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Old 22nd Jan 2022, 2:41 pm   #1
regenfreak
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Default Intuitive understanding of Friis cascade formula

Sorry to ask a nerdy question but it has been bugging me for a few days. Friss came up with his cascade noise figure equation in a 1944 IEEE paper.

Take a simple example, a 2-stage VHF amplifier, the overall noise factor F is:

F=F1+(F2-1)/G1

F1, F2 are linear noise factor
G1 is linear power gain

Case1:
Stage 1, noise figure 3db, gain 20db
Stage 2, noise figure 12db, gain 20db

The total noise figure is 3.3117db, overall gain 40db.

Note the terminology can be confusing, some websites mix up "factor" with "figure" when they refer to F, I don't thnk they are the same. Figure is in db; factor is linear.

Case2:
I swap the amplifiers in case 1 (e.g. a triode and pentode),
stage 1, noise figure 12db, gain 20db
stage 2, noise figure 3db, gain 20db

The total noise figure is 12.0027db, overall gain 40db.

Clearly the noise figure of the first stage has biggest influence on the overall noise.

When I first saw Friis equation, I thought it is a bit counter-intuitive because the overall noise figure is independent of the linear gain of the last stage. In the above example, the overall noise factor is the same regardless of how large G2 is. If there is n stage, the n-th stage gain is invariant. So if you have a superhet with a low-noise front end RF amp, mixer, IFs, detector, audio amp, the overall noise figure is dictated by the first RF front end. No matter how noisy and lousy the audio amp stage is, it does not seem to make a great impact on the overall chain, and yet the audio amp is closest to the output.

Have I missed something? Is there an intuitive explanation why G2 plays no part in the overall noise figure?
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Old 22nd Jan 2022, 3:22 pm   #2
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Default Re: Intuitive understanding of Friis cascade formula

You've missed something.

Noise factor/Noise figure is a somewhat 'processed' parameter, which works usefully for comparing devices, but is a bit painful for system design. Noise gets added in in different amounts at each stage, while signal gets scaled by gain/loss ~This makes the equations awkward to manage.

So do what the astronomers do. Convert noise figures into noise temperatures. You can still multiply by gains where needed, but temperatures add simply once you'veaccounted for different gains. All of a sudden, things become intuitive.

As a bonus, noise temperature doesn't carry an artificial reference temperature of 290K along with it. This is what makes NF verycounter intuitive.

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Old 22nd Jan 2022, 5:33 pm   #3
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Default Re: Intuitive understanding of Friis cascade formula

Quote:
Noise factor/Noise figure is a somewhat 'processed' parameter, which works usefully for comparing devices, but is a bit painful for system design. Noise gets added in in different amounts at each stage, while signal gets scaled by gain/loss ~This makes the equations awkward to manage.

So do what the astronomers do. Convert noise figures into noise temperatures. You can still multiply by gains where needed, but temperatures add simply once you'veaccounted for different gains. All of a sudden, things become intuitive.

As a bonus, noise temperature doesn't carry an artificial reference temperature of 290K along with it. This is what makes NF verycounter intuitive.
Thanks. It is good to know that I am not the only one finding it counter intuitive. Having said, I still do not understand how the equation is derived from the first principle. I have looked at Friis 1944 paper and struggled with its derivation. In the following Wiki page, it does not really explain where the first equation coming from and G3 "magically" is cancelled out in the last line of the derivation:

https://en.wikipedia.org/wiki/Friis_formulas_for_noise

The Friss noise temperature equation of a two stage amp:

TN=T1 + T1/G1

Once again G3 "cheats" its way out of it not appearing in the 3-stage cascade equation.



In this article, there is a conversion table between noise temperature and noise figure:
https://www.rfcafe.com/references/el...ise-figure.htm

So 1db noise figure is equivalent to 75K or -198.15C. It is still a abstract figure. Manufacturers don't really mention the noise temperature of a RF stage or the whole system in radio receivers. Perhaps I can relate better to noise voltage Vn:

(Vn^2)/B = 4KbRT

where B is bandwidth,
R is the equivalent resistance of the device
Kb Boltzmann constant
T noise temperature.

