Physics Electronics PMDC Conceptual Practice
PMDC Verified Question 291 of 494
In an LC resonant tank circuit used for RF tuning, a reverse-biased varactor diode is used in place of a mechanical tuning capacitor. What property allows the resonant frequency to be tuned electronically?
A
The transition capacitance \( C_T \) decreases as reverse bias voltage increases, shifting the resonant frequency \( f_0 \)
B
The diode emits photons that alter the inductance of the coil
C
The diode's forward resistance increases to infinity
D
The diode converts DC into nuclear energy
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: The transition capacitance \( C_T \) decreases as reverse bias voltage increases, shifting the resonant frequency \( f_0 \)
Concept:

A varactor diode operates in reverse bias as a voltage-controlled capacitor: \( C_T \propto (V_0 + V_R)^{-1/2} \). Varying \( V_R \) changes the tank capacitance and tunes the resonant frequency \( f_0 = 1 / (2\pi\sqrt{L C}) \).

Formula:

$$f_0 = \frac{1}{2\pi \sqrt{L \cdot C_T(V_R)}} \implies \text{Increasing } V_R \implies C_T \downarrow \implies f_0 \uparrow$$

Solution:

  • Increasing the reverse voltage \( V_R \) widens the depletion layer, decreasing the transition capacitance \( C_T \).


  • Because resonant frequency is inversely proportional to \( \sqrt{C_T} \), adjusting the DC control voltage provides electronic frequency tuning.


Why other options are incorrect:

  • Option B: Varactor diodes do not emit light and cannot alter coil inductance.
  • Option C: The varactor is operated in reverse bias; its forward resistance is not part of normal operation.
  • Option D: Varactors operate purely via solid-state electrostatics.

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