# Why aren't log taper pots smooth?

B taper pots are linear, A taper pots are "log", and used for volume controls and such. But the actual specified taper, and what I've measured, is piece-wise linear, not a smooth curve.

Any idea why this would be? I can't imagine it being any more difficult to make pots with a completely smooth curve.

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I'm guessing this is because they can plunk down a few different segments of pre-mixed material, but smoothly mixing and laying it down at the same time sounds difficult. Log pots are for volume controls and only need to be roughly right. Nowadays, volume is set digitally anyway, even if from a pot. Log pots are going the way of the dinosaur. –  Olin Lathrop May 10 '12 at 14:46
I'd guess it's to save costs. Materials have fixed resistivity, so you have to get a bunch of "strips" of varying resistivity and join them together. The more strips you use, the smaller the parts become and the more complex your manufacturing process. The less strips you use, the "rougher" your pots perform. They tend to do the job fine as long as they're "roughly log", since it's a human controlling the device and they will intuitively compensate for any offset or skew. –  Polynomial May 10 '12 at 14:47
@stevenvh: Nope. I vaguely recall someone saying the designations were swapped decades ago, though. Ah, here: sound.westhost.com/pots.htm#markings –  endolith May 10 '12 at 14:59
@Polynomial: Ok, but I don't know why that would save costs. With some explanation of how pots are made and why it needs strips of fixed resistivity, that would make a good answer. –  endolith May 10 '12 at 15:07
@endolith Did a bit of research and provided an answer. Enjoy :) –  Polynomial May 10 '12 at 16:04
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## 1 Answer

Cheap log potentiometers are a trick. In fact, lot of cheap log pots aren't actually log at all - they're linear pots with an ordinary resistor attached to create the effect of a log pot. This saves the manufacturers a lot of money, because they produce almost exactly the same product for both the linear and log pots, and just solder a resistor in there on the log one.

Another method of producing cheap log pots is to use two materials of different resistivity to produce a rough log-shape resistance graph. This, again, is pretty inaccurate and only gives you a rough log shape.

True log pots use tapering to turn a single fixed-resistivity material strip into a logarithmic resistance source. Resistance can be calculated as the following:

$$R = \rho\frac \ell A$$

where R is resistance in Ω, ρ is resistivity in Ωm, l is length in meters, A is cross-section area in m2.

So, if you have a strip of material with a fixed area and fixed resistivity, resistance is directly linearly proportionate to length, giving us a linear potentiometer. In order to make a true log potentiometer, we need to have one of these variables change over the length of the material.

The easiest method is to have the area change over the length of the material. This can be done by simply changing the height of the material and keeping the depth fixed. The height of the material isn't directly proportional to log because the height of all points previous to it have to be taken into account too. It's relatively easy to calculate the required gradient at any point by doing some calculus, but I won't cover that here.

Of course, anything that involves extra work will increase the price of production. Creating the curved material requires a CNC milling machine (or similar) to produce the curve, and involves more waste than perfectly flat circles.

As I mentioned in an earlier comment, all of this doesn't particularly matter for most purposes. Controlling audio volume only requires that the perceived volume gradient is linear. We're also very good, as humans, at "faking it" by physically compensating for fluctuations when manually altering volume.

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"Creating the curved material requires a CNC milling machine (or similar) to produce the curve, and involves more waste than perfectly flat circles." I would think this only needs to be done once, though, and then mass production would be with some kind of stencil or printed board? Like it doesn't cost any different to have curvy traces on a PCB vs straight traces. –  endolith May 10 '12 at 16:23
@endolith creating traces on a PCB and shaping a 3D resistive material are very different processes... –  NickHalden May 10 '12 at 18:17
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