Exercise 7.1 Stability for a trans impedance amplifier configuration

See the opamp circuit below.

The opamp is almost ideal ($r_{\mathit{in}}\to \infty$, $t_{\mathit{out}}=0\mathrm{\Omega }$), but it has a frequency dependent gain according to $A(\mathit{j\omega })=\frac{A_0}{1+\mathit{j\omega }∕{\omega }_0}$, with $A_0\gg 1$.

a)

Derive an equation for the loop gain of this circuit.

We now define an (angular) frequency ${\omega }_1=\frac{1}{R_2\cdot C_1}$

b)

With $A_o\gg 1$, is it possible to get a phase margin of $45°$ if ${\omega }_0={\omega }_1$?

c)

With $A_o\gg 1$, is it possible to get a phase margin of $45°$ if ${\omega }_0\gg {\omega }_1$?

d)

With $A_o\gg 1$, is it possible to get a phase margin of $45°$ if ${\omega }_0\ll {\omega }_1$?

e)

Calculate for one of the cases above where $45°$ phase margin can be obtained, the corresponding/required ${\omega }_1$. The properties of the opamp are fixed.