For the circuit shown in the figure below, assume that diodes $${D_1},\,{D_2}$$ and $${D_3}$$ are ideal.

The $$DC$$ components of voltages $${v_1}$$ and $${v_2},$$ respectively are

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

The transfer function of the system $$Y\left( s \right)/U\left( s \right)$$ , whose state-space equations are given below is:
$$\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet \left( t \right)} \cr {\mathop {{x_2}}\limits^ \bullet \left( t \right)} \cr } } \right] = \left[ {\matrix{ 1 & 2 \cr 2 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] + \left[ {\matrix{ 1 \cr 2 \cr } } \right]u\left( t \right) \cr & y\left( t \right) = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] \cr} $$