Thermal Noise Tutorial and Noise Figure Tutorial

I have finished two tutorials on noise.

the first one is here:

http://www.fourier-series.com/Noise/index.html

This covers thermal noise, and contains several interactive flash
programs.  included is insight into the thermal noise equation, rms
voltage calculations, examples of correlation and how independent
(uncorrelated) noise adds together. All the programs have extensive
audio explanations.

The second one is here:

http://www.fourier-series.com/Noise/NoiseFigure.html

This covers The basic noise model of an amplifier.  Spectrum analyzer
representations of input signal and noise and output signal and noise
are presented with interactive features to allow the user to modify
signal levels, gain and noise figures of the amplifier.  A full
explanation of the noise factor model and derivation of Friis formula
using interactive programs and audio explanations are provided.

brent

------------------------------
PS I posted several times to comp.dsp and sci.electronics.design to
get clarity on a few topics contained in this tutorial.  So thanks.

A small hint for noise figure in run-of-the-mill radio engineering:
In my opinion, once noise voltage comes in, most first time readers will
already be hopelessly confused (at least, I was, in the lecture).

There are two equations one should remember. Neither of them needs noise
voltage or resistance, but we can get there easily using Ohm's law as a
third equation.

The first one is:
Nth = k B T

Explanation:
In an observation bandwidth of B Hz, an object at temperature T dissipates
N watts into a matched load.
Note that the power transfer works both ways. If object and load are at the
same temperature, the net exchange of power is zero. If my load is colder,
for example, it will slowly heat up towards thermal equilibrium (basic
thermodynamics at work).

The "matched" load concept here avoids the need for voltages, currents
etc.

The second one is:
NTot = k B T F

It states:
The total input-referred noise of an amplifier with noise figure F (linear
scale) is NTot, when connected to a termination at temperature T. This
includes source noise Nth and amplifier-contributed noise Nadd.

There is some small print here which I'll ignore, if you have the freedom
to modify the terminating impedance.

Since we already know the noise from the termination is K B T, the noise
-contribution- of the amplifier follows as Nadd = NTot - Nth = (F - 1) k B
T.

With those two equations and Ohm's law, one can derive almost anything
using one or two steps.

On Nov 28, 3:08�pm, "mnentwig"
<markus.nentwig@n_o_s_p_a_m.renesasmobile.com> wrote:
> A small hint for noise figure in run-of-the-mill radio engineering:
> In my opinion, once noise voltage comes in, most first time readers will
> already be hopelessly confused (at least, I was, in the lecture).
>
> There are two equations one should remember. Neither of them needs noise
> voltage or resistance, but we can get there easily using Ohm's law as a
> third equation.
>
> The first one is:
> Nth = k B T
>
> Explanation:
> In an observation bandwidth of B Hz, an object at temperature T dissipates
> N watts into a matched load.
> Note that the power transfer works both ways. If object and load are at the
> same temperature, the net exchange of power is zero. If my load is colder,
> for example, it will slowly heat up towards thermal equilibrium (basic
> thermodynamics at work).
>
> The "matched" load concept here avoids the need for voltages, currents
> etc.
>
> The second one is:
> NTot = k B T F
>
> It states:
> The total input-referred noise of an amplifier with noise figure F (linear
> scale) is NTot, when connected to a termination at temperature T. This
> includes source noise Nth and amplifier-contributed noise Nadd.
>
> There is some small print here which I'll ignore, if you have the freedom
> to modify the terminating impedance.
>
> Since we already know the noise from the termination is K B T, the noise
> -contribution- of the amplifier follows as Nadd = NTot - Nth = (F - 1) k B
> T.
>
> With those two equations and Ohm's law, one can derive almost anything
> using one or two steps.

Thanks for the feedback.  I realized in doing this how subtle and
difficult it is to explain noise voltage vs. noise power.  I chose to
go with noise voltage and then tie in noise power afterwords.  When I
started doing this tutorial I expected it to be pretty easy (as was
say the decibel tutorial).  It turned out to be more difficult than I
expected.  Hopefully the interactive nature of the programs will do a
better job of explaining than my audio explanations.

