UK Vintage Radio Repair and Restoration Powered By Google Custom Search Vintage Radio and TV Service Data

Go Back   UK Vintage Radio Repair and Restoration Discussion Forum > General Vintage Technology > Components and Circuits

Notices

Components and Circuits For discussions about component types, alternatives and availability, circuit configurations and modifications etc. Discussions here should be of a general nature and not about specific sets.

Closed Thread
 
Thread Tools
Old 23rd Jan 2022, 3:10 pm   #21
G0HZU_JMR
Dekatron
 
Join Date: Sep 2010
Location: Cheltenham, Gloucestershire, UK.
Posts: 3,077
Default Re: Intuitive understanding of Friis cascade formula

The spreadsheet converts Noise Figure in dB (in column E) to Linear Noise Factor in column H.

A noise figure of 3.01dB would therefore calculate to be 10^(3.01/10) = a linear noise factor of 2.

To do it the other way around a linear noise factor of 2 converts to Noise Figure 10*log(2) = 3.01dB.

The aim of column J is to convert the noise to a power in Watts.

Stage 1 has a noise figure of 3dB so this is a linear factor of 2. This therefore adds 'double' the thermal noise (converted from -173.9dBm/Hz to Watts) from cell E14. So it adds 2* 4.0020E-21W = 7.9850E-21W.

Stage 1 then amplifiers this noise power with a linear gain of 15.8489 to produce a noise power of 1.2655E-19 Watts at the output of stage 1.

Stage 2 has a noise figure of 8dB = 6.311 Linear Noise Factor. So its excess noise will contribute noise power at 6.311 * E14 = 2.1249E-20W but this also needs to be summed with the 1.2655E-19 noise power output from stage 1. It then gets amplified in stage 2 with a linear gain of 15.8489 to produce a noise power of 2.3425E-18 Watts at the output of stage 2.

Stage 3 has a noise figure of 11dB = 12.59 Linear Noise Factor. So it will contribute noise power at 12.59 * E14 = 24.6380E-20Watts but this needs to be summed with the 2.3425E-18W noise power output from stage 2. It then gets amplified in stage 3 with a linear gain of 15.8489 to produce a noise power of 3.7862E-17 Watts at the output of stage 3.

This is equivalent to a power level of -134.22dBm/Hz at the output of stage 3.

The system gain is 12dB + 12dB + 12dB = 36dB.

The system noise figure will therefore be 173.98 - 36 - 134.22 = 3.759dB.



.
__________________
Regards, Jeremy G0HZU
G0HZU_JMR is offline  
Old 23rd Jan 2022, 3:18 pm   #22
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: Intuitive understanding of Friis cascade formula

Quote:
The spreadsheet converts Noise Figure in dB (in column E) to Linear Noise Factor in column H.

A noise figure of 3.01dB would therefore calculate to be 10^(3.01/10) = a linear noise factor of 2.

To do it the other way around a linear noise factor of 2 converts to Noise Figure 10*log(2) = 3.01dB.

The aim of column J is to convert the noise to a power in Watts.



Thanks. Let me have a second look.

I think I understand how y-method works.

Let Po output thermal noise output
Ps is the input source noise power
Pt is the unknown noise power of DUT of thermal noise temp Tn
G is the stage gain

Po = GPs + GPt
=GKBT + GkBTn

The equation of a straight line is:

y = kx + c
k = slope = GKB
intercept is c= GkBTn

To get the two-point measurements, apply the input Ps with and without noise source.
regenfreak is offline  
Old 23rd Jan 2022, 3:29 pm   #23
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: Intuitive understanding of Friis cascade formula

Quote:
Stage 1 has a noise figure of 3dB so this is a linear factor of 2. This therefore adds 'double' the thermal noise (converted from -173.9dBm/Hz to Watts) from cell E14. So it adds 2* 4.0020E-21W = 7.9850E-21W.
Many thanks I understand now
regenfreak is offline  
Old 23rd Jan 2022, 3:52 pm   #24
G0HZU_JMR
Dekatron
 
Join Date: Sep 2010
Location: Cheltenham, Gloucestershire, UK.
Posts: 3,077
Default Re: Intuitive understanding of Friis cascade formula

Sorry, I wrote the previous explanation too hastily as I for got to include the '-1' term for the noise factor for the noise contribution from stages 2 and 3.
The spreadsheet has the '-1' term included so it should still be OK.

