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

Choices:  
A: Through a tapped coil  
B: Through link coupling  
C: Through a capacitive divider  
D: Through a neutralizing capacitor    

Correct Answer is  C: Through a capacitive divider  

Correct answer: C — Through a capacitive divider

Why C is correct:
- A Colpitts oscillator uses two capacitors in series across the tank inductor. The junction of these capacitors feeds a fraction of the RF voltage back to the active device (emitter/source), providing the required positive feedback.
- The two series capacitors form a capacitive voltage divider; their ratio sets the feedback fraction.
- Resonant frequency and divider relations:
  - $$C_{eq} = \frac{C_1 C_2}{C_1 + C_2}$$
  - $$f_0 = \frac{1}{2\pi\sqrt{L C_{eq}}}$$
  - Voltage division at resonance:
    $$\frac{V_{C1}}{V_{total}} = \frac{C_2}{C_1 + C_2}, \quad \frac{V_{C2}}{V_{total}} = \frac{C_1}{C_1 + C_2}$$
  - Smaller capacitance sees the larger RF voltage; choose the ratio to set the feedback level.

Why the others are incorrect:
- A: Through a tapped coil — That’s the Hartley oscillator (inductive divider), not the Colpitts.
- B: Through link coupling — A separate loosely coupled coil used for coupling or tickler feedback (e.g., Armstrong), not the Colpitts method.
- D: Through a neutralizing capacitor — Neutralization cancels unwanted interelectrode capacitance (negative/canceling feedback), not the intentional positive feedback in a Colpitts.

Useful rules of thumb:
- Feedback fraction in a Colpitts is set by the capacitor ratio; typical design uses $C_{small}:C_{large} \approx 1:3$ to $1:10$ to ensure reliable start-up without excessive loop gain.
- Barkhausen criterion for oscillation:
  $$|A\beta| \ge 1, \quad \angle A\beta = 0^\circ \text{ (or } 360^\circ)$$
- Ensure device and network phasing so the capacitive divider provides the correct-phase feedback at $f_0$.