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Why is the noise gain of an op amp always constant at $$1+\frac{R_1}{R_2}$$ and independent of configuration, unlike signal gain?

Null
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user3668717
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2 Answers2

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There are two unwanted opamp properties - effective at the input nodes of the opamp: Noise and input offset voltage. When the opamp has negative resistive feedback, both voltages (noise, offset) are amplified with the factor (1+R2/R1).

This is obvious (typical non-inv. gain formula) if we allocate these voltages to the non-inverting terminal only (assuming no signal input voltage at this node). However, it is easy to show by calculation that the result is the same if such an unwanted noise or offset source is located directly at the inverting terminal (between the inv. input and the common node where the feedback resistors meet).

Calculation (edit): Assuming no signal input (non-inv. input node and R1 grouded) and a finite output voltage Vout, the corresponding voltage at the common point of R1 and R2 is Vo=Vout*R1/(R1+R2). Solving for Vout/Vo=1+R2/R1 gives the relation between Vout and a corresponding voltage Vo between the common point and the "virtual ground" potential at the inverting input node.

LvW
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    I think this is correct as far as it goes but I don't think it spells out the implications enough for other configurations ... i.e. actually answers the question. –  Oct 26 '14 at 10:45
  • In the question the expression (1+R2/R1) is explicitely mentioned. Thus, the question is related to resistive feedback only - and not to "other configurations". – LvW Oct 26 '14 at 12:13
  • OK but I got the impression that illustrating how - and why - signal gain and noise gain are different in another configuration would help the questioner. (I can't see how to easily express it to my satisfaction, or I'd simply add my own answer!) –  Oct 26 '14 at 13:00
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(This will general, if you have a specific circuit you want to ask about, you should link to it or the discussion of it.) Noise gain of an opamp circuit tells you how the circuit responds to the various noise sources at it's inputs. (not just the signal which is usually just at one input.) All the instances I can think of involve the voltage noise gain. Generally one is most concerned with the opamp noise, though noise from resistors could also be important. I think the most insidious noise gain comes in transimpedance amps, where capacitance on the inverting input can lead to oscillations if not controlled. Sergio Frano's opamp book has some very clear discussions.

George Herold
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