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Question about analogue potentiometers

Discussion in 'd.i.y.' started by ToTo Man, Feb 7, 2019.

  1. ToTo Man

    ToTo Man the band not the dog

    I'm trying to understand how analogue potentiometers operate as volume controls in audio amplifiers.

    I understand they have a logarithmic taper function (or in the case of cheaper pots, two linear tracks are used to effectively approximate a log function).

    Assuming the amplifier has unity gain (i.e. input voltage = output voltage when the pot is turned to max), I'd like to be able to relate the position of the pot to the amount of dB applied to the signal.

    One information source stated that the halfway (6 o'clock) position is -20dB attenuation, which equates to 1/10th of input voltage.

    Another information source stated that the halfway (6 o'clock) position is calibrated to sound half as loud to the human ear as the max position. IIRC correctly, the human ear perceives SPL in such a way that 10dB sounds like a doubling of SPL. Thus the halfway position on an analogue log pot would be -10dB.

    Which information source is correct?

    Also, is there a formula that can be used to estimate the dB level of attenuation at different positions on the pot?
  2. Vinny

    Vinny pfm Member

    I don't see how two linear tracks can approximate to anything but another linear track.
    That aside, 10dB increase is doubling of the signal (that can be anything, not just sound). That being so 20dB is 4 times, 30dB is 8 times etc. By similar logic -10dB is half the volume, etc. (Contrary to common belief, 0dB is not silence, it is just a very low volume.)

    A log10 scale (as this is what we are talking, as opposed to loge) has the same distance between powers of 10, so 1 to 10 is the same distance as between 10 and 100, and 100 and 1000, etc. (Apologies for lack of subscripts there - can't find it....)
  3. ToTo Man

    ToTo Man the band not the dog

    See here: http://www.resistorguide.com/potentiometer-taper/

    I don't think that's correct, it depends what you're doubling. Doubling the power = 3dB increase, doubling the voltage = 6dB increase, doubling the SPL that the ear hears = 10dB increase. The first two are objective and measurable, the last one is somewhat subjective.
  4. Vinny

    Vinny pfm Member

    Things are going to get mighty complicated unfortunately........
    The dB scale can be applied to absolutely anything and a 10dB increase is a doubling of that thing alone, forget what effect that doubling might have elsewhere. Again, that said, the commonest use for dB scales in everyday life is for signals of any and all kinds.

    In the case of power being fed to a speaker, doubling the input (increasing it by 10dB), produces a 3dB increase in the speaker volume. Add to this the complication of how the ear perceives increasing volume, from very quiet to very loud.................... (3dB is around 23% change)

    If you wanted a 10dB increase in volume (a doubling), you would need in the order of 35dB increase in amplifier output - just over 11 times the power.

    I see what is meant by two linear tracks, but what it produces is two linear tracks, one after the other. Poor terminology I suppose, but a poor approximation of true log is arguably achieved.
    Last edited: Feb 7, 2019
  5. John Phillips

    John Phillips pfm Member

    Here's an empirical formula that approximates to the shape of the log curve on this page.

    Gain (linear units) = (81^rotation - 1) / (81 - 1)​

    It spans rotation values from 0% to 100% rather than the more practical 5% to 95% limits as in the graph. It goes through -20 dB (0.1 in linear units) at rotation=50%.

    EDIT: note that actual values of rotation are 0 to 1 and the value 81 is the square of (1/mid-gain - 1).
    ToTo Man likes this.
  6. davidsrsb

    davidsrsb pfm Member

    If the pot is at 10% resistance midway, you will get 10% input channel ie -20dB voltage
    Barrymagrec and ToTo Man like this.
  7. Vinny

    Vinny pfm Member

    I am unsure what precisely is being referred to, but -20dB is a 75% cut in signal strength - a quarter the volume for instance. -10db is a reduction to half, -20dB is to a quarter, -30db is to an eighth, -40dB is to a sixteenth etc.
  8. martin clark

    martin clark pinko bodger

    Vinny I think are thinking of the rough perceptual effect on changes in SPL; because in voltage terms a change of 6dB is a doubling (or -6dB a halving): 20*log10 (v1/v2)
  9. John Phillips

    John Phillips pfm Member

    AFAICS you can make a choice. See for example this datasheet for a Bourns professional potentiometer. There are several "A series" log-like tapers with mid-position-gain values from 5% to 30%.

    I am also aware that Alps (datasheet here) seems to offer either 15A or 3B tapers. The 15A taper has mid-position gain of 15% (-16.5 dB). But they label the "B series" 3B taper as "vol.control" with mid-position gain of 50% (-6 dB).

