A weird degenerated amplifier with an NPN

Exercise 5.2 A weird degenerated amplifier with an NPN

Given is the circuit schematic below. The transistor in this schematic has current gain $βfe$ and has a finite output resistance; the collector current can be written as:

i_{C} = I_{C 0} (e^{\frac{q V_{BE}}{kT}} - 1) (1 + \frac{V_{CE}}{V_{A}})

with $V_{A}$ the Early Voltage, $k = 1.38 \cdot 1 0^{- 23} [m^{2} \cdot kg \cdot s^{- 2} \cdot K^{- 1}]$ (Boltzmann constant) and $q = 1.6 \cdot 1 0^{- 19} C$ (elementary charge). Consequently, $\frac{kT}{q} ≃ 25 mV$ at room temperature, $T = 290 K$ . You can assume the components $L_{1}$ , $C_{E}$ , and $C_{out}$ to be “large” for the signal frequencies of interest. We will ignore the output impedance of the BJT for all sub questions except for (d).

pict

a): Derive an expression for the bias collector current $I_{C}$ expressed in properties or values of the various components. Do not neglect the base current.
b): Find an expression for the bias collector voltage $V_{C}$ .
c): What amplifier topology is this (no motivation needed)?
d): Explain what you have to assume to be able to neglect the output impedance of the BJT in small signal derivations of e.g. voltage gain and output impedance.
e): Draw a small-signal equivalent circuit of this amplifier.
f): Calculate the output impedance of this amplifier.
g): Calculate the small-signal voltage gain of this amplifier.

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