The attenuation factor of the output signal at the summing point of the amplifier (the negative input terminal of the op-amp) is called beta (a Greek letter) and is given by the ordinary divider equation as
beta = Rin / (Rin + Rfb)
The so-called “loop gain” (more precisely the open loop gain) is the gain around the loop as the product of the intrinsic open-loop gain of the op-amp itself and the attenuation factor beta, as
Go = A * beta = A * Rin / (Rin + Rf)
For the inverting circuit, the signal gain is given more exactly with a correction factor for the finite gain of the op-amp itself and we can write the corrected signal gain as
Gs = - (Rfb / Rin ) * (1/ (1 + (1/Go))
Looking at the equation above the last one we can see that the quantity Go takes into account the finite gain of the op-amp and the beta factor.
Let the gain correction factor be written as gcf, then we can write Gs as
Gs = - (Rfb / Rin) * gcf
where gcf is approximately 1.0 or a little less than 1.0.
For the non-inverting amplifier, we still have the same value for beta or the attenuation factor from the output to the summing point as
beta = Rin / (Rfb + Rin)
and we will have the same correction factor for signal gain as we had above. Therefore the non-inverting signal gain is given by
Gs_ni = ((Rin + Rfb) / Rin) * gcf
So what is noise gain? Noise gain is defined as the inverse of the beta factor or
NG = 1 / beta
In the case of unity gain amplifier circuits, if we consider the non-inverting unit gain circuit, the noise gain is
NGni = (Rin + Rfb) / Rin = 1 / beta
and Rfb is zero or Rin is infinite, so
NGni = 1 /1 = 1
So the noise gain for the non-inverting amp is 1.0.
For the unity gain inverting amplifier we have
NGi = (Rin + Rfb) / Rin
and Rin = Rfb , so
NGi = (Rin + Rin ) / Rin = 2.0
Therefore the noise gain of the non-inverting amplifier is lower than the inverting amplifier in the unity gain configuration. Why is this important? Because the noise gain will act on the voltage and current off-set errors of the op-amp as well as other op-amp noise sources. For a sensitive low level amplifier circuit we should therefore prefer the non-inverting configuration.
beta = Rin / (Rin + Rfb)
The so-called “loop gain” (more precisely the open loop gain) is the gain around the loop as the product of the intrinsic open-loop gain of the op-amp itself and the attenuation factor beta, as
Go = A * beta = A * Rin / (Rin + Rf)
For the inverting circuit, the signal gain is given more exactly with a correction factor for the finite gain of the op-amp itself and we can write the corrected signal gain as
Gs = - (Rfb / Rin ) * (1/ (1 + (1/Go))
Looking at the equation above the last one we can see that the quantity Go takes into account the finite gain of the op-amp and the beta factor.
Let the gain correction factor be written as gcf, then we can write Gs as
Gs = - (Rfb / Rin) * gcf
where gcf is approximately 1.0 or a little less than 1.0.
For the non-inverting amplifier, we still have the same value for beta or the attenuation factor from the output to the summing point as
beta = Rin / (Rfb + Rin)
and we will have the same correction factor for signal gain as we had above. Therefore the non-inverting signal gain is given by
Gs_ni = ((Rin + Rfb) / Rin) * gcf
So what is noise gain? Noise gain is defined as the inverse of the beta factor or
NG = 1 / beta
In the case of unity gain amplifier circuits, if we consider the non-inverting unit gain circuit, the noise gain is
NGni = (Rin + Rfb) / Rin = 1 / beta
and Rfb is zero or Rin is infinite, so
NGni = 1 /1 = 1
So the noise gain for the non-inverting amp is 1.0.
For the unity gain inverting amplifier we have
NGi = (Rin + Rfb) / Rin
and Rin = Rfb , so
NGi = (Rin + Rin ) / Rin = 2.0
Therefore the noise gain of the non-inverting amplifier is lower than the inverting amplifier in the unity gain configuration. Why is this important? Because the noise gain will act on the voltage and current off-set errors of the op-amp as well as other op-amp noise sources. For a sensitive low level amplifier circuit we should therefore prefer the non-inverting configuration.
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