Question E7H01:
What are three common oscillator circuits?  

Choices:  
A: Taft, Pierce, and negative feedback  
B: Pierce, Fenner, and Beane  
C: Taft, Hartley, and Pierce  
D: Colpitts, Hartley, and Pierce    

Correct Answer is  D: Colpitts, Hartley, and Pierce  

Correct answer: D — Colpitts, Hartley, and Pierce

1) Why D is correct
- These are the three classic RF oscillator topologies you’re expected to recognize:
  - Colpitts: Uses a capacitive voltage divider ($C_1$ and $C_2$) in the feedback network with an inductor $L$ for resonance.
  - Hartley: Uses an inductive divider (split inductor $L_1$, $L_2$ or tapped coil) with a capacitor $C$ for resonance.
  - Pierce: A crystal-controlled variant (essentially a Colpitts form) using a quartz crystal to set frequency.

Key relationships:
- Barkhausen criterion (for sustained oscillation):
  $$|A\beta| \ge 1 \quad \text{and} \quad \angle(A\beta) = 0^\circ \ (\text{mod } 360^\circ)$$
- Resonant frequency:
  $$f_0 = \frac{1}{2\pi\sqrt{LC}}$$
- Colpitts equivalent capacitance:
  $$C_{\text{eq}} = \frac{C_1 C_2}{C_1 + C_2}$$
- Hartley equivalent inductance (with coupling):
  $$L_{\text{eq}} = L_1 + L_2 + 2M \quad (\approx L_1 + L_2 \text{ if } M \text{ small})$$
- Pierce relies on the crystal’s series/parallel resonance near its marked frequency; the loop uses small capacitors to bias the crystal as the frequency-determining element.

Rules of thumb:
- Colpitts feedback ratio set by $C_1/C_2$.
- Hartley feedback ratio set by $L_1/L_2$ or tap position.
- Pierce provides very stable frequency due to the crystal’s high $Q$.

2) Why the other choices are incorrect
- A: Taft, Pierce, and negative feedback
  - “Taft” is not a standard oscillator type.
  - “Negative feedback” is not an oscillator topology; oscillators require net positive feedback meeting Barkhausen.
- B: Pierce, Fenner, and Beane
  - “Fenner” and “Beane” are not recognized oscillator types.
- C: Taft, Hartley, and Pierce
  - Includes Hartley and Pierce, but “Taft” is not a standard oscillator.

3) Useful exam pointers
- The “big three” you should instantly recognize: Colpitts (capacitive divider), Hartley (inductive divider), Pierce (crystal-based Colpitts).  
- Also know Clapp (a Colpitts variant with an additional series capacitor for improved stability), but it’s not listed here.