Question E7H08:
Which of the following components can be used to reduce thermal drift in crystal oscillators?  

Choices:  
A: NP0 capacitors  
B: Toroidal inductors  
C: Wirewound resistors  
D: Non-inductive resistors    

Correct Answer is  A: NP0 capacitors  

To reduce thermal drift in a crystal oscillator, use capacitors with near-zero temperature coefficient so the load/reactive network seen by the crystal doesn’t change with temperature.

Why A (NP0 capacitors) is correct:
- NP0 (a.k.a. C0G) ceramic capacitors have a near-zero temperature coefficient, typically $0 \pm 30$ ppm/°C.
- In crystal oscillators (e.g., Colpitts/Clapp), the frequency depends on the load capacitance. Keeping that capacitance stable with temperature minimizes frequency drift.
- Rule of thumb: Use NP0/C0G for all capacitors in the crystal’s frequency-determining network.

Why the others are incorrect:
- Toroidal inductors: The inductance and core permeability change with temperature; this can add drift. Toroidal form reduces stray fields, not temperature drift.
- Wirewound resistors: Have significant temperature coefficient and parasitic inductance; they don’t stabilize oscillator frequency.
- Non-inductive resistors: “Non-inductive” addresses inductance, not temperature coefficient. Their resistance can still vary with temperature and they don’t control the crystal’s load capacitance.

Useful formulas/rules:
- Temperature coefficient (TC): 
  $$TC = \frac{1}{X}\frac{dX}{dT} \quad \text{(ppm/°C)}$$
- Fractional frequency drift roughly follows the drift of the frequency-determining reactances:
  $$\frac{\Delta f}{f} \propto \sum S_i \cdot TC_i \cdot \Delta T$$
  where $S_i$ is the sensitivity of $f$ to component $i$. Keeping capacitor $TC_i \approx 0$ (with NP0) minimizes drift.
- Avoid high-K ceramics (X7R, Z5U, etc.) in oscillator networks; they have large tempco and voltage dependence.