Theoretical limits 1kOhm - Page 1
Forum section: electronics / general

author: luky315
author_rank: Regular Contributor
timestamp: July 07, 2022, 06:37:00 pm
content: What is the smallest possible resistance change on a 1k resistor ("perfect" PT1000) that could be measured? This ist only a theoretical exercise, I want to unterstand what the limits in metrology are. Where can I find more informations on this sort of topic? All of my textbooks are only talking about more or less ideal components with maybee one or two offset voltages to make the (manual) calculations more difficult :-(

author: MK
author_rank: Regular Contributor
timestamp: July 07, 2022, 08:24:42 pm
content: You need to consider johnson noise as well as the bandwidth required, just how quickly do you need your answer, and how quickly can the temperature of the body/item you are measuring can change.

author: Gyro
author_rank: Super Contributor
timestamp: July 07, 2022, 08:32:26 pm
content: The Keithley -> Tektronix Low Level Measurements Handbook is more or less the standard (and free) metrology reference unless you want to get deep into a particular area...https://www.tek.com/en/documents/product-article/keithley-low-level-measurements-handbook---7th-editionEdit: In fact Section 1.2 probably gets you what you want.

author: langwadt
author_rank: Super Contributor
timestamp: July 07, 2022, 09:16:26 pm
content: Quote from: MK on July 07, 2022, 08:24:42 pmJohnson noise for 1K is ~4nV per square root Hertz so at thermal time scales is that really an issue?

author: dietert1
author_rank: Super Contributor
timestamp: July 07, 2022, 10:13:44 pm
content: Self heating also limits precision. That will depend on how low you can make thermal resistance between sensor and DUT. If the DUT is a metal body, people drill a hole and glue the sensor inside.One also needs to consider the sensor wiring. Some thermal fluctuations arrive to the sensor from elsewhere. One can glue the first centimeters of the wiring to the surface of the DUT, if possible with a metal cover. Probably that is the idea of sensors that already come in a short metal tube.Regards, Dieter

author: TiN
author_rank: Super Contributor
timestamp: July 08, 2022, 12:23:40 am
content: Measurements to 0.1-0.05ppm are somewhat practical with common metrology laboratory for 1 kOhm standard. Obviously you'll need stable temperatures, high quality standards and DUT, careful shielding and proper equipment. Better is also doable with quantum hall effect reference and cryogenic comparators, uncertainties down to <10 ppb were achieved at national laboratories. So your question is bit too wide to answer.Here was 9 hour measurement span withGuildline 9330-1kfixed resistance standard in DIY air bath and commercial bridge. Vertical scale is deviation in ppm from median. Orange is resistance, black chart is temperature. Green is reference ESI SR104 primary standard (assumed perfect for purpose of transfer, measured annual drift <0.05ppm).I'd say anything below 0.5ppm is already good enough for 98% of metrology use cases.

author: MiDi
author_rank: Frequent Contributor
timestamp: July 08, 2022, 07:20:14 am
content: For the capabilities and uncertainties (CMCs) of metrology institutes,KCDB from BIPMseems to be a good source.

author: 2N3055
author_rank: Super Contributor
timestamp: July 08, 2022, 09:13:59 am
content: Quote from: luky315 on July 07, 2022, 06:37:00 pmLimits in metrology of RTD1000 are dominated with other factors, not theoretical limits pure resistance can be measured in ideal laboratory conditions... Attached is nice document that scratches the surface.. (It is a PDF zipped to get under 4MB limit.)

author: KT88
author_rank: Frequent Contributor
timestamp: July 08, 2022, 10:08:38 am
content: QuoteI would interpret this as a question about maximum resolution not nescesarily about absolute accuracy...To gain the maximum resolution within given power dissipation constraints for RTDs, I would propose to build a full H-bridge with one RTD and three very stable (Vishay Bulk Metal-) resistors.Using AC-excitaion would remove DC errors by parasitic TCs.To increase the possible resolution, zeroing the bridge at the temperature that has to be monitored.From here a lock-in amplifier and a lot of averaging time would score results way below the noise floor...

author: dietert1
author_rank: Super Contributor
timestamp: July 08, 2022, 11:01:14 pm
content: Here a small exercise in temperature measurements.It's a chinese ADS1256 board (available at ebay or the like). It implements the datasheet circuit with a buffered 2.5 V reference. There is a red LED (power indicator) fed from 3.3 V, voltage about 1.85 V. I inserted a 10K NTC B3950 and a 10K resistor and connected AINCOM to the reference output. Sorry i don't have a PT1000 right now.At 1 second integration time i am getting the difference 2.5 - 1.85 V = 0,65 V with 1 ppm standard deviation. The NTC voltage divider gives about 1.17 V on the NTC, as the temperature is a bit more than 25 °C, with a lot more noise. Slope as expected from the B3950 resistance table is -2.18 % / °C.First diagram shows a log of the two voltages normalized to their average, over several hours. The plots both demonstrate the same ambient temperature variation of 0.55 °C during the day. The correlation diagram shows that the NTC gives 7.1 times more signal. But the LED voltage yields much better temperature resolution with a standard deviation of 0.0003 °C. The LED will exhibit aging though. A thin film PT1000 sensor will probably drift, too.There are some quiet sections in the NTC measurement, at 11 000 seconds. Maybe one should add a capacitor to get a clean measurement.Regards, Dieter