I think it should be described as below. Note that this is my understanding of how the noise powers sum in each stage and I'm not sure I've ever seen it presented in a breakdown like this before. I hope it is all OK.
Quote:

Stage 1 has a noise figure of 3dB so this is a linear factor of 2. This therefore adds 'double' the thermal noise (converted from -173.9dBm/Hz to Watts) from cell E14. So it adds 2* 4.0020E-21W = 7.9850E-21W.

Stage 1 then amplifiers this noise power with a linear gain of 15.8489 to produce a noise power of 1.2655E-19 Watts at the output of stage 1.

Stage 2 has a noise figure of 8dB = 6.311 Linear Noise Factor. So its excess noise will contribute noise power at (6.311 - 1) * E14 = 2.1249E-20W but this also needs to be summed with the 1.2655E-19W noise power output from stage 1. It then gets amplified in stage 2 with a linear gain of 15.8489 to produce a noise power of 2.3425E-18 Watts at the output of stage 2.

Stage 3 has a noise figure of 11dB = 12.59 Linear Noise Factor. So it will contribute noise power at (12.59 - 1) * E14 = 24.6380E-20Watts but this needs to be summed with the 2.3425E-18W noise power output from stage 2. It then gets amplified in stage 3 with a linear gain of 15.8489 to produce a noise power of 3.7862E-17 Watts at the output of stage 3.

This 3.7862E-17 Watt power level is equivalent to a power level of -134.22dBm/Hz at the output of stage 3.

dBm/Hz =(10*LOG(3.7862E-17))+30 = -134.22dBm/Hz

The system gain is 12dB + 12dB + 12dB = 36dB.

The system noise figure will therefore be 173.98 - 36 - 134.22 = 3.759dB.
__________________
Regards, Jeremy G0HZU
G0HZU_JMR is offline  
Old 23rd Jan 2022, 3:54 pm   #25
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: Intuitive understanding of Friis cascade formula

Thanks I can sum up your updated explanation below:

thermal noise power at T= 290k is defined as Pt
Pt = kBT

stage 1:

since NF1 = P1/Pt therefore P1 = NF1 X Pt

output thermal power P1o = G1 X P1

stage 2:
P2o = [(NF2-1) X Pt + P1o]G2

stage 3:
P3o = [(NF3-1) X Pt + P2o] G3

Please correct me if i mess it up.

Quote:
Sorry, I wrote the previous explanation too hastily as I for got to include the '-1' term for the noise factor for the noise contribution from stages 2 and 3.
The spreadsheet has the '-1' term included so it should still be OK.
I was wondering as well. My understanding is -1 is to knock off the NF contribution from the previous stage.

Last edited by regenfreak; 23rd Jan 2022 at 4:03 pm.
regenfreak is offline  
Old 23rd Jan 2022, 4:06 pm   #26
Radio Wrangler
Moderator
 
Radio Wrangler's Avatar
 
Join Date: Mar 2012
Location: Fife, Scotland, UK.
Posts: 22,800
Default Re: Intuitive understanding of Friis cascade formula

All the above works fine if things like the signal source have background noise associated with resistors at room temperature (290K) and then a device with 3dB NF will reuce your S/N ratio by 3dB.

Where you suddenly get into deep water is when you have to deal with a system whose antenna sees a fair amount of sky or cold ground. The incoming S/N ratio can be quite a bit better than room temperature, and consequently there is a lot more benefit from ultra low noise devices than you'd think.

