Consider the following circuit using an ideal Op-Amp. The I-V characteristics of the diode is described by the relation $$$I = {I_0}\left[ {{e^{{V \over {VT}}}} - 1} \right], where \,{V_T}\,\, = \,\,25mV,{I_0}\,\, = 1 \mu {\rm A}$$$

and V is the voltage across the diode (taken as positive for forward bias). For an input voltage $${V_i}\,\, = \,\, - 1V,$$ the output voltage V₀ is

The Op-Amp circuit shown above represents a

Consider the Schmitt trigger circuit shown below.

A triangular wave which goes from -12V to 12V is applied to the inverting input of the OP-AMP. Assume that the output of the OP-AMP swings from +15V to -15V. The voltage at the non-inverting input switches between.

In the Op-Amp circuit shown, assume that the diode current follows the equation I = I_s exp (V/V_T) . For V_i = 2V, V_o = V₀₁, and for V_i = 4 V, V_o = V₀₂. The relationship between V₀₁ and V₀₂ is