Since the gain of the amp is a factor in the S/N calculations it obviously has an impact on the S/N. When designing the preamp stage of a multi stage amp, what factors into the decision for setting the gain of the preamp? Does higher gain degrade the S/N? Should the preamp have a lower gain compared to following stages?
I'm building a very high gain amp (x 1250) using OP270G op amps and currently I have only two stages, the preamp has a gain of 50 and the main amp 25. Would the overall S/N be better or worse with a different gain distribution pattern on the two stages?

thanks

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The normal design for a low noise amp is to use a low noise input stage with sufficient gain so that the noise from the following stages is negligible, and the total S/N is then mainly determined by the S/N of the first stage. Thus the gain of 50 for the first stage will cause the noise contribution to the S/N by the second stage to be 1/50 as compared to the first stage (for equal input noise level of both stages). Using that you can determine how much gain you need for the first stage so that the second stage contribution to the S/N is negligible.

Edit: Since random noises combine as the square root of the sum of the squares, 1/50 would subtract about 1.7e-3 dB from the overall S/N, for example.

 

That's an interesting insight, that one needs to focus on the first contact with the data, to separate the wheat from the chaff as early as possible. Reminds me of computer databases and the old adage of shinola in, shinola out. The computer almost always does what you tell it to, but so often it'ss errors - noise - in the signal that causes so many headaches.

 

Here it is pretty easy to understand. Noise is added pretty much by every part of the circuit, but the input sections of each amplifier stage is generally the dominant noise source for that stage. Once noise enters the system, it becomes part of the signal (not "signal" as in "signal-to-noise", but just the generic time-varying signal that the electronics are processing). So noise at the input of an amplifier (or "input-referred noise" regardless of where in the stage it originates) is amplified by that stage and all subsequent stages. Since the signal (as in "signal-to-noise) is amplified by all the stages, the dominant noise is also, generally, only the noise that is amplified by all the stages which means the noise in the first stage. So you spend a LOT of effort making a good low-noise amplifier (LNA) for your first stage and get to be quite a bit looser with later stages.

 

All very good points and makes sense to me and I thank you for the feedback. However I still have a question regarding the direct affect of gain on S/N. For example, what is the point in having multiple stages if all the gain you need can be accomplished in one stage? Granted high value feedback resistors introduce noise but lets assume for the moment that is not a problem. And also lets assume that distortion is not a problem. Is there any negative affect on S/N if the preamp gain is 50 vs 100 or even 1000? I'm assuming that any degredation of S/N would be the result of some aspect of the op amp itself and I'm curious what that would be. Again, talking only about noise here not distortion due to insufficient slew rate or such.

In the preamp stage, are the higher voltages associated with higher gain going to contribute in any way to internally generated noise? Are there higher currents associated with the higher voltages that will contribute to internal noise? Or are these factors insignificant in a quality op amp? Or is all of this already factored into the noise rating on the op amp's datasheet?


Thanks

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Ping......

 

For example, what is the point in having multiple stages if all the gain you need can be accomplished in one stage?

Op-amps have a "gain-bandwidth product", so increasing the gain reduces the bandwidth. Using more than one stage can get around this.

And sometimes it's useful to have stages with different properties, e.g. for particular input impedences, or filtering.

 

If one stage gives you the gain and bandwidth you need, then you don't need two stages.

Edit: An additional factor is op amp input offset voltage. A high gain could cause a high DC level at the output from this offset. Using multiple op amps with capacitor DC blocks between stages will prevent this problem. Alternately you can use DC feedback (low-pass filter) around the one stage to minimize the output offset.