Be aware of the reference temperature built-in to the definitions of noise factor and noise figure and check that it is relevent to the system in-hand.

With a Y factor measurement rig, a calibrated noise source is turned on and off. Off isn't all that off. There is still the thermal noise from the resistors setting its output impedance. Y-factor instruments need the equipment temperature entering. A great many users either don't know to fo this or just guess. When measuring a reasonable low noise transistor, a 6 degree error in the guess can give 0.1dB error in the noise figure result, comparable to the errors in the rest of the equipment. Some people leave it set at the default. Well, they get a number and that's what they want. But they have no idea of how far off it could be. THese errors can easily be bad enough to make noise figure show as a negative number. Unfortunately bad software suppresses this and you just lost the big clue that something is badly wrong.

In terms of accuracy, noise figure is one of the worst measurements regularly made.

Agilent application notes AN57/1 and AN57/2 take you through this. You may be best looking for the versions from around 2001. Later versions got re-written with a view to selling NF options in spectrum analysers and network analysers. Convenient, but a step down in accuracy from the HP8970 and the Agilent N897x family.

Bruce Ericksson wrote AN57/1 and Ian White (G3SEK) Wrote AN57/2.

David
__________________
Can't afford the volcanic island yet, but the plans for my monorail and the goons' uniforms are done
Radio Wrangler is offline  
Old 23rd Jan 2022, 4:34 pm   #27
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: Intuitive understanding of Friis cascade formula

Quote:
ith a Y factor measurement rig, a calibrated noise source is turned on and off. Off isn't all that off. There is still the thermal noise from the resistors setting its output impedance. Y-factor instruments need the equipment temperature entering. A great many users either don't know to fo this or just guess. When measuring a reasonable low noise transistor, a 6 degree error in the guess can give 0.1dB error in the noise figure result, comparable to the errors in the rest of the equipment. Some people leave it set at the default. Well, they get a number and that's what they want. But they have no idea of how far off it could be. THese errors can easily be bad enough to make noise figure show as a negative number. Unfortunately bad software suppresses this and you just lost the big clue that something is badly wrong.

In terms of accuracy, noise figure is one of the worst measurements regularly made.

Agilent application notes AN57/1 and AN57/2 take you through this. You may be best looking for the versions from around 2001. Later versions got re-written with a view to selling NF options in spectrum analysers and network analysers. Convenient, but a step down in accuracy from the HP8970 and the Agilent N897x family.

Bruce Ericksson wrote AN57/1 and Ian White (G3SEK) Wrote AN57/2.
Thanks. AN57/1 and AN57/2 cover lots of stuff. It does mention that noise figure is independent of type or fidelity of modulation and demodulation. Also the noise factor should be considered separated from the gain and is independent of input level.
regenfreak is offline  
Old 23rd Jan 2022, 5:17 pm   #28
G0HZU_JMR
Dekatron
 
Join Date: Sep 2010
Location: Cheltenham, Gloucestershire, UK.
Posts: 3,077
Default Re: Intuitive understanding of Friis cascade formula

I can post up a worked system example as I've dug out a couple of test amplifiers and a calibrated 20dB attenuator.

Stage 1 is a Minicircuits PGA103+ amplifier
Stage 2 is a very accurate 20dB attenuator
Stage 3 is a Minicircuits GALI-51 amplifier

The minicircuits data suggests 25.98dB gain at 104MHz for the PGA103+ and 18.19dB gain at 100MHz for the GALI-51 amp.

So the system gain ought to be just under 24.2dB.

The claimed noise figure for the PGA103+ is 0.45dB at 100MHz
The claimed noise figure for the GALI-51 is 3.72dB at 100MHz

If I connect up the real amplifiers in a short chain with the 20dB attenuator in the middle of the two amplifiers using SMA connectors and measure the gain and noise figure on my spectrum analyser I see 23.94dB gain and 2.30dB noise figure for the entire 3 stage combination.