I can relate the noise voltage more easily, for example, the equivalent resistance (compared with an ideal resistor at 20C) of an ECC85 is 500 ohms, the noise voltage is 2.1175 uV at temperature of 50C and bandwidth of 500kHz. This figure gives me more intuitive value rather than a noise temperature number. But then it assumes the device is mostly resistive and it does not work well for devices with dominantly reactive components
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Old 22nd Jan 2022, 8:42 pm   #4
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Default Re: Intuitive understanding of Friis cascade formula

Quote:
Have I missed something? Is there an intuitive explanation why G2 plays no part in the overall noise figure?
It's best to think of noise figure as the change (degradation) in signal to noise ratio after a signal has passed through a system. Therefore, it does make sense that the final gain G2 plays no part because this term just amplifies the signal and the noise by the same amount. So the ratio between them is unchanged. Therefore it doesn't affect the system noise figure.

This can easily appear counter-intuitive because when you listen to a receiver on a quiet frequency and increase the volume/gain level the noise level goes up. However, if there had been a signal there it would also have got louder too. So the ratio stays the same even at the louder volume level.

Note: I think you made a typo with the temperature equation as it contains two T1 terms.
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Old 22nd Jan 2022, 9:31 pm   #5
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Default Re: Intuitive understanding of Friis cascade formula

Quote:
Originally Posted by G0HZU_JMR View Post
Quote:
Have I missed something? Is there an intuitive explanation why G2 plays no part in the overall noise figure?
It's best to think of noise figure as the change (degradation) in signal to noise ratio after a signal has passed through a system. Therefore, it does make sense that the final gain G2 plays no part because this term just amplifies the signal and the noise by the same amount. So the ratio between them is unchanged. Therefore it doesn't affect the system noise figure.

This can easily appear counter-intuitive because when you listen to a receiver on a quiet frequency and increase the volume/gain level the noise level goes up. However, if there had been a signal there it would also have got louder too. So the ratio stays the same even at the louder volume level.

Note: I think you made a typo with the temperature equation as it contains two T1 terms.

Thanks. But then stage one gain G1 amplifies the signal and the noise by the same amount too. I still dont get it. I am not sure I am making a straw man argument here. The formula looks simple but it doesnt.

Here is a sample calculation of the cascade noise figure of a receiver:

https://www.techplayon.com/noise-fig...eceiver-chain/

Yes I made a typo mistake in temperature Friis equation. Temperature noise does make lots of sense in the context of cryogenic FET LNA amps used in Astro radio telescopes and quantum computing, but it is also little hard to relate to ordinary receivers
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Old 22nd Jan 2022, 9:41 pm   #6
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Default Re: Intuitive understanding of Friis cascade formula

Quote:
But then stage one gain G1 amplifies the signal and the noise by the same amount too.
It might be helpful to look at a single stage on its own first.

If a single stage amplifies by a gain of G1 (dB) and it has a noise figure of 1dB then the signal to noise ratio at the output will be degraded by 1dB. The value of G1 doesn't need to be known for this to hold true. It applies if the G1 gain is 6dB, 12dB, 19dB or 40dB for example.

This stuff becomes more complicated if there is another amplifier after this because then the G1 term does play a role in the overall system noise figure. The only amplifier stage whose gain doesn't affect the system noise figure is that last amplifier and this holds true even if there is only one amplifier in the whole system as this single amplifier is also the last amplifier.
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Old 22nd Jan 2022, 9:41 pm   #7
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Default Re: Intuitive understanding of Friis cascade formula

I remember seeing this guy putting 100 megaphones in a chain:

https://youtu.be/XKFKPQHdWRI

Based on Friss equation, the gain of the last megaphone has no contribution to noise of the whole chain.
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Old 22nd Jan 2022, 9:44 pm   #8
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Default Re: Intuitive understanding of Friis cascade formula

Quote:
Originally Posted by G0HZU_JMR View Post
Quote:
But then stage one gain G1 amplifies the signal and the noise by the same amount too.
It might be helpful to look at a single stage on its own first.

If a single stage amplifies by a gain of G1 (dB) and it has a noise figure of 1dB then the signal to noise ratio at the output will be degraded by 1dB. The value of G1 doesn't need to be known for this to hold true. It applies if the G1 gain is 6dB, 12dB, 19dB or 40dB for example.

This stuff becomes more complicated if there is another amplifier after this because then the G1 term does play a role in the overall system noise figure. The only amplifier stage whose gain doesn't affect the system noise figure is that last amplifier and this holds true even if there is only one amplifier in the whole system as this single amplifier is also the last amplifier.
Thanks. I need to go away and think about what you have written.
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Old 22nd Jan 2022, 10:58 pm   #9
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Default Re: Intuitive understanding of Friis cascade formula

I have various MiniCircuits MMIC amplifiers here including one of their official GALI-51+ eval modules so I can use a spectrum analyser to demo how it degrades the signal to noise ratio because of its noise figure.

