Signal to Noise Ratio

Concert Hall

Signal to Noise Ratio (SNR), or Dynamic Range, is a measure of the maximum resolution of a piece of audio gear.  The larger the number, the greater the possible range from very, very quiet sounds to very, very loud sounds.  It is easy to calculate, for example:

Noise level with no input signal = 70uVrms
Signal level at full output = 1000Wrms into 4Ω → 63.25Vrms
SNR = 20 log (63.25Vrms / 70uVrms) = 119dB

Pretty simple, huh?

Now sometimes the Signal to Noise Ratio may mention that it is “A-Weighted“.  This is an attempt to adjust the value based (very roughly) on the way we hear – i.e. the “Fletcher-Munson” curves.  The end result is a higher Signal to Noise Ratio than if no weighting were used.  Is this simply cheating to improve the on-paper specifications?  Probably, but at least it has some basis in psychoacoustics.

Speaking of cheating, I came across an amplifier with the following specifications:

Noise level with no input signal = 90uVrms (A-Weighted)
Signal level at full output = 1000Wrms into 4Ω → 63.25Vrms
SNR (according to specifications) = 120dB (A-Weighted)
SNR (according to calculations) = 20 log (63.25Vrms / 90uVrms) = 117dB (A-Weighted)

What’s going on here?  There’s a 3dB discrepancy between the spec sheet SNR and the calculated SNR!  The trick in this case is that the manufacturer is using the peak output power (2000Wpeak) of the amplifier instead of the RMS output power (1000Wrms).  It is then compared against the RMS noise level – i.e. it’s not comparing apples to apples!  Here’s the calculation:

Noise level with no input signal = 90uVrms (A-Weighted)
Signal level at full output = 1000Wrms into 4Ω → 2000Wpeak into 4Ω → 89.44Vpeak
SNR = 20 log (89.44Vpeak / 70uVrms) = 120dB (A-Weighted)

There it is now!  So if you are simply “creative” with you calculations, you too can add 3dB to your amplifier’s SNR.  Is this cheating?  Yes, I believe it is.  However, you are now armed to check if the SNR numbers add up for a prospective piece of audio gear, to help weed out the cheaters.  Good luck!

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