*Question E7H01:
What are three common oscillator circuits?*  

*Correct Answer is  D: Colpitts, Hartley, and Pierce*  

### AI Response: (may contain errors)  

The correct answer to the question about common oscillator circuits is **D: Colpitts, Hartley, and Pierce**. Let's break down why this answer is correct and why the others are not.

### Correct Answer: Colpitts, Hartley, and Pierce
- **Colpitts Oscillator**: This oscillator uses a combination of capacitors and an inductor to determine its frequency. It is known for its stability and is widely used in RF applications.
- **Hartley Oscillator**: Similar to the Colpitts, but it uses two inductors and one capacitor. It is also popular for generating sine waves in RF circuits.
- **Pierce Oscillator**: This is a type of crystal oscillator that uses a crystal for frequency stability. It is commonly used in applications requiring precise frequency control.

### Why the Other Choices Are Incorrect
- **A: Taft, Pierce, and negative feedback**: 
  - The Taft oscillator is not a recognized standard oscillator type in the same way as the others. Negative feedback is a technique used in many circuits but does not refer to a specific oscillator type.

- **B: Pierce, Fenner, and Beane**: 
  - While Pierce is correct, Fenner and Beane are not standard oscillator types. This choice includes non-existent or less common names in oscillator theory.

- **C: Taft, Hartley, and Pierce**: 
  - Again, Taft is not a recognized oscillator type. Hartley and Pierce are valid, but the inclusion of Taft makes this choice incorrect.

### Useful Formulas and Rules of Thumb
- The frequency of oscillation for a Colpitts oscillator can be approximated by the formula:
  
  $$f = \frac{1}{2\pi\sqrt{L \cdot C_{total}}}$$

  where:
  - $L$ = inductance in henries
  - $C_{total}$ = total capacitance in farads (considering the capacitors in series and parallel).

- For a Hartley oscillator, the frequency can be calculated similarly, but it uses two inductors:

  $$f = \frac{1}{2\pi\sqrt{(L_1 + L_2) \cdot C}}$$

  where:
  - $L_1$ and $L_2$ are the inductances,
  - $C$ is the capacitance.

These formulas help in understanding how the frequency of oscillation is determined in these circuits, which is crucial for their application in radio frequency systems.