See the amended excel spreadsheet below and see also my attempts to measure the gain and noise figure of each amplifier and the combined system.

The spreadsheet predicts 24.13dB gain and 2.31dB noise figure. That is a very close result!

The results do agree very well with the excel spreadsheet and also with the datasheet as long as you also accept that it is very difficult to measure noise figure with great accuracy. My noise figure setup here at home is very good and the next significant step up in capability would probably be a thermally controlled and screened RF lab using a £250k analyser.
Attached Thumbnails
Click image for larger version

Name:	PGA103_20dB_GALI51.jpg
Views:	39
Size:	71.3 KB
ID:	250290   Click image for larger version

Name:	combined.gif
Views:	37
Size:	10.6 KB
ID:	250291   Click image for larger version

Name:	pga103.gif
Views:	31
Size:	10.6 KB
ID:	250292   Click image for larger version

Name:	gali51.gif
Views:	34
Size:	10.6 KB
ID:	250293  
__________________
Regards, Jeremy G0HZU

Last edited by G0HZU_JMR; 23rd Jan 2022 at 5:38 pm.
G0HZU_JMR is offline  
Old 23rd Jan 2022, 5:30 pm   #29
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: Intuitive understanding of Friis cascade formula

Quote:
See the amended excel spreadsheet below and see also my attempts to measure the gain and noise figure of each amplifier and the combined system.

The spreadsheet predicts 24.13dB gain and 2.31dB noise figure. That is a very close result!

The results do agree very well with the excel spreadsheet and also with the datasheet as long as you also accept that it is very difficult to measure noise figure with great accuracy. My noise figure setup here at home is very good and the next significant step up in capability would probably be a thermally controlled and screened RF lab using a £250k analyser.
Attached Thumbnails
Woww! Thats very impressive! Thanks for the demo. I can only dream one day getting a entry level Rigol DSA815-TG. But my Scrooge side controls my spending and I dont want to depart with my hard earned money. Honestly noise measurements would not be something appeal to me, it is my nerdy mind gets me to read about it. I would prefer to do frequent sweep of filters, less stressful than thinking about noises!
regenfreak is offline  
Old 23rd Jan 2022, 5:43 pm   #30
G0HZU_JMR
Dekatron
 
Join Date: Sep 2010
Location: Cheltenham, Gloucestershire, UK.
Posts: 3,077
Default Re: Intuitive understanding of Friis cascade formula

Thanks. I think I measured the noise figure of the GALI-51 a bit too quickly without letting the module fully warm up. MiniCircuits provide this demo amp on a chunky metal heat spreader and it takes a while to warm up. I measured 3.45dB noise figure and was expecting 3.7dB. I suspect it would have increased closer to 3.7dB had I been a bit less impatient/lazy and let it settle to a steady thermal state. The PGA103 LNA amp is on a skinny PCB without a chunky metal heat spreader so it settles quite quickly.
__________________
Regards, Jeremy G0HZU
G0HZU_JMR is offline  
Old 23rd Jan 2022, 8:55 pm   #31
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: Intuitive understanding of Friis cascade formula

There is a very good diagram in AN57/1 that illustrates the same steps as your excel spreadsheet (attached).
cheers
Attached Thumbnails
Click image for larger version

Name:	cascade.jpg
Views:	44
Size:	55.8 KB
ID:	250313  
regenfreak is offline  
Old 23rd Jan 2022, 10:08 pm   #32
G0HZU_JMR
Dekatron
 
Join Date: Sep 2010
Location: Cheltenham, Gloucestershire, UK.
Posts: 3,077
Default Re: Intuitive understanding of Friis cascade formula

Thanks! That gives me a bit of peace of mind.

I tried measuring the noise figure of the GALI-51 amp using the RSP1A SDR and the 346A noise source. Sadly, the RSP1A only resolves down to 0.1dB and even with lots of averaging there is about +/-0.2dB variation in the hot and cold readings. However, with a noise source ENR of 5.73dB the Y factor ratio was typically 4.0dB.

