1. Consider the circuit as shown in Fig. 1. NPN transistors Q1...Q4 have an VA = 50V and \(\beta\) = 40. The reference current $I_{ref}$ is always maintained at a constant value, typically at 1 mA.
(i) Derive an expression for R as a function of $I_{ref}$, $I_O$ and the reverse saturation current $I_S$.
(ii) If $I_O = 24 \,\mu A$, then what is the value of R?
(iii) Based on your answer to part (ii) of this question, determine the small signal resistance $R_{out}$.