Concept:Dynamic conductance (\(g_d\)) is the reciprocal of dynamic resistance (\(r_d\)). Differentiating the Shockley diode equation with respect to voltage yields a dynamic conductance directly proportional to the forward bias current.
Formula:$$I_D \approx I_s e^{\frac{V_D}{\eta V_T}} \implies g_d = \frac{d I_D}{d V_D} = \frac{I_D}{\eta V_T}$$
$$r_d = \frac{1}{g_d} = \frac{\eta V_T}{I_D}$$
Solution:- Differentiating forward diode current \(I_D\) with respect to forward voltage \(V_D\):
- $$\frac{d I_D}{d V_D} = \frac{1}{\eta V_T} \left( I_s e^{\frac{V_D}{\eta V_T}} \right) = \frac{I_D}{\eta V_T}$$
- Therefore, the dynamic conductance is \(g_d = \frac{I_D}{\eta V_T}\).
Why other options are incorrect:- Option A: \(V_T / I_D\) is the dynamic resistance (\(r_d\)), not conductance.
- Option B: Conductance has units of Siemens (\(\text{A/V}\)); \(I_D^2 / V_T\) has incorrect dimensions of \(\text{A}^2 / \text{V}\).
- Option D: Multiplying \(V_T\) by \(I_D\) gives power dimensions (\(\text{Watts}\)), not conductance.
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