In the figure shown, assume that the zener diode and operational amplifier to be ideal.

$$(a)$$ 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.

Figure shows a common emitter amplifier

$$(a)$$ 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.

Which of the following is the transfer function of a system having the Nyquist plot shown in Fig. below.

A unity feedback system has an open-loop transfer function of the form $$KG\left( s \right) = {{K\left( {s + a} \right)} \over {{s^2}\left( {s + b} \right)}};\,\,\,\,b > a$$ Which of the loci shown in Fig. can be valid root-loci for the system?