How do I calculate the inherent noise of this amplifier? - diyAudio
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Old 7th April 2015, 09:24 PM   #1
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Default How do I calculate the inherent noise of this amplifier?

I'm getting barely audible static noise from my amplifier, but I don't know how I can find the source. I don't have equipment to measure levels this low, so I don't know how loud the noise actually is. Here's a quick circuit:

Click the image to open in full size.

I don't know much about noise sources or how to calculate them, but I would like to be able to calculate the inherent noise created by the amplifier itself (while the input pot is turned all the way down). The only noise sources I know of is the inherent noise of the op-amp itself and the thermal noise caused by the external resistors. Here's some figures from the datasheet of the op-amp:

Click the image to open in full size.

I found a formula for thermal noise on wikipedia: v^2=sqrt(4kB*TR). For room temperature and 100kOhm (input resistor) value gives a result of 40nV/sqrt(hz).

The datasheet gives an inherent noise density figure of 35nV/sqrt(hz) @ 10kHz. Adding these two figures together gives sqrt(40^2+35^2)=53nV/sqrt(hz). Since this is an audio amplifier my bandwidth is 20kHz so total noise is 53*sqrt(20000)=7495nV. With a gain of 3 the resulting output noise should be 22uV or are my calculations way of? I'm just taking a shot in the dark here, could someone help me out? :P Is 22uV of noise really audible?
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Old 7th April 2015, 10:23 PM   #2
rayma is offline rayma  United States
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Quote:
Originally Posted by Plecto View Post
I'm getting barely audible static noise from my amplifier, but I don't know how I can find the source.
That level of noise is not audible. Why just the 100k at the positive input - what's the source impedance?

Last edited by rayma; 7th April 2015 at 10:33 PM.
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Old 7th April 2015, 11:36 PM   #3
wwenze is offline wwenze  Singapore
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Use diodes instead of resistors for biasing your output. If resistors are used it's more sensitive to power supply noise - since you have just a voltage divider any variation in supply voltage would simply show up at the base of your transistors, giving you in this case a whopping -26dB PSRR.

22uV is -93dB relative to 1V, can be heard as a whisper on ear/headphones. Inaudible on speakers usually unless you put your ears against the tweeter.
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Old 8th April 2015, 06:17 AM   #4
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Quote:
That level of noise is not audible. Why just the 100k at the positive input - what's the source impedance?
The source impedance will depends upon the source though, won't it? It has a 3.3uF input cap as well, but I've shorted the input pot to ground in this example so the 3.3uF didn't have much going for it.

Quote:
Use diodes instead of resistors for biasing your output. If resistors are used it's more sensitive to power supply noise - since you have just a voltage divider any variation in supply voltage would simply show up at the base of your transistors, giving you in this case a whopping -26dB PSRR.
Having diodes will seriously cripple the amplifier output voltage capabilities compared to having a voltage divider though, won't it? How did you come up with -26dB PSRR? I know that there's about 1Vpp of ripple on the supply, but humming is not audible. I did some testing with my most sensitive headphones and a gain of as much as 25, humming could barely be heard, but at this level the static hissing was completely dominant.

I would like to know if my calculations are correct and if the two noise sources that I have included are the only ones? The noise is really really low and I'm testing with headphones that has a sensitivity of 109dB SPL/V.
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Old 8th April 2015, 09:18 AM   #5
wwenze is offline wwenze  Singapore
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This picture gives a better... picture... than words:

Click the image to open in full size.
Source

-26dB is based on open-loop. With feedback the amp will try to correct it and greatly reduce the output error, assuming the amp and feedback loop is fast enough. Usually for audio frequencies it is fast enough, but RF not always.

Anyway, consider the open-loop case, with your op-amp output at ground. We make an assumption here: Output voltage = Voltage at Base of transistor minus Vbe. If you're biasing using voltage divider, then voltage at Base = Power supply voltage multiply by (some value). Meaning any fluctuation in power supply causes the Base voltage and subsequently output to fluctuate at 1/(some value). That (some value) is -26dB based on those resistor values.

