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15th January 2014, 12:08 AM  #1 
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Join Date: Dec 2009
Location: Md

SNR from noise density
A bit if a gap in my expertise here.
OK, My amp has an output of 22V RMS Spice tells me my noise density is 112 nV/sqrt Hz Divide 112 by sqrt of 20K or 141, I get .794nV Here is where I go wrong. I am off by a factor of 1000. If I plug this into 20 log (22/.794 ee9) I get 208. Of I do 20 Log (22/.794 ee6) I get 148 dB which is the believable value. I tried to follow Cordell in his spice section and I believe his example is off by 10, so even more confused. Maybe I am totally confused. 
15th January 2014, 01:36 AM  #2 
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Where you went wrong is on the 4th line. You're supposed to multiply by sqrt(20k), not divide by it. The noise spec is nanovolts per rootHertz. So to get to nanovolts you must multiply by the denominator units.
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15th January 2014, 10:45 PM  #3 
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OK following this.
Spice gives the output noise density. I need to reference the input, so divide spice supplied number by the system's gain. 112nVperHz / 27 is 4.148nVper Hz Multiply by the number of sqrt increments, or 141 gives me 585nV 20 log Vout / Vnoise or 20 log (22/585 ee9 is 151 dB Do I have this? Makes more sense today. 
15th January 2014, 11:26 PM  #4 
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151dB seems impressively high for an SNR but yep you nailed the calculation ISTM.
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16th January 2014, 01:16 AM  #5 
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Nope, still wrong.
If you want to calculate the signal to noise ratio, you need to either: a) Compare output signal voltage to output noise or: b) Compare input signal voltage to inputreferred noise You compare output signal voltage to inputreferred noise. 
16th January 2014, 01:57 AM  #6 
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Ha good point  I'd missed that  it explains why the 151dB looks too impressive. So subtract 20log(27) from 151 to get the correct answer. 27 being the system gain.
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16th January 2014, 01:11 PM  #7 
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Even that might be optimistic. You need to add the voltage noise component, the current noise component (in, pA per rt Hz, times Rs gives volts), and the Johnson noise of the source resistance itself. All 3 components add RMS. If the source resistance is low (like 1020 ohms) the last two aren't really big players, but get it up into the k ohms and it can doiminate.

16th January 2014, 01:42 PM  #8 
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4.something is about the noise level of a good low noise opamp.
4nanovolts/root Hertz is the medium frequency and high frequency levels for a 5334. Expect a low noise discrete Power Amp to be in the range 8nV to 20nV per root Hertz. Excluding avoidable Hum and buzz. A chipamp is of the order of 20nV to 100nV per root Hertz. Including avoidable Hum and Buzz can make those Power Amplifier number tens of times worse. That's why I keep asking for Numbers when Builders claim their new builds have no Hum. To me 1mVac of hum is NOT = no Hum. <0.1mVac is my definition of no Hum. ~0.3mVac is hum, but almost inaudible. 20nV/root Hz is 0.08mVac in a 27 gain Power Amplifier over the 20Hz to 20kHz frequency range
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16th January 2014, 02:28 PM  #9 
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I've seen as low as 2nv/rt Hz for state of the art op amps, and 1.7nv/rt Hz is the theoretical limit for a bipolar transistor. Something like that on >100 ohm source resistance (inclusing the feedback of course) is d*** quiet. Stick your ear up to the tweeter and hear NOTHING kind of quiet.

16th January 2014, 02:58 PM  #10 
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In LTspice, you specify a noise simulation. Run it, click on the output of your circuit and a graph of noise versus frequency will appear. It will most likely rise significantly at lower frequency, say below 100Hz. Now control click on the graph label. A little window will appear. Type in the stop and start frequencies. LTspice will then calculate the total RMS noise voltage for you.
As an example, I get 25.234uV for a circuit I am working on, for 20Hz to 20kHz. Peak output voltage is 34.6217V, or 24.28V RMS. S/N ratio is 20 * log(24.28/25.23E6) = 119dB. Not bad
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