This gives an uncorrected noise figure of 3.93dB for the GALI-51 at 103MHz. This reading will be very slightly high because it is uncorrected but it is fairly close. However, the RSP1A could benefit from having the ability to improve the averaging to get a more consistent reading for hot and cold down to a resolution of <0.1dB.

See below for a screenshot of the noise floor of the RSP1A with a terminated input at 103MHz. I'm not sure I trust the accuracy of the FFT window function but it implies the RBW is about 7.63Hz and the marker indicates -160dBm noise power in this RBW. This implies the noise figure is very low. It's almost as sensitive as my Agilent analyser although the input VSWR of the RSP1A will probably be quite poor at these settings.
Attached Thumbnails
Click image for larger version

Name:	RSP1A_Noise_Floor.jpg
Views:	28
Size:	55.9 KB
ID:	250318  
__________________
Regards, Jeremy G0HZU
G0HZU_JMR is offline  
Old 23rd Jan 2022, 10:37 pm   #33
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: Intuitive understanding of Friis cascade formula

Quote:
See below for a screenshot of the noise floor of the RSP1A with a terminated input at 103MHz. I'm not sure I trust the accuracy of the FFT window function but it implies the RBW is about 7.63Hz and the marker indicates -160dBm noise power in this RBW. This implies the noise figure is very low. It's almost as sensitive as my Agilent analyser although the input VSWR of the RSP1A will probably be quite poor at these settings.
This is still very impressive considering the price of a cloned RSP1A. I remember looking at Steve Andrew software last year and was tempted but forgot about it. For educational purpose, it is justifiable to get a RSP1A for the sake of just using spectrum analyzer software, without all the features of Malahit
regenfreak is offline  
Old 23rd Jan 2022, 11:09 pm   #34
G0HZU_JMR
Dekatron
 
Join Date: Sep 2010
Location: Cheltenham, Gloucestershire, UK.
Posts: 3,077
Default Re: Intuitive understanding of Friis cascade formula

I haven't used the latest version of the Steve Andrew analyser program very much but my overall impression of the previous version was that it was a bit buggy and the RSP1A hardware can introduce lots of spurious terms. Also the spurious free dynamic range can change a lot depending on the reference level setting. There are a few controls that don't operate in a conventional manner but apart from that I was extremely impressed because the Steve Andrew program really transforms this £100 SDR into a useful test instrument. It's a shame the development of the program seemed to stop a while back.

On the whole this package is fine if you just want to use it as a narrowband signal analyser. Even so, some experience is needed to know the best settings to get the best dynamic range out of it. Otherwise it can perform quite poorly.

If I try and use it as a conventional swept spectrum analyser on wider spans it quickly loses performance because of the hardware limitations. It becomes slow and has lots of internal spurious terms even with no signal input. It's very much a niche device for doing specific narrowband measurements in my opinion.

The display update rate can be very fast/fluid even on narrow spans because it uses the FFT function. See below for a link to an old youtube demo where I used the little RSP1A to explore the Bessel nulls on a very scruffy and battered IFR3416 signal generator. I wrote a quick windows app to remotely control the IFR3416 to adjust the AF modulation frequency to explore for the Bessel nulls predicted at the settings in the lower left corner of the windows app.

https://www.youtube.com/watch?v=6gSw5QjOonU

The accuracy of the FM on this generator is very good according to the tests I did here. Very impressive in this respect compared to other sig gens. You can also see how fluid the display is on the RSP1A analyser.
__________________
Regards, Jeremy G0HZU
G0HZU_JMR is offline  
Old 23rd Jan 2022, 11:29 pm   #35
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: Intuitive understanding of Friis cascade formula

Quote:
I haven't used the latest version of the Steve Andrew analyser program very much but my overall impression of the previous version was that it was a bit buggy and the RSP1A hardware can introduce lots of spurious terms. Also the spurious free dynamic range can change a lot depending on the reference level setting. There are a few controls that don't operate in a conventional manner but apart from that I was extremely impressed because the Steve Andrew program really transforms this £100 SDR into a useful test instrument. It's a shame the development of the program seemed to stop a while back.
I have been using poorman's NWT200 cheapo spectrum analyzer with built-in tracking generator. It is great for aligning HF bandpass filters with 50 ohms input and output.

