EEVblog Electronics Community Forum
EEVblog => EEVblog Specific => Topic started by: EEVblog on April 10, 2015, 09:32:21 am
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Fundamentals Friday
What is Sheet Resistance?
Did you know that the resistance of a square copper PCB trace is the same regardless of the size?
Dave explains the theory behind this rather counter-intuitive concept called Sheet Resistance, and demonstrates that it is in fact true.
What is the ohms per square of 1oz copper-clad PCB material and how can you use this concept to calculate the resistance of a PCB trace?
Thin Film Precision Resistor Network video: https://www.youtube.com/watch?v=Rxy-VpSDPg4 (https://www.youtube.com/watch?v=Rxy-VpSDPg4)
EEVblog #732 - PCB Sheet Resistance (https://www.youtube.com/watch?v=ME4Xe53TMxI#ws)
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Nice video Dave, I work with sheet resistances almost every day, so nothing new for me, however I would have loved to see you attempt to measure the PCBs instead ;)
Don't you have a constant current source which can give a few amps and then a multimeter with sub uV resolution?Maybe an excuse for using the Keithley or Keysight DMMs?
I am guessing that you would get reasonable values by soldering a thick copper wire along the entire length of the side of the PCB connected to the current source, then an extra sens-wire to the DMM.
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I am guessing that you would get reasonable values by soldering a thick copper wire along the entire length of the side of the PCB connected to the current source, then an extra sens-wire to the DMM.
Perhaps, but I wasn't keen to try, I think the results would be quite muddy.
Would have been nice to have some nichrome sheet.
I had another idea to demo it, but would have required a lot of prep work.
The foam was quick and effective I think.
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Does that "black conductive foam for ICs" have a name?
Can it be found and purchased on Digi-Key or Farnell?
Many thanks.
EDIT:
Conductive antistatic mat (says in the video, sorry)
Is this it? http://export.farnell.com/vermason/l250622/mat-foam-high-density/dp/175847 (http://export.farnell.com/vermason/l250622/mat-foam-high-density/dp/175847)
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What is the difference between conductive and dissipative? I know this was mentioned in some video but I can't recall.
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Does that "black conductive foam for ICs" have a name?
Can it be found and purchased on Digi-Key or Farnell?
Many thanks.
EDIT:
Conductive antistatic mat (says in the video, sorry)
Is this it? http://export.farnell.com/vermason/l250622/mat-foam-high-density/dp/175847 (http://export.farnell.com/vermason/l250622/mat-foam-high-density/dp/175847)
Yes, http://au.element14.com/static-protection_foam (http://au.element14.com/static-protection_foam)
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Why is the DURATOOL so expensive?
100$ DURATOOL
1.6$ MULTICOMP
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I am guessing that you would get reasonable values by soldering a thick copper wire along the entire length of the side of the PCB connected to the current source, then an extra sens-wire to the DMM.
Perhaps, but I wasn't keen to try, I think the results would be quite muddy.
...
I took your statement as a challenge, I hope you don't mind ;)
With just handheld multimeters and a homebuilt power supply I had at home, I decided to prove that it would not be hard to measure the resistance of the square of copper on a PCB (0.036 mm thick). However I did not have any empty PCBs at home so I had to use an even more difficult "sample". A sheet of 0.1 mm thick pure Silver, which would have only ca. 30 % of the resistance as the PCB! :-+
0.0001 m thick Silver with a resistivity of 15.87 [nOhm m] would have a sheet resistance of only 0.0001587 Ohm/sq, that is only 158.7 uOhm/sq.!
Challenge Accepted!
(https://www.eevblog.com/forum/blog/eevblog-732-pcb-sheet-resistance/?action=dlattach;attach=146464)
I made a 17 mm by 17 mm square of the Silver sheet and soldered a 0.75 sq.mm copper cable along the length of two sides. Then I soldered thinner sense wires on the opposite side of the sheet (important to solder them directly to the Silver and not the copper wire, in order to eliminate the resistance from the solder joint).
(https://www.eevblog.com/forum/blog/eevblog-732-pcb-sheet-resistance/?action=dlattach;attach=146466)
I used my Fluke 289 which has 1 uV resolution for the sense-wire measurement (zeroed the reading first, I had an offset of 4 uV), and I then used my Fluke 179 for the current reading.
(https://www.eevblog.com/forum/blog/eevblog-732-pcb-sheet-resistance/?action=dlattach;attach=146468)
And the final results:
(https://www.eevblog.com/forum/blog/eevblog-732-pcb-sheet-resistance/?action=dlattach;attach=146470)
Calculation:
0.001535 V / 9.86 A = 0.0001557 Ohm. = 155.7 uOhm/sq.
Compare that to the theoretical 158.7 uOhm/sq., less than a 2 % error with only very crude tools and a quick and dirty soldering job. :-+
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Compare that to the theoretical 158.7 uOhm/sq., less than a 2 % error with only very crude tools and a quick and dirty soldering job. :-+
Nice work, better than I expected.
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So, using this formula every time you double the width of your PCB trace since you are modifying the ratio of trace length/width, you are dividing the resistance of your trace in half?
At least until the point where the width of the trace is larger than the length and then you start going in the opposite direction.
