'Ohms per Square'. Huh?

[David G4EBT]

I've see the term 'Ohms per square' used to describe the conductive properties of metallic paint used on valves and for other RF shielding applications. I've never quite understood it - Ohms Per square what? CM, Metre? etc. Surely if one applied the prods an Ohm-meter to either side of say a 2cm square, (4 sq cms that is), the resistance would be less than across a 10cm square. (100 sq cms). The resistance of wire is expressed in Ohm's/Metre - easier enough to grasp, but for me, the term 'Ohms/Sq' goes whoosh over my head.

Any thoughts anyone?

Just curious really - it isn't keeping me awake at night, and it's so expensive that I'm never likely to buy any. On the odd occasions I've felt the need to repair/replace shielding on a valve, I've used silver conductive paint as used for repairing heated car windshield tracks etc. Cheap enough online, and a little bottle goes a long way. I overspray it whatever colour is called for to neaten it up. Silver grey, matt red or whatever.

[Radio Wrangler]

Ah, it's easy!

Any unit of measurement is fine.

If I make a square of material one inch square and connect across one full side, and make the other connection across the other full side. I measure X Ohms. I have 1 inch wide of the resistance material, and whatever the thickness is, and I pass current through 1 inch of length.

So now I make a 1mm square. The width has dropped so the resistance per length ahs gone up pro-rata.... but it's square, so the length has gone down pro rata. The two effects cancel and I'm left with X Ohms again, the same value as before.

Works for a 1 kilometre square or a light year (you may have to wait a while for the ohmmeter to settle).

So any size square comes out the same unless you change the material or the thickness.
What units you use don't matter, what size you make it affects power dissipation versus temperature capability, but not resistance.

BUT notice that you have to connect across a full side all at once. Point contact from a prod doesn't work the same.

David

[LeakyGrid]

'Ohms per Square' is the unit of Sheet Resistance, usually applicable to thin films of uniform thickness. A Google for Sheet Resistance will probably turn up a number of references.

Roger

[GMB]

Slightly off topic, but following on from the point made above...

Given that using prods is way easier than connecting a whole side together with super-conductor (required to get the exact same answer), it raises the question as to what is the conversion that relates the ohms/sq figure with using prods at two points on an infinite area of the stuff?

On thinking about it I have the feeling that it must be a simple constant that doesn't depend on the distance, for a similar reason. If that's true I think that is really interesting.

[GrimJosef]

I haven't worked through the maths but I fear that a problem will arise relating to the contact area of the probe tip. If the area was infinitesimally small then the current density around it would be infinitely large and this would give an infinitely large voltage drop in any material with non-zero resistivity. An infinite voltage and a finite current would correspond to an infinite resistance. It's a bit like asking what happens to the electric potential as you approach a point charge.

In the real world of course all test probes have finite contact areas. But the local current density around them will still be very high and this may contribute significantly to the overall voltage drop and therefore to the overall measured resistance. I suspect, though, that as long as the probe contact area is scaled in proportion to the overall area of the resistive square then you are correct that the conversion constant will be scale-invariant.

As far as establishing a uniform voltage along the whole side of a square is concerned, it's actually not that hard. One way to do it would be to etch a wide gap in the copper coating of a pcb and then to paint a square across the gap. As long as the resistivity of the copper was much lower than that of the paint (and if it wasn't you could solder a length of wire onto the copper close to and parallel to the edge) any voltage variations in the copper should be negligible.

If I remember correctly resistive paint and resistive paper (cut to shape with scissors) could be and were used for EM field modelling in complicated 2-D geometries.

Cheers,

GJ

[woodchips]

That is a coincidence. Just last evening I found a couple of Servomex Field Plotters which I think are for plotting flow lines using Teledeltos (?) conductive paper.

Gazing soulfully at one of them wondering where on earth you buy Teledeltos paper, and are they any use now anyway. Isn't all this done mathematically now?

Took a few hours to remember the name of the paper, not quite on the tip of the tongue!

[kalee20]

Originally Posted by GrimJosef

I haven't worked through the maths but I fear that a problem will arise relating to the contact area of the probe tip. If the area was infinitesimally small then the current density around it would be infinitely large and this would give an infinitely large voltage drop in any material with non-zero resistivity. An infinite voltage and a finite current would correspond to an infinite resistance.

My thoughts exactly - but the infinite current density only applies for an infinitesimally small radial distance from the point-contact. So you could still end up with a finite answer. Definitely have to try the maths...

Originally Posted by woodchips

Gazing soulfully at one of them wondering where on earth you buy Teledeltos paper

Try £24 for 10 sheets here.

[David G4EBT]

Thanks everyone for your input and explanations. The penny has now dropped!

The sort of stuff I had in mind has very low resistance and high conductivity. I first noted the term 'Ohms per square'. I came across it when I was searching internet to see if there was a sensibly priced RF shielding paint or spray for renovating valves that have lost all or part of their metalising. As I suspected, there isn't, or if there is, I've not found it. Lot's of stuff available, but not really to fit our pockets or in small quantities.

Here's an example of a product in which the resistance is expressed in Ohms/Sq and is said to be no greater than 0.066 Ohms/Sq. It also states the conductivity in 'Siemens'. (I won't ask!):

Quote:

Super Shield™ Silver Conductive Coating 842:

The 842 Silver Conductive Coating is a very highly conductive acrylic paint designed to reduce electromagnetic or radio frequency interference (EMI/RFI). Long-term protection from EMI/RFI is assured by its durable acrylic resin that minimizes loss of metallization through rubbing, and by the oxidation resistant silver that slows down conductivity degradation with age. The flake shape helps ensure maximum points of contact to ensure better conductivity. In addition, loss of shielding through paint peeling is unlikely since the acrylic resin system was shown, in UL related testing, to adhere to even difficult substrates like ABS and polycarbonates.

High Conductivity (≥15 Siemen)—Low Surface resistance of ≤0.066 Ω/sq for a 1 mil coat
Tough and durable coating
Rub off resistant
Corrosion resistant coating
Stronger adhesion than water based coatings
Low VOC’s
Median attenuation 75 dB ±20 dB per 25.4 μm (~1.0 mil) for frequency range of 10 MHz to 18 GHz

End quote.

See: http://www.mgchemicals.com/products/....mPyY3UYh.dpuf

[Dave Moll]

Siemens correctly pronounced [ˈziːmɛns] (or more prosaically, "zeemens") is the SI unit of electrical conductance.

[Radio Wrangler]

Formerly known as the 'Mho' the reciprocal of resistance.

David