Electrical – single pole roll off model for an operational

I would expect the gain-bandwidth product to be a constant, but it's worth comparing the two on the bench before designing it in (I suggest measuring both the gain-of-10 -3dB point and the gain-of-0.1 -3dB point to have a point of comparison with the datasheet limits).

Note that the slew rate is typically a fairly good 5V/us, but you'll run into that at high amplitudes.

If you use this circuit on a regular basis I guess it would be worth to calculate its transfer function once and for all, so you can just easily evaluate it given the concrete component values. Doing the math you get (assuming an ideal OP)

$$H(\omega)=\frac{j\omega R_1C_1}{1+j\omega R_1C_1}\left(1+\frac{j\omega R_4C_2}{1+j\omega R_2C_2}\right)\tag{1}$$

A plot of (1) in dB with the specified component values looks like this (|H|/db vs f in Hz):

from which you can see that the -3dB point is at about \$250\,\text{Hz}\$.

If you further assume that

$$R_1C_1=R_2C_2=\tau$$

and if you denote the gain at large frequencies by

$$g=1+\frac{R_4}{R_2}$$

then with a bit more math you get this exact expression for the 3dB cut-off frequency in radians

$$\omega_c=\frac{1}{\tau}\sqrt{1-\frac{1}{g^2}+\sqrt{\left(1-\frac{1}{g^2}\right)^2+1}}\tag{2}$$

which with the given component values gives

$$\omega_c=2\pi\cdot 247.28$$

For a large gain \$g\gg 1\$, formula (2) is closely approximated by

$$\omega_c=\frac{1}{\tau}\sqrt{1+\sqrt{2}}\approx\frac{1.55}{\tau}\tag{3}$$