Measuring a Crystal

This tutorial explains how to measure quartz crystals with the NanoVNA-H and extract their motional parameters (Fs, Fp, Lm, Cm, Rm, and Q).

What You Will Learn

• Understanding crystal equivalent circuit parameters
• Measuring series and parallel resonant frequencies
• Using the NanoVNA’s crystal measurement mode
• Matching crystals for filter construction

Crystal Fundamentals

A quartz crystal has an equivalent circuit with these parameters:

Parameter	Symbol	Description
Series resonant frequency	Fs	Frequency where crystal acts as a short
Parallel resonant frequency	Fp	Frequency where crystal acts as open
Motional inductance	Lm	Equivalent series inductance
Motional capacitance	Cm	Equivalent series capacitance
Motional resistance	Rm	Equivalent series resistance (ESR)
Parallel capacitance	C0	Physical holder capacitance
Quality factor	Q	Lm / Rm at Fs

Note

Crystals have very high Q (10,000 to 100,000+), making them useful for precise frequency control and narrow filters.

Test Fixture Options

Crystals are typically packaged in HC-49 or similar holders with leads. You need a test fixture to connect them to the NanoVNA.

Simple Fixture

Through-hole crystal:

• Solder short leads to two SMA connectors
• Keep leads as short as possible
• Connect in series between Port 1 and Port 2

SMD crystal:

• Use a small PCB with SMA connectors
• Solder crystal between center conductors

Pi Network Fixture

For more accurate measurements:

• Build a Pi-network fixture with 12.5-ohm resistors
• This transforms the 50-ohm ports to a more suitable impedance
• Reduces measurement errors from crystal ESR

Schematic:

Port1 ---[12.5]--- XTAL ---[12.5]--- Port2
              |         |
           [12.5]    [12.5]
              |         |
             GND       GND

Basic Crystal Measurement

1. Set the frequency range

   Center the sweep around the crystal’s nominal frequency with a narrow span.

   For a 10 MHz crystal:

   • CENTER: 10M
   • SPAN: 50k (50 kHz span = 25 kHz each side)

   Tip

   Start with a wider span to find resonance, then narrow down for accurate measurements.

2. Reduce IF bandwidth

   Crystals are very narrow. Reduce IF bandwidth for accurate measurements:

   Go to DISPLAY > IF BANDWIDTH > 100 Hz or 30 Hz

   The sweep will be slower but much more accurate.

3. Configure traces

   • Trace 1: S21 LOGMAG (transmission)
   • Trace 2: S21 PHASE (optional, for verification)

4. Calibrate with THRU

   With fixture in place (no crystal), perform THRU calibration.

5. Insert the crystal

   Install the crystal in your fixture.

6. Find series resonance (Fs)

   Look for the peak in S21 (maximum transmission). This is the series resonant frequency where the crystal acts like a low impedance.

7. Find parallel resonance (Fp)

   Look for the dip in S21 (minimum transmission). This is the parallel resonant frequency where the crystal acts like a high impedance.

Using the Crystal Measurement Mode

The NanoVNA firmware includes a dedicated crystal measurement function that calculates motional parameters automatically.

1. Enable crystal measurement

   Go to MARKER > MEASURE > SERIES XTAL (S21)

2. Place the marker at series resonance

   Move the marker to the S21 peak (Fs).

3. Read the calculated parameters

   The display shows:

   • Fs: Series resonant frequency
   • Rm: Motional resistance (ESR)
   • Cm: Motional capacitance
   • Lm: Motional inductance
   • Q: Quality factor

4. Record the values

   Note all parameters for your records.

Note

The measurement accuracy depends on proper calibration and fixture quality. For critical applications, verify with multiple measurements.

Measuring Multiple Crystals for Matching

When building crystal filters, you need crystals matched in Fs within a few Hz.

1. Set up a narrow sweep

   For matching 10 MHz crystals:

   • SPAN: 10k (10 kHz)
   • IF BW: 30 Hz or 10 Hz

2. Measure each crystal

   Record Fs and Rm for each crystal in your batch.

3. Sort by Fs

   Group crystals with Fs within 20-50 Hz of each other.

4. Check Rm consistency

   Crystals for the same filter should have similar Rm values.

Example Measurement Log

Crystal #	Fs (Hz)	Rm (ohms)	Group
1	10,000,145	15.2	A
2	10,000,167	14.8	A
3	10,000,312	16.1	B
4	10,000,158	15.0	A
5	10,000,298	15.5	B

Understanding the Results

Typical Parameter Ranges

Crystal Type	Fs	Rm	Cm	Q
32.768 kHz watch	32.768 kHz	30-50k ohms	~3 fF	50k-100k
4 MHz HC-49	4 MHz	20-50 ohms	~15 fF	50k-100k
10 MHz HC-49	10 MHz	10-30 ohms	~10 fF	50k-150k
20 MHz HC-49	20 MHz	10-20 ohms	~5 fF	50k-100k

What the Parameters Tell You

Motional Resistance (Rm)

Low Rm (5-20 ohms): Good for oscillators, low insertion loss filters

High Rm (50+ ohms): More loss, may need different filter topology

Rm is determined by the crystal’s physical construction and cannot be changed.

Quality Factor (Q)

Q = 2 * pi * Fs * Lm / Rm

Higher Q means:

• Sharper resonance
• Lower phase noise in oscillators
• Narrower filter bandwidth capability

Typical crystals have Q of 50,000-200,000.

Holder Capacitance (C0)

C0 is the parasitic capacitance across the crystal terminals.

Typical values: 2-7 pF

C0 affects the spacing between Fs and Fp:

• Fp - Fs approximately = Fs * Cm / (2 * C0)

Troubleshooting

No clear resonance visible

• Check crystal is properly connected
• Widen frequency span to find resonance
• Crystal may be damaged

Resonance is very weak

• Crystal may have high Rm (damaged or low-quality)
• Fixture losses are too high
• Reduce IF bandwidth further

Multiple resonances appear

• Crystal may have spurious modes
• This is normal for some crystal types
• Choose the dominant (strongest) mode

Fs differs from marked frequency

• Crystals are specified with a particular load capacitance
• Measure at actual operating conditions for accuracy
• Tolerance is typically 20-100 ppm at room temperature

Measuring Load Capacitance Effect

Crystals for oscillators are often specified with a “load capacitance” (CL).

1. Measure Fs with crystal only

2. Add a capacitor in series with the crystal

   Use a value close to the specified CL (commonly 12 pF, 18 pF, or 20 pF).

3. Measure the new resonant frequency

   This is the frequency the crystal will oscillate at in a circuit with that load capacitance.

4. Calculate the pulling range

   The difference shows how much the crystal can be “pulled” by changing CL.

Calculating Filter Parameters

Once you have crystal parameters, you can design crystal filters:

Ladder Filter Design

For a 4-crystal ladder filter:

• Bandwidth approximately = 1.5 * Rm / Lm (in Hz)
• Wider bandwidth requires lower-Q crystals or more complex topologies

Coupling Capacitors

The coupling capacitors between crystals set the bandwidth:

• Larger capacitors = wider bandwidth
• Typical values: 30-100 pF depending on crystal parameters

Tip

Many online calculators exist for crystal filter design. Input your measured Lm, Cm, and Rm values for accurate results.

Next Steps

• Characterizing a Filter - Measure your finished filter
• Your First S21 Measurement - Basic transmission measurements
• Full Calibration - Ensure accurate measurements