Noise Figures
I am working on an amplifier, and I am wondering how to measure and interpret noise figures for the preamp stage...
The preamplifier involves a JFET front end, and a directcoupled class A bipolar transistor second stage. I have run the circuit through Circuitmaker and have nice simulation results. Now.... What the heck is pV^/Hz ? It is a noise figure, but I'm not sure what it means in the real world. Does anyone have any information on what this is, how I could measure it on my finished amp, and what I'm looking for for noise figures? Even a place to research this and learn it for myself would be AOK. Thanks 
PV^/Hz is the noise voltage density in a one Hz bandwidth. you have to integrate it over the whole bandwidth to obtain a total noise voltage. With a preamp this is tricky because of the equalization.
Dr. Leach has a very good dissertation on noise on his website, but you now need a password for access. Possibly if enough people ask him he might make it available to the public again. Several years ago I asked him to post the schematic of his MM phono preamp and he did it. I have a very effective grovel and beg. Regards, Ray 
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Basically, you can use this figure to determine how much noise will be present, based on amplifier bandwidth. Ex. if you have 4.5 nV/sqrt(Hz), and a bandwidth of 20 kHz, then you will have 4.5 nV * sqrt(20000) = 636 nV or 0.6 uV of noise. Note that this figure is usually referenced to the input of the amp, so now multiply it by the voltage gain of the amp, say 20 (which is 26 dB gain). Now you have 12 uV of noise at the output of the amp. But to caculate the noise accurately, you will need to account for noise sources other than the inputreferenced voltage noise. These include the inputreferenced current noise (input impedance of the amp converts this into voltage noise), resistor selfnoise (thermal noise), etc. I would imagine that you could find some noise application notes or design guides at Analog Devices or TI or Linear Tech that will go into lots of practical detail about noise sources. Take a look. 
You guys (& gals) rock
Once again, this helps immensely.
The graph at the output node in Circuitmaker shows the noise level rolling up to @ 4.5 pV^2/Hz down towards 15Hz with the node designated to the signal generator and measured at the final simulated load resistor. so I'll assume that my minimum noise level will be 5 pV^2/Hz, and my realistic voltage gain will be about 15. that's: 25pV/Hz 25pV / 20,000 Hz (bandwidth) =.00125 .00125*15 (gain) =.01875 pV That's tested with an input of 2mV and an output of over 30mV, so my theoretical noise output is @ 240db? This seems kinda low... I'm guessing that there will me much more noise than that from other sources. Or, maybe my analysis is set up wrong... Ok, I'll double the noise level to 10pV^2/Hz 100pV/Hz 100pV / 20,000 (bandwidth) =.005 pV .005 pV * 15 (gain) =.075 pV out of 30 mV that's still 230dB for a noise floor. 
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I use Circuitmaker all the time, and I have used the noise simulation often to optimize designs.
here's what I think is the right way to do it 5pV^2/Hz you need to SQuarerRooT it .. for nV/sqrt(hz) that is 70nV/sqrt(Hz) (that's quite a lot for a low noise design) multiply with the sqrt (bandwidth) say sqrt(20e3) = 141 70 * 141 = 10uV total noise grz, Thijs 
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You need units of Volts in the result, not Volts^2, so take the square root of the noise figure you have (5 pV^2/Hz): 5 pV^2/Hz can be expressed as: 5e12 (V^2)/Hz sqrt( 5e12 (V^2)/Hz ) is 2.24e6 V/sqrt(Hz) The voltage noise figure is 2.24 uV/sqrt(Hz). Note the significant change in the exponent; you were about 5 orders of magnitude off. Now use that in your calculations. 
Hmmm.... Hmmm....
so 5pV^2/Hz
= SQRT .000000000005 / (SQRT Hz) =2.236 uV / 141 (SQRT Hz) =.01585 uV .01585 uV * 15 (power) =.238 uV noise Did I do that right? Now I'm getting @ 100dB noise figure. Yes, this is bad. I'm looking for @ 115dB. or  infinity dB of course... ;) Well, it's my first attempt at a JFET front end, so back to the drawing board. 
Re: Hmmm.... Hmmm....
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Also, The noise figure of 5 pV^2/Hz, I assume that you got this from simulations? Is this figure for noise at the output, or is it referenced to the input? This is important, because in the former case, you do not multiply it by the amplifier's gain, but in the latter case you do. Commercial opamps give noise figures referenced to the input because they have no control over how you use the amplfier (gain, etc.), but I would suspect the simulations might give a noise figure directly at the output. That makes a big difference. But probably not enough. 
LTSpice has an example of a phono preamp using an LT1027. I modified the example by adding a phono cartridge and plotted the output noise. It was very high at 20 Hz and decreased in a concave curve to 20kHz. This is to be expected because the gain decreases about 40 dB from 20 Hz to 20kHz. What this tells you is that you need an input stage with very low noise voltage and decent noise current. The noise voltage dominates at low frequencies due to the low cartridge impedance. The cartridge impedance doubles in each octave and so does the current noise.
Suggest you use the same JFETS as in the Leach preamp at http://users.ece.gatech.edu/~mleach/. The JFETs are old but still good and readily available from many sources. In this case the low transconductance and gain of the JFETs is an advantage because you have little Miller effect capacity. Regards, Ray 
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