I have been testing homebrew FM two-pole Butterworth bandpass filters for the RF front end of a DIY valve tuner with it. They are designed with Elsie software with input and output impedance of at least 3k ohms. It is very difficult to get accurate response even with tapped input and output for the inductor coils of the double tuned LC network bandpass. I use variable series resistors to get closer to input and output impedance but the dynamic range of the cheap machine is a limiting factor.

Last edited by regenfreak; 23rd Jan 2022 at 11:36 pm.
regenfreak is offline  
Old 24th Jan 2022, 5:44 am   #36
Radio Wrangler
Moderator
 
Radio Wrangler's Avatar
 
Join Date: Mar 2012
Location: Fife, Scotland, UK.
Posts: 22,800
Default Re: Intuitive understanding of Friis cascade formula

Quote:
Originally Posted by regenfreak View Post
There is a very good diagram in AN57/1 that illustrates the same steps as your excel spreadsheet (attached).
cheers
This diagram can be rather misleading. Note that the thermal noise term coming from the signal source or termination has a bandwidth factor in it.

Noise doesn't have a unique power level in plain terms. It is distributed, so you get a noise power density. So many Watts per Hertz. The noise created in your amplifier stages is no different, but the diagram shows the amounts without bandwidth terms.

Things now get a lot more difficult looking as different stages are likely to have different bandwidths, and the history of different noise contributions will include different combinations of bandwidth.

One way to simplify this is to have a defining bandwidth at the detector and to pitch it narrower than the preceding stages. You can now use this bandwidth for everything and get a sensible noise density figure for that bandwidth.

This isn't so limiting, because having a defining narrowest bandwidth later is typical of the vast majority of receiver systems, and is also used in noise figure measurement systems.

The old gold standard, the HP8970A had a fixed 4MHz bandwidth. Fine for microwave systems of the day. It was needed because the local oscillator in this instrument was a free-running YIG which was periodically tuned to find the zero-Hz response peak in an attempt to rein-in the drift a bit.

In the later noise figure analyser, it can do narrower bandwidths, and the LO is synthesised. Watch out that narrower bandwidths will create more statistical jitter on results unless the measurement time is scaled up. One trick considered at the time was to FFT the IF and so measure, say, 20 100kHz slots at once. This didn't happen because the shape of the 4MHz analogue IF wasn't flat enough to avoid added errors, so the instrument just does narrower BWs centred. Some fancier software and a scan across the calibrator to integrate the noise bandwidths of offset narrow BWs could have done this.

David
__________________
Can't afford the volcanic island yet, but the plans for my monorail and the goons' uniforms are done
Radio Wrangler is offline  
Old 24th Jan 2022, 1:18 pm   #37
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: Intuitive understanding of Friis cascade formula

Quote:
This diagram can be rather misleading. Note that the thermal noise term coming from the signal source or termination has a bandwidth factor in it.

Noise doesn't have a unique power level in plain terms. It is distributed, so you get a noise power density. So many Watts per Hertz. The noise created in your amplifier stages is no different, but the diagram shows the amounts without bandwidth terms.

Things now get a lot more difficult looking as different stages are likely to have different bandwidths, and the history of different noise contributions will include different combinations of bandwidth.

One way to simplify this is to have a defining bandwidth at the detector and to pitch it narrower than the preceding stages. You can now use this bandwidth for everything and get a sensible noise density figure for that bandwidt
Thanks. Noise is a difficult subject as it is a stochastic process and I dont like statistics at school. If i were to plot the instantaneous noise voltage in a time domain, the probability distribution would be like a Guassian bell curve (attached). So the noise power measurements would be dependent on the time-averaged statistics sampled over bandwidth of random fluctuations of the noises.

