Question E7H12:
Which of the following ensures that a crystal oscillator operates on the frequency specified by the crystal manufacturer?  

Choices:  
A: Provide the crystal with a specified parallel inductance  
B: Provide the crystal with a specified parallel capacitance  
C: Bias the crystal at a specified voltage  
D: Bias the crystal at a specified current    

Correct Answer is  B: Provide the crystal with a specified parallel capacitance  

To set a crystal oscillator on the manufacturer’s specified frequency, you must present the crystal with its specified load capacitance (for a parallel-resonant crystal). That’s why the correct answer is: Provide the crystal with a specified parallel capacitance.

Why the correct answer is correct
- Most modern crystals are specified for parallel resonance with a given load capacitance, often noted as “CL = 18 pF,” “20 pF,” etc.
- The oscillator circuit (e.g., Pierce) must present that effective parallel load capacitance to the crystal. When CL is correct, the oscillator runs at the crystal’s marked frequency.

Why the other choices are incorrect
- Provide the crystal with a specified parallel inductance: Manufacturers don’t specify a required parallel inductance. Adding inductance changes (pulls) the frequency rather than ensuring the nominal marked frequency.
- Bias the crystal at a specified voltage: A crystal is a passive resonator; DC bias is applied to the active device, not the crystal. Voltage bias does not set the crystal’s operating frequency.
- Bias the crystal at a specified current: Similarly, there’s no DC “bias current” for the crystal. While drive level (RF power) is specified to avoid overstress and frequency pulling, it does not establish the nominal frequency like the load capacitance does.

Useful formulas and rules of thumb
- Crystal model: a motional series RLC (Rm, Lm, Cm) in parallel with shunt capacitance C0.
- Series-resonant frequency:
  $$f_s = \frac{1}{2\pi\sqrt{L_m C_m}}$$
- Parallel (antiresonant) frequency with load capacitance CL (approx.):
  $$f_p \approx f_s \sqrt{1 + \frac{C_m}{C_0 + C_L}} \approx f_s\left(1 + \frac{C_m}{2(C_0 + C_L)}\right)$$
- Effective load capacitance in a Pierce oscillator with two caps to ground:
  $$C_L \approx \frac{C_1 C_2}{C_1 + C_2} + C_{\text{stray}}$$
  Rule of thumb: If CL is 18 pF and Cstray ≈ 3 pF, choose C1 ≈ C2 ≈ 27–33 pF so that their series combination plus stray equals about 18 pF.

Note: Some crystals are specified for series resonance (no CL). In that case, use a series-resonant oscillator. For parallel-resonant crystals, correct CL is the key to hitting the marked frequency.