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be careful with things like sheet resistance.
that is only true for DC and relatively low currents.
once you start playing with higher currents they will not utilise the entire area but run in a bundle.
the same goes for high frequency signals. above 100khz they start coupling into an underlying plane pretty good.
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Robert Murray-Smith has made a nice block just checking square conductance.
http://youtu.be/1M9EhLTmNoQ?t=1m44s (http://youtu.be/1M9EhLTmNoQ?t=1m44s)
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Very interesting episode. Thanks.
BTW, I didn't expect that black foam to be so conductive.
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Very interesting episode. Thanks.
BTW, I didn't expect that black foam to be so conductive.
Well, it has to be and making it resistive isn't too hard since all they have to do is take some sponge and spray some graphite paint on it.
Much like they do with antistatic bags, they just mix some graphite into the plastic and Bob's your uncle.
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be careful with things like sheet resistance.
that is only true for DC and relatively low currents.
once you start playing with higher currents they will not utilise the entire area but run in a bundle.
the same goes for high frequency signals. above 100khz they start coupling into an underlying plane pretty good.
To my knowledge this is not true, all thin film resistors are sheets of conductive metal, and they are good for high currents and high frequencies?! As long as the thickness of the sheet is less than the skin depth for the particular frequency you are using, then there should be no problem.
Do you know of any particular application where there would be a problem using sheet resistance instead of resistivity and also specifying the thickness?
Or maybe you are confusing it with surface resistivity? It also has the unit of ohm/sq. but is mostly used for "almost" insulating materials where migration of electrons on the surface is higher than inside the material, e.g. due to adsorbed water or some other aspect.
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Take a 20cm x 20 cm square of 4 ounce copper foil. Connect on diagonally opposite corners. Send 50 ampere.
The current densitiy is not uniform. the outlying tips conduct much less current than the 'line' connecting the corners.
you can check with a IR camera. the outlying tips run cooler than the centerline.
electrons tend to run in straight lines.
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Take a 20cm x 20 cm square of 4 ounce copper foil. Connect on diagonally opposite corners. Send 50 ampere.
The current densitiy is not uniform. the outlying tips conduct much less current than the 'line' connecting the corners.
you can check with a IR camera. the outlying tips run cooler than the centerline.
electrons tend to run in straight lines.
Thus the requirement for connections running the full length of the board.
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Very nice video and great explanation.
Great idea with the black foam to prove a point.
Your Keithley DMM7510 and your Keysight 34470A would have been great tools to measure the uV across the copper clad.
In "Trend Chart" mode you should even be able to see a noticeable change by laying your hand on to the copper surface.
I think I will give this a try with my 34470A.
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Connect on diagonally opposite corners.
Well, there's your problem.
The current densitiy is not uniform. the outlying tips conduct much less current than the 'line' connecting the corners.
Correct me if I'm wrong, but isn't the current density non-uniformity pattern independent of the current, unlike the skin depth which varies with "its" parameter (frequency)? If anything, a bigger current should in practice make the current density slightly more uniform, as the center heats up and increases its resistance slightly, encouraging more of the current to take an outer path.
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Point contacts instead of a line of ideally zero resistance, transforms from a uniform sheet to one where current density varies according to the distance normal to the line connecting the points. If you have the 50A connected to the ends of the sheet with either a busbar ( lower resistance than the copper foil as it is thicker) or with multiple vias to a top busbar or cable then you get a better approximation.
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A sheet of metal can be seen as a grid of identical resistors like in the picture below.
It behaves exactly like a sheet of conductive material.
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Wouldn't a bunch of wires of the same length soldered along the edges be adequate terminals? I assume 10-20 wires per side are a good enough approximation of an edge contact.
I'd also love to see Dave pay some nearby physics department a visit where they can deposit superconductors and do cryogenic measurements.
oh, and by the way ... (https://xkcd.com/356/)
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Nice video. As I was watching it, I realized I was wearing the same shirt. This is nerd heaven.
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Hey Dave, +1 for Fundamental Friday! Do it again!
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Not only true for PCB's but the same fundamentals apply inside on the chips. Designing IC's we run across sheet Rho all the time. In fact the resistivity and capacitance that is associated with any conductive element dominates many of the IC design exercises (digital timing or analog analysis). Great fundamental and appreciate the effort.
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Reminds me of an exam question - take a 1 metre diameter circular piece of a material of 1 ohm/cm2. What is the resistance across two point contacts placed on its surface?
It's one of those questions. No points for trying to hit it head on with mathematics. some points for noticing that there doesn't seem to be enough information in the question for an answer - although you might get unsure if you remember that resistance across a square of a conductor is invariant wrt size.
You win if you spot that theoretical points have no area, so will have infinite resistance no matter what you do with them. (You can also get there with the maths, but it will hurt and you will cry.)
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Do larger sheets handle more wattage? 1/4 of a larger sheet 1/4 the watts?
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Do larger sheets handle more wattage? 1/4 of a larger sheet 1/4 the watts?
Basically, yes, exactly. More pedantically, if sheet B is twice as wide and twice as long as sheet A, sheet B will have almost four times the current handling capacity of sheet A (for a given temperature rise). Why not exactly four times? Because the edge of the sheet has slightly better ventilation that the center areas, which are surrounded by hot metal on all sides. The larger sheet has a smaller perimeter-to-area ration, so not quite as good at rejecting heat per unit area.