100uV, 50kHz Signal: theoretical limits - Page 1
Forum section: electronics / general

author: luky315
author_rank: Regular Contributor
timestamp: June 30, 2022, 04:54:27 pm
content: I have a signal with 100uVpp, 50kHz bandwidth and 500 Ohm impedance.What are the theoretical limits when measuring this signal?And what would be practically possible with <100€/$ in parts?

author: TimFox
author_rank: Super Contributor
timestamp: June 30, 2022, 07:37:08 pm
content: The theoretical limit would be the Johnson/Nyquist thermal noise at room temperature in 500 ohms, with a 50 kHz measurement bandwidth.At 20oC, that would be 636 nV rmshttps://www.electronics-notes.com/articles/basic_concepts/electronic-rf-noise/thermal-noise-calculations-calculator-formulas.phpThis assumes that your measuring device has 0 dB noise figure.If not, add the noise figure (only a few dB, hopefully) to the value above.However, if your signal be truly constant, not a modulated signal, you can extend the average in computing the "m" in "rms" and the thermal noise will reduce accordingly. Note that you have to extend the averaging inside the root-mean-square computation to get a valid answer.In this bandwidth, you could build a cheap audio (non-inverting) amplifier based on a low-noise op amp (5534 or similar), inside an aluminum box, powered by batteries, to amplify the signal to the point where it can be read by a decent TRMS voltmeter or DSO with rms measurement.

author: Marco
author_rank: Super Contributor
timestamp: June 30, 2022, 08:43:47 pm
content: Lets assume the signal is normally distributed and pseudo-random, so ~100/6 uV RMS. SNRdb = 20*log((100/6)/0.636) = 28.37. Source noise starts to dominate at around 4.42 ENOB ADC without oversampling.So use the lowest noise amplifier you can afford (probably a LT1028 class BJT opamp, unless your time is free) with basically any MSPS ADC (even one in a micro).

author: luky315
author_rank: Regular Contributor
timestamp: July 01, 2022, 10:19:20 am
content: Shouldn't the SNR be more in the region of 20*log(100uV/0.6uV) = 44.4dB and therefore arround 7Bits? Still not great, but I am more concerned by the offset voltage of the amplifier. Only very slow ones have offsets in the sub uV region, but I need quite a high gain. The best compromise I have found is the OPA388 (GBP 10MHz, slew rate is ok and ±0.25 μV Offset). With this a gain of 200 should be possible. Or am I missing something? Is a multi-stage design better?

author: Kleinstein
author_rank: Super Contributor
timestamp: July 01, 2022, 11:12:22 am
content: The Johnson resistor noise applies if the impedance is resistive. With a capacitive or inductive source impedance the noise can be lower.There is no need for a sub µV offset, as long as it is stable even 100 µV of offset would only require a slightly larger resolution for the ADC.Especially older OPs can have an option to adjust the offset. The question is also of the frequency range goes all the way to zero or if AC coupling (especially between 2 stages) is possible.An Az OP can also be used just to correct for the low frequency part, with the main part of the frequency band still covered by a more normal OP amp or even a discrete JFET.Because of the bandwidth one may want to use a 2 stage design if the gain is high (like > 100 fold).

author: Marco
author_rank: Super Contributor
timestamp: July 02, 2022, 10:43:16 am
content: Quote from: luky315 on July 01, 2022, 10:19:20 amYou're dividing P2P by RMS, so if the signal is normally distributed then no.If the signal is a FM modulated sine of 100uv P2P, then the math gets hard.

author: Henrik_V
author_rank: Regular Contributor
timestamp: July 04, 2022, 02:19:36 pm
content: Do you know more about the signal?If periodic you can use/build a lock-in-amplifier

author: luky315
author_rank: Regular Contributor
timestamp: July 07, 2022, 02:40:10 pm
content: The Signal is unknown and it can be DC - so unfortunately no AC coupling is possible