Question E7H05:
How is positive feedback supplied in a Pierce oscillator?  

Choices:  
A: Through a tapped coil  
B: Through link coupling  
C: Through a neutralizing capacitor  
D: Through a quartz crystal    

Correct Answer is  D: Through a quartz crystal  

To understand a Pierce oscillator, remember the Barkhausen criterion:  
$$|A\beta| \ge 1 \quad \text{and} \quad \angle (A\beta) = 0^\circ \ (\text{mod } 360^\circ)$$

Why D (Through a quartz crystal) is correct:
- In a Pierce oscillator, the quartz crystal is connected between the amplifier output and input, forming the feedback path.
- At the crystal’s resonant frequency, it provides the correct phase shift and a low-impedance path, creating the required positive feedback so oscillation can sustain.
- The crystal also sets a very stable frequency:
  - Series resonance: $$f_s = \frac{1}{2\pi\sqrt{L_m C_m}}$$
  - Parallel resonance (approx.): $$f_p \approx f_s \sqrt{1 + \frac{C_m}{C_0}}$$
  where $L_m$, $C_m$ are motional parameters and $C_0$ is shunt capacitance.

Why the other choices are incorrect:
- A: Through a tapped coil — That’s the Hartley oscillator’s feedback method (inductive tap). The Pierce uses a crystal for feedback, not a tapped inductor.
- B: Through link coupling — Link coupling is for energy transfer between circuits (e.g., tank to load), not the positive feedback network in a Pierce.
- C: Through a neutralizing capacitor — Neutralization cancels unwanted feedback (often negative feedback to prevent oscillation in RF amplifiers), not to create positive feedback.

Rules of thumb:
- Pierce = crystal provides the feedback path.
- Hartley = tapped coil feedback.
- Colpitts = capacitive divider feedback.
- Clapp = Colpitts with series-tuned capacitor to improve stability.