Conversion of mV to dB

06-30-12: Actusreus
Thank you both. I agree the KAB calculator needs to be used with caution as it does not take into consideration all of the parameters that might come into play when trying to convert different values. It appears that an accurate calculation can be done using the formula of 20 log (V1/V2) where V1 is the preamp's nominal output in terms of V rms and V2 is the sensitivity setting that is being converted. The preamp's nominal output is listed as 2V rms so let's say for the 1.4 mV setting, the gain would be 63 dB. This perfectly reflects the range provided by the manufacturer of 52-76 db from the lowest to the highest setting.

No, I'm afraid that you did not get this right. From my experience a 1.4mV output cartridge does not need 63dB of gain. It needs much less - more like 45-47dB. A 1.4mV output cartridge in not exactly hi-output MC (which is usually around 2.5mV) but neither is it low output MC (which is sub 1mV). MM cartridges are often in the 4-6mV which need 40dB of phono preamp gain.
You could use a phono preamp that has 63dB of gain for a 1.4mV cartridge at your peril as it will trend towards overloading the linestage that follows the phono preamp & will most likely give you high hiss.
The assumption that's wrong in your calc is that a phono preamp outputs 2Vrms. Reading that it appears that you are thinking that a phono pre connects directly to the power amp. It does not. A phone preamp usually outputs a voltage that is in the 100s of mV. This output is fed into a linestage preamp & further amplified before feeding into the power amp. A phono preamp cannot output more than a few 100s of mV as it will overload the linestage pre.
For example, My power amp has an input sensitivity of 1V. Imagine if a preamp output 2Vrms - I'd have 300W into 8Ohms & I would blow my eardrums & fry my speakers! And, I know that this does not happen.
I'm quite sure that your preamp is set for 60dB gain at the 0.3mV setting & for 40dB gain at the 5mV setting. I did calculate the ratios of 0.4/0.3, 0.6/0.4, 0.9/0.6 & they are all close to sqrt(2). The ratio 1.4/0.9, 2.5/1.4 are slightly higher than sqrt(2) & of course, 5/2.5 = 2.
So, I would say:
0.3mV would be 60dB gain
0.4mV would be 57dB gain
0.6mV would be 54dB gain
0.9mV would be 51dB gain
1.4mV would be 47dB gain
2.5mV would be 42dB gain
5mV would be 36dB gain.
Of course all of this at 5cm/s.

I owe credit for this to, and would like to thank, Al (Almarg), whose advice has been absolutely invaluable to me since becoming an Audiogon member. Thanks Al!

yeah, I agree Almarg is a very nice fellow who genuinely wants to help fellow Audiogoners & is very knowledgeable. He's kept me honest a few times! ;-)

Thanks very much for the nice words, guys.

Bombaywalla, thanks for your comment, with which I essentially agree. However, note that the question was not what gain setting to use with a cartridge having a given output. The intent of the question was to determine the gain in db that corresponds to each of the gain settings provided by the phono stage, which are marked in millivolts, rather than in db.

The phono stage is an RCM Sensor Prelude, which is indeed specified to have a 2 volt nominal output. So, for example, the gain setting that is marked as 1.4 mv provides a gain of 20 x log (2000/1.4) = 63.1 db.

That interpretation can be confirmed by noting in the data sheet that the range of possible gain settings is specified as 52 to 76 db, corresponding to markings of 5 mv and 0.3 mv respectively. 20log(2000/5) = 52.04 db, and 20log(2000/0.3) = 76.48 db.

I agree that generally a 2 volt nominal phono stage output will be much too high, so the mv marking of the gain setting that is used should be significantly higher than the rated cartridge output.

Thanks again. Best regards,
-- Al

Thanks Al. Let me just add that the designer himself stated to me that the setting of 1.4 mV corresponds to approximately 70 dB of gain, and 0.6 mV to approximately 68 dB, which essentially matches to the values obtained by using the formula.

Also, the assertion that "[a] phono preamp cannot output more than a few 100s of mV as it will overload the linestage pre" surely cannot be true. The Parasound JC-3 has a nominal output of 1V, and it will probably output way more than that in peaks. The Sensor is listed to have the max output of a whopping 8V, which I don't quite understand, but certainly the designer would not design it this way if it was likely to be incompatible with most of the line preamps on the market. I certainly didn't experience any incompatibility with my line preamp, which btw outputs 1.5V whereas my power amps are listed as having input sensitivity of 1V, and they are all from the same manufacturer. Needles to say, they work very well together. Sounds like the issue is more complicated than just pure numbers on paper. I also apologize for not providing more information to begin with, which is never a good way to ask for advice. However, I simply and honestly did not know what information was pertinent to the answer.

As a follow up, I looked up specifications for some phono and line preamps out of curiosity. My Rogue preamp has "rated" output of 1.5V, but "maximum" output of 30V PP ("peak power"?)!!! With the power amps listed as having input sensitivity of 1V RMS, it sounds like a bad match, on paper, but definitely not in reality.

Also, the Rogue Ares phono preamp, is listed as having rated output of 1V and maximum output of 8V RMS @ 1KHz. Based on this, and in light of our conversation, I would venture an uneducated guess that the max values are not truly relevant in real life conditions, and even the nominal value in case of the phono pre would depend on either the cartridge's output or the gain setting. So Bombaywalla's assertion might as well be true in that under real life conditions a phono pre will not output 2 or more V's. Otherwise, these figures wouldn't make much sense...

Thanks for the followups, Marek. A point to keep in mind is that the specs for maximum output, for both phono stages and line stages, refer to the maximum output that the component is capable of (without clipping or a severe rise in distortion). And in the case of a line stage, it is based on the volume control being turned all the way up, as is the specified gain of a line stage.

So that number should be much greater than the maximum output level that would ever actually be used, and it should also be much greater than the input sensitivity of the next component in the chain.

Also, "rated output" tends to not be a particularly useful figure, at least without being put into the context of the input level it is based on. The output level will be the input level factored up by the gain (expressed as a voltage ratio), and (in the case of a line stage) factored down by whatever amount of attenuation is provided by the volume control at the setting that is being used.

Finally, I believe that the reference to 70 db in the first paragraph of your post immediately following mine is a typo, and perhaps should be 60 db.

Glad the new phono stage is working out well. Best,
-- Al