Practical measurement methods for the post "Optimising quartz crystals for ICs" - Section B
To the encyclopaedia article : Matching crystals optimally to ICs
What it's all about
The load capacitance CL defines the operating point of a quartz crystal and thus its actual frequency in the circuit, also known as the operating frequency. Each crystal is trimmed to a specific CL (typically 6 pF, 8 pF, 12 pF, 16 pF, 18 pF or 20 pF for MHz quartz crystals / 4 pF, 6 pF, 7 pF, 9 pF and 12.5pF for 32.768kHz clock crystals). If the CL specification of the crystal and the effective load capacitance of the circuit do not match, a systematic frequency shift occurs - often in the range of a few ppm to several tens of ppm.
This practical post shows how the effective load capacitance can be checked and validated in a real circuit.</p
<h2>Physical background
The effective load capacitance that the crystal "sees" in the circuit results from the series connection of the two external capacitances C1 and C2 plus the parasitic capacitances (stray).
CL_eff = (C1 - C2) / (C1 + C2) + Cstray
Cstray is made up of IC pin capacitance, track capacitance and pad capacitance. Typical guide values in a real layout are 2 pF - in compact, layout-optimised designs sometimes only 1 pF, in unfavourable layouts or with IC pin capacitances up to 7 pF correspondingly higher.
Why a pure calculation is not enough
The calculation from the data sheet provides a good starting value, but is not a guarantee. Deviations arise due to:
- Serial dispersion of the IC pin capacitance (typ. ±30 %)
- Layout variants (trace lengths, number of layers, number of via, proximity to ground planes)
- Fabrication tolerances of the circuit capacitors (C0G/NP0 typ. ±5%, standard ±10%, ±1% for precise applications such as those required in radio applications)
- Temperature and voltage dependence of the pin capacitance
Verification in the real circuit is therefore mandatory if the frequency accuracy is relevant (wireless, USB, Ethernet, timer).
Measurement method A: Frequency method (recommended in series)</h2
<h3>Measurement principle
The actual frequency of the running circuit is measured and compared with the specified nominal frequency. The effective load capacity can be calculated back from the frequency deviation.</p
<h3>Required equipment
Frequency counter with ≥ 0.1 ppm resolution and GPS or OCXO reference (e.g. Keysight 53230A, Pendulum CNT-90)
Probe active, low-capacitive (< 1 pF, e.g. FET probe), e.g. FET probe. e.g. FET probe) so as not to falsify the measurement
Temperature chamber recommended for reference measurement at +25 °C ±1 °C
Execution
Commission the circuit at +25 °C and nominal voltage. Allow to warm up for at least 60 s.
Tap XOUT (oscillator output) with a low-capacitance probe. Do not touch XIN - this is where the probe disturbs the operating point the most.
Average the frequency over ≥ 10 s gate time and note: fmess.
Calculate the deviation: Δf/f = (fmess - fnenn) / fnenn - 10⁶ [ppm]
Calculate the effective CL back from Δf/f (see formula below).
Recalculate CL from Δf/f
Approximation formula (valid in the usual range around CL_spec):
Δf / f ≈ - C1_motional / (2 - (C0 + CL_eff)²) - (CL_eff - CL_spec)
With typical quartz parameters (C1_motional ≈ 3 fF, C0 ≈ 1 pF), the following is a practical rule of thumb:
ΔCL [pF] ≈ Δf/f [ppm] - (CL_spec + C0)² / (C1_motional - 10⁶ / 2)
Simpler and more precise: Read the pull sensitivity from the quartz data sheet (typically -15 to -25 ppm/pF) and use it to convert.
ΔCL = Δf/f / S (S = pull sensitivity in ppm/pF)
Measurement method B: Variation method (to determine Cstray)
This method is the most accurate variant if the parasitic capacitance of the circuit is to be determined:
Set C1 and C2 to a symmetrical test value (e.g. 12 pF each, C0G ±2 %).
Measure the frequency f1.
Switch C1 and C2 to a second value (e.g. 22 pF each). e.g. 22 pF each), measure frequency f2.
Cpar and effective load capacitance can be analytically resolved from two measurement points.
Well suited for initial sample debugging because it also characterises the layout and the determined Cpar values can be reused for similar layouts.
Typical values and acceptance limits
| Criterion | Green area | Assessment / Measure |
|---|---|---|
| |Δf/f| at +25 °C | < 5 ppm | In order |
| |Δf/f| at +25 °C | 5 - 15 ppm | Adjust C1/C2 |
| |Δf/f| at +25 °C | > 15 ppm | check CL variant, determine Cpar |
| Difference XIN / XOUT | < 2 ppm | Symmetrical layout |
| Cpar (from variation method) | 1 - 3 pF | Typical normal range |
| Cpar | > 5 pF | Check layout (short leads, no GND area under quartz) |
Example calculation
Quartz: 26,000 MHz, CL_spec = 8 pF, pull sensitivity S = -18 ppm/pF.
Measurement in the circuit: fmess = 26,000 234 MHz → Δf/f = +9 ppm.
ΔCL = +9 ppm / (-18 ppm/pF) = -0.5 pF
Interpretation: The effective load capacitance is 0.5 pF below target. Remedy: Increase C1 and C2 slightly. With C1 = C2, +1 pF per capacitor causes ≈ +0.5 pF at CL_eff - i.e. increase by +1 pF each.
Practical note For applications with high long-term accuracy (e.g. ISM band wire), it is advisable to use the e.g. ISM band wireless, LoRaWAN, precise time base), we recommend 1%-tolerated C0G/NP0 capacitors for C1 and C2. This limits the dominant external influences on CL_eff to < 0.1 pF dispersion. Do not measure the actual frequency directly on the XIN pin. The capacitive entry of the probe immediately falsifies the result by several ppm. XOUT or a downstream IC pin is the better measuring point. It is best to check the IC data sheet to see whether the frequency can be output via a separate pin. In this case, the operating frequency of the crystal can be measured without influencing the test equipment/probes. |
Further information
The formula used here and the relationships between CL, C1, C2 and the parasitic capacitances are described in detail in the practical guide "Matching quartz crystals optimally to ICs" (sections B and C). This post supplements the guide with specific measurement practice.</p
<p>You have questions about implementation
Our frequency experts will support you in selecting the right crystal, taking measurements in your circuit and providing design-in support through to series release.
- Request technical advice
- Discuss your application with us
- Define and order a sample crystal
- Request an alternative via cross reference
Phone: +49 8191 305395 Email: info@petermann-technik.de
Your success is our goal.
