Load Capacitance and Crystal Frequency Pulling Calculator

1. Load capacitance and pulling calculator

Enter the frequency at the specified reference load, the two external capacitors, an effective stray-capacitance estimate, and crystal model parameters. All preset values are illustrative, not specifications or measurements of an FCom product. Replace them with values for your design.

Capacitances are in pF except motional capacitance, which is in fF (1,000 fF = 1 pF). For a 32.768 kHz crystal, enter 0.032768 MHz. Positive pulling means a higher frequency than the reference.

Interactive calculation requires JavaScript. The formulas and worked example below remain available without it.

2. Understand the capacitances

A common first estimate combines the two capacitors from the crystal nodes to ground as a series equivalent, then adds effective stray capacitance. This is the external load seen by the crystal. [1]

Cs is an effective contribution, not a simple sum of every pin capacitance. Parasitics from each node to ground belong in the corresponding branch before taking the series equivalent. This simplified calculator folds their net contribution into Cs. Do not include the same capacitance twice. Reassess Cs when the layout or capacitor balance changes.

The crystal model contains a motional branch and a parallel shunt capacitance. These describe resonator behavior; neither replaces the specified external load. [2]

3. Frequency pulling formulas

For a single resonance in the lossless equivalent circuit, the loaded frequency is approximated by the expression below. Taking the ratio at two loads eliminates the series-resonant frequency, fs. The calculator uses this ratio. [3]

Use the same capacitance unit throughout the formulas. When Cm is much smaller than C0 + CL, a useful first-order check is:

Δf (ppm) ≈ 500,000 × Cm × [1 / (C0 + CLactual) − 1 / (C0 + CLref)]

Smaller Cm reduces pulling sensitivity; a larger C0 + CL also reduces sensitivity to a small load change. The calculation excludes amplifier phase shift, crystal losses and mode interactions. It cannot establish whether oscillation will start. [3]

4. Worked example

Assume fref = 16 MHz at CLref = 12 pF, with CA = CB = 18 pF, Cs = 2 pF, C0 = 2 pF and Cm = 10 fF = 0.010 pF.

1. Actual load: (18 × 18) / (18 + 18) + 2 = 11 pF.
2. The load is 1 pF below the specified value, so the model predicts a positive shift.
3. The ratio formula gives approximately +27.45 ppm, or +439.24 Hz.
4. The modeled frequency is approximately 16.00043924 MHz.
5. To target 12 pF with the same Cs, equal external capacitors would be 20 pF each.

The first-order formula gives about +27.47 ppm. Its small difference from the ratio result reflects the approximation. Neither result includes the crystal’s initial frequency tolerance or measurement uncertainty.

5. Select and validate capacitors

1. Confirm the specification. Match nominal frequency, resonance mode and CL. Ask for Cm and representative C0 if pulling matters; a maximum C0 limit is not necessarily the actual value. [4]
2. Check the oscillator IC. Account for internal load settings and pin capacitances before choosing external components. Use its recommended circuit and layout.
3. Evaluate tolerances. Repeat the calculation with capacitor and parasitic limits. Keep load mismatch separate from initial tolerance, temperature drift and aging in the frequency budget.
4. Check startup and drive. Loading changes can affect negative resistance, startup time and crystal drive. Follow the IC manufacturer’s validation procedure across operating conditions. [1]
5. Measure the assembled board. Prefer a buffered clock output or the manufacturer’s measurement method. Account for probe loading and instrument accuracy. Record supply, temperature and fitted capacitor values.

A model based on measured frequency-versus-load data can improve parameter estimates, but the result remains tied to the tested circuit and conditions. Validate the final design rather than treating calculated digits as guaranteed accuracy. [5]

6. Frequently asked questions

Does a 12 pF crystal need two 12 pF capacitors?

No. Two equal 12 pF capacitors contribute a 6 pF series equivalent before effective stray capacitance is added. Calculate the complete load.

Can I estimate ppm from CL alone?

No. CL determines loading, but pulling sensitivity depends on Cm and C0. Request model parameters or a measured pulling curve if they are unavailable.

What if the specified load is at or below Cs?

The equal-capacitor formula cannot produce positive external values for that target. Recheck the parasitic model and internal settings, or reconsider the layout and crystal specification.

Does this calculator apply to an active oscillator module?

It is intended for a passive crystal in a compatible oscillator circuit. A module’s output-load rating describes a different interface and should not be entered as crystal CL.

Will correcting CL remove every frequency error?

No. It addresses modeled load mismatch. Initial tolerance, temperature behavior, aging and circuit effects still need separate assessment.