Resistors: Composition, Tolerance, and Noise

[343 Salty Beans]

About 45 minutes ago I was sitting in my really boring sociology class (every class is a 2 hour lecture  ), and was pondering the whole 'metal-film is the best craze.' It's generally agreed that metal film resistors create less noise than carbon film or carbon comp resistors. Since there's a bunch of engineers and smart guys in here who seem to agree, I was wondering what causes the noise. Is it:

a)  carbon film or carbon comp resistors have more leakage than metal film?

or

b) tolerances? By tolerance, carbon film resistors have 5% differences. a resistor labeled 100K that is only 95K might have enough of an effect on the circuit to where too much voltage may be getting where it's not supposed to be. With 1% tolerance, a 100K metal film resistor that's actually only 99K wouldn't have as much of an effect?

[R.G.]

It's neither one.

A resistor IS a leakage. One can't have more leakage than another of the same value. And tolerance is merely a measure of what the exact resistance is, not whether only part of the material is using the voltage.

It's the material and the construction.

Every material has a property called its resistivity. If you take a solid, rectangular block of the material of dimensions L, W, and H, and measure the resistance, you will always come up with R = L/(W*H) times some constant. That constant is the specific resistivity of the material, called "rho". For all resistors of that material, R = rho*L/A.

So I want to make a resistor. No problem, I just take a block of stuff the right size and I got it. But what if I want to make a whole range of resistors and have them all be the same size for the same power dissipation? Ooops... I'm changing the size, and hence the power dissipation ability to make them different resistances. They can't all be the same size.

They can if you work out a way to use more or less material inside the resistor body in a more or less diffuse manner. Carbon composition resistors are made of a dispersion of carbon particles in a settable gook which is poured into a cylindrical body. The size of the body sets the power rating, and the density of the carbon in the gook sets the resistance up to the point that it's pure carbon. The granules of carbon only contact each other intermittently inside the gook, so the path an electron takes inside is tortuous and long. If there are few granules, it's a long, skinny path. If there are many granules, there are many, fat paths.

And that's what the industry standardized on, and they worked and worked and worked to make them perfect. The problem is, they could not be perfect. Carbon granules touching only at a few points have intermittent contacts that cause excess noise, over and above the thermal noise that is a inescapable property of the physics of resistance. So carbon comp has both thermal noise and excess noise because of the way they're made.

Metal film has only thermal noise, because the resistor is a continuous film of metal alloy. It has only its resistivity, no point contacts and internal intermittents. Even carbon film has lower excess noise than carbon comp.

Noise comes from random processes. Conductors have thermally agitated outer electrons just because they're at temperatures above absolute zero, and this is a property of resistance and temperature only. The material may contribute additional excess noise over and above the thermal noise if it has other random processes that go on. Carbon comp does.

It's a material property. Bad construction can make that worse, of course.

[343 Salty Beans]

I understood that all things have resistance to begin with, but the way carbon comp resistors work is brand-new to me. Kind of strange, kind of neat.

Okay, that makes a good amount of sense...so are carbon film resistors just strips of carbon (kind of like metal film)? I thought carbon comp and carbon film were two different things.

[markm]

R.G.,
I always end up learning something from your responses!
Very interesting,
   Thanks! 

[zpyder]

Interesting...

I had a related-ish question pop into my head earlier today.  Last week I was putting together a circuit, but I didn't have any 33k resistors, so I ended up using 2 15k plus 3 1k resistors all in series to make up the 33k.  I've read before that larger-value resistors create more self-noise.  I wondered, "could I replace all the large-value resistors in circuits with a series of smaller-values that add up to the large-value in order to reduce noise?"  I figure the answer is probably no, as the aggregate of the noise of all the smaller-value resistors is likely to be higher than that of a single higher-value one.  But that is a pure guess with no real academic basis.

zheers,
cpyder