Question about the slew rate

Question

Let's consider an op-amp:

From basic courses of electronics, we know that the output voltage as a function of the differential input is given by the following picture:

Now, assuming that:

• the op-amp is closed with negative feedback;
• the output voltage has a finite value;
• the open-loop gain is large enough (ideally infinite);

then

and Vin1 and Vin2 are almost equal (virtual short-circuit).

Question: when I turn on a given circuit containing an op-amp with negative feedback, the op-amp in general will not work exactly and immediately in the linear region of its characteristic. Does the op-amp go into the linear region thanks to the slew rate due to some parasitic capacitors (which are always present)?

This idea has come to my mind after reading the following example taken from Razavi's book:

Thanks to the load capacitor CL indeed we have that the output voltage either increases or decreases and, as a consequence, the difference between the two inputs of the differential pair returns small, thus restoring linearity.

Answer 1

The large swing slew Rate is always limited by drive current limit and load capacitance which near 0 ESR compare to load R.

Thus dV/dt = Ic/C. Where Ic=V/R where for FETs, R = RdsOn or Ron and for BJT drivers , Ic is an active current limiter with the bulk Rce added to it.

Where f(-3dB)=0.35/Tr , and Tr= 10~90% rise time, this is always less than the small signal f-3dB .

Closed loop gain is limited by small internal capacitance and feedback ratio where more -ve feedback results in lower output impedance. Thus more feedback with lower Zout and lower forward gain. Acl*f = GBW.

In other words, for small signals, the Negative feedback (NFB) always reduces the output impedance for small signals which enables mor BW, but for large sig. the slew rate is limited by charge current Ic(max)=dV/dt= V/(R’C’) as the driver becomes saturated and cannot drive any more current to match the input risetime.

BJT OA’ s may have active current limiting of 30mA and slew rate is thus is defined for a fixed load like 30~100pF while FET drivers have Ron limits. Since the cap ESR is lower than the load R, this if often the limiting factor. But then FET’s with lower Ron also higher Coss, so max slew rate includes other variables of the FET & Load pF.