author: David Hess
author_rank: Super Contributor
timestamp: July 09, 2022, 01:21:05 am
content: Quote from: luky315 on July 07, 2022, 06:37:00 pmOver a typical measurement bandwidth of 10 Hz, the peak-to-peak noise of a 1 kilohm resistance would be about 25 nanovolts. DC measurements below this have questionable meaning, and even achieving this is difficult.A chopper based method, AC or double sampling, can have a much smaller bandwidth limiting noise, and removes thermocouple errors and offset. The resolution then depends on measurement bandwidth which is arbitrary. How long do you want to wait?Self heating in a PT1000 sensor limits practical resolution. A larger current increases measurement resolution, but decreases accuracy because of self heating.

author: Andreas
author_rank: Super Contributor
timestamp: July 09, 2022, 04:43:13 am
content: Quote from: dietert1 on July 08, 2022, 11:01:14 pmHello,I fear you will need some cloth as wind shield to get a quieter measurement.Due to self heating the NTC might be very sensitive to air drafts.with best regardsAndreas

author: Sengcid
author_rank: Regular Contributor
timestamp: July 09, 2022, 04:43:35 pm
content: Herewith a link. See part 1, monograph 1.https://drive.google.com/folderview?id=1TbomXeoBbIe-IVADaOOmyyLH9le-3wAt

author: Echo88
author_rank: Frequent Contributor
timestamp: July 09, 2022, 07:44:56 pm
content: Is it christmas already? A full 35 pages of analysis of the MicroK (which im interested in at the moment), not to mention the rest of this goodness ive yet to discover.Is there a way to thank you, perhaps paypal?

author: dietert1
author_rank: Super Contributor
timestamp: July 09, 2022, 10:43:44 pm
content: Quote from: Andreas on July 09, 2022, 04:43:13 amNo need to be afraid. For the measurements above i already did that. In addition there was a metal enclosure as electrical shield. It won't get much better.Meanwhile i turned on the chopper stabilized input buffer of the ADS1256. This increases input impedance from about 250 KOhm to 80 MOhm. Now the RMS noise of the NTC temperature measurement is 3 times lower than with the LED, so my experimental limit with this 30 € setup would be around 0.0001 K.In order to do this with a platin RTD one needs a 0.4 ppm setup, probably a resistance bridge. I think the ADS1256 with its built-in PGA can implement that, too.Regards, Dieter

author: luky315
author_rank: Regular Contributor
timestamp: July 10, 2022, 12:54:34 pm
content: I did know "theoretically" that there is a lot of noise, but calculating it for myself was ... educating.The bridge calculations by themselves are also very interesting. If I have a bridge with 4 identical elements R, the effective resistance for the noise calculations would be only R/2, correct?I found another interesting problem: How would you theoretically measure this 1k resistor without a bridge? Or with a bridge with the elements not at the same temperature? Is a current source then a better solution?So if I would have a PT1000 resistor with a few meter of 4 (kelvin sensing) wires?What are the basic differences when measuring a 100Ohm resistor (the hypothetical "ideal" PT100)? Can this be more precise because you have less noise or would the other effects like contact resistance negate the positive effect?

author: KT88
author_rank: Frequent Contributor
timestamp: July 10, 2022, 02:50:24 pm
content: The basic trade-off is noise vs. self heating: Noise scales linear with resistance while self heating squares - given the same delta-V/°C is assumed.Depending on the measured medium - a gas, a solid or liquid and whether gas or liquid are moving or not, a larger RTD could reduce the self heating by providing a lower thermal resistance to the medium...In a practical implementation multiple 1k RDTs could be paralleled for example.

author: dietert1
author_rank: Super Contributor
timestamp: July 10, 2022, 10:14:33 pm
content: This is a log of the temperature difference between the LED and the NTC (as shown above). There are enough samples to show a band of about 6 times 0.3 mK = 2 mK peak-to-peak. 0.3 mK is the RMS resolution of the LED temperature measurement. Calibration is simple and will hide a constant temperature offset between the two measurements. The log has about 22 hours and exhibits a drift of about 5 or 10 mK.During this log the DUT was subject to a temperature cycle of about 1 K. Part of the deviations stem from thermal propagation delays, e.g. at the beginning of the log. This is to emphasize that a high resolution resistance measurement won't guarantee a temperature measurement of similar quality. That was mentioned more than once before in the context of ovens for voltage references: There is a difference between on-board and on-chip temperature sensing.Regards, Dieter