Exercise 5.3 A common-collector amplifier

Given is the circuit in the figure below. The element equations of the BJT (for the region of operation assumed in this question) are:

The transistor is biased at a collector bias current $I_C=10\mathit{mA}$ for which (for this particular transistor) $V_{\mathit{BE}}=0.7V$. The current gain $\mathit{\beta fe}$ is 49. Furthermore, circuit operates at $300K$, $R_{B1}=15k\mathrm{\Omega }$, $R_{B2}=20k\mathrm{\Omega }$ and $V_{\mathit{CC}}=10V$.

a)

Derive an expression for $R_E$ and (after that) determine the numerical value of $R_E$.

b)

Explain briefly when we may use a small-signal approach for a BJT.

c)

Draw the small-signal equivalent circuit and derive an expression for the small-signal output resistance.