Multiple choice

In the Op-Amp circuit shown, assume that the diode current follows the equation I = Is exp (V/VT). For Vi = 2V, V0 = V01, and for Vi = 4 V, V0 = V02. The relationship between V01 and V02 is

  1. V02 = $\sqrt2$V01

  2. V02 = e2 V01

  3. V02 = V01 In 2

  4. V01 - V02 = VT In 2
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D Correct answer
Explanation

Here the inverting terminal is at virtual ground and the current in resistor and diode current is equal i.e.

$$ \begin{aligned} I_R = & \quad I_D \\ or \qquad \dfrac{V_i}{R} = & \quad I_s e^{\frac{V_0}{V_r}} \\ or \qquad V_D = &\quad V_T\ ln \dfrac{V_i}{I_sR} \\ \text{For the first condition}\\ V_D = 0 - V_{o1} = V_T \ ln \ \dfrac{2}{I_sR}\\ \text{For the first condition}\\ V_D = 0 - V_{o1} = V_T \ ln \ \dfrac{4}{I_sR}\\ \text{Subtracting the above equation}\\ V_{o1} - V_{o2} = &\quad V_T\ ln\dfrac{4}{I_sR} - V_T\ ln \dfrac{2}{I_sR} \\ or \quad V_{o1} - V_{o2} = &\quad V_T\ ln\dfrac{4}{2} = V_T\ ln 2 \end{aligned} $$

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