On Mon, 28 Nov 2011 15:20:14 -0800, brent wrote:

> On Nov 28, 3:08 pm, "mnentwig"
> <markus.nentwig@n_o_s_p_a_m.renesasmobile.com> wrote:
>> A small hint for noise figure in run-of-the-mill radio engineering: In
>> my opinion, once noise voltage comes in, most first time readers will
>> already be hopelessly confused (at least, I was, in the lecture).
>>
>> There are two equations one should remember. Neither of them needs
>> noise voltage or resistance, but we can get there easily using Ohm's
>> law as a third equation.
>>
>> The first one is:
>> Nth = k B T
>>
>> Explanation:
>> In an observation bandwidth of B Hz, an object at temperature T
>> dissipates N watts into a matched load.
>> Note that the power transfer works both ways. If object and load are at
>> the same temperature, the net exchange of power is zero. If my load is
>> colder, for example, it will slowly heat up towards thermal equilibrium
>> (basic thermodynamics at work).
>>
>> The "matched" load concept here avoids the need for voltages, currents
>> etc.
>>
>> The second one is:
>> NTot = k B T F
>>
>> It states:
>> The total input-referred noise of an amplifier with noise figure F
>> (linear scale) is NTot, when connected to a termination at temperature
>> T. This includes source noise Nth and amplifier-contributed noise Nadd.
>>
>> There is some small print here which I'll ignore, if you have the
>> freedom to modify the terminating impedance.
>>
>> Since we already know the noise from the termination is K B T, the
>> noise -contribution- of the amplifier follows as Nadd = NTot - Nth = (F
>> - 1) k B T.
>>
>> With those two equations and Ohm's law, one can derive almost anything
>> using one or two steps.
> 
> Thanks for the feedback.  I realized in doing this how subtle and
> difficult it is to explain noise voltage vs. noise power.  I chose to go
> with noise voltage and then tie in noise power afterwords.  When I
> started doing this tutorial I expected it to be pretty easy (as was say
> the decibel tutorial).  It turned out to be more difficult than I
> expected.  Hopefully the interactive nature of the programs will do a
> better job of explaining than my audio explanations.

You may want to re-think (I know, you're already done and it works).

Noise power is the more fundamental quantity -- until you start hitting 
bandwidth constraints, in fact, the power/hz is just a basic physical 
constant (Plank's) times the temperature.  As long as you keep that in 
mind, you can always figure out the noise voltage using various bits of 
circuit theory.

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

On Nov 28, 7:14&#4294967295;pm, Tim Wescott <t...@seemywebsite.com> wrote:
> On Mon, 28 Nov 2011 15:20:14 -0800, brent wrote:
> > On Nov 28, 3:08&#4294967295;pm, "mnentwig"
> > <markus.nentwig@n_o_s_p_a_m.renesasmobile.com> wrote:
> >> A small hint for noise figure in run-of-the-mill radio engineering: In
> >> my opinion, once noise voltage comes in, most first time readers will
> >> already be hopelessly confused (at least, I was, in the lecture).
>
> >> There are two equations one should remember. Neither of them needs
> >> noise voltage or resistance, but we can get there easily using Ohm's
> >> law as a third equation.
>
> >> The first one is:
> >> Nth = k B T
>
> >> Explanation:
> >> In an observation bandwidth of B Hz, an object at temperature T
> >> dissipates N watts into a matched load.
> >> Note that the power transfer works both ways. If object and load are at
> >> the same temperature, the net exchange of power is zero. If my load is
> >> colder, for example, it will slowly heat up towards thermal equilibrium
> >> (basic thermodynamics at work).
>
> >> The "matched" load concept here avoids the need for voltages, currents
> >> etc.
>
> >> The second one is:
> >> NTot = k B T F
>
> >> It states:
> >> The total input-referred noise of an amplifier with noise figure F
> >> (linear scale) is NTot, when connected to a termination at temperature
> >> T. This includes source noise Nth and amplifier-contributed noise Nadd.
>
> >> There is some small print here which I'll ignore, if you have the
> >> freedom to modify the terminating impedance.
>
> >> Since we already know the noise from the termination is K B T, the
> >> noise -contribution- of the amplifier follows as Nadd = NTot - Nth = (F
> >> - 1) k B T.
>
> >> With those two equations and Ohm's law, one can derive almost anything
> >> using one or two steps.
>
> > Thanks for the feedback. &#4294967295;I realized in doing this how subtle and
> > difficult it is to explain noise voltage vs. noise power. &#4294967295;I chose to go
> > with noise voltage and then tie in noise power afterwords. &#4294967295;When I
> > started doing this tutorial I expected it to be pretty easy (as was say
> > the decibel tutorial). &#4294967295;It turned out to be more difficult than I
> > expected. &#4294967295;Hopefully the interactive nature of the programs will do a
> > better job of explaining than my audio explanations.
>
> You may want to re-think (I know, you're already done and it works).
>
> Noise power is the more fundamental quantity -- until you start hitting
> bandwidth constraints, in fact, the power/hz is just a basic physical
> constant (Plank's) times the temperature. &#4294967295;As long as you keep that in
> mind, you can always figure out the noise voltage using various bits of
> circuit theory.
>
> --
> My liberal friends think I'm a conservative kook.
> My conservative friends think I'm a liberal kook.
> Why am I not happy that they have found common ground?
>
> Tim Wescott, Communications, Control, Circuits & Softwarehttp://www.wescottdesign.com

