Exercise 6.11 Non linear feedback around an opamp configuration

Given is the circuit below; for the op-amp

• the voltage gain is $A_o$ (finite)

• the output resistance is $r_{out}$.

• the input resistance $r_{in}\to \infty$.

The element equation of the BJT is $i_C=I_{C0}\cdot e^{}$

q$\cdot v_{BE}kT$.

a)

Derive an expression for the transfer of $v_{out}(v_{in})$ of the circuit. You may assume that the input voltage $v_{in}$ is positive. For simplicity, you may use $r_{out}=0\mathrm{\Omega }$ and $A_0\to \infty$ for this question.

b)

Derive an expression for the (small signal) output resistance $r_{out,circuit}$ of the circuit as a function of the input voltage of the circuit.