What is the resistance of a typical PCB?

Question

What is the typical resistance between two points on a "typical" PCB? Let's say the points are 1mm apart and let's assume a normal office environment.

I've noticed that resistors come in many values, but resistors larger than 10 megaohm are rare or hard to find.

I suppose that a circuit with a 10 gigaohm resistor would be kind of sensitive and probably not a good design (under "normal" circumstances).

Is it somehow understood that resistances more than 10 megaohm would be too affected by electrolytes in the form of grime, pollution and moisture? Or is there some other reason >10 megaohm resistor parts are so rarely used? Noise perhaps?

Edit: It seems my question is partly resting on a false premise. Apparently >10 megaohm resistors aren't that hard to source. I was looking at surface mount thin film resistors at Farnell (www.farnell.com), and those only go to 10 megaohm. But I see now that there are "thick film" resistors above 10 gigaohm.

Answer 1

The resistance between any two points is infinite.

In the real world, you can't make a true point contact. It will always have some diameter or other finite dimensions. Those dimensions relative to the separation distance are required to determine the resistance between, given the resistivity of the material.

Let's say your "points" really have 1 mm edges facing each other, and that the separation is also 1 mm. Consider how the resistance would change if those edges were instead 1/2 mm. You can think of the original set of points of being made up of two of these smaller ones in parallel. This means the resistance between the 1/2 mm edges would be twice that as between the 1 mm edges, all else being held the same.

Now consider what happes when you move the original 1 mm points farther apart, to 2 mm. You can now think of this new configuration as being two of the previous in series, so must have twice the resistance as the original.

The relative geometry matters. Hopefully you can see by now that as the "points" are shrunk smaller and smaller, the resistance goes up. When they become infinitely small true points, the resistance is infinite.

So how do you quantify all this? Consider doubling everything about the original configuration so that you now have 2 mm edges separated by 2 mm. Each 1 mm slice looks like two of the original in series, so twice the resistance. However, you have two of these slices in parallel, so that doubled resistance is halved again, getting you back to the original value. In fact, for uniform surface conductivity on a infinite plane (or close enough, a PC board much larger that the dimensions of your test area), the resistance stays the same when all the linear dimensions are scaled uniformly.

This is why surface resistivity is usually quoted in Ohms per square. That would be two 1 mm edges separated by 1 mm, two 7.3 mm edges separated by 7.3 mm, etc. As long as you measure the resistance between opposite sides of a square, you will get the same answer regardless of the size of that square.

Well made and clean PC boards can have surface resistivity in the 10s of GΩ per square. It goes down from there with moisture, accumulated dirt, and poor PCB fab processes that leave ions on the surface or in the mix. Solder mask helps with this for traces that can be covered, but surface dirt accumulation will be a long term problem for anything not covered. This is the main reason for large creapage distance requirements where even small leakage currents can be a problem, like in patient-touching medical equipment.

Answer 2

A clean PTFE circuit board could be as high as 10^17 ohms between a couple small pads spaced by a mm or two. If the board has contamination (especially ionic contamination) it could be much less. A clean FR board should be > 10G ohms. If you really need high impedance for fA measurements, PTFE standoffs or air connections are better than FR4.

You can buy a 5G 1% SMT resistors from Digikey (plenty in stock and only a few dollars), and up to 25G with 10% tolerance.

If you're using a 10M resistor and want to maintain 0.1% tolerance (e.g. for a DMM input divider) that means that the board resistance certainly can't be less than 10G ohms.

Edit: Unless you really need to have high impedances, it's best to stick to 1M ohm maximum. G-ohm resistances and nA or fA leakages demand heroic precautions including cleanliness (standoffs, air connections) and may well have issues outside a clean dry lab environment (or even long-term in a lab environment).