Electronic – Capacitor into resistor to ground

The transfer function of the inverting amplifier is

\$ V_{OUT} = -\dfrac{R_{feedback}}{R_{in}} \cdot V_{IN} \$

For the non-inverting amplifier it is

\$ V_{OUT} = \left(1 + \dfrac{R_{feedback}}{R_{g}}\right) \cdot V_{IN} \$

where \$R_g\$ is the resistor to ground.

So the gain is determined by a resistance ratio, where a higher feedback resistance gives a higher gain. About the choice for higher or lower resistance values: lower is better, because at higher resistances the input bias current may begin to play a role. But don't overdo it: if your inverting amplifier would have a 1 kΩ feedback resistor and you want a gain of 10 \$\times\$, then the input resistance should be 100 Ω, and that may be a bit too little for the signal source. So see how much current the source can supply, and calculate the feedback resistor from that.

The non-inverting amplifier doesn't have that problem: the input signal feeds directly to the high impedance of the non-inverting input. To minimize offset error you'll have to make the input impedances for both inputs equal, that means on the signal input a series resistance equal to \$R_{feedback}\$ and \$R_g\$ in parallel. Example: if the feedback resistor is 10 kΩ and \$R_g\$ 1 kΩ then place a 9.1 kΩ in series with the source.

By the way, that equal impedance rule also goes for the inverting amplifier. You'll often see the non-inverting input directly connected to ground, but again placing a resistor between the input and ground will reduce offset error. Again the resistance is the parallel of the other two resistors.

There is an outer loop provided by Rf and an inner loop provided by the local integrator capacitor Cf. At low frequencies Cf has effectively a high impedance and the outer loop dominates. This can be approximated by an open Cf and zero value Rf (since Rf impedance would be much lower than OpAmp input impedance).

While at high frequencies CF has lower impedance than Rf path and the inner loop dominates. This can be approximated as shorted Cf and open Rf.