The official Minicircuits data for the GALI-51 amplifier can be found here:

https://www.minicircuits.com/pdfs/GALI-51+.pdf

The first image below is from the link above at 65mA bias at room temperature and shows a claimed gain of 18.19dB at 100MHz and a noise figure of 3.72dB for the GALI-51 amplifier. If I measure my eval module here at home on a decent VNA I see a gain of 18.13dB as in the second image below. The third image below shows a noise figure measurement I made of this amplifier a while back at 146MHz and this showed a gain of 18.16dB and a noise figure of about 3.6dB at 146MHz. I think it is safe to assume the GALI-51 I have here is healthy and working as it should.

If I turn on the preamp of my spectrum analyser and fit a 50 ohm termination at the input and reduce the attenuator to 0dB it has a noise floor of about -170dBm/Hz. This means it has an effective noise figure of about 4dB as thermal noise is close to -173.9dBm/Hz. See the next plot below that shows a screenshot of my analyser at 100MHz with a -170dBm/Hz reading using the noise marker function in the top right hand corner of the plot. The next plot is the one that is the most interesting. You can see what happens to the noise floor of the analyser when I insert the GALI-51 amplifier in between the 50 ohm termination and the analyser input. The noise floor marker (see the top right hand corner of the plot for the noise marker data) is now up at -152.08dBm/Hz and this can be rounded to -152.1dBm/Hz.

Thermal noise power at a warmish room temperature is -173.9dBm/Hz. The gain of the amplifier is known to be about 18.1dB from my VNA measurement. If the amplifier had a noise figure of 0dB the noise level on the analyser would be close to -173.9 + 18.1dB = -155.8dBm/Hz.

However, the marker shows -152.1dBm/Hz so the noise figure is approximately -152.1 - -155.8 = 3.7dB. In reality there will be a small contribution from the 4dB noise figure of the analyser to this number but it will be negligible in this case.

This shows that the GALI-51 added 18.1dB gain but degraded the potential signal to noise ratio of the system by about 3.7dB as demonstrated by the -152.1dBm/Hz noise floor seen on the spectrum analyser. This noise level is 3.7dB higher than thermal noise plus the 18.1dB gain of the amplifier.

If this amp had 28.1dB gain the noise floor seen on the analyser would be -173.9 + 28.1 + 3.7dB = -142.1dBm/Hz. The degradation is still only 3.7dB despite the extra 10dB gain of the amplifier.

If you think of the role of the noisy amplifier as being something that degrades the signal to noise ratio due to its noise figure and then boosts everything in level by its gain then this stuff might make more sense because the final amplifier gain figure doesn't affect the signal to noise ratio of the overall system. It just makes everything bigger including the signal and the noise.
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Old 22nd Jan 2022, 11:41 pm   #10
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Default Re: Intuitive understanding of Friis cascade formula

Quote:
Originally Posted by regenfreak View Post
Have I missed something? Is there an intuitive explanation why G2 plays no part in the overall noise figure?
It does seem counter-intuitive that G2 plays no part, or Gn in the case of an n-stage chain. After all, G2 (or Gn) is not noiseless, so must add some noise to the signal that wasn’t there when it [the signal] arrived at G2 (Gn).

My interpretation of Moxon’s writings (next attachment) on the subject is that it is simply that the noise contribution of the later stages in the chain are so small that they may be neglected. For wideband amplifiers (presumably as used in radar applications), he suggested that only the first three stages need be considered.

Moxon pp.18,19 Partial Noise Factors.pdf


The whole of Moxon’s treatment of the subject may be worth reading:

Moxon front matter.pdf


As far as I know, this book is readily available on the SH market.


Cheers,
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Old 23rd Jan 2022, 12:08 am   #11
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Default Re: Intuitive understanding of Friis cascade formula

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Originally Posted by regenfreak View Post
So if you have a superhet with a low-noise front end RF amp, mixer, IFs, detector, audio amp, the overall noise figure is dictated by the first RF front end. No matter how noisy and lousy the audio amp stage is, it does not seem to make a great impact on the overall chain, and yet the audio amp is closest to the output.
Empirically not so. Consider an FM tuner with fully variable output connected to an amplifier. Turn the tuner output down so low that the amplifier needs to be operated at the upper end of its volume control range for adequate volume. Likely the noise level will be higher than with “normal” settings of both controls. It’s an extreme example, and a measure of attenuation has been introduced. Perhaps this breaks the chain, and so separate calculations are required for each part? But then the FM tuner output might have been an inverting opamp with adjustable gain (via the feedback loop) down to fractional, so that there then there would have been no passive attenuation between two amplifier stages….

