# Total Noise Calculation, NF & RMS Voltage noise

1. ## Total Noise Calculation, NF & RMS Voltage noise

Hi,

I'm calculating the noise of an inverting opamp followed by a variable gain amplifier. The opamp's noise sources are stated by its input current noise and input voltage noise in pA/sqrt(Hz) and nV/sqrt(nV), respectively. I calculated the opamp's output rms noise voltage.

The output of the opamp (1st stage) is connected to a variable gain amplifier (2nd stage). I calculated the cascaded output noise caused bei the 1st stage (opamp) by Vn_opamp^2 * G(x), where the VGA amplification G(x) is a function of the gain control setting x.

Now I'm getting a little bit confused. The VGA noise is given by its noise figure NF in dB. This noise figure is also a function of the gain setting x and decreases with increasing gain. How can I convert the noise figure into a rms voltage noise, to calculate the total noise of stage 1 and stage 2?

The VGA has an input impedance of 200 Ohm, if this helps.

Can anyone tell me how to calculate the total noise?

BR

2. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Noise figure is the usual way to specify amplifier noise in RF engineering. You should be able to calculate the amplifier noise density by simply referring to the definition of Noise Figure, see e.g. https://en.wikipedia.org/wiki/Noise_figure. Verbose explanations with calculation examples in RF engineering text books.

Noise figure refers to a nominal source impedance rather than actual amplifier input impedance, first point to check if it's actually 200 ohms for the said VGA.

3. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Hi,

and for the OPAMP circuit noise: https://www.edaboard.com/showthread.php?t=371938

Klaus

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4. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Hi, thank you for the quick replies!

@FvM: I know how the noise figure is defined, but how can I calculate the output noise, if I have no information of the input noise?

Originally Posted by FvM
Noise figure refers to a nominal source impedance rather than actual amplifier input impedance, first point to check if it's actually 200 ohms for the said VGA.
So the input noise of a noise figure is provided by the source load, usually 50 Ohm? Therefore the input noise is Vn,in = sqrt(4*k*T*R_source*B*pi/2)?!
I'm analyzing the AD8367, from Analog Devices. According to figer 45 on page 20, the device is characterized with two matching networks, to use 50 Ohm equipment.

BR

5. ## Re: Total Noise Calculation, NF & RMS Voltage noise

To calculate noise u should know:
- oamp gain
- resistors value

for example :)
for 1Mhz, and gain = 10, oamp noise hm,. f.e 10nV/√Hz, resistor 50 ohm,

rms noise for resistor is: 0.89970847 uV
http://www.sengpielaudio.com/calculator-noise.htm
your gian is 10x, so 0,89 * 10 = 8,9uV

rms noise for oamp is: 10nV/√Hz = 10nV * sqrt(1Mhz) ~ 10uV

To add noise: sqrt(10uV^2 + 8,9uV^2) =~ rms 13uV
probability of rms noise, for 6 sigma 98% is 13uV * 6 = 78uV ...

To do this properly you must consider noise for loopback resistor and the current noise. That's why it's best to do it in LTSpice.
Remember!! Noise is added with square root and it depends on the bandwidth value! The smaller the bandwidth, the smaller the output noise.

btw: for example:
noise for resistor 50 ohm, for badwith 1Mhz is 0,89uV and badwith 1khz is 0.028 uV.
Reducing bandwidth from 1MHz to 1kHz your noise is smaller 31x, not 1000 times. (0,89/0,028 = 31)

6. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Hi,

Sorry.
I corrected it now.

Klaus

7. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Hi,

@ karbiuch & KlausST: thank you for your replies! I have no problem at all to calculate the noise of an opamp or cascaded opamps, as long their noise characteristics are given in nV/sqrt(Hz) and pA/sqrt(Hz).

I still have problem to calculate the overall gain if the noise characteristics of the second stage is ONLY given by its noise figure.

BR

8. ## Re: Total Noise Calculation, NF &amp; RMS Voltage noise

AD8367 datasheet says "system impedance Z0 200 ohm" on top of the specifications, that's what noise figure refers to, about 2 nV/√Hz resistor noise.

I still have problem to calculate the overall gain if the noise characteristics of the second stage is ONLY given by its noise figure.
Not sure what the problem is. Noise figure versus VGA gain is specified in the datasheet, also NF versus frequency, so you can calculate input (or output referred) noise voltage density and noise voltage for any operation point.

AD8367 is basically an amplifier with preceding variable attenuator, so you get roughly a constant output noise contribution of VGA + a gain dependent contribution of first stage, only significant at highest gain settings.

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9. ## Re: Total Noise Calculation, NF & RMS Voltage noise

@ FvM: Thank you for the reply. I know how the AD8367 works, and that the noise due to the resistive variable attenuator is larger for low gain settings (large attenuation). I also know the definition of noise factor and noise figure.

My problem until now was, how the "test conditions look like". If I understand your answer correct, the VGA is shorted at its input, thus the input impedance creates the noise (as it is for an inverting opamp) and the output noise is determined. And finally stated as the ratio (noise factor) F = N_out/(Gain * N_in), where N_in is the 200 Ohm input noise.

I hope I understood you correct!?

Is there a text book or publication where noise figure/factor measurement or calculation is explained? Everey time I made a web research I only found the definition of F and NF e.g. on wikipedia. Sometimes I found examples, using an amplifier (triangle symbol) in combination with a (additional) 50 Ohm resistor as input resistor. But it was never mentioned (or I haven't got it ) that this resistor is the opamps input resistor. Which is obvious now, if I consider RF components only (with a typical input resistance of 50 Ohm), instead an ordinary opamp.

