For the given differential amplifier:

a$.$ Determine the D$.$C$.$ current through Q$1$ with Vinl $=$Vin$2=0V.[1]$

b$.$ Determine the D$.$C$.$ output voltage at Vout$2$ with Vin$1=$Vin$2=0V.[1]$

c$.$ Determine the value of $r_e^{\text{'}}$ for Q$1.[1]$

d$.$ Determine the magnitude of the single$-$ended Av$.[1]$

e$.$ Sketch one cycle of the output waveform for the following sine$-$wave inputs. Label your maximum voltage. Assume Vin $=0$ and is rising at the origin $($centre of graph$).$

$[3]$

$V_{IN1}=V_{IN2}=1m{V}_{PK}$

Sketch Vout$2-$ Vout$1$