From crest25@sbcglobal.net Wed Jan 28 09:17:42 2004
Subject:Re: Speakeasy gain structure?

Claire,

Discussing db is always tricky and I think you did a pretty good job in your explanation. I used to have similar discussions like this with my submarine commanding officer. As a submarine sonarman, why do I have to wait to detect a 3db gain to determine whether the sound target is approaching or leaving our operating area or just changed the "Angle on the Bow" or pictoral attitude compared to us. Underwater sound theory is a total new ballgame from our surface friends. I once heard and monitored an empty tanker from Cape Horn in Africa go up the coast all the way to the UK area. I was underwater at all times off Nassau near Florida. I'm straying off topic a little so I'll end it there. I just wanted to compliment you on your db explanation.

Ed

claire_trikes_aust wrote:
Strictly speaking, 'Gain' is simple.

Its the output/input. (i.e. Output divided by Input).

Thats where it should end. If you want to understand it a bit more, read on
at your own risk !

Both the Input and Output have to be in the same units, which is why gain
does not have units (they canel out).

Lets take a piece of wire. For all (simplistic) intents and purposes, the
output is the same as the input so it has a gain of "One".

If only half as much came out, the gain would be 0.5 or 1/2. If the result
is larger than 1 we usually refer to it as "gain", if it is less than 1 as
"loss".

If the units are voltage, we are talking voltage gain. If both output and
input are in amps we are talking current gain. If the units are watts we
are talking power gain.

Typically a preamp has very high voltage gain. It might accept a microphone
input, say .5mV and put out say 1V. A gain of 2000 times. It doesn't have
much current gain so it also doesn't have much power gain.

Typically a power amplifier has moderate voltage gain: Input say 1V, Output
say 75V = Voltage Gain 75 Times.
It has a considerable current gain however as the input current might be say
.2mA and the output current say 5 Amps = 25,000 times. Therefore the power
gain is 75x35,000 = 1,875,000 times. (!)

If you are still with me, this is where it starts to get tricky....
Because there are such large variations (ratios from unity to millions) it
is usually easier to measure gain on a logarithmic scale. When using a
logarithmic scale it is normal to ascribe the units dB (decibel). (I'm
taking a huge amounts of short-cuts here, so I hope all the purists will cut
me some slack in trying to keep it reasonably simple).

Voltage gain in dB=20 x log (Output Voltage/Input Voltage)

Power Gain in dB=10 x Log (Output Power/Input Power)

Some interesting (sort of unrelated) facts come out here.

It is generally accepted that the smallest change in volume of a sound a
normal person (not a musician) can detect is around 3dB. This equates to
*Double* the power level. (A 100W amp will be just noticably louder than a
50W amp (3dB difference in a steady state condition i.e. producing a
continuous tone at maximum output ). I can hear the arguments starting
already, but please note this is under steady state conditions. The
realistic peaky, transient performance will be much different (hence ratings
in Peak Music Power). It takes a power gain of 6dB to cause a subjective
increase of "double the volume" which equates to 4 times the power. (try it
in the equations above....)

Note that in our example of the power amplifier above it has a power gain of
about 60dB (which is somewhere around what you would expect).

I'm going to leave it here (for my own safety) I think !

Regards,
Claire

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