Dimension external capacities C1/C2 and determine Cstray

Dimension external capacities C1/C2 and determine Cstray

Practical measurement methods for the post "Optimising quartz crystals for ICs" - sections C and 5

To the encyclopaedia article : Matching crystals optimally to ICs

What it's all about:

The two external circuit capacitors C1 and C2 on the Pierce oscillator together with the parasitic capacitances of the circuit (stray) determine the effective load capacitance. A simple formula value from the data sheet is usually not sufficient because each circuit board has an individual stray. This post shows how C1 and C2 are correctly dimensioned and verified in the circuit.

Initial formula for dimensioning

For symmetrical wiring (C1 = C2 = CX) the following applies:

CL = CX / 2 + Cstray ⇒ CX = 2 - (CL - Cstray)

The following rule of thumb is given as the starting value in many data sheets (CL and CX in pF):

CX = 2 - CL - 2 - Cstray (Cstray typ. 2 pF)

From the original article, the following results for CL = 12 pF: 2-12 - 2-2 = 20 pF. With an average stray of 2 pF, the calculation example in the lexicon (18 pF per side) leads to the identical effective operating point - depending on the actual pin capacitance of the IC.

Step 1: Calculate starting value from data sheet

Dimensioning always starts with two data sheet values:

  • CL of the crystal (e.g. 8 pF, 12 pF, 16 pF, 20 pF)
  • Capacitive load of the IC at XIN/XOUT (usually 1 - 7 pF per pin; usually specified in the MCU data sheet as "CIN/COUT" or "CLoad")
Quartz-CLCstray (typ.)CX start value C1/C2Range
6 pF2 pF8 pF7 - 12 pF
8 pF2 pF12 pF10 - 15 pF
10 pF2 pF16 pF15 - 18 pF
12 pF2 pF20 pF18 - 22 pF
12.5 pF2 pF21 pF18 - 22 pF
16 pF2 pF28 pF22 - 30 pF
20 pF2 pF36 pF33 - 39 pF

Important before dimensioning

Check the MCU data sheet to see what pin capacity the manufacturer specifies for XIN/XOUT. Some modern low-power MCUs deliberately have increased pin capacitances of up to 7 pF, others only 1-2 pF. Calculate with the actual value, not the rule of thumb.

Step 2: Determine the stray of the PCB (variation method)

On the target board, Cstray is determined by two frequency measurements at different C1/C2 values. This is the simplest and most reliable laboratory method.</p

<h3 class="text-justify">Measurement setup

  • Two sets of C0G/NP0 capacitors (±2 %) of significantly different values, e.g. 10 pF and 22 pF

  • Frequency counter ≥ 0.1 ppm resolution with external reference

  • Low-capacitance FET probe (< 1 pF)

Implementation

  1. Fitting 1: C1 = C2 = C_A (e.g. 10 pF) → measure frequency f_A.

  2. Fitting 2: C1 = C2 = C_B (e.g. 22 pF) → measure frequency f_B.

  3. Express both frequencies as a deviation from the nominal frequency: Δf_A, Δf_B in ppm.

  4. Determine the stray from the system of equations.

Calculating equation

From the two measurements, the pull sensitivity S and the parasitic capacitance Cstray follow:

S = (Δf_B - Δf_A) / (CL_B_eff - CL_A_eff) [ppm/pF]

Where CL_eff = CX/2 + Cstray. Equating the specified pull sensitivity (from the crystal data sheet) and resolving according to Cstray results in a unique value. In practice, developers usually use a small Excel spreadsheet or an MCU manufacturer app for this purpose.

Step 3: In-circuit measurement of the effective capacitance

Very elegant and without soldering: The capacitance between XIN (or XOUT) and GND is measured with a precise LCR meter when switched off.

Measurement procedure

  1. Supply voltage to 0 V, circuit completely de-energised.
  2. Desolder (or do not equip) the crystal - only C1, C2, IC pin and traces in the measurement path.
  3. Measure the capacitance XIN → GND and XOUT → GND with an LCR meter (1 MHz measurement signal, ≤ 100 mV).
  4. Measured values should correspond to the calculated CX values + 1...3 pF (IC pin).

Caution with the LCR measurement

The IC pin capacitance is voltage-dependent. The LCR measurement in the switched-off state therefore does not provide the exact operating value. For precision designs, the frequency method (step 2) is the more reliable reference.

Step 4: Check symmetry

Unbalanced wiring (C1 ≠ C2) worsens the starting behaviour and drive level distribution. In practice, we recommend:

ParametersTarget valueBoundary value
Deviation C1 to C2≤ 2 %≤ 5 %
Tolerance C0G (NP0)±2 %±5 %
Tolerance standard ceramic X7Rnot recommended-
Voltage coefficient≤ 1 % at Voperation-

Example calculation using the variation method

Quartz: 24,000 MHz, CL = 8 pF, pull sensitivity S = -20 ppm/pF (from data sheet).

PopulationC1 = C2measured frequencyΔf/f
Measurement A10 pF24,000 042 MHz+1.75 ppm
Measurement B22 pF23.999 928 MHz-3.00 ppm

Between the two placements, CX/2 changes by (22-10)/2 = 6 pF. The measured frequency change is -4.75 ppm → S_measured = -0.79 ppm/pF - (1/6) = actually around -19.8 ppm/pF, matches the data sheet.

With Δf_A = +1.75 ppm at CX = 10 pF: CL_eff_A = 10/2 + Cstray = 5 + Cstray. From Δf = S - (CL_eff - CL_spec) follows CL_eff_A ≈ 8 - (1.75/-20) = 7.91 pF → Cstray ≈ 2.9 pF.

Result: The circuit board has Cstray ≈ 2.9 pF. Target value CX = 2-(8 - 2.9) = 10.2 pF. An assembly with 10 pF ±2 % is therefore almost exactly on target.

Further information

The formulas and the relationship between CL, C1/C2 and Cstray are explained in the practical guide "Optimally matching quartz crystals to ICs" (sections B, C and 5). This post shows the laboratory measurement with which the calculation is compared on your real PCB.

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