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A Practical Guide To Key Audio Calculations
Thanks to modern technology, you can do dB calculations without knowing a thing about the mathematics of logs, anti-logs, ratios, exponents, or even much about math
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GAIN
Your amplifier puts out 70V with a 1.4V input. How much gain does it have?
Formula: dB = 20 x Log (volts1/volts2) or 20 x Log (70/1.4)
Enter 70 (volts1)
Hit the divide key
Enter 1.4 (volts2)
Hit the = key
Your answer should be 50.00
Hit the Log key
Your answer should be 1.69
Hit the multiply key
Enter 20
Hit the = key
Your answer should be 33.97 dB gain

Suppose you only knew your amplifier had 33.97 dB voltage gain (we’ll round this up to 34 dB). What would its maximum output voltage be?
Formula: Multiplier = 10^(dB/20) or 10^(34/20)
Enter 34 (dB)
Hit the divide key
Enter 20
Hit the = key
Your answer should be 1.7
Hit the 10x key
Your answer should be 50.11

The voltage at the output will be 50.11 times bigger than the voltage at the input. (Note: this number appeared during the first calculation for this amplifier as 50.00 but we rounded up the gain from 33.97 dB to 34 dB.)

Take the next step. The input sensitivity on the amplifier is 1.4 volts.
Formula: Volts Out = Multiplier x Volts In or 50.11 x 1.4
With the 50.11 (multiplier) still displayed, hit the multiply key
Enter 1.4 (volts in)
Hit the = key
Your answer should be 70.16 volts

Thus, your amplifier will put out 70.16 volts with a 1.4 volt input with the input control at maximum. If you wanted to put 8 volts in your amplifier it will clip unless you turn the input control down. But, your control is marked in dB, so how far do you turn it down? Not a problem to figure out. Read on.

VOLTAGE TO dB
The question is what is the difference in dB between 1.4 volts and 8 volts?
Formula: dB = 20 x Log (volts1/volts2) or 20 Log (1.4/8)
Enter 1.4 (volts1)
Hit the divide key
Enter 8 (volts2)
Hit the = key
Your answer should be 0.17
Hit the Log key
Your answer should be -0.75
Hit the multiply key
Enter 20
Your answer should be -15.13 dB

So guess what? Turn your input control down to the -15 dB point and now when you put 8 volts in, the amplifier will put out its full 70.16 volts. Why? Back to the calculator.

You amplifier has 34 dB gain. You turn your input control down 15 dB so now it effectively has 34 dB - 15 dB = 19 dB gain between the input jack and the output.
Formula: Multiplier = 10^(dB/20) or 10 ^ (19/20)
Enter 19 (dB)
Hit the divide key
Enter 20
Hit the = key
Your answer should be 0.95
Hit the 10x key
Your answer should be 8.91

Your output will now be 8.91 times bigger than the input. Your input is 8 volts so multiplying 8 times 8.91 gives you 71.30. Well, that’s not exactly the 70.16 volts we got before. Why? Because the numbers were chopped off in these calculations. If you used the numbers with all the digits, the answer would have come out as 70.16621271 volts which is the precise answer arrived at previously. Is this difference significant? No. You can find out why it isn’t by using the next example calculation to find the dB difference between 71.30V and 70.16V.

Suppose you have one device that has a maximum 15.5 volt output and the device you wish to drive with it accepts a maximum input of only 7.75 volts. What is the dB difference?
Formula: dB = 20 x Log (volts1/volts2) or 20 x Log (15.5/7.75)
Enter 15.5 (volts1)
Hit the divide key
Enter 7.75 (volts2)
Hit the = key
Your answer should be 2
Hit the Log key
Your answer should be 0.30
Hit the multiply key
Enter 20
Hit the = key
Your answer should be 6.02 dB
The output of the first device is 6 dB more than what the second device can accept.

You’ll notice that in the first voltage to dB calculation you ended up with a minus dB number and in this one a plus or positive dB number.
+dB AND -dB

In the last example, if you used the formula 20 x Log (7.75/15.5), your answer would be -6.02 dB. It simply depends whether a larger number is divided by a smaller one (answer is always +dB) or a smaller one is divided by a larger one (answer is always -dB). The basic number will be the same no matter which way you divide. Try reversing the 7.75 and 15.5 in the last example. You should get -6.02 as the answer.

Also, if you calculated the dB difference between the 71.30V and the 70.16V for the amplifier outputs, you would have gotten 0.139 dB or -0.139 dB, depending on which number you divided by which. This is why the difference was not significant: you can not hear a 0.139 dB difference.

The main reason for dividing a smaller by a larger number when calculating dB is to figure out the LOSS in dB. You will see this in the SPL and amplifier calculations below.


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