Virtual Earth Summing - Noise Calcs

http://www.sengpielaudio.com/calculator-volt.htm

I found this article to be enormously helpful to understanding opamp noise calculations:
http://www.analog.com/static/imported-files/rarely_asked_questions/moreInfo_raq_opAmpNoise2.html

The 3 main sources of noise being: Johnson noise,  current noise, and voltage noise. As others have pointed out, they combine as the root sum of squares - see the attached image of that equation.

R =  source resistance, which in a summing amp is all the summing resistors in parallel
In = current noise density in nA/√Hz (from opamps's datasheet)
Vn = voltage noise density in nV/√Hz (from opamps's datasheet)

The Johnson noise term is simplified in this equation, and it assumes an absolute (Kelvin) temperature of 290 (aka 17ºC or 62ºF). That's close enough, and using the simplified version means you don't have to plug in Boltzmann's Constant yourself.

I set this equation up in a spreadsheet, concerned that the summing amp IC I had chosen, with a BJT front end, was going to adversely affect the noise with its high current noise density. Turns out that with a source resistance of around 400 ohms, that the InR term was by far the lowest of the 3 contributing noise sources, and that the opamp I had chosen was overall the quietest option of the ICs I was surveying. Hooray for math for putting my mind at ease.

While the author dismisses using NF to characterize noise performance, he is talking from the perspective of an op amp salesman.

I like using NF to evaluate a circuit design because it clearly states how far from ideal (noiseless) it is. 

JR

JohnRoberts said:

While the author dismisses using NF to characterize noise performance, he is talking from the perspective of an op amp salesman.

I like using NF to evaluate a circuit design because it clearly states how far from ideal (noiseless) it is. 

JR

Click to expand...

NF calculation is relevant to optimizing a circuit's operation for a given source impedance and BW. It's adequate for optimizing a discrete design, not so much for opamps which, in most cases do not let the user vary its operating point.
Personally, I like the Vn-In method where te contributins of noise voltage, current voltage and source noise are clearly identifiable and comparable.
In RF design, the NF method is adequate because one has generally control of the operating point AND the source Z.

I guess it depends on what are the variables you can adjust.

Op amps can and do have optimal source impedances, and in VE applications you can tweak those impedances (over a range) with resistor value choices. 

In mic preamps, even though the source impedance of the microphone is a given, using a step up transformer can adjust that source impedance to better match a given op amp.

While I think talking about (optimizing) noise too much in the context of VE summing is missing the rest of the story (phase shift and distortion). The noise floor of most consoles is dominated by other circuitry.

I preferred NF when talking about mic preamps because consumers were generally confused by dBu numbers that were not always comparable apples to apples, due to different measurement bandwidths or other factors (shorted input, etc). NF reveals how close the preamp is to ideal so  hyperbolic claims in advertising were easier to negate.

JR

JohnRoberts said:

I guess it depends on what are the variables you can adjust.

Op amps can and do have optimal source impedances, and in VE applications you can tweak those impedances (over a range) with resistor value choices. 

In mic preamps, even though the source impedance of the microphone is a given, using a step up transformer can adjust that source impedance to better match a given op amp.

While I think talking about (optimizing) noise too much in the context of VE summing is missing the rest of the story (phase shift and distortion). The noise floor of most consoles is dominated by other circuitry.

I preferred NF when talking about mic preamps because consumers were generally confused by dBu numbers that were not always comparable apples to apples, due to different measurement bandwidths or other factors (shorted input, etc). NF reveals how close the preamp is to ideal so  hyperbolic claims in advertising were easier to negate.

JR

Click to expand...

I believe we would agree that both methods are aimed at different evaluations. I guess that's why we learnt both and have found out when one is more useful than the other.

JohnRoberts said:

While the author dismisses using NF to characterize noise performance, he is talking from the perspective of an op amp salesman.

I like using NF to evaluate a circuit design because it clearly states how far from ideal (noiseless) it is. 

Click to expand...

Hmmm, I didn't get the impression that he was dismissing using NF out of hand. I thought he was just saying that you can't quote NF for a given op amp the way you can quote other specs, since it depends on the "environment" (signal source resistance). And, therefore, that salesmen who do quote NF are assuming some standard 50Ω or 75Ω resistance, or perhaps some other unnamed resistance that most flatters their product.

In any case, he does then show how to calculate NF for a given op amp with a given source resistance. And, I agree with you, it's useful to have a figure which clearly compares the ideal noise level vs the actual.

So, I added a row on my op amp comparison spreadsheet for NF as well. And was pleased to see that my summing op amp of choice for the Trident S65, the LME49710, has a NF of 0.31 dB when used with a 400Ω source resistance. This was the lowest NF of the bunch, with the NE5534A in a close second with 0.47 dB.

All that said, John, I know that NF for a summing amp isn't necessarily (and probably isn't) the most important spec. But if everything else is looking and sounding good, it's nice to know that noise level isn't suffering as a result.