Consider this one – and I don’t know the answer:

In FM stereo (Zenith-GE system), a stereo signal arrives at the receiver with a signal-to-noise ratio (on a demodulated and decoded basis that is theoretically 23 dB worse (*) than a mono signal of similar strength. But with a good quality receiver, this difference is diminished to just a few dB by the time the incoming signal gets to somewhere a little below the 1 mV level.

Click image for larger version

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Where does this convergence of noise floors take place? Probably not in the front end, as 1 mV or thereabouts is a typical threshold for the commencement of RF AGC action, where provided. So is it in the IF amplifier/limiter, or in the demodulator/decoder, or both?


(*) 23 dB applies to the 75 µs pre-emphasis case. The pertinent equations are shown in the attached paper.


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Old 23rd Jan 2022, 12:32 am   #12
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Default Re: Intuitive understanding of Friis cascade formula

Quote:
I have various MiniCircuits MMIC amplifiers here including one of their official GALI-51+ eval modules so I can use a spectrum analyser to demo how it degrades the signal to noise ratio because of its noise figure.
Thank you very much for the demo. It is very interesting.

Quote:
If I measure my eval module here at home on a decent VNA I see a gain of 18.13dB as in the second image below.
Can it be done by cheap NanoVNA F or V2? I have done quite a bit SMD soldering and can repeat your measurement with GALI-51+

Quote:
If I turn on the preamp of my spectrum analyser and fit a 50 ohm termination at the input and reduce the attenuator to 0dB it has a noise floor of about -170dBm/Hz. This means it has an effective noise figure of about 4dB as thermal noise is close to -173.9dBm/Hz. See the next plot below that shows a screenshot of my analyser at 100MHz with a -170dBm/Hz reading using the noise marker function in the top right hand corner of the plot.
I dont have a proper spectrum analyzer so the concept of noise floor expressed in noise power in dbm per one hertz bandwidth is new to me. I guess the one Hertz unit is a convenient normalised unit. I will need to go away to read about it.

noise floor dbm = 10log(KTx1000)+NF+logBW

Quote:
If this amp had 28.1dB gain the noise floor seen on the analyser would be -173.9 + 28.1 + 3.7dB = -142.1dBm/Hz. The degradation is still only 3.7dB despite the extra 10dB gain of the amplifier.

If you think of the role of the noisy amplifier as being something that degrades the signal to noise ratio due to its noise figure and then boosts everything in level by its gain then this stuff might make more sense because the final amplifier gain figure doesn't affect the signal to noise ratio of the overall system. It just makes everything bigger including the signal and the noise.
I am sort of getting the idea . I understand the derivation now (see below)

Quote:
It does seem counter-intuitive that G2 plays no part, or Gn in the case of an n-stage chain. After all, G2 (or Gn) is not noiseless, so must add some noise to the signal that wasn’t there when it [the signal] arrived at G2 (Gn).

My interpretation of Moxon’s writings (next attachment) on the subject is that it is simply that the noise contribution of the later stages in the chain are so small that they may be neglected. For wideband amplifiers (presumably as used in radar applications), he suggested that only the first three stages need be considered.
Many thanks. Now I understand the derivation of Friis equation by re-arranging the equations backward to get the definitions of noise figure of each stage. From the derivation in the Moxon attachment:

Additional noise from 1st stage = input noise x N1 - input noise

re-arranging:

N1 =( additional noise from 1st stage + input noise)/ input which is the definition.

Therefore the first two lines of the Moxon derivation make sense now.

In the third equation in Moxon:

additional noise by 2nd =( input noise X N2 - input noise)/G1

re-arranging

N2=(additional noise by 2nd x G1 + input noise)/input noise

So it all make senses now
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Old 23rd Jan 2022, 12:37 am   #13
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Default Re: Intuitive understanding of Friis cascade formula

Things will quickly get in a muddle if you start including demodulation because you get capture effect with FM. It's best to stick to simple gain and loss stages.