    So the question is what do kit manufacturers typically specify as a volume control? I don't know but others may.
    ToTo Man likes this.
  10. ToTo Man

    ToTo Man the band not the dog

    Presumably the formula becomes less accurate at very high levels attenuation, due to the logarithmic function changing to a straight "walk off to zero" line?

    Out of interest, are most of the analogue pots used as volume controls in stereo amplifiers: log curves with a straight walk of to zero near the very bottom; or two linear curves that change over near the halfway point to approximate a log curve?
  11. Vinny

    Vinny pfm Member

  12. Arkless Electronics

    Arkless Electronics Trade: Amp design and repairs.

    First of all ignore everything Vinny said as it is all spectacularly wrong!

    I would personally never think in terms of attenuation at a given point etc for a potentiometer used in audio. They are not intended for that sort of precision. You need a switched attenuator for that and can then mark it of in dB's BUT only for a known impedance load and source.
  13. Vinny

    Vinny pfm Member

    Thanks for the input Arkless.
    Perhaps you'd explain precisely what is wrong?
  14. Arkless Electronics

    Arkless Electronics Trade: Amp design and repairs.

    Sorry but lifes too short....
  15. ToTo Man

    ToTo Man the band not the dog

    In my case I don't need a high level of precision, I'm really just wanting to ballpark the level of attenuation provided by a 10% or 15% resistance ratio analogue pot at say a quarter, half, and three quarters of its turning range and use this info, in conjunction with the strength of input voltage, internal gain ratio of the amp, and headphone voltage sensitivity, to predict whereabouts I'm likely to be on the volume control with a particular headphone. I appreciate there are a heap of assumptions required for this which prevents an exact answer to the problem.
  16. Arkless Electronics

    Arkless Electronics Trade: Amp design and repairs.

    'Fraid I can't get my head around what you are trying to do or why here.... it's not something I've ever known anyone want to do before! Vol control position will vary hugely with the input source material anyway! I have some CD's recorded so quiet that if I left the vol where it was and put a loud recorded level CD on it could blow the speakers!
  17. Barrymagrec

    Barrymagrec pfm Member

    3dB is half or double the power.

    6dB is half or double the voltage.

    10dB is 1/10th or 10 times the power

    20dB is 1/10th or 10 times the voltage.
    ToTo Man and Arkless Electronics like this.
  18. Jim Audiomisc

    Jim Audiomisc pfm Member

    Two sources of potential (pun alert!) confusion here.

    Firstly, values in dB have a specific meaning in terms of *power* ratio. So as Barry has said, 10dB corresponds to a change in power by a factor of 10, etc. *However* human perception of 'loudness' is *also* quasi-logarithmic. So it may sound like a change in 'how loud something is' by more like a factor of 2 or so.

    Secondly, the 'law' of 'log pots' isn't normally truly logarithmic, but a near-fake of it over a portion of the rotation. Not all pots, in use, will give the same 'law'. Nor need they all reduce the level by 20dB when wound down 'half way' in terms of rotation.

    So in practice if you really want to know this you may have to measure it. Unless you have one of the volume controls that was made in a carefully calibrated and stated manner. Alps used to make these decades ago, but they are rare now. And as Arkless says, the level you get depends on what goes in anyway.
  19. ToTo Man

    ToTo Man the band not the dog

    True, lots of variables are at play here! AIUI, ideally an amp should be gain-staged so that it delivers its full output voltage with the pot set full. This is of course impossible in practice because source output voltages vary significantly, as do the levels at which digital music is mastered, so you need to include excess gain in the design so that the amp can still be driven to its full output voltage capability with weaker sources.

    Gain is an especially important consideration for headphone amps because headphones vary so much in their voltage sensitivity (there can be over 25dB difference in sensitivity between headphones!). If the amp's gain is too high for your headphone, you will be trapped within a narrow range of the volume pot, making fine volume adjustments difficult and perhaps increasing the audibility of tracking errors etc. A good solution is an amp with two ore more gain settings that can be selected by the operator to best match the source input voltage and output voltage sensitivity of the headphones so that there's a decent turning range on the volume pot but still enough gain on tap if needed.

    EDIT - TBH I experience a similar problem with loudspeakers. I used to attribute it to the fact that vintage integrated amplifiers and receivers were designed with line input sensitivities of around 150mV, not the 2V that later became the standard line output voltage. But what's the excuse for modern-day amplifiers exhibiting the very same issue, being unable to crank the volume above halfway even on a relatively quite recording? I suspect it's because the manufacturers are scared that lowering the input gain will give the impression that their product has less output power than their competitors!...
  20. Arkless Electronics

    Arkless Electronics Trade: Amp design and repairs.

    All fair enough and agreed with but still don't see what your OP was about....:confused:

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