy.

John

 

[Joerg]

If you do that, I'd love to get a copy.

Sorry if this spoils the fun with Maxwell's equations:
http://www.mentor.com/products/pcb/pads/techpubs/index_noflash.cfm?baseurl=

Scroll down to "Pad Capacitance Extraction for IBIS Models", select and
request the paper at the bottom. But check whether they charge for it.

John, if there is a charge maybe they give you access to that for free
since you are a PADS customer.

 

[Tom Bruhns]

Sorry if this spoils the fun with Maxwell's equations:http://www.mentor.com/products/pcb/pads/techpubs/index_noflash.cfm?ba...

Scroll down to "Pad Capacitance Extraction for IBIS Models", select and
request the paper at the bottom. But check whether they charge for it.

John, if there is a charge maybe they give you access to that for free
since you are a PADS customer.

Well, it's not Maxwell's equations I'm using directly, but ADS, to do
what the abstract for the paper you reference suggests. I just put an
ideal 1uH inductor in series with 50 ohms to a pad whose size I can
vary easily, and look for the resonance, indicated by a sharp dip in
S11. It's just a bit tedious. It does suggest that even with a pad
an inch square on 1/16-inch thick FR4, the fringing is still a
moderately significant effect. I got sidetracked and didn't finish
the work today. Maybe next week.

Cheers,
Tom

 

[Fred Bartoli]

Tom Bruhns a écrit :

Well, it's not Maxwell's equations I'm using directly, but ADS, to do
what the abstract for the paper you reference suggests. I just put an
ideal 1uH inductor in series with 50 ohms to a pad whose size I can
vary easily, and look for the resonance, indicated by a sharp dip in
S11. It's just a bit tedious. It does suggest that even with a pad
an inch square on 1/16-inch thick FR4, the fringing is still a
moderately significant effect. I got sidetracked and didn't finish
the work today. Maybe next week.

Cheers,
Tom

Tom,

what I'd try is to adapt the microstrip formula.

With the ustrip you get the fringing correction value along the
perimeter of your square pad. I'll be twice the value of the ustrip line
of your pad width. Then you'd have to correct for the 'corner effect',
which we can assume to be reasonably constant, given your pad width is
sufficiently larger than the plane-pad separation. You just have to
evaluate this corner effect with a solver, for a few height of interest
and maybe add a curve fitting there for fanciness and voilà.

 

[Joerg]

Tom Bruhns a écrit :


Tom,

what I'd try is to adapt the microstrip formula.

With the ustrip you get the fringing correction value along the
perimeter of your square pad. I'll be twice the value of the ustrip line
of your pad width. Then you'd have to correct for the 'corner effect',
which we can assume to be reasonably constant, given your pad width is
sufficiently larger than the plane-pad separation. You just have to
evaluate this corner effect with a solver, for a few height of interest
and maybe add a curve fitting there for fanciness and voilà.

Possibly. Initially I thought to post a microstrip link but it won't
take the corner distortion into effect. Anyhow, for microstrip this can
help:
http://www.emclab.umr.edu/pcbtlc2/index.html

And here is a collection of FEM routines and field solvers:
http://www.emclab.umr.edu/codes.html

 

[joseph2k]

Anyone have any favorite reasonably accurate applets or formulas or
the like for calculating the capacitance of a small rectangular
surface against an extensive ground plane? That is, for example, the
capacitance of the pad for a surface-mount part, where there's a
ground plane about 1.5mm behind the pad, through FR4 PC board
material, er about 4.5.

I have a clue that the fringing effects for small pads is significant,
in that I can use a simple-minded calculator that only uses the plate
area for a cap with two equal size plates, and doesn't consider
fringing effects, and get one value -- and then look at the pad as if
it were a short section of microstrip transmission line, calculate the
capacitance per unit length of that geometry line, and multiply by the
length of the pad to get an estimate of the pad capacitance. For one
example get about two times higher capacitance than the "dumb" plate
area/separation applet gives. Given that there is additional fringing
for the pad versus what's considered in the microstrip, I suppose the
actual capacitance is even higher.

I know there are full-blown geometry calculators, some available for
free, but I'm hoping for something simpler to use, along the lines of
typical microstrip applets where you enter length, width, dielectric
thickness, pad thickness, and dielectric relative permittivity, and an
answer with perhaps 10% accuracy pops out.

Cheers,
Tom

Not speaking for anyone else it sounds like simple paper and pencil from
basic physics is the fastest approach. Get your answer, optionally
including fringing, in less time than firing up and inputting the geometry
into a program.

 

[Tom Bruhns]

Not speaking for anyone else it sounds like simple paper and pencil from
basic physics is the fastest approach. Get your answer, optionally
including fringing, in less time than firing up and inputting the geometry
into a program.

Hi Joseph,

Thanks for your posting. At the very least, it's gotten me thinking
more deeply about the calculation, which is of a sort I seldom need to
deal with.

I suppose I could assume the charge is distributed uniformly over a
rectangular surface, and get an approximation of the capacitance, and
compare that for a few cases against a numerical fields solver to see
what error there is. Did you have in mind anything more complicated
than the assumption of uniform charge distribution? I'm pretty sure
that there are cases where that won't be very accurate.