One thing to consider is what you think would happen to the system noise figure if the final amplifier had (say) 30dB gain and you measured the noise figure of the system and then fitted a passive 15dB attenuator after the final amplifier. The net system gain is now 15dB lower.

Do you think this passive attenuator at the output will affect the system noise figure because the effective gain of the final stage just changed down by 15dB? It's now a 15dB gain stage rather than 30dB.

It shouldn't make any difference to the system noise figure when this happens.

Edit: I see from your post above you are now getting the hang of this stuff now so no need to answer the question above. I'm glad my analyser demo was helpful.
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Old 23rd Jan 2022, 12:42 am   #14
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Default Re: Intuitive understanding of Friis cascade formula

Quote:
Empirically not so. Consider an FM tuner with fully variable output connected to an amplifier. Turn the tuner output down so low that the amplifier needs to be operated at the upper end of its volume control range for adequate volume. Likely the noise level will be higher than with “normal” settings of both controls. It’s an extreme example, and a measure of attenuation has been introduced. Perhaps this breaks the chain, and so separate calculations are required for each part? But then the FM tuner output might have been an inverting opamp with adjustable gain (via the feedback loop) down to fractional, so that there then there would have been no passive attenuation between two amplifier stages….

Consider this one – and I don’t know the answer:

In FM stereo (Zenith-GE system), a stereo signal arrives at the receiver with a signal-to-noise ratio (on a demodulated and decoded basis that is theoretically 23 dB worse (*) than a mono signal of similar strength. But with a good quality receiver, this difference is diminished to just a few dB by the time the incoming signal gets to somewhere a little below the 1 mV level.

Click image for larger version

Name: Revox A76 S-N Curves.gif
Views: 0
Size: 71.3 KB
ID: 250235


Where does this convergence of noise floors take place? Probably not in the front end, as 1 mV or thereabouts is a typical threshold for the commencement of RF AGC action, where provided. So is it in the IF amplifier/limiter, or in the demodulator/decoder, or both?


(*) 23 dB applies to the 75 µs pre-emphasis case. The pertinent equations are shown in the attached paper.
Thanks again for the paper. I will go away and read it.

I dont know the answers of your questions. I need to think about them.
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Old 23rd Jan 2022, 12:47 am   #15
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Default Re: Intuitive understanding of Friis cascade formula

Obviously you would be able to measure the gain of the amplifier quite accurately using your nanovna so maybe a combination of the nanovna and the RSP1A could measure the gain and noise figure. However, the absolute level accuracy of the RSP1A will not be good so it won't be able to deliver the same accuracy as my Agilent spectrum analyser. However, if the RSP1A is used with a noise source to measure the Y factor then it only has to make relative measurements to perform an uncorrected noise figure measurement. As long as the gain of the test amplifier is high compared to the (4dB?) noise figure of the RSP1A then a reasonable result should be achieved.

I'll try this RSP1A setup tomorrow with a noise source and show you the result for the GALI-51.
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Old 23rd Jan 2022, 12:56 am   #16
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Default Re: Intuitive understanding of Friis cascade formula

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Quote:
Can it be done by cheap NanoVNA F or V2? I have done quite a bit SMD soldering and can repeat your measurement with GALI-51+
I've not used those nanovna models but I doubt you would succeed. I think they will be too noisy.

At a push you might be able to do it using an RSP1A SDR when it is running the Steve Andrew spectrum analyser program. I've got this setup here and could have a play tomorrow. I suspect it will prove to be a bit imprecise but still educational. I've used this RSP1A SDR setup to measure the noise figure of an amplifier via the Y factor method with a noise source and it worked quite well.
Thanks!!!! I have never heard of it.

Quote:
e-arranging

N2=(additional noise by 2nd x G1 + input noise)/input noise
Hang on a minute, why it is not multiplied by G2? Now I am back to where I was. Stage 1 cannot amplify the noise of stage 2
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Old 23rd Jan 2022, 4:52 am   #17
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Default Re: Intuitive understanding of Friis cascade formula

Steer clear of FM systems, as Jeremy says, they will confuse you. Not just with the capture effect, but also because the gain profile of the receiver changes as the IF limiters go critical in different stages depending upon level. To make sense of them you usually work only in the minimum signal condition where operating points are stable. Similarly, linear sets with AGC are handled before AGC comes in, in their low signal region where gains are maxed-out.

