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.

Find the output voltage, V₀ in the following circuit assuming that the Op-Amps are ideal.