Reference: http://sound.westhost.com/project01.htm
The volume control in a hi-fi amp or preamp (or any other audio device, for that matter), is a truly simple concept, right? Wrong. In order to get a smooth increase in level, the potentiometer (pot) must be logarithmic to match the non-linear characteristics of our hearing. A linear pot used for volume is quite unsatisfactory.
Unless you pay serious money, the standard "log" pot you buy from electronics shops is not log at all, but is comprised of two linear sections, each with a different resistance gradient. The theory is that between the two they will make a curve which is "close enough" to log (or audio) taper. As many will have found out, this is rarely the case, and a pronounced 'discontinuity' is often apparent as the control is rotated.
As with all pots used as volume controls, the first 10% of rotation causes a very large variation in level (essentially from 'off' to quietly audible). A 'true' log response over the full range of perhaps 100dB is not really useful, because most of the time the gain is varied over a relatively small range. 25dB of variation is a power ratio of 316:1 - this will normally be the range over which any volume control is used.
Figure 1 - Circuit of the Log Pot Approximation
Take a 100k linear pot (VOL), and connect a resistor (R = 10k - 15k, 12k used to produce Figure 2) as shown above to achieve the curve shown. It should be a straight line, but is actually still far more logarithmic than a standard log pot. For stereo, use a dual-gang pot and treat both sections the same way. Use of a 1% resistor for R is recommended. Different values can be used for the pot, but keep the ratio between 6:1 to 10:1 between the value of VOL and R respectively. While 8.33:1 (as shown) is close to a real log curve, it may still allow excessive sensitivity at low levels. Higher ratios than 10:1 can be used, but will cause excessive loading of the driving stage, or necessitate the use of a pot whose resistance is too high.
Figure 2 - The Transfer Curve in dB
Provided the gain structure of the preamp is set up properly, a good approximation to true log pot operation is obtained over at least a 25dB range, which is sufficient for the normal variations one requires.
The gain structure of the preamp is correct when the pot spends the vast majority of its time between the 10 and 2 o'clock positions. If the volume is often below or above this range, consider changing the preamp gain. The gain can be switched to give a 'two-stage' volume control, so that the optimum setting is always available.
The other advantage of the 'fake' log pot is that linear pots usually have better tracking (and power handling) than commercially available 'log' pots, so there will be less variation in the signal between left and right channels. This is improved even further by the added resistor, which will allow a cheap carbon pot to equal a good quality conductive plastic component (at least for accuracy - I shall not enter the sound quality debate here).
Make sure that the source impedance is low (from a buffer stage) and that it can drive the final impedance when the control is fully advanced (it may be as low as 9k Ohms with a 100k pot). Use of a high impedance drive will ruin the law of the pot, which will no longer resemble anything useful.