Non-linearities and AGC action make a right mess of Y-factor method noise figure measurement, anyway. Any non-linearities produce grossly exaggerated errors.

Also, when combining stages, remember that a device does not have a simple noise figure (or temperature) value. What you do get is a contour overlay on a Smith Chart of presented source impedance. The gain parameter can be represented as another 3-D contour map on the same Smith chart.

Where life seems really unfair is that best gain and best noise figure rarely are at close impedance values. So in designing a cascade of amplifiers you have to decide on a compromise. Going close to the gain peak better disguises the noisiness of the following stage at the expense of the noisiness of the stage you're looking at.

Subsequent stages need to be designed to handle larger signals because of the effect of the gain of the earlier stages, so inevitably, they tend to be noisier.

Some low noise parts are rather low in gain, so that in a cascade arrangement they may not have enough gain to get close to dominating the overall noise figure.

As far as understanding goes, take a few steps backwards. Convert the data for your stages into linear power gain numbers and noise temperature numbers. Noise temperatures get multiplied by linear gains, signals get multiplied by linear gains. Noise temperatures can be added in, stage by stage.

Let's say you have a 3-stage cascade where the amplifiers have power gains of 10, 20, and 30 respectively as well as noise temperatures of 100, 200, 300 Kelvins respectively.

So the noise of the first amp is 100K. This gets x10 in the first stage, x20 in the second and x30 in the third. so 100x10x20x30 = 600,000K at the output of the third stage.

The noise of the second stage is 200K and gets multiplied x20 and x30 giving a contribution of 120,000K at the output of the third stage

The noise of the third stage gets multiplied by only the third stage gain so 300 x 30 = 9,000K at the output of the third stage.

So, the cascade of amolifiers with these imagined out of nowhere parameters works. The noise contributions of later stages are progressively less significant than the earlier stages. 600,000 + 120,000 +9000 = 729,000K

But this is at the end of the amplifiers and noise figures, factors, or temperatures are considered in the plane of the input. So we calculate back to the input

792,000 / (30 x 20 x 10) = 121.5K

So the first stage dominates the noise performance, but the second stage is not insignificant. The third stage is pretty insignificant.

This calculation could have also been done by calculating each contribution temperature back to the input and adding them there. I did it this way round to follow natural signal flow.



Now, all three contributions are there at the third stage output.

If 729,000 Kelvin seems rather hot, well, the signal has had 10 x 20 x 30 = times 6000 power gain by this point.

This method can be shown to be mathematically equivalent to the Friis equations. Use it as a proof of Friis, use it instead, but it is a more intuitive way into cascaded noise calculations. It does, however, allow you to keep contributions seperate until the end, and allows you to see which stages are critical, and by how much.

20+ years ago I built a monster spreadsheet and used it in designing the Agilent Noise Figure Analyser. It allowed me to keep tabs on noise contributions as I played with stage gains/losses and looked at levels throughout the structure, making compression estimates stage by stage. It didn't just calculate overall noise figure, it produced bar charts showing which stages were critical for each of several parameters.

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Old 23rd Jan 2022, 1:06 pm   #18
regenfreak
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Default Re: Intuitive understanding of Friis cascade formula

Many thanks for the example, it is more intuitive than Friss NF formula derivation. From your example, the noise temperature is:

T = ( T1G1G2G3 + T2G2G3 + T3G3 )/ G1G2G3

If I multiply all terms inside the bracket by G1G2G3, I get the Friis noise temperature forumla:

T = T1 + T2/G1 + T3/G1G2

So this is a more intuitive way to derive the equation

How would you figure out the noise temperature of each stage?


Quote:
Steer clear of FM systems, as Jeremy says, they will confuse you. Not just with the capture effect, but also because the gain profile of the receiver changes as the IF limiters go critical in different stages depending upon level.
Lots of FM tuners has progressive hybrid limiters that IF stages act as both IF amp and limiters.

Quote:
Non-linearities and AGC action make a right mess of Y-factor method noise figure measurement, anyway. Any non-linearities produce grossly exaggerated errors.

Also, when combining stages, remember that a device does not have a simple noise figure (or temperature) value. What you do get is a contour overlay on a Smith Chart of presented source impedance. The gain parameter can be represented as another 3-D contour map on the same Smith chart.
3D Smith chart sounds scary. I gather y-method is a sort of two-point linear correlation method based on x- , y-incepts and slope of a straight line.

