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Author Topic: Proper Gain Staging Considerations?  (Read 2706 times)

Offline natpub

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Proper Gain Staging Considerations?
« on: October 04, 2004, 01:31:58 am »
Quote: "....And lets start another thread on proper gain staging… That is also a very good subject..."


Welcome Dan, and I will take you up on your offer above:

Can you discuss some basic considerations in gain staging, and things folks might want to keep in mind when working in signal paths that are digital, analog, or a comination of the two?

Thank you for commenting and for modertating this month! Smile

--KT
Kurt Thompson
Vibrational Arts, Inc.
Blue Skyway Music
Sonic Sorcery Studios
Austin,TX/Columbus,OH

Offline Brian Roth

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Re: Proper Gain Staging Considerations?
« Reply #1 on: October 04, 2004, 02:35:17 am »
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.

IOW, if a signal source clips at +24 dBu, then the destination/input should be happy with +24 dBu and clip at that point as well.

IE, source and destinations clip at the same point.

Reality...just because a given signal source grossly clips at some specified signal level does NOT mean it is linear at levels somewhat the clipping point.  IE, the distortion level may creep up (a typical result) in some fashion as the clipping level is approached.

This is TOTALLY a function of the circuit design.  Hence, one circuit might, say, produce 0.01% THD at +10 dBu, 0.5% THD at +15 dBu, and 10% THD at +24 dBu.  Another might provide this series under the same output conditions: 0.1%, .01%, 1%.

That being said, clipping levels in/out should be semi-closely matched to optimize dynamic range.  That says NOTHING about the sonics of the analog circuit at levels well-below clipping.

Bri



Brian Roth Technical Services
Oklahoma City, OK
www.BrianRoth.com

Offline danlavry

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Re: Proper Gain Staging Considerations?
« Reply #2 on: October 06, 2004, 04:45:24 pm »
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

Offline Sahib

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Re: Proper Gain Staging Considerations?
« Reply #3 on: October 06, 2004, 05:26:52 pm »
Dan,

I am enjoying all your topics immensely and this is no exception. I would like to go in deeper and please do continue if you can.

Many thanks.

Cemal Ozturk

Offline weihfool

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Re: Proper Gain Staging Considerations?
« Reply #4 on: October 06, 2004, 06:50:04 pm »
I don't know about anyone else, but I'm eagerly awaiting the next installment of this thread.  Thank you, Dan, for taking your free time to educate those of us who don't have a handle/grasp/understanding/knowledge of this subject.  

Offline Barish

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Re: Proper Gain Staging Considerations?
« Reply #5 on: October 07, 2004, 05:56:37 am »
Yes, Dan, please carry on. We've read so many books about opamps and gain staging but no one has ever explained it from this point of view before. Thank you for sparing your time and opening up your expertise for public domain here, that's really appreciated and respected.

Eagerly looking forward to the second installment.

Regards,

Mahcem Ozturk
M Ozturk

Offline wireline

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Re: Proper Gain Staging Considerations?
« Reply #6 on: October 07, 2004, 10:00:31 am »
Quote:

Again, noise is not really additive


OK, this I understand...but is distortion additive, multiplicative, exponential, or what?  

Say you have .005% distortion coming from gain stage A...which is sent to gain stage B, which adds its own .005% distortion...

Is the distortion at that point .010%?  .025%?

Ken Morgan
Wireline Studio, Midland, TX
Authorized Sales Agent, WWW.Soundpure.Com

Offline danlavry

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Re: Proper Gain Staging Considerations?
« Reply #7 on: October 08, 2004, 12:23:40 pm »
wireline wrote on Thu, 07 October 2004 15:00

Quote:

Again, noise is not really additive


OK, this I understand...but is distortion additive, multiplicative, exponential, or what?  

Say you have .005% distortion coming from gain stage A...which is sent to gain stage B, which adds its own .005% distortion...

Is the distortion at that point .010%?  .025%?




I am sure we will talk about distortion more. But unlike noise, you really can relay on distortion figures to predict anything about how distortion will "accumulate". You will have to know more then just the distortion figures. In fact, distortion may add in some cases, and cancel out in other cases. The circuit designer often "weaves the circuits" to do exactly that, cancel distortions.

I hope I did not confuse anyone talking about noise. I was talking a bout the noise generated by the circuits themselves (resistor noise, semiconductor noise...). This is not about the noise you get when your mic picks up say a car driving by. The car noise is a signal. Circuit noise is random and unpredictable. There are no recognizable patterns in it...

BR
Dan Lavry