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Signal to Noise Ratio

The signal to noise ratio is the difference between the noise floor and the reference level. The reference level is determined by the person making the measurements. For amplifiers, the reference may be, full power, one volt, one watt into a given load or any number of other things. For you to compare two pieces of equipment which were tested by different methods, you must know precisely what reference was used.

Common Misconception:
Many people believe that a piece of electronic equipment (equalizer, amplifier, crossover...) with a slightly higher signal to noise (s/n) ratio is infinitely better than one with a slightly lower s/n ratio. Many people don't realize how much a 30 or 40 dB ratio is. A piece of electronic equipment with a S/N ratio of 80dB may be good enough for all but the best systems.

Example:
If you were looking at 2 amplifiers and one had a S/N ratio of 102dB and the other was rated at 80db. You'd probably think that the amp with the higher ratio was quieter (and better). If both amplifiers were rated at 600 watts and the amp with the higher S/N ratio was rated at full power but the amp with the lower S/N ratio was rated at 1 watt, we could use the formula dB=10*log(value1/value2) to find the difference in decibels between 600 watts and 1 watt (so that we could compare apples to apples).

dB = 10*log(value1/value2)
dB = 10*log(600/1)
dB = 27.78

We can see that the difference in 600 watts and 1 watt is 27.78dB. To compare the 2 amplifiers, we have to subtract 27.78 from 102dB. This gives us a S/N ratio of 74.22dB for the amp with the 102 dB S/N ratio when its reference is changed from full power output to 1 watt. When both amplifiers are measured with the same reference, the amplifier that you thought was noisier (and a total piece of junk) is actually quieter.

Test Tones:
The links below show you the difference between a 250hz tone recorded at 0dBfs (0dB full scale) which we will call the reference and a tone recorded at a specified lower level. It plays the reference for 2 seconds then the quieter part of the of the tone at xdB lower for 2 seconds. It plays each twice. Consider the louder part to be the 'signal' and the lower part to be the 'noise'. The difference is specified on the link.

Warning!
Set the volume control on your computer to approximately 10% of its maximum level before clicking on the links below. Adjust the volume as needed after the file has begun playing.

Even at a 50dB ratio, there is a significant difference between the 2 levels. With most computer speakers, anything more than a 50dB would be difficult to reproduce.

Calculators

Calculator 1:
This calculator will tell you the dB gain when you know the input and output voltages. This is useful when you know the input voltage and output voltage of any signal processor and you need to know how much gain you're getting from the processor.

 Find dB gain by entering input and output voltage Data Input: Input Voltage? = Volts Output Voltage? = Volts Data Output: Gain = Decibels

Calculator 2:
This calculator will calculate (big surprise!) the dB gain when you tell it the before and after power. This means that if you have a 100 watt amp (before) and you are going to buy a 350 watt amp (after), it will tell you the dB increase (approximately) that you can expect.

 Find dB gain by entering before and after power Data Input: Power Before? = Watts Power After? = Watts Data Output: Gain = Decibels

Calculator 3:
This calculator will tell you the output voltage you would get with a given input voltage and a given number of dBs.

 Find output voltage by entering input voltage and dB gain Data Input: Input Voltage? = Volts Desired Gain? = Decibels Data Output: Output Voltage = Volts

Calculator 4:
This calculator will tell you how much power you'll need if you tell it how much power you have and the desired gain in dBs. Say you have 1 watt of noise (what a crappy system). If you wanted to see how much power would be needed to achieve a 100 dB signal to noise ratio, you could find it here. I think you may be surprised.

 Find output power by entering input power and dB gain Data Input: Input power? = Watts Desired Gain? = Decibels Data Output: Output power = Watts

 You should remember: Because a 90 dB s/n ratio is so high already, another 10 dB (for a 100 dB s/n ratio) is not going to be noticeable and you should not decide to purchase a piece of audio equipment solely based on that specification. In amplifiers, you wouldn't likely be able to pick out the noisier amp if one amp had a s/n ratio of 60 dB and another had a 90 dB s/n ratio (as long as all else remained equal). This, of course, excludes all of the 13, 14 and 15 year old guys out there because, as we aaalllll know, they know more than anyone (especially their elders). :- ) I can just imagine all the email I'll get from that!

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