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Old 15th January 2014, 12:08 AM   #1
tvrgeek is offline tvrgeek  United States
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Default 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 ee-9) I get 208.

Of I do 20 Log (22/.794 ee-6) 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.
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Old 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 root-Hertz. So to get to nanovolts you must multiply by the denominator units.
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Old 15th January 2014, 10:45 PM   #3
tvrgeek is offline tvrgeek  United States
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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 ee-9 is 151 dB

Do I have this? Makes more sense today.
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Old 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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Old 16th January 2014, 01:16 AM   #5
godfrey is offline godfrey  South Africa
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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 input-referred noise

You compare output signal voltage to input-referred noise.
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Old 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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Old 16th January 2014, 01:11 PM   #7
wg_ski is offline wg_ski  United States
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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 10-20 ohms) the last two aren't really big players, but get it up into the k ohms and it can doiminate.
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Old 16th January 2014, 01:42 PM   #8
AndrewT is offline AndrewT  Scotland
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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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Last edited by AndrewT; 16th January 2014 at 01:50 PM.
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Old 16th January 2014, 02:28 PM   #9
wg_ski is offline wg_ski  United States
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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.
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Old 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(24.28/25.23E-6) = 119dB. Not bad
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