Tim,
Wikipedia starts with voltage noise as do many others.  Some start
with power.  Perhaps power is the better starting point. I think the
thing that I found most intriguing about this tutorial is that it
seems like a simple subject, but there are so many subtle aspects and
different problems require a different approach.  For instance, most
engineers like to deal with noise figure and noise figure works for
98% of all analysis, but when doing cascaded noise figures then you
have to convert to noise factor.  Knowing when to switch back and
forth was more subtle than I thought.  I actually thought this
tutorial was going to be a cake walk, and it was perhaps my most
difficult one to do.  I still have to go back and clean up some
explanations on correlation that I am not satisfied with.

it's a great tutorial ...

there is another subtle point about noise figure that confuses a lot
of people..

the DEFINITION of noise figure depends upon the noise of the source
signal feeding the system (typically an antenna) being at the the
standard 290K.

 This works great for most terrestrial systems where the antenna is
"warm"  but if you are working on a sat system and the Rx antenna is
aimed up into the cold sky, noise figure doesn't work so well.  I
first struggled to understand this (many years ago) when you could buy
a 1.2 dB noise figure LNA for say $100 but a 0.8 dB noise figure LNA
cost $1000 and people still bought them.  Was 0.4 dB in SNR worth
$900?.  The answer of course is that noise figure does not accuratly
represent the situation and the improvement exceeds 0.4 dB becasue the
antenna is cold.  Noise temperature works betterin tese cases.

Mark

On Nov 28, 9:07&#4294967295;pm, Mark <makol...@yahoo.com> wrote:
> it's a great tutorial ...
>
> there is another subtle point about noise figure that confuses a lot
> of people..
>
> the DEFINITION of noise figure depends upon the noise of the source
> signal feeding the system (typically an antenna) being at the the
> standard 290K.
>
> &#4294967295;This works great for most terrestrial systems where the antenna is
> "warm" &#4294967295;but if you are working on a sat system and the Rx antenna is
> aimed up into the cold sky, noise figure doesn't work so well. &#4294967295;I
> first struggled to understand this (many years ago) when you could buy
> a 1.2 dB noise figure LNA for say $100 but a 0.8 dB noise figure LNA
> cost $1000 and people still bought them. &#4294967295;Was 0.4 dB in SNR worth
> $900?. &#4294967295;The answer of course is that noise figure does not accuratly
> represent the situation and the improvement exceeds 0.4 dB becasue the
> antenna is cold. &#4294967295;Noise temperature works betterin tese cases.
>
> Mark

Thanks,

I was debating to myself to do the noise temperature thing.  I may
come back to this topic and do it later.

>> the DEFINITION of noise figure depends upon the noise of the source
signal feeding the system (typically an antenna) being at the the
standard 290K.

that is correct. Change the reference temperature and the noise figure will
change. 

The historical explanation goes more or less like this: 
I've got a directional antenna and point it towards a transmitter, which is
located on the ground (think 1930ies or earlier, no satellites yet).

