A part of a communication system consists of an amplifier of effective noise temperature, $$Te = \,\,21\,\,{}^ \circ K\,$$, and a gain of 13 dB, followed by a cable with a loss of 3 dB. Assuming the ambient temperature to be $$300{}^ \circ \,K$$, we have for this part of the communication system,

In order to stabilize the system shown in fig. T_i should satisfy:

From the Nicholas chart, one can determine the following quantities pertaining to a closed loop system:

Nyquist plot consider a feed back system where the OLTF is: $$G(s) = {1 \over {s\left( {2s + 1} \right)\left( {s + 1} \right)}}.$$ Determine the asymptote which the nyquist plot approaches as $$\omega \to 0.$$ Find also the range of 'k' in terms of the cross over frequency $${\omega _{PC}}$$ for stability.