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10. ## Re: Total Noise Calculation, NF & RMS Voltage noise

@ FvM: regarding my previous reply, are my conclusions correct?

Further, can anyone recomment publications or text books, where NF/F measurements, especially the measurement setup, are explained in detail.

BR stenzer

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11. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Profound RF engineering text books should contain a detailed discussion of noise factor, I have it e.g. in the German Taschenbuch der Hochfrequenztechnik by Meinke, Gundlach et al ("RF engineering pocket book"). Perhaps other users can suggest an English text book.

A derivation of noise factor and other noise parameters can be also found in specialized text books, e.g. Razavi, RF Microelectronics.

An amplifier has both voltage and current input noise, in so far shorting the input won't give the complete amplifier noise. The referenced "noiseless amplifier output" is essentially a calculated quantity, it requires an accurate measurement of DUT gain.

12. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Hi, thank you FvM, I will have a look at Razavi, RF Microelectronics.

Originally Posted by FvM
An amplifier has both voltage and current input noise, in so far shorting the input won't give the complete amplifier noise. The referenced "noiseless amplifier output" is essentially a calculated quantity, it requires an accurate measurement of DUT gain.
I know from "ordinary" opamp noise calculations that bot, voltage input noise and current input noise have to be considered. This leads to my dilemma. I do not know those quantities for the VGA. The only reference point until now is the input impedance of 200 Ohm, which leads to a input voltage noise of about 2 nV/√Hz, as you already stated.

So is it valid, to assume the input voltage noise to be 2 nV/√Hz, to calculate the output voltage noise? As I do not have any further information.

BR

13. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Hi,

No, 2nV/sqrt(Hz) is the 200 Ohms reference noise. This is equals 0dB noise.
Now including the amplifier you get 2dB (or whatever) noise in total.

So the 2dB result in 2nV/sqrt(Hz) x 1.259 = 2.51nV/sqrt(Hz)

Now you just have to take your bandwidth into account.

Klaus

14. ## Re: Total Noise Calculation, NF & RMS Voltage noise

The datasheet specifies a noise figure with 200 ohm source impedance, you don't (and don't need to) know which part is caused by noise current and which by noise voltage. The question would be relevant for a variable source impedance.

15. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Hi, now I'm totally confused by the last two replies.

Originally Posted by KlausST
Hi,

No, 2nV/sqrt(Hz) is the 200 Ohms reference noise. This is equals 0dB noise.
Now including the amplifier you get 2dB (or whatever) noise in total.

So the 2dB result in 2nV/sqrt(Hz) x 1.259 = 2.51nV/sqrt(Hz)

Now you just have to take your bandwidth into account.

Klaus

According to Klaus the output noise is direct proportinal to the VGA gain, but the NF decreases with increasing gain. By having a look at figure 7 and the definition of the noise figure/noise factor,( F = (S_in/N_in)/(S_out/N_out) = (S_in/N_in)/(S_in*G/N_out) = N_out/(G * N_in)), the output noise can not be direct proportional due to the decreasing noise figure. So the noise figure/ noise factor is "missing". So the equation to calculatethe output noise should look like N_out = F * G * N_in = F * G * 2nV/sqrt(Hz).

Originally Posted by FvM
The datasheet specifies a noise figure with 200 ohm source impedance, you don't (and don't need to) know which part is caused by noise current and which by noise voltage. The question would be relevant for a variable source impedance.
@ FvM: I was already convinced, by your reply and, your other replies, that input noise referes to a 200 Ohm input load. Thus leading to a output noise following N_out = F * G * N_in = F * G * 2nV/sqrt(Hz). Is this conclusion correct?

BR

16. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Hi,

According to Klaus the output noise is direct proportinal to the VGA gain
No. I never said this.
I assume you mix noise_figure (in dB) with VGA_gain (in dB).

The VGA noise is given by its noise figure NF in dB. This noise figure is also a function of the gain setting x and decreases with increasing gain.
How can I convert the noise figure into a rms voltage noise
Klaus

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17. ## Re: Total Noise Calculation, NF & RMS Voltage noise

@ Klaus: Sorry, I really mixed the VGA gain and the Noise Figure, in your reply (#13). So the output noise is given be N_out = 2 nV/sqrt(Hz) x 10^(NF/20)

Thank you

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18. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Hi,

So the output noise is given be N_out = 2 nV/sqrt(Hz) x 10^(NF/20)
No, this is the equivalent input noise. "200 Ohms" is the source impedance = input impedance.
Multiply this with the VGA gain and get the output noise.

Klaus

19. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Originally Posted by KlausST
Hi,

No, this is the equivalent input noise. "200 Ohms" is the source impedance = input impedance.
Multiply this with the VGA gain and get the output noise.

Klaus

Hi Klaus,

I already asked in reply #9 and #15 if the output noise can be calculated by N_out = G x N_in x F. Where N_out is the output noise in V/sqrt(Hz), G is the linear VGA gain, F the noise factor and N_in the input noise in V/sqrt(Hz). Wher N_in = 2 nV/sqrt(Hz).

So, again, can the output noise be calculated by N_out = G x N_in x F? As be intended by the last reply (#18).

20. ## Re: Total Noise Calculation, NF & RMS Voltage noise

Hi,

Yes, N_out = G x N_in x F seems to be correct.

I was confused, because the formula in post#9 made no sense to me (F = ...) but now I see it´s basically the same. Sorry.

Klaus

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