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# Noise Figure (NF) of Low Noise Amplifier (LNA)

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#### exp

##### Full Member level 1
Pretty stupid question: What are the integration bounds for the NF of an LNA? (direct conversion receiver)?

Suppose frf=1GHz with 200 MHz signal bandwidth (900 - 1100 MHz). Would I integrate then from 900-1100M or all the way from 1 to many GHz? How many?

A simple cross capacitively cross-coupled differential LNA gives me NF=1.65dB between 900-1100M and NF=2.61dB if I integrate from 1 Hz to 10GHz. Clearly Flicker noise kicks in a lot (corner at 1-10MHz).

PS: I do not have any bandlimitation such as SAW filter in front of the LNA (I do not have blockers, it's not a conventional RF receiver).

Pretty stupid question: What are the integration bounds for the NF of an LNA? (direct conversion receiver)?

Suppose frf=1GHz with 200 MHz signal bandwidth (900 - 1100 MHz). Would I integrate then from 900-1100M or all the way from 1 to many GHz? How many?

A simple cross capacitively cross-coupled differential LNA gives me NF=1.65dB between 900-1100M and NF=2.61dB if I integrate from 1 Hz to 10GHz. Clearly Flicker noise kicks in a lot (corner at 1-10MHz).

PS: I do not have any bandlimitation such as SAW filter in front of the LNA (I do not have blockers, it's not a conventional RF receiver).

Similar situation ocurs with microwave radiometers. The LO is in the center of the RF spectrum, and both sidebands are converted to IF. This is why we name the system noise figure DSB.
In communication receivers, to reduce out-of-band interference, we use a RF band-pass filter and convert only one RF "sideband" to IF. Then NF is increased by 3 dB.

Including lower RF or IF section of the spectrum worsens the system RF exactly as you indicated, by low.frequency noise contribution. Some is "flicker", some (lowest) is 1/f noise.

When one measures NF of such wideband receiver as yours, be aware of FM and TV VHF and UHF transmitters around, now also cell phone base stations. Such interference also travels alomg power lines. I found it difficult even when I measured a LNA in a good Faraday cage.

Shouldn't the NF be just the one integrated from 1900M-2100M? After conversion, you no longer see what was there at DC before LNA in the frequency band of interest. You can confirm this by measuring the NF at the output of the Mixer or the TIA following the Mixer.

and NF=2.61dB if I integrate from 1 Hz to 10GHz.

You might have misunderstood the concept of noise figure, or the meaning of bandwidth in this context. The reference for noise figure is thermal noise, measured with the same (channel) bandwidth. If you double the bandwidth, noise power will double for both LNA and thermal noise => noise figure unchanged.

Shouldn't the NF be just the one integrated from 1900M-2100M?

I guess you mean 900 - 1100M (=my numbers)?
Then it is true what I said?

You might have misunderstood the concept of noise figure, or the meaning of bandwidth in this context. The reference for noise figure is thermal noise,

Hence I am asking here and even mark the question as stupid.
In a baseband system this is all easier to follow but here frequency translation happens.
And my question is if for the LNA only the RF bandwidth matters (because it is subsequentially downconverted to baseband) or something else.

measured with the same (channel) bandwidth. If you double the bandwidth, noise power will double for both LNA and thermal noise => noise figure unchanged.

This is actually something I wanted to ask some time ago. In the classical setup of channel "bandwidth" this makes sense.
But what if there is no channel in the classical sense? For example, a non-flat channel such as an integrator?

Suppose I want to integrate a signal up to 100 MHz and hence I set the unity crossover of my integrator to 100 MHz. Is the bandwidth for the noise calculation still 100 MHz although it is not a flat channel? What if I set the unity crossover of the integrator to 10 MHz. Is the bandwidth for noise calculation still 100 MHz or 10 MHz?

And my question is if for the LNA only the RF bandwidth matters (because it is subsequentially downconverted to baseband) or something else.

Let me repeat: bandwidth matters for total noise power, but not for noise figure.

This is actually something I wanted to ask some time ago. In the classical setup of channel "bandwidth" this makes sense. But what if there is no channel in the classical sense? For example, a non-flat channel such as an integrator?

Maybe you are not interested in the noise figure, but in total noise power? If you detect the total power over all frequencies, yes then your total input band range matters.