The spectral noise power is the power per unit bandwidth. The noise power P is:

P=KTBW

At 20C, and 50 ohms:

At 1 Hz noise power is -174dbm
2 Hz -170.9dbm
FM wide 200kHz -120.9dbm
FM narrow 10Khz -133.9dbm
4MHz -107.9dbm

If PBW is the noise power in dbm with bandwidth BW and P1HZ per 1Hz bandwidth

PBW=P1HZ+10log(BW)

For any two bandwdith BW1 and BW2

PBW2=PBW1+10log(BW2/BW1)
Attached Thumbnails
Click image for larger version

Name:	agilent.jpg
Views:	25
Size:	40.4 KB
ID:	250395  

Last edited by regenfreak; 24th Jan 2022 at 1:24 pm.
regenfreak is offline  
Old 24th Jan 2022, 1:51 pm   #38
Radio Wrangler
Moderator
 
Radio Wrangler's Avatar
 
Join Date: Mar 2012
Location: Fife, Scotland, UK.
Posts: 22,800
Default Re: Intuitive understanding of Friis cascade formula

Rather amusingly, if someone sends you a true noise voltage along a cable and you can see only the far end...

What's the average voltage? Zero!
What's the peak voltage? Well, both plus and minus infinity!

Oh, can you attenuate it by 10dB?

Sure.

What's the average voltage? Zero!
What's the peak voltage? Well, both plus and minus infinity!

Are you sure you put that attenuator in?

THe only tools that can get any grip on noise are statistical. RMS voltage for example... it's very closely related to the standard deviation.

The noise business has so many counter-intuitive quirks, you can have a lot of fun with it.

David
__________________
Can't afford the volcanic island yet, but the plans for my monorail and the goons' uniforms are done
Radio Wrangler is offline  
Old 24th Jan 2022, 4:24 pm   #39
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: Intuitive understanding of Friis cascade formula

Quote:
The only tools that can get any grip on noise are statistical. RMS voltage for example... it's very closely related to the standard deviation.

The noise business has so many counter-intuitive quirks, you can have a lot of fun with it.
Statistics is often counter-intuitive. There is a famous Birthday paradox:

"In a room of just 23 people there’s a 50-50 chance of at least two people having the same birthday. In a room of 75 there’s a 99.9% chance of at least two people matching."

A lots of musicians have intuitive understanding of music theory without knowing sine waves, Fourier series etc.. Pigeons have intuitive navigation skills based on sensing of Earth magnetic field.

Speaking of under sea cables, there was a counter-intuitive video about electricity that generates lots of interest and discussions over all internet:

https://youtu.be/bHIhgxav9LY

I am not sure this was posted in this forum before.

Throwing in IM noises, crosstalk, impulses into the consideration on top of thermal noise, you are starting into the abyss.
regenfreak is offline  
Old 24th Jan 2022, 10:47 pm   #40
Radio Wrangler
Moderator
 
Radio Wrangler's Avatar
 
Join Date: Mar 2012
Location: Fife, Scotland, UK.
Posts: 22,800
Default Re: Intuitive understanding of Friis cascade formula

Some of us had to squeeze into the bathyscape and go exploring the abyss for work-work.

Turned out it was weird and counter intuitive, but not actually hard.

David
__________________
Can't afford the volcanic island yet, but the plans for my monorail and the goons' uniforms are done
Radio Wrangler is offline  
Closed Thread

Thread Tools



All times are GMT +1. The time now is 9:28 pm.


All information and advice on this forum is subject to the WARNING AND DISCLAIMER located at https://www.vintage-radio.net/rules.html.
Failure to heed this warning may result in death or serious injury to yourself and/or others.


Powered by vBulletin®
Copyright ©2000 - 2024, vBulletin Solutions, Inc.
Copyright ©2002 - 2023, Paul Stenning.