(Solved): Q1. (80) Consider the BJT amplifier seen in fig. 1. The input AC voltage give ...

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Q1. (80) Consider the BJT amplifier seen in fig. 1. The input AC voltage given by \( v_{i}(t)=10 \sin \left(2 \pi 10^{3} t\right), m V \) is applied to the amplifier and the \( \mathrm{AC} \) output voltage obtained is given with the expression \( v_{o}(t)=-1.2 \sin \left(2 \pi 10^{3} t\right) \). Perform the followings: a) (05) Calculate the value of the \( \mathrm{AC} \) voltage gain \( A_{v} \). b) (05) Draw the AC equivalent circuit. c) (10) Derive the mathematical expression of \( \mathrm{AC} \) voltage gain \( A_{v} \) using the \( \mathrm{AC} \) equivalent circuit you have drawn in b). d) (12) Calculate the value of the emitter dynamic resistance \( r_{e} \) in \( \mathrm{k} \Omega \). (VT=26 \( \mathrm{mV} \) at room temperature 27C). e) (13) Determine the value of the DC emitter current \( I_{E Q} \) at operating point \( Q \). Then, determine the value of the DC currents \( I_{B Q}, I_{C Q} \) at operating point Q. (Hint: Assume \( \beta=100 \) ). f) (12) Determine the VCEQ and then write down operating point \( Q \). g) (23) Assuming the ratio between \( \mathrm{R} 1 \) and \( \mathrm{R} 2 \) is given as \( a=\mathrm{R} 1 / \mathrm{R} 2=29.97 \), derive an expression for \( \mathrm{R} 2 \) and then determine the value of R2 and R1 in k \( \Omega \). Find Thevenin voltage VTH and resistance RTH.