Assume that the OP_AMP in the figure, ideal

(a) Obtain an expression for V₀ in terms of V_s, R, and the reverse saturation current I_s of the transiostor.

(b) If R = 1$$\Omega $$, I_s = 1pA and the thermal voltage V_T = 25mV, then what is the value of the output voltage V₀ for an input voltage V_s = 1V?

(c) Suppose that the transistor in the feedback path is replaced by a p-n junction diode with a reverse saturation current of I_s. The p-side of the diode is connected to node A and the n-side to node B. Then what is the expression for V₀ in terms V_s, R and I_s ?

Consider the circuit given in fig. using an ideal operational Amplifier.

The characteristics of the diode are given by the relation I = I_s $$\left[ {{e^{{{qV} \over {KT}}}} - 1} \right],$$

Where V is the forward voltage across the diode
(a)Express V₀ as a function of V_i assuming V_i> 0.
(b)If R = 100K$$\Omega $$ , I_s = 1$$\mu $$A and $${{KT} \over q}\,\, = \,\,25mV$$

Shown that the system in Fig. is a double integrator. In other words, prove that the transfer gain is given by $${{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}} = {1 \over {{{\left( {CRs} \right)}^2}}},$$ assume ideal OP -AMP

Find the output voltage of the following circuit assuming ideal op-amp behavior.