I AGREE! <g> I have my own "rules of thumb" and am always interested in seeing if my thumbs are broken <g>.
A very simplistic mindset is that:
Any given signal source at clipping point should hit the clipping point of the destination's input.
Well, I would not call it simplistic. I would call it “theoretical”. Indeed in an “ideal world” that would work fine, from gain staging stand point.
Lets assume we are in a noise free and distortion free world. Your AD takes 10V and your mic puts out a maximum of 10mV so you need a gain of 1000 (60dB).
Say we have a 3 stage amplifier. We could set the gain at (for example)
A. 10 X 10 X 10 =1000
B. 1 X 100 X 10 =1000
C. 50 X 10 X 2 = 1000.
With theoretical amplifiers we do not care. In fact we only need one theoretical amplifier…
But there are practical reasons why we go for three consecutive amps instead of one. 60dB gain is a lot to ask for from a single amplifier. Why? There are real world tradeoffs.
The basic concept is about “Gain Bandwidth” product – the more gain, the less bandwidth. The whole subject is a bit outside this conversation. But one important point: An amplifiers circuits has some “Open loop gain”, that is the “potential amplification”. Some amps, though not common, have as much as 120dB gain capability. Why so much gain? Most audio amplifiers use some negative feedback. Negative feedback helps linearize circuits, reducing all sorts of problems, from distortions to flatness response and more. So “all that open loop gain” is “split 2 ways” – Part of it goes toward signal gain, and what is left will be available as feedback. Say you have an open loop gain of 80dB and you are going for 60dB signal gain. You have only 20dB left for feedback. But let us go for 3 stages of amplification, each is 20dB (combined they yield 60dB signal gain). Now each stage has 60dB feedback. Thus the 3 stage approach yields a lot more “distortion removal”. 60dB left for the feedback reduces to distortion by a factor of 1000!
So from amplifier distortion standpoint, it seems like a good idea to spread the gain into equal stages. But there are of course other considerations as well, such as noise.
Lets revisit the above examples A, B and C. But this time we will include the fact that each amplifier input has 1mV noise at the input. There is no signal, and we are going to compute the output noise.
Example A was 3 gain stages, 10 X 10 X 10. The noise at the input to the first stage is 1mV, so at the 1st output it is 10mV. There it adds to the second stage noise for a total of 11mV. The 2nd stage amplifies it to be 110mV, there it adds with the 3rd stage input noise to 111mV. A final amplification yields 1.11V noise.
Example B was 3 gain stages, 1 X 100 X 10. The noise at the input to the first stage is 1mV, so at the 1st output it is 1mV. There it adds to the second stage noise for a total of 2mV. The 2nd stage amplifies it to be 200mV, there it adds with the 3rd stage input noise to 201mV. A final amplification yields 2.01V noise.
Example C was 3 gain stages, 50 X 10 X 2. The noise at the input to the first stage is 1mV, so at the 1st output it is 50mV. There it adds to the second stage noise for a total of 51mV. The 2nd stage amplifies it to be 510mV, there it adds with the 3rd stage input noise to 511mV. A final amplification yields 1.022V noise.
Again, noise is not really additive (it adds as square root of the sum of the square, and I am assuming most people here don’t wish to “go there”). Also 1mV in the example is too high. While crude, it does serve to demonstrate the fact that different gain stages do have a lot of impact on noise. Example A yielded about 1V noise, exampl B yielded 2V noise. The bottom line is - the early stages (where signals are low) require amplifiers and devices with very low self generating noise. From noise standpoint, it is best to have as much of the amplification as possible at the first stage, getting to higher signal levels as soon as possible. Larger signals can than work with nosier circuits…
So far I touched on the fundamentals of gain staging form distortion standpoint and from noise standpoint. These are just the basics, and there is a lot more to say, yet we already see a conflict (compromise) between distortion and noise.
I will be glad to continue is there is enough interest in the subject.
BR
Dan Lavry
