Calculator Inputs
Enter the crystal equivalent circuit values. The page estimates series resonance, parallel resonance, loading effects, and error against a target frequency.
Formula Used
1. Load capacitance
CL = (C1 × C2) / (C1 + C2) + Cstray
2. Series resonant frequency
fs = 1 / (2π √(Lm × Cm))
3. Parallel resonant frequency
fp = fs × √(1 + Cm / (C0 + CL))
4. Quality factor
Q = (1 / Rm) × √(Lm / Cm)
This equivalent-circuit model is useful for quartz crystal estimation, loading checks, oscillator trimming studies, and comparing expected operating frequency against a design target.
How to Use This Calculator
- Enter the crystal motional inductance, motional capacitance, and motional resistance from the datasheet or equivalent circuit model.
- Add the shunt capacitance, both external load capacitors, and estimated stray capacitance from traces, pads, and input pins.
- Enter a target frequency if you want a ppm error check against the intended oscillator operating point.
- Press Calculate Frequency to display results below the header and above the form.
- Use the CSV or PDF buttons to export the calculated output table for documentation, reporting, or design review.
Example Data Table
| Lm | Cm | Rm | C0 | C1 | C2 | Stray | Target | Estimated fp |
|---|---|---|---|---|---|---|---|---|
| 19.8 mH | 20 fF | 30 Ω | 3 pF | 18 pF | 18 pF | 2 pF | 8 MHz | 8.005716 MHz |
This sample shows how external loading and parasitic capacitance slightly move the crystal from its series resonance toward the operating parallel resonance.
Frequently Asked Questions
1. What does this calculator estimate?
It estimates series resonance, parallel resonance, effective load capacitance, frequency shift, quality factor, and ppm error from crystal equivalent-circuit inputs.
2. Why are series and parallel frequencies different?
Series resonance depends mainly on motional elements. Parallel resonance also includes shunt and load capacitances, so the operating frequency usually shifts slightly upward.
3. Why is stray capacitance important?
PCB traces, package pins, and oscillator input capacitance add extra loading. Ignoring them can produce optimistic frequency estimates and poor trimming decisions.
4. What values should I use for C1 and C2?
Use the external load capacitors actually fitted in the oscillator network. Their series combination, plus stray capacitance, forms the effective crystal load.
5. Is the Q factor exact?
It is an equivalent-circuit estimate based on Lm, Cm, and Rm. Real oscillators also depend on drive level, temperature, aging, and amplifier conditions.
6. Can I use this for ceramic resonators?
Yes, if you have an equivalent circuit. However, ceramic resonators often show lower stability and different tolerances than quartz devices.
7. What does ppm error tell me?
PPM error compares the estimated parallel frequency with your target. It helps judge whether loading or trimming adjustments are needed.
8. Does this replace laboratory measurement?
No. It is best for design estimation and sensitivity checks. Final validation should still use measured frequency on the real board.