I am buliding a device with 24bit ADC, and would like to be able to measure the noise level on the analog supply rails. For this I want to build a low noise preamp to be able to better feed the signal into a spectrum analyser.

Here is the general layout of the first stage, and my question is, how much does the thermal noise of R3 contribute?
Or more to the point, am I correct to think that the impedance of the noise contributed by R3 is 10k and therefore this noise will be attenuated by the impedance of the capacitor? (assuming the impedance of the measured signal to be 0 ohms)

 

Here is the general layout of the first stage, and my question is, how much does the thermal noise of R3 contribute?

The noise voltage density of a 1 kΩ resistor is about 4 nV/√Hz, so the noise density of a 10 kΩ resistor would be √10 times that, or ≈13 nV/√Hz.

Or more to the point, am I correct to think that the impedance of the noise contributed by R3 is 10k and therefore this noise will be attenuated by the impedance of the capacitor? (assuming the impedance of the measured signal to be 0 ohms)

Yes. For frequencies above (1/2 * pi * R * C) ≈ 16 Hz, the capacitor will tend to shunt away the resistor's noise. The effective noise bandwidth of a 1-pole RC filter is about 1.57 times the filter cutoff frequency, or 16 Hz * 1.57 ≈ 25 Hz.

Since the bandwidth is 25 Hz, and the noise density of the resistor is 13 nV/√Hz, the net RMS noise will be

13 nV/√Hz * √25 Hz = 13 nV * 5 = 65 nV rms.

 

I assume that your circuit resistors R1 & R2 should be 10kΩ & 90kΩ respectively.
Noise from these components needs to be considered as well as the op-amp (8nV√Hz – typical).

You might find that your circuit is introducing more noise than is on the supply rails.

Why would a scope trace (on mV/div scale) not be adequate to indicate the noise levels?
Why do you require knowing the frequency-domain of the noise?

 

If you have a DSO set it to infinite persistence and look at supply rails. This will
give you pk-pk noise.

Most spectrum analyzers have low noise preamps in their frontend. What model/
manufacturer do you have.

Regards, Dana.

 

Interestingly, the noise in in RC circuit is independent of the resistor value and depends only on the value of the capacitor and the temperature (often called kt/C noise).
The voltage noise is:

For a 1μF at room temperature, this gives vn = 64nV, essentially the same value as OBW0549 calculated by a different method.

 

I assume that your circuit resistors R1 & R2 should be 10kΩ & 90kΩ respectively.

For lowest noise these should be in the k ohm region, not tens of k ohms. such as 1kΩ and 10kΩ.

 

I am buliding a device with 24bit ADC, and would like to be able to measure the noise level on the analog supply rails. For this I want to build a low noise preamp to be able to better feed the signal into a spectrum analyser.

I don't know how low a noise level you want, maybe you don't need that much as many power supply rails are pretty noisy. Others have given you good advice, but the choice of op amp is also critical. There is also a trade-off in the input impedance and noise level. If you are measuring power rail noise then the input impedance is not critical.

The OP1177 is pretty noisy (8nV/√Hz), there are much better options e.g. the ADA4898 has 0.9nV/√Hz.
http://www.analog.com/media/en/technical-documentation/data-sheets/ADA4898-1_4898-2.pdf
The datasheet also gives details of how to make a gain stage with low noise (i.e. discusses resistor values).

The LT1028 is similar, and the datasheet also has lots of useful info:
http://www.analog.com/media/en/technical-documentation/data-sheets/1028fd.pdf

If you want to go even lower, there is Charles Wenzel's design:
http://www.wenzel.com/wp-content/uploads/lowamp.pdf
which he claims is 0.6nV/√Hz

 

You might find that your circuit is introducing more noise than is on the supply rails.

Why would that be? The power supply in question will have a first stage of an isolated buck converter at around 800kHz, where I measured roughly 100mV pk-pk. After this I plan a linear regulator down to 5V for the analog rail. This I expect to be at least an order of magnitude lower noise, but that would most likely be beyond the capabilities of the instrumenst I have available, definitely for the scopes. I was thinking about the spectrum analyzer beacuse it should have lower noise than a scope, I don´t really need to see frequency domain.

I am not sure how much noise exactly I can tolerate, but the ADC ADS1257 has PSRR of 60dB, so with 5V full scale measured signal I need the noise at around 300uV to be at the 24th bit. Is that correct?
The required precision will be more like 18-19 bits, so the noise needs to be less than 10-20mV?

The opamp I have samples of comes from TI´s appnote http://www.ti.com/lit/ug/tidu016/tidu016.pdf and is OPA211 with 1.1 nV/√Hz at 1 kHz.

 

The noise power in an RC circuit is independent of R,
but the noise voltage is still very much present in the
form of

.

http://www.dsplog.com/2012/05/06/thermal-noise-rc-low-pass-filter/

Regards, Dana.