$$(a)$$ Draw the equivalent circuit and evaluate the gain $$\left( {{V_0}\,\,vs\,\,{V_i}} \right)$$ of the circuit for

$$(i)$$ $${V_i} \le 0$$ $$\,\,\,\,\,\left( {ii} \right)\,\,\,0 < {V_i} < 5V\,\,\,\,\,\,$$ $$\,\,\,\,\,\left( {iii} \right)\,\,\,{V_i} > 5V\,\,\,\,\,\,$$

$$(b)$$ Sketch the gain $$\left( {{V_0}\,\,\,{V_s}\,\,\,{V_i}} \right)$$ characteristics of the above circuit and label the salient features.

$$(a)$$ Simplify the circuit by applying thevenin's theorem to biasing network $${R_1},{R_2}$$ at

$$\,\,\,\,\,\,\,$$ the base of the transistor.

$$(b)$$ Assuming $${C_s}$$ to be a short for frequency range considered. Draw the small signal

$$\,\,\,\,\,\,\,$$ $$a.c.$$ model of the circuit obtained in $$(a)$$ by using the simple model for the

$$\,\,\,\,\,\,\,$$ transistor shown in figure.

$$(c)$$ Evaluate the small signal gain $$\left( {{{{V_0}} \over {{V_i}}}} \right)$$ of the amplifier.