How the depletion width of varactor diode is releated to its capacitance?Adirectly proportionBinversely portionCequal

Understanding the Relationship Between Depletion Width and Capacitance in Varactor Diodes

1. Break Down the Problem

   • We want to determine the relationship between depletion width and capacitance in a varactor diode. This involves understanding both how capacitance is defined in the context of a diode and how the depletion width affects this parameter.

2. Relevant Concepts

   • The capacitance $C$ of a varactor diode can be expressed using the formula: $C = \frac{\varepsilon A}{W}$ where:
     • $\varepsilon$ is the permittivity of the dielectric material,
     • $A$ is the junction area, and
     • $W$ is the depletion width.
   • From this equation, it's clear that capacitance is inversely proportional to the depletion width $W$.

3. Analysis and Detail

   • When the depletion region width $W$ increases, the capacitance $C$ decreases. Conversely, if the depletion width decreases, the capacitance increases. This is because a greater width means that the charge plates (the p-n junction in this case) are further apart, thus reducing the ability to store charge and leading to lower capacitance.

4. Verify and Summarize

   • The relationship can be mathematically verified through the formula $C = \frac{\varepsilon A}{W}$. As $W$ increases, $C$ falls, confirming that capacitance is inversely proportional to the depletion width.

Final Answer

The correct choice is B: inversely proportional. The depletion width of a varactor diode is inversely related to its capacitance.