A typical signal path has, say, 100 dB loss.
What the receive antenna "sees" is 0.0000000001 transmitter and
0.9999999999 atmosphere and background. In other words, we're basically
looking into a resistive termination that has a negligibly small signal
source hidden in it. 
Now the average noise power out of that "termination" (the atmosphere) can
be expressed equivalently as a temperature. Since the weather is different
in different places, a reference temperature of 290 K was agreed for most
terrestrial applications. "Noise figure" means we're comparing the noise
contribution of a device to the environmental / atmospheric noise at the
agreed temperature.

Now a satellite dish is a highly directional antenna that's pointed up into
cold space. The atmosphere suddenly gets rather thin - just a few
kilometers of air: Walking outside on a clear night, the sky seems to be
"radiating cold". The "termination" of the antenna is interstellar space,
which is pretty cold. A 290 degree reference temperature is not the best
choice here, even though the marketing department may disagree.



Again, dealing with noise power instead of voltage/current allows for some
very straightforward calculations. For example, let's say I've got a source
at 10000K (a typical laboratory noise source with ENR=15 dB) and a 6 dB
attenuator in the temperature chamber at 350 K.
6 dB is 1/4 in terms of power. Looking into the attenuator, we'll observe a
noise power equivalent to 10000K * 1/4 + 350 K * 3/4. 

On Nov 27, 6:46&#4294967295;pm, brent <buleg...@columbus.rr.com> wrote:
> I have finished two tutorials on noise.
>
> the first one is here:
>
> http://www.fourier-series.com/Noise/index.html
>

> This covers thermal noise, and contains several interactive flash
> programs. &#4294967295;included is insight into the thermal noise equation, rms
> voltage calculations, examples of correlation and how independent
> (uncorrelated) noise adds together. All the programs have extensive
> audio explanations.
>
> The second one is here:
>
> http://www.fourier-series.com/Noise/NoiseFigure.html
>
> This covers The basic noise model of an amplifier. &#4294967295;Spectrum analyzer
> representations of input signal and noise and output signal and noise
> are presented with interactive features to allow the user to modify
> signal levels, gain and noise figures of the amplifier. &#4294967295;A full
> explanation of the noise factor model and derivation of Friis formula
> using interactive programs and audio explanations are provided.
>
> brent
>
> ------------------------------
> PS I posted several times to comp.dsp and sci.electronics.design to
> get clarity on a few topics contained in this tutorial. &#4294967295;So thanks.

Brent,

You may wish to describe the noise as being Johnson noise named for
its discoverer. If you are curious as to where the Johnson formula
comes from, you may find it here:

http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf

IHTH,
Clay

On Nov 29, 10:01&#4294967295;am, Clay <c...@claysturner.com> wrote:
> On Nov 27, 6:46&#4294967295;pm, brent <buleg...@columbus.rr.com> wrote:
>
>
>
>
>
>
>
>
>
> > I have finished two tutorials on noise.
>
> > the first one is here:
>
> >http://www.fourier-series.com/Noise/index.html
>
> > This covers thermal noise, and contains several interactive flash
> > programs. &#4294967295;included is insight into the thermal noise equation, rms
> > voltage calculations, examples of correlation and how independent
> > (uncorrelated) noise adds together. All the programs have extensive
> > audio explanations.
>
> > The second one is here:
>
> >http://www.fourier-series.com/Noise/NoiseFigure.html
>
> > This covers The basic noise model of an amplifier. &#4294967295;Spectrum analyzer
> > representations of input signal and noise and output signal and noise
> > are presented with interactive features to allow the user to modify
> > signal levels, gain and noise figures of the amplifier. &#4294967295;A full
> > explanation of the noise factor model and derivation of Friis formula
> > using interactive programs and audio explanations are provided.
>
> > brent
>
> > ------------------------------
> > PS I posted several times to comp.dsp and sci.electronics.design to
> > get clarity on a few topics contained in this tutorial. &#4294967295;So thanks.
>
> Brent,
>
> You may wish to describe the noise as being Johnson noise named for
> its discoverer. If you are curious as to where the Johnson formula
> comes from, you may find it here:
>
> http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf
>
> IHTH,
> Clay

Thanks for the link to your paper.  I did make a make a modification
to the intro page that stated what you said above.