Quote:
Thermal noise power at a warmish room temperature is -173.9dBm/Hz. The gain of the amplifier is known to be about 18.1dB from my VNA measurement. If the amplifier had a noise figure of 0dB the noise level on the analyser would be close to -173.9 + 18.1dB = -155.8dBm/Hz.
I was like a deer in headlights when I saw the unit dbm/Hz, now I understand after reading about it.


The thermal noise power at temperature standard T with 50 ohms input, Boltzmann constant k and bandwidth

PT=KTB


Noise power of a device P at noise temperature Tn:
P = KTnB

So the output power Po
Po=( PT + P ) G

=GKB (T +Tn)

The sensitivity of a receiver is

=10log(kTb)+NF+C/N

C/N is carrier to noise ratio.
The spectral density is like bell shape Gaussian curve as thermal noise is like white noise. The thermal noise is proportional to bandwidth. If the bandwidth is doubled, the power is doubled or 3db.

The noise floor = 10log(thermal noise floor)=10log(kTB) At 1 Hz bandwith 290K,
noisefloor = -203.9dBW/Hz

To change from dbWatts to dbm
-203.9 + 30db = -173.9dBm/Hz.



Quote:
Obviously you would be able to measure the gain of the amplifier quite accurately using your nanovna so maybe a combination of the nanovna and the RSP1A could measure the gain and noise figure. However, the absolute level accuracy of the RSP1A will not be good so it won't be able to deliver the same accuracy as my Agilent spectrum analyser. However, if the RSP1A is used with a noise source to measure the Y factor then it only has to make relative measurements to perform an uncorrected noise figure measurement. As long as the gain of the test amplifier is high compared to the (4dB?) noise figure of the RSP1A then a reasonable result should be achieved.

I'll try this RSP1A setup tomorrow with a noise source and show you the result for the GALI-51.
Thanks.

Since GALI-51 has 50 ohms input and output impedance, I could just add attenuator at the input to stop the LNA overloaded by the nanoVNA getting false readings. In what way a £2000 spectrum analyzer is superior than a cheapo VNA in gain measurement? Does the measurement affect by the noise floor and noise figure of the measuring device?

Last edited by regenfreak; 23rd Jan 2022 at 1:23 pm.
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Old 23rd Jan 2022, 1:59 pm   #19
G0HZU_JMR
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Default Re: Intuitive understanding of Friis cascade formula

Another way to analyse the system would be to work out the noise power contribution at each stage in excel. If this is done the signal to noise ratio (for a -130dBm test tone) can be computed for the input and the output and these can be compared in dB. This dB ratio can then be compared to the Noise Figure (in dB) computed by the Friis equation. They should both agree.

I've had a quick go and see the attached excel spreadsheet. I guess the interesting stuff happens in column J and you can see how the various noise powers are calculated at each gain stage.

You can see the S/N degradation for the test tone is the same (in dB) as the noise figure (in dB) calculated by Friis.

Both methods show that the gain of the final stage doesn't affect the overall system noise figure. I hope the spreadsheet is OK, I've written it quickly and not done much testing on it... Obviously, it's best to stick to sensible values for gain and noise figure for each stage.

Quote:
In what way a £2000 spectrum analyzer is superior than a cheapo VNA in gain measurement? Does the measurement affect by the noise floor and noise figure of the measuring device?
The cheapo VNA should be superior at measuring the gain. It's the ability to measure noise power accurately that would let it down compared to a decent spectrum analyser. However, I believe that the most accurate noise figure measurements now use the 'cold source' method and this requires a very expensive VNA that can measure noise very accurately.
Attached Files
File Type: xlsx Friis Noise Figure1.xlsx (10.8 KB, 21 views)
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Old 23rd Jan 2022, 2:29 pm   #20
regenfreak
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Default Re: Intuitive understanding of Friis cascade formula

Quote:
've had a quick go and see the attached excel spreadsheet. I guess the interesting stuff happens in column J and you can see how the various noise powers are calculated at each gain stage.
Thanks. I struggle with column J, I dont understand why the noise power = NF x 10^(NF/10)?

I have found this Y-method, it is quite involved:

https://www.rohde-schwarz.com/uk/app...280-15484.html

There is a nice figure showing the SNR of input and output (attached).

Quote:
How would you figure out the noise temperature of each stage?
I guess it is from noise figure:

T = To ( 10^(NF/10) - 1)
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Last edited by regenfreak; 23rd Jan 2022 at 2:42 pm.
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