# Level of johnson-Nyquist noise in analog voltmeter

1. Dec 1, 2011

### tommyli

Hello,

I was wondering if anybody could answer a quick question:

What is the typical level of Johnson-Nyquist noise in an analog voltmeter in equilibrium (short circuited)? Is it millivolts?

What is the level for an AC current of order mA at 50Hz?

2. Dec 2, 2011

### jsgruszynski

It's more complicated than this because it depends on the effective bandwidth. (Not the frequency of measurement but the bandwidth of the measurement)

http://en.wikipedia.org/wiki/Johnson–Nyquist_noise

If you measure an AC current that is at 50 Hz, you have to specify a resistance to have a measurable voltage. The effective bandwidth depends on how you "box" the 50 Hz with a bandpass filter: if it's 50 Hz (25Hz above and below), that will be the bandwidth (at least) for the noise measurement.

You have to plug in bandwidth into the equation. The resistance seen also enters the picture.

If the meter is designed for it, the measurable noise can be very low, for example:

http://www.home.agilent.com/agilent/product.jspx?pn=34420A&cc=US&lc=eng

100 pV resolution and 2.5 nV accuracy (limited by thermal noise floor) - assuming you understand the difference between resolution and accuracy. Of course to attain this accuracy when actually measuring something depends a lot on how you fixture/connect the meter to the device under test. BTW this is DC only, not AC though there is an AC spec as well.

But another meter that isn't specifically design for this won't achieve the same thing because its *internal* effective bandwidth won't be small enough for the noise to be low enough to allow measurement at that level - thus the meter noise floor will be spec'ed for resolution and accuracy at a higher level.

You can often adjust the effective bandwidth with a setting called "integration time" or "NPLC" (same thing, different name). This is a post-processing way of getting around the analog limits but effectively you could have to integrate for a very long time.

3. Dec 3, 2011

### tommyli

Hi jsgruszynski,

Thankyou for your quick reply. For AC voltage I understand; however even when there is no voltage applied, you should be able to detect thermal fluctuations in a voltmeter (?) If I integrate the signal in time-domain over a "box" of size 1 millisecond, the effective bandwidth will be 1kHz, is this the bandwidth that should enter the equation? This should mean I can detect thermal fluctuations in a shorted circuit of the order of microvolts if the resistance is 1 kOhm?

4. Dec 4, 2011

### jsgruszynski

Yes, but.

The problem becomes: what (who's) noise are you measuring: the device's or the instrument's (or one of many subcomponents in the instrument). You have "dead shorts" within the instrument as well: the wiring from the DUT and all the traces up to the transistors that amplify the DUT's signal/noise.

I'm not trying to joke or dismiss your question but this literally is the issue.