# A mistake in "Op Amps for Everyone" about op amp attenuators

In Texas Instruments' book "Op Amps for Everyone" (5th edition, link, see page 347), in chapter 25 "Common Application Mistakes" I believe there is a mistake (ironically).

It states that it's wrong to use a unity-gain stable opamp for an attenuator like this:

I believe the statement is wrong, because that attenuator have the noise gain of $$\1+\frac{R_F}{R_G}\$$ which is always $$\\ge 1\$$. Opamp stability is determined by the noise gain (i.e. the gain with respect to the non-inverting input), not the gain of a desired signal (opamp doesn't know what the desired signal is). There is even a compensation technique which increases the noise gain preserving the signal gain (e.g. add a resistor between the opamp's inputs in fig. 25.1). Surprisingly, even in the same book in chapter 7, sect. 7.4, there is a highlighted statement, quoute:

Several things must be mentioned at this point in the analysis. First, the transfer functions for the noninverting and inverting equations, (7.13) and (7.18), are different. For a common set of $$\Z_G\$$ and $$\Z_F\$$ values, the magnitude and polarity of the gains are different. Second, the loop gain of both circuits, as given by Equations (7.15) and (7.19), is identical. Therefore the stability performance of both circuits is identical although their transfer equations are different. This makes the important point that stability is not dependent on the circuit inputs.

It means that an inverting amp (like in fig. 25.1) has the same stability as a non-inverting amp with the same resistors (as if $$\V_{IN}\$$ be grounded).

Also, I sometimes see attenuators like in fig. 25.1 in real-world circuits designed by professionals. For example, in Agilent 6060B there are some examples, e.g. an inverting amp with the signal gain of $$\-\frac 16\$$ (the noise gain of $$\1+\frac 16\ge 1\$$):

Does this a real mistake in the book (survived for the 5th edition!), or I miss something?

• Please provide a link to the on-line version of the book and state the page number. Jan 24, 2021 at 9:45
• Opamp stability is NOT determined by the noise gain. It is the LOOP GAIN - as for each system with feedback - that is the basis for the stability criterion.
– LvW
Jan 24, 2021 at 9:51
• @LvW: doesn't matter. Loop gain of the amp in fig. 25.1 is the same as for a non-inverting amp with the same resistors, which is stable (for a unity-gain stable opamp). Jan 24, 2021 at 9:54
• Please provide an accessible link to the on-line version of the book Jan 24, 2021 at 10:49
• Put it simply, that statement is wrong. Any writing can be crept by mistakes and TI is everything but immune. Jan 24, 2021 at 12:01

# TL;DR

It's a mistake in the book.

# Details

After some googling (and pirating for different editions of "Op Amps for Everyone") I found that the original editor of "Op Amps for Everyone" (1-2 editions) was Ron Mancini. These editions doesn't contain the caution about $$\R_G > R_F\$$.

At 3rd editions the editor of the book was changed to Bruce Carter, and "Texas Instruments" label from the title is gone. He placed that caution in many places around the book. He didn't remove the old material though, like the quote above about inverting and non-inverting circuits has the same loop gain (so the stability), which directly contradicts with the Carter's caution.

There are some other discussions on web, e.g. this with Ron Mancini itself, and this where Michael Steffes (from Texas Instruments) wrote:

This actually was a classic mistake by Bruce Carter that Mancini seems to paper over for some reason. Somewhere Bruce got the idea that an inverting configuration had a noise gain of Rf/Rg instead of the correct 1+Rf/Rg. Bruce Trump and I wasted about an hour one day trying to explain that error to him with no luck.

As the author of one the book's chapter "Active Filter Design Techniques", I did advise B. Carter not to publish this nonsense, as it is simply wrong. I also advised him not to use the term "gain" repeatedly, but to distinguish between open-loop gain, closed-loop gain and loop-gain. A concept he seems to be opposed to.

Whether an op-amp circuit, (inverting or non-inverting amplifier) is stable or not, solely depends on its loop-gain, A x b, where A is the op-amp's open-loop gain and b is the feedback factor RF/(RF+RG). A very good treatise on op-amp stability is Jerald Graeme's book "Optimizing op-amp performance".

• sorry Thomas, but the feedback factor b = RG/(RF+RG) Jul 26 at 22:10

When a data sheet says "Unity Gain Stable" it is referring to the non-inverting, buffer, unity gain configured amplifier which is the least stable of all the configurations and is less stable than an inverting amplifier configured for a closed loop gain of less than 1.

It is loop gain, B.Aol which determines stability. The lower the loop gain, the more stable the amplifier. B is equal to 1/(noise gain) which is equal to Rg/(Rf+Rg) and so the higher the noise gain, the more stable the amplifier. The lowest the noise gain can be is unity as in the case of the buffer amp (non-inverting amp configured for unity closed loop gain) but an inverting amplifier configured with a closed loop gain of less than one has a noise gain of greater than 1 (beta less than one) and so is a more stable configuration than a "unity gain" amplifier, (a buffer). The beta of an inverting amplifier, configured for a closed loop gain of 1/10, is equal to 10/11. This is less than 1 and so it is more stable than a non-inverting buffer because BAol is less.

Therefore if an amplifier is specified as "unity gain stable" (stable as a non-inverting buffer) it should be even more stable (further from instability) when configured as an inverting amplifier with a closed loop gain of less than unity.

• So the caution "$R_G>R_F$ is WRONG!!!" in the fig. 25.1 above is wrong? Jan 24, 2021 at 11:41
• Yes - I think you are right. An inverting opamp with a gain <1 is more stable if compared with the case of 100% feedback (zero inverting gain)
– LvW
Jan 24, 2021 at 15:08
• @LvW Yes, zero inverting gain (output at 0V) has the same B = 1, the same loop gain = Aol and therefore the same stability margins as unity, non-inverting gain. So for the inverting amplifier, increasing the closed loop gain to anything above zero improves stability beyond that of unity non-inverting gain or zero inverting gain. Jan 24, 2021 at 15:37