The circuit shown in the figure uses matched transistors with a thermal voltage $${V_T} = 25\,mV.$$ The base currents of the transistors are negligible. The value of the resistance $$R$$ in $$k\Omega $$ that is required to provide $$1\,\,\,\mu A$$ bias current for the differential amplifier block shown is ____________.

The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

For a system having transfer function $$G\left( s \right) = {{ - s + 1} \over {s + 1}},$$ a unit step input is applied at time $$t=0.$$ The value of the response of the system at $$t=1.5$$ sec (round off to three decimal places) is __________.

The transfer function of a system is given by $${{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}} = {{1 - s} \over {1 + s}}$$

Let the output of the system be $${v_0}\left( t \right) = {v_m}\sin \left( {\omega t + \phi } \right)$$ for the input $${v_i}\left( t \right) = {v_m}\sin \left( {\omega t} \right).$$ Then the minimum and maximum values of ϕ (in radians) are respectively