Now, one interesting thing about this noise, is that it goes away if the same noise is on both + and - supply rails. If the noise is only present on one rail (say the +), the higher Base voltage of one transistor cause more current on one transistor compared to the other - this causes output voltage to shift from ground. But if both transistors get higher Base voltage at the same time, current through both is increased, the voltage changes are symmetrical, so output voltage is unaffected.
With most audio power supplies a center-tapped transformer is used so the charging cycle for both + and - rails happen at the same time and this noise cancels out.

So I've mentioned why the 50Hz hum isn't audible, but random noise behaves differently and hence can still show up. One, if random noise is on both + and - rails, it will not cancel out like in the previous case, but would instead add together. Second, random noise is across all frequencies including RF - which can modulate some way some how and affect the audio frequencies, and may not be filtered away by your feedback and etc.

Well that's my hypothesis.
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Old 9th April 2015, 10:11 AM   #6
AndrewT is offline AndrewT  Scotland
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There are many more noise sources around the first stage opamp, than you have allowed for.

I recently stumbled up a Ti pdf that gave a very thorough, but understandable, analysis for predicting the noise output of their opamps. It was linked for us from a Thread here.

I'll see if I can find the copy on my HDD, but that won't have the link to the original.

However, if you have ONE dominant noise source and use that, the error in your prediction as a result of ignoring all the other non dominant noises, is very small.
With 100k tacked onto your opamp, then I would guess you have correctly identified the dominant noise.

But like the other Member I have to ask, why 100k, what's wrong with 6k666? (to match 10k||20k0)

Would that be the dominant noise now?
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Old 9th April 2015, 11:04 AM   #7
AndrewT is offline AndrewT  Scotland
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Ti doc:
www.ti.com/lit/an/sboa066a/sboa066a.pdf

noise analysis
Attached Files
File Type: pdf TiNoiseANsboa066a.pdf (256.8 KB, 6 views)
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Last edited by AndrewT; 9th April 2015 at 11:07 AM.
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Old 9th April 2015, 11:51 AM   #8
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Quote:
But like the other Member I have to ask, why 100k, what's wrong with 6k666? (to match 10k||20k0)

Would that be the dominant noise now?
The input bias current of this op-amp is so small that it doesn't matter. I just smacked on the 100k to make sure the cutoff frequency was well below 20hz. I could reduce the 100k resistor just to see what happens to the noise. I'll take a look at that pdf also, thanks a lot AndrewT

Also, how do I determine what noise is caused my the amplifier itself and what comes from the outside? With input cables connected and volume turned all the way up the hissing is intense, but disconnecting the input cables removes the hiss, but I'm not sure what this means? The internal input wires run from the back of the box, past the mains transformer and to the front amplifier PCB, but how do I isolate the noise that this cable is picking up (if any)?

Last edited by Plecto; 9th April 2015 at 11:56 AM.
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Old 9th April 2015, 12:32 PM   #9
AndrewT is offline AndrewT  Scotland
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if the input cable is open ended then you are hearing/measuring the noise of the smallest resistor across the input. If that resistor is 1M (to discharge the leakage of the DC blocking cap) then you have a lot of noise.
If the vol pot is the smallest resistance then you have 100k (10dB quieter than the 1M).
If the input to the full open vol pot is shorted or connected to a Rs=100r, then that short becomes the smallest input resistor and the noise disappears below audibility.
Quote:
how do I isolate the noise that this cable is picking up
Just pace a "short" across the far end.

One never has an open ended input with a "connected" system, provided the Source is powered ON.

Your 109dB/V headphones when fed with a noise of -93dB below 1Vac will reproduce ~16dB SPL at your ears.
That may not be audible. It depends on the background noise, how recently you listened to louder noises, how fast/hard your heart is pumping, etc.
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Last edited by AndrewT; 9th April 2015 at 12:37 PM.
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Old 9th April 2015, 02:55 PM   #10
johnr66 is offline johnr66  United States
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No drivers for the output? It might be current starved. Of course I don't know what it will be driving or the supply rails. What about thermal stability?
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