Once I decided to do it, it wasn't difficult to fire up ADS and get it
to run the calcs for me. It's certainly faster than _I_ could do it
with paper and pen.

But seriously, I'd be happy to know if there's something I'm missing
about doing it with a simple calculation.

Cheers,
Tom

 

[Tom Bruhns]

Tom Bruhns a écrit :






Tom,

what I'd try is to adapt the microstrip formula.

With the ustrip you get the fringing correction value along the
perimeter of your square pad. I'll be twice the value of the ustrip line
of your pad width. Then you'd have to correct for the 'corner effect',
which we can assume to be reasonably constant, given your pad width is
sufficiently larger than the plane-pad separation. You just have to
evaluate this corner effect with a solver, for a few height of interest
and maybe add a curve fitting there for fanciness and voilà.

Thanks for the ideas, Fred. I thought some about that, but actually,
now that I have ADS set up to do it for me, it's no trouble to put in
any particular pad size, thickness, and dielectric constant. And in
surface-mount work, I am often dealing with pads whose dimensions are
similar to or smaller than the separation to the ground plane.

Cheers,
Tom

 

[John Larkin]

Not speaking for anyone else it sounds like simple paper and pencil from
basic physics is the fastest approach. Get your answer, optionally
including fringing, in less time than firing up and inputting the geometry
into a program.

Suppose we have a 62 mil square pad on a 62 mil thick FR-4 pcb with
ground plane on the far side. How would you go about computing total
pad capacitance (including to the air) with pencil and paper?

John

 

[Rich Grise]

Not speaking for anyone else it sounds like simple paper and pencil from
basic physics is the fastest approach. Get your answer, optionally
including fringing, in less time than firing up and inputting the geometry
into a program.

Suppose we have a 62 mil square pad on a 62 mil thick FR-4 pcb with
ground plane on the far side. How would you go about computing total
pad capacitance (including to the air) with pencil and paper?[/QUOTE]

I'd measure the capacitance, get out the lab notebook, and write down the
answer. ;-)

Cheers!
Rich

 

[Fred Bartoli]

Rich Grise a écrit :

I'd measure the capacitance, get out the lab notebook, and write down the
answer. ;-)

Doing this is certainly even not an easy task. I mean measure the
capacitance

 

[Marra]

The cheap little AADE cap-meter is great for 2-wire stuff like this.
It resolves 10 fF.

If somebody posts a prediction, I'll confirm it with a measurement.

John

The word negligible comes to mind at 1.5mm
If your having problems I would look elsewhere.

 

[John Larkin]

Rich Grise a écrit :

Doing this is certainly even not an easy task. I mean measure the
capacitance

The cheap little AADE cap-meter is great for 2-wire stuff like this.
It resolves 10 fF.

If somebody posts a prediction, I'll confirm it with a measurement.

John

 

[John Larkin]

The word negligible comes to mind at 1.5mm
If your having problems I would look elsewhere.

It's about 0.06 pF without fringing, so may get up towards 0.1 pF
with. Sometimes that matters. With thinner dielectrics, like on a
multilayer, c will go up but fringing will be somewhat less.

John

 

[joseph2k]

Suppose we have a 62 mil square pad on a 62 mil thick FR-4 pcb with
ground plane on the far side. How would you go about computing total
pad capacitance (including to the air) with pencil and paper?

John

In some cases, like yours, the typical basic equation c=e'e(r)A/d fails to
give better than correct order of magnitude. It includes the usually
unstated assumption that A >>> d^2. For various symmetrical cases for A >=
3*d^2 the fringing can be shown to be equivalent to the base equation. For
cases like yours where A~=d^2 obtaining C from the work equation can be
made to do but the time required quickly becomes more than using a finite
element solver. I am not usually pushing the dimensions quite that hard.

Just the same, i am glad that i had the limitations of my usual methods
pointed out to me, and even happier that i got others to step back and
re-check the limits of their typical practices as well.

 

[Fred Bartoli]

John Larkin a écrit :

The cheap little AADE cap-meter is great for 2-wire stuff like this.
It resolves 10 fF.

If somebody posts a prediction, I'll confirm it with a measurement.

I wasn't speaking of measurement instrument capabilities, I can easily
get down to the fF, but rather meant: how do you measure it without
introducing perturbations, i.e. field modification with your probe,
wire, whatever...?

At this pad size I guess you can't neglect this anymore.

The true test would be a check between a field solver and a careful
measurement, but we also need to accurately measure Er.

 

[MassiveProng]

It's about 0.06 pF without fringing, so may get up towards 0.1 pF
with. Sometimes that matters. With thinner dielectrics, like on a
multilayer, c will go up but fringing will be somewhat less.

John

We used an embedded pad on our HV circuits (those that needed it) to
achieve a feed forward effect on our feedback loop. It was in
parallel with our HV feedback resistor voltage divider network.

It gave us about 15 pF for a quarter inch wide pad at about just
under an inch length. One "plate" was embedded, and the other was top
side. Of course where in the embedding makes a huge difference for,
as we all know, plate proximity distance directly affects capacitance
achieved.