About "Always inverting except when you can't" of OPA

 I answered this SE EE question yesterday.

Short explanation

Non-inverting configuration. Simply put, the problems of the non-inverting configuration come from the op-amp inputs being at some voltages and, even worse, those voltages are changing. And when there are voltages, all kinds of parasitic leakages and stray capacitances "attack" and change them. The differential input has also been a problem in the past and they used a single-ended input. In addition, the differential input cannot be fully balanced and a voltage appears at the op-amp output even when the two input voltages are exactly the same (the so-callel "common-mode error"). The good things are that the differential voltage (between the two inputs) is close to zero and the input resistances are high.

Inverting configuration. In contrast, all input voltages in the inverting configuration are zero and parasitic leakages and capacitances (to ground), even if they vary, do nothing. But this configuration has one peculiarity - the input source and the op-amp output are connected through an R1-R2 resistor network and interact (oppose). As a result, R2 "disappears" (it is neutralized by the op-amp output voltage) and a point with zero voltage (virtual ground) appears in the middle of the resistor network. This creates the illusion that R1 is grounded, but in fact it has no connection to ground. The problem with R1 is that it has to be high (because it determines the input resistance of the inverting configuration) but if we want gain, R2 needs to be even higher... and it will have parasitic leakage and capacitance.

Basic idea

Now I want to add a little more general explanations of these two basic negative feedback configurations. This would be of interest to OP and visitors because it reveals the logic behind the emergence of these configurations. I will do it by showing, step by step, their evolution.

Zero voltage stabilizer

This is the most basic negative feedback circuit. We can do it easily by simply connecting the output of a very high gain inverting amplifier to its input. Thus we force it make its input voltage (almost) equal to zero. For this purpose, the (op-)amp decreases its output voltage (almost) up to zero. So to make an op-amp keep its input voltage zero, just connect its output to its input.

Such a circui producing zero voltage is not very useful for us but it is needed as a starting point for building negative feedback circuits. We rather need an amplifier circuit. Let's see how we can do it.

Disturbed zero voltage stabilizer

To make the circuit above amplify, we can apply a well-known trick from life - if we disturb the op-amp, it will react to this intervention and restore the zero voltage at its input. How can we disturb it?

For example, we can add an external (input) voltage as a disturbance to op-amp input. As a response, the op-amp will subtract its output voltage and its input voltage will be zero again. So, we can use the disturbance as an input and the op-amp reaction as an output in this negative feedback amplifier. We can say that the input voltage of a negative feedback amplifier is a disturbance and its output voltage is a reaction to this disturbance.

Implementation

How can we add the input voltage? We can do it in two ways:

In series (according to KVL). Here, the external input voltage source and the op-amp output are connected in series (through the ground) and have the same polarity (referenced to ground). So their voltages are subtracted (as needed) in the loop and the circuit is non-inverting.

In parallel (according to KCL). Now, the external input voltage source and the op-amp output are connected through resistors in parallel and have opposite polarities (referenced to ground). So their voltages are subtracted by the R1-R2 network and the circuit is inverting.

Inverting circuits do not need an amplifier with differential input; they can be implemented by a simple amplifier with single-ended input. But since there are none today, they are implemented by op-amps with a differential input with the unused non-inverting input grounded.

Inverting vs non-inverting

The inverting and non-inverting amplifiers are two implementations of the same idea. Structurally, they differ only in the way they subtract the input and output voltages (type of summer). But this leads to the following functional differences:

• The inverting amplifier inverts since the resistor summer needs input voltages with opposite polarities to subtract them; the non-inverting amplifier does not invert since the series summer needs input voltages with the same polarity to subtract them.
• In the inverting amplifier, the virtual ground voltage (usually zero) is between the input and output voltage (usually with opposite polarity); in the non-inverting amplifier, the input and output voltage have the same polarity.
• The inverting amplifier can be implemented by an op-amp with a single-ended input since the result of subtraction is referenced to ground; the non-inverting amplifier requires an op-amp with a differential input since the result of subtraction is "floating".
• Both circuits can be single-supplied - the inverting amplifier needs a bias voltage appled to the non-inverting input; the non-inverting amplifier is "self-biased" and does not need biasing.
• All input voltages in the inverting amplifier are zero so parasitic leakages and capacitances do not affect the input; in the non-inverting amplifier the op-amp inputs are at some voltages that are changing so that they are under the influence of leakages and capacitances.
• Since in an inverting amplifier the input voltages are zero (or fixed), there is no common-mode error; in a non-inverting amplifier, there is a common-mode error because of the varying input voltages.
• In an inverting amplifier, the op-amp output voltage is added to the input voltage so the input current increases; in a non-inverting amplifier, a part of the op-amp output voltage is subtracted from the input voltage so the input current decreases.
• The input resistance of the inverting amplifier seen by the input voltage source is equal to R1 since R2 is neutralized by the op-amp output voltage... but R1 cannot be very high because R2 will be even higher; the input resistance of the non-inverting amplifier is high because it is the op-amp input resistance.