Hmm, maybe I misunderstand something but ... what is then the number "NF" all these thousands of papers refer to?
They do not say "NF at 1 GHz" or "NF in the middle of the signal bandwidth" or give a plot of NF vs Frequency. They give one NF number.

It would make sense only if NF(f) = const. But if I plot the noise figure NF in Cadence (no matter if for LNA, Mixer, baseband amplifier) it's all but constant.

Maybe you are not interested in the noise figure, but in total noise power? If you detect the total power over all frequencies, yes then your total input band range matters.

But NF is defined as "Total output noise/total output noise due to the source".
Total implies something at all frequencies of interest.

Another definition is NF=SNRin/SNRout. SNR contains all frequencies ... we integrate either in the time domain or in the frequency domain.

EDIT: Yes, I have seen some NF numbers with "dBm/Hz" or so but most of them were just "dB". I'm totally confused now. Maybe you can shed light on this.

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According to this old paper from HP/Agilent/Keysight (page 7) noise figure is independent from the bandwidth:

Anyway, read this paper and you will understand everything about noise figure (faithfully).

According to this old paper from HP/Agilent/Keysight (page 7) noise figure is independent from the bandwidth:

Anyway, read this paper and you will understand everything about noise figure (faithfully).

There is a common misunderstanding in generally giving one number for a device NF. In fact, any device has its NF as a function of frequency. Look at any LNA specifications.

LNA or MMIC manufacturers typically achieve the lowest NF over an application frequeny range, say 800 to 2200 MHz. At lower frequencies the NF rises due to various reasons. One is matching, another may be materials used (FETs and HEMTS are poor below say 10 MHz).

If you extend the LNA bandwidth over which NF is measured, usually you get poorer NF numbers at lower part of spectrum. Most LNAs are designed to a specific RF frequency range only.

It would make sense only if NF(f) = const. But if I plot the noise figure NF in Cadence (no matter if for LNA, Mixer, baseband amplifier) it's all but constant.

That is possible and expected. We usually look at narrow band systems and noise figure is specified for some design frequency (or frequency range). Within that band, it is independent of bandwidth.

One example for a device with frequency independent noise figure from DC to GHz is an attenuator. 3dB attenuator has 3dB noise figure, regardless of frequency and bandwidth.

But NF is defined as "Total output noise/total output noise due to the source".
Total implies something at all frequencies of interest.

True - but in your simple math from post #1, doubling the bandwidth would also double the thermal noise power at the input ("due to the source"). So noise figure would not change in this simplified calculation.

Another definition is NF=SNRin/SNRout. SNR contains all frequencies ... we integrate either in the time domain or in the frequency domain.

Same thing: if you double the frequency range, noise power at both input and output doubles, so that SNR doesn't change.

Yes, I have seen some NF numbers with "dBm/Hz" or so but most of them were just "dB". I'm totally confused now. Maybe you can shed light on this.

Noise figure has no units in linear scale, so that we have dB in log scale. The dBm/Hz is phase noise, which is a measure of spectral signal purity.

That is possible and expected. We usually look at narrow band systems and noise figure is specified for some design frequency (or frequency range). Within that band, it is independent of bandwidth.

One example for a device with frequency independent noise figure from DC to GHz is an attenuator. 3dB attenuator has 3dB noise figure, regardless of frequency and bandwidth.

True - but in your simple math from post #1, doubling the bandwidth would also double the thermal noise power at the input ("due to the source"). So noise figure would not change in this simplified calculation.

Same thing: if you double the frequency range, noise power at both input and output doubles, so that SNR doesn't change.

Noise figure has no units in linear scale, so that we have dB in log scale. The dBm/Hz is phase noise, which is a measure of spectral signal purity.

This long discussion shows what happens when one did not study the problem before asking questions. Beginners are confused, at least.

Units dBm/Hz refer to phase noise, or the specific power density over frequency.

Thermal noise power can be calculated from the popular equation

Pn = -174 + NF + 10 log BW, plus any gain in dB before the point of interest.

Pn is in dBm, -174 is logarithmed (kT), the product of Boltzmann constant times ambient temperature (290 Kelvis), and BW is the bandwidth in Hertz. NF here is in dB.

The wider the bandwidth, the higher the Pn. But NF is used as "spot noise figure" for one spot in frequency spectrum.

Noise figure is defined from the Pn as a device¨s addition of noise. One can and does use also noise temperature if higher than the ambient.

volker@muehlhaus

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