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Noise Gain (NG)

The first aid to analyzing op amps circuits is to differentiate between noise gain and signal gain. We have already discussed the differences between non-inverting and inverting stages as to their signal gains, which are summarized in Equations 1-2 and 1-4, respectively. But, as can be noticed from Fig. 1-6, the difference between an inverting and non-inverting stage can be as simple as just where the reference ground is placed. For a ground at point G1, the stage is an inverter; conversely, if the ground is placed at point G2 (with no G1) the stage is non-inverting.
Note however that in terms of the feedback path, there are no real differences. To make things more general, the resistive feedback components previously shown are replaced here with the more general symbols ZF and ZG, otherwise they function as before. The feedback attenuation, β, is the same for both the inverting and non-inverting stages:
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Noise gain can now be simply defined as: The inverse of the net feedback attenuation from the amplifier output to the feedback input. In other words, the inverse of the β network transfer function. This can ultimately be extended to include frequency dependence (covered later in this chapter). Noise gain can be abbreviated as NG.
As noted, the inverse of β is the ideal non-inverting op amp stage gain. Including the effects of finite op amp gain, a modified gain expression for the non-inverting stage is:
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where GCL is the finite-gain stage's closed-loop gain, and AVOL is the op amp open-loop voltage gain for loaded conditions.
It is important to note that this expression is identical to the ideal gain expression of Eq. 1-4, with the addition of the bracketed multiplier on the right side. Note also that this right-most term becomes closer and closer to unity, as AVOL approaches infinity. Accordingly, it is known in some textbooks as the error multiplier term, when the expression is shown in this form (Some early discussions of this finite gain error appear in References 4 and 5 (References 4 and 5: Frederick E. Terman, "Feedback Amplifier Design," Electronics, Vol. 10, No. 1, January 1937, pp. 12-15, 50 and Julian M. West, "Wave Amplifying System," US Patent 2,196,844, filed April 26, 1939, issued April 9, 1940). Terman uses the open-loop gain symbol of A, as we do today. West uses Harold Black's original notation of μ for open-loop gain. The form of Eq. 1-9 is identical to Terman's (or to West's, substituting μ for A)).
It is useful to note some assumptions associated with the rightmost error multiplier term of Eq. 1-9. For AVOLβ >> 1, one assumption is:
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This in turn leads to an estimation of the percentage error, ε, due to finite gain AVOL:
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Gain Stability
The closed-loop gain error predicted by these equations isn't in itself tremendously important, since the ratio ZF/ZG could always be adjusted to compensate for this error. But note however that closed-loop gain stability is a very important consideration in most applications. Closed-loop gain instability is produced primarily by variations in open-loop gain due to changes in temperature, loading, etc.
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From Eq. 1-12, any variation in open-loop gain (ΔAVOL) is reduced by the factor AVOLβ, insofar as the effect on closed-loop gain. This improvement in closed-loop gain stability is one of the important benefits of negative feedback.
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