As known there are inverting and non-inverting summing circuits, such as below:
What's their cons and pros?
I'm only going to bother with the main con of the non-inverting summing amplifier because it renders it fairly useless in many applications. So....
The big disadvantage of the non-inverting summing amp is that if you disconnect one of the inputs, the gain of the circuit doubles for the remaining connected channel. This is not the case with the inverting summing amplifier because it generates a virtual earth summing point.
Implications that follow: -
None of the above happens with the inverting summing amplifier.
In addition to the pros/cons already mentioned I like to add the following:
The bandwidth of the inverting circuit is - depending on the number of input resistors - much smaller than for the non-inverting configuration. More than that, also the noise at the output will much larger.
The reason for this effect is the feedback factor (resp. the loop gain of the inverting circuit).
(1) For the non-inverting configuration, the feedback factor is simply Rin/(Rfeedback+Rin). [in the example: 100k/200k=0.5]
(2) In contrast, for the inverting circuit the feedback factor is Rp/(Rp+R4) with Rp=R1||R2||R3. This reduced value of Rp lowers the feedback signal (without influence on the forward gain) and - at the same time - the loop gain.
Hence, taking the real frequency-dependent gain of the opamp into account, the available bandwidth is reduced correspondingly. At the same time, the reduced feedback factor is connected with a noise gain increase (Noise gain=1/feedback factor)
Comment: In the answer from JWRM22 we can read "inverting amplifiers are more stable". Although this is not true for a comparison between inverting and non-inverting amplifiers (both have the same feedback path), it is true for the summing applications as discussed here. As explained above in (2), inverting summing blocks have comparable less feedback and, hence, the stability margin is increased.
Of course, all comparisons between both circuit alternatives assume equal or - at least - similar gain values.
For simplicity I answer for normal amplifier circuit (one input and one output). R2 is the feedback resistor.
Inverting amplifier: Vout = Vin * -(R2/R1)
Inverting amplifiers gain is easily adjusted. Double R2 is double the gain. Also Inverting amplifiers are more stable.
Noninverting amplifier: Vout = Vin * (1+ (R2/R1))
Noninverting amplifiers have a very high input impedence. It needs little (nano Amps) of input current. This means you can measure a circuit without influencing it.
In analog circuitry its mix and match. Add a line follower before the inverting amplifier to get the best of both worlds.