*Question E7H04:
How is positive feedback supplied in a Colpitts oscillator?*  

*Correct Answer is  C: Through a capacitive divider*  

### AI Response: (may contain errors)  

In a Colpitts oscillator, positive feedback is essential for sustaining oscillations. Here's how it works:

### Correct Answer: C: Through a capacitive divider

1. **Why the correct answer is correct:**
   - A Colpitts oscillator uses a capacitive divider to provide the necessary positive feedback. This divider is typically formed by two capacitors in series, connected across the inductor in the tank circuit. The junction of these two capacitors is connected to the transistor's base (or gate), providing the feedback needed to maintain oscillations.
   - The capacitive divider allows a portion of the output signal to be fed back in phase with the input, which is crucial for sustaining oscillations.

### Why the other choices are incorrect:

2. **A: Through a tapped coil**
   - A tapped coil is used in a Hartley oscillator, not a Colpitts oscillator. In a Hartley oscillator, the feedback is provided through an inductive divider (a coil with a tap), not a capacitive one.

3. **B: Through link coupling**
   - Link coupling involves using a separate coil to transfer energy between circuits, which is not the method used in a Colpitts oscillator for feedback. This method is more common in RF amplifiers and other types of oscillators.

4. **D: Through a neutralizing capacitor**
   - A neutralizing capacitor is used to cancel unwanted capacitance or feedback, often in amplifiers, to prevent oscillations. It is not used to provide positive feedback in a Colpitts oscillator.

### Useful Formula:

- The frequency of oscillation for a Colpitts oscillator is determined by the tank circuit and can be calculated using:
  $$ f = \frac{1}{2\pi\sqrt{L \cdot C_{\text{total}}}} $$
  where:
  - $L$ is the inductance of the coil.
  - $C_{\text{total}}$ is the equivalent capacitance of the capacitive divider, calculated as:
    $$ C_{\text{total}} = \frac{C_1 \cdot C_2}{C_1 + C_2} $$
  - $C_1$ and $C_2$ are the capacitances of the capacitors in the divider.

Understanding these concepts will help you identify the correct feedback mechanism in a Colpitts oscillator and distinguish it from other types of oscillators.