What is GAIN?

Just what is this thing called gain that yours truly keeps rattling on about?

Gain is the amount of amplification - think of it as magnification like a lens can make things bigger.

If a phono cartridge puts out say 0.4mV (milli-volts), that's like saying 400uV (micro-volts), or even 0.0004 volts - and in this example I'm talking about a moving coil cartridge - how much gain will be required to "magnify" its output to 500mV (that's half a volt) to go into the input of a line stage or the aux input of an integrated amplifier?

Believe it or not it's dead easy to work out...

You want 500mV out - you have 0.4mV going in - so it's 500 divided by 0.4. Let's shift the decimal point to make it really easy...

5000 / 4

and 5000 / 4 = 1250

So that's how much gain you require to "magnify" 0.4mV to 500mV.

OK, that explains gain but often you find it expressed in decibels (dB), and that isn't very fair to the customer is it?

But what if you had the keystroke sequence for a scientific calculator to enable you to work it out?

Let's give it a go with a gain of 1250...

On your calculator press [log] then enter 1250 then [=]

the answer is 3.096910013

now press [x] and enter 20 then [=]

the answer is 61.93820026

this is in dB and you always try to round dB to the nearest whole number so that makes it 62dB

so you need 62dB of gain to "magnify" 0.4mV to 500mV

now we'll work that backwards...

key in 62 followed by [÷] and enter 20, then press the [=] key

you get 3.1

now press the [shift] key followed by the [log] key (this selects the anti-log) then the [=] key

the answer is 1258.925412 - not far off our initial 1250 is it?

Engineers use dB's to get a very good approximation that although isn't bang-on it's close enough for "rock and roll" (and rock bands are serious!)

The above calculations refer to voltage gain decibel calculations - power is expressed a bit different, but I'm not going to complicate matters any further - we'll leave that for another time.