Practical measurement methods for the post "Optimising quartz crystals for ICs" - Sections F and F.3
To the encyclopaedia article : Matching crystals optimally to ICs
What it's all about
The ESR (Equivalent Series Resistance) represents the mechanical and dielectric losses of the quartz crystal. It is one of the most important parameters for the transient behaviour: A low ESR means lower losses, higher transient response reliability, faster start-up time and more stable oscillation over temperature.</p
<p class="text-justify">MCU manufacturers usually specify a maximum ESR in their data sheets (typically 40 - 100 Ω for MHz crystals, 30 - 90 kΩ for 32.768 kHz crystals). If the real ESR of the crystal is higher, the oscillator will not start reliably.
This post shows how to correctly measure the ESR in single piece and sample testing.
Measurement method A: Network analyser (IEC 60444-5, reference method)
Network analysis is the reference method - precise, reproducible and the basis of all quartz data sheets. It is used exclusively in measurement laboratories.
Equipment
Vector network analyser (VNA), e.g. Keysight E5061B, Rohde & Schwarz ZNLE, or specialised quartz test bridge (Saunders 250C, Saunders 260)
π network socket (quartz test jig) according to IEC 60444-5 with defined load capacity
Precision reference and OSL calibration up to the quartz frequency range
Procedure
Calibrate the π network: Short-Open-Load-Through (SOLT) with precision standards at the target frequency.
Insert the crystal into the test socket. The socket defines a suitable load capacitance for the measurement.
Set the drive level to the measurement level specified in the quartz data sheet (typically 10 µW or 100 µW).
Carry out transmission measurement S21, search for minimum at series resonance.
Calculate ESR from insertion loss at resonance minimum.
ESR = 2 - R₀ - ( 10^(-|S21|/20) - 1 ) (with R₀ = 50 Ω for an open π-network)
Measurement method B: Active bridge / Saunders method (production and QA method)
Commercial quartz measuring bridges (Saunders, TTi) directly measure ESR, series resonance frequency fs, load resonance frequency fL and motional parameters L1, C1, C0. They are used in incoming goods and QA testing.</p
<p class="text-justify">Advantage: direct display of the ESR in ohms, automatic drive level control, measurement time a few seconds per crystal.
Method C: In-circuit estimation (field method, only for plausibility checks)
If only one oscilloscope is available, the ESR can be narrowed down indirectly using the series resistance method. This method is primarily used to determine the transient response safety (see separate post on -Rneg) and provides an upper estimate of the ESR as a secondary result.
Principle
A variable series resistor Rtest is looped in between the crystal and one of the capacitance nodes (usually the XOUT side). The resistance value at which the oscillation just stops corresponds to the limit value:</p
<p class="text-centre">Rtest_max + ESR ≈ |-Rneg|
If |-Rneg| is known from the oscillator specification, an upper ESR limit can be estimated from this. This method is not sufficient for a precise absolute measurement.
Typical ESR values
| Quartz type | Frequency range | ESR typical | ESR max (data sheet) |
|---|---|---|---|
| 32,768 kHz watch quartz standard (depending on case version) | 32,768 kHz | 35 - 65 kΩ | 70 - 90 kΩ |
| 32.768 kHz Clock Quartz LRT-Low-ESR | 32.768 kHz | 40 - 45 kΩ | 50 kΩ |
| MHz quartz SMD 3.2 × 2.5 mm | 8 - 50 MHz | 40 - 80 Ω | 100 Ω |
| MHz quartz SMD 2.0 × 1.6 mm | 16 - 54 MHz | 60 - 120 Ω | 150 Ω |
| LRT quartz SMD03025/4 | 8 - 60 MHz | 20 - 50 Ω | 80 Ω |
| LRT-Quartz SMD02016/4 | 16 - 60 MHz | 30 - 70 Ω | 100 Ω |
| MHz quartz in 5032 THT package | 4 - 40 MHz | 20 - 40 Ω | 60 Ω |
Rating rule
Rule of thumb for robust design If the MCU specifies a maximum ESR_max_IC, the real ESR of the crystal used should be no more than 50 - 70 % of this value. Example: MCU data sheet says ESR_max = 70 Ω → desired quartz ESR 30 - 50 Ω. This leaves a reserve for temperature and ageing drift, component scattering and a possibly low |-Rneg|. |
.
Influence of temperature on the ESR
The ESR is higher at low temperatures. For 32.768 kHz crystals, the ESR at -40 °C can increase to 2 - 3 times the +25 °C value. For MHz crystals, the temperature coefficient is typically +10 - 20 % between +25 °C and -40 °C.
The following therefore applies: The measurement and the data sheet evaluation must always cover the specified temperature range.</p
| Quartz | ESR at +25 °C | ESR at -40 °C (typ.) | Factor |
|---|---|---|---|
| 32,768 kHz default (depending on version) | 45 - 70 kΩ | 100 - 130 kΩ | ×2.2 - 2.9 |
| 32.768 kHz LRT-Low-ESR | 35 kΩ | 50 kΩ | ×2,0 - 2,6 |
| MHz standard 25 MHz | 40 Ω | 45 - 48 Ω | ×1.1 - 1.2 |
| LRT SMD03025/4, 25 MHz | 25 Ω | 28 - 30 Ω | ×1,1 - 1,2 |
Frequent errors in the ESR measurement
Measurement with incorrect drive level: ESR is drive-dependent. Always adhere to the measurement level specified in the data sheet.
Missing calibration of the π network: leads to systematic errors of 20 - 50 %.
Mixing of R1 and ESR: Data sheets sometimes specify R1 (series RLC branch), sometimes ESR at the load resonance frequency. Both differ slightly (ESR ≈ R1 - (1 + C0/CL)²). Check which value is meant.
In-circuit measurements without taking into account the parasitic track resistances that are included in the path.
LRT technology: Low-ESR as standard
All oscillating crystals supplied by PETERMANN-TECHNIK utilise the exclusive LRT technology (Low ESR Resonator Technology). Due to their design, these crystals have very low ESR values over the entire specified temperature range, which ensures the circuit designer has sufficient swing reserve even with weak oscillator stages in modern low-power MCUs.
Further information
The significance of the ESR for the transient response and the relationship with the negative input resistance are described in detail in the practical guide "Optimally tuning crystals to ICs" (sections F and F.3). This post provides measurement practice and specific limit value recommendations.</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.
