Consider the circuit given in the figure is using an ideal operational amplifier.
The characteristics of the diode are given by the relation $\mathrm{I}=\mathrm{I}_{\mathrm{S}}\left(\frac{\mathrm{V}}{e^{\mathrm{kT}}}-1\right)$ where $V$ is the forward voltage across the diode.
- Express $V_{u}$ as function of $V_{i}$ assuming $V_{1}>0$
- If $\mathrm{R}=100 \; k \Omega, I_{s}=1 \; \mu \mathrm{A}$ and $\frac{k \mathrm{T}}{q}=25 \mathrm{~mV}$, find the input voltage $V_{i}$, for which $V_{0}=0$.