Can anyone give me a laymans explanation of the "nV/rtHz" specification/measure?

[gerrysweeney]

Hi all,

I am working one some low noise circuitry and I keep on coming across the "nV/rtHz" spec, i.e.  1.2nV/rtHz and I have no idea what this actually means. If its not too dumb a question can someone please break it down for me?

Thanks

Gerry

[rolycat]

Gerry,

I think it's spectral noise density, measured in nanoVolts per root Hertz. There's a useful explanation here:

http://www.ecircuitcenter.com/Circuits/Noise/Noise_Analysis/res_noise.htm

[ejeffrey]

This is somewhat easier to understand in the world of RF where everything is in impedance matched lines.  In that case, the real quantity of interest is "watts / Hz" -- how much noise power there is in a given bandwidth.  If you take your circuit and send its output through a bandpass filter with a given bandwidth, then onto a power meter, the signal detected will depend on the bandwidth of the filter.  You just multiply by the bandwidth BW to get watts: the signal from your meter.  The tricky part comes when you want to find out what the voltage is.  With a fixed impedance (say 50 ohm), watts = V^2/R.  Thus, you can see that the voltage noise is simply:

Vn^2 = noise_power_density (W/Hz) * BW * R.

Now, we can't resist the temptation to take the square-root of this, and solve for the RMS voltage noise.  Then we get this funny unit "volt / sqrt(Hz)"  what that means is that you take that quantity, multiply by the square-root of the bandwidth to get the noise voltage.  This means that if you double the bandwidth, you double the noise power, but the RMS noise voltage only goes up by sqrt(2).  You need to quadruple the bandwidth to get the voltage to double.

The nice power analogy doesn't quite apply as cleanly in non-impedance matched systems, but the basic scaling remains.  If you have a random noise voltage source, the RMS noise voltage is proportional to the square root of bandwidth.

[gerrysweeney]

Hi,

Thanks for the responses, that sort of makes sense, noise power in a given spectrum. I was reviewing this data sheet: http://www.thatcorp.com/datashts/THAT_1510-1512_Datasheet.pdf and under the heading Noise Performance on page 4 I found the statement:

Both parts exhibit excellent voltage noise performance of ~1 nV/?Hz at high gains

but I guess what I am not understanding is how gain and bandwidth affect this measure, and the way i read the description in the data sheet, the measure seems to go up at lower gains which seems counter-intuative to me.  I am reading 0db to be a lower gain than 60db but perhaps I have that the wrong way around?

So it would seem that both gain and the specific frequency would impact the noise figure, and both and increase in gain or an increase in frequency will increase the noise power or voltage?

Does that sound about right?

Thanks,

Gerry

[Zad]

Gain has no effect. v/sqrt(bandwidth) is a measurement of noise generated within the op-amp. As you might expect, it increases as the square root of the bandwidth. Four times the bandwidth gives twice the measured noise voltage.

[poptones]

Gain does have a practical effect, because the noise current is converted to voltage in both the input impedance and in the gain setting network.

Also, I have a problem witht he way they present this without any spectral plots. Virtually every design has a 1/f figure where noise begins rising pretty much exponentially, and this spec sheet makes no mention of it. The higher the 1/f the higher the overall noise density and the greater its audibility. Some designs have great noise voltage and current specs at higher frequencies but a 1/f pole at 1KHz or higher, which makes them essentially no better than a 5534 or an ancient LM381A.