Johnson Nyquist Noise

Started by Clay December 30, 2006
Hello All,

I had a recent situation where I needed to write a paper explaining the
why's and wherefores of Johnson noise. So if you are interested, the
following link will take you to my paper.

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


Any and all comments welcome.

Thanks,

Clay

Clay wrote:

> http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf
I'll keep that, thanks! Noticed a typo though -- the left equation in the penultimate formula on page 3 has a factor 1/2 missing. Martin -- The difference between genius and stupidity is that genius has limits.
Martin Eisenberg wrote:
> Clay wrote: > > > http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf > > I'll keep that, thanks! Noticed a typo though -- the left equation in > the penultimate formula on page 3 has a factor 1/2 missing. > > > Martin > > -- > The difference between genius and > stupidity is that genius has limits.
Hello Martin, Thanks for reading my paper. And yes I see the typo and I'm fixing it. Again thanks, Clay
On 30 Dec 2006 17:10:02 -0800, "Clay" <physics@bellsouth.net> wrote:

> >Hello All, > >I had a recent situation where I needed to write a paper explaining the >why's and wherefores of Johnson noise. So if you are interested, the >following link will take you to my paper. > >http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf > > >Any and all comments welcome. > >Thanks, > >Clay
Definitely a keeper! According to the analysis and last figure the noise is reduced at 60GHz? Do I understand correctly that that's really just a failing of the approximation and the thermal noise is really independent of frequency? Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org
Eric Jacobsen wrote:
> On 30 Dec 2006 17:10:02 -0800, "Clay" <physics@bellsouth.net> wrote: > > > > >Hello All, > > > >I had a recent situation where I needed to write a paper explaining the > >why's and wherefores of Johnson noise. So if you are interested, the > >following link will take you to my paper. > > > >http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf > > > > > >Any and all comments welcome. > > > >Thanks, > > > >Clay > > > Definitely a keeper! > > According to the analysis and last figure the noise is reduced at > 60GHz? Do I understand correctly that that's really just a failing > of the approximation and the thermal noise is really independent of > frequency? >
Hello Eric, Actually, the Johnson formula is the approximation - it assumes the noise power is constant across all frequencies. Basically a conductor at room temperature would have little noise power up above 60GHz. At light frequencies (~10^14 Hz), there is almost none. Of course, just heat up the conductor to several thousand Kelvins, and the situation changes. But at room temperature and constraining one's self to frequencies < 10GHz, the Johnson formula is quite good. The exact power is given by an integral of hf/(exp(hf/kT)-1) df over the band of interest. It is just that this integral does not have a nice closed form solution, so we look to approximations or numerical solutions. Clay p.s. Thanks for reading.
On 31 Dec 2006 11:24:18 -0800, "Clay" <physics@bellsouth.net> wrote:

> >Eric Jacobsen wrote: >> On 30 Dec 2006 17:10:02 -0800, "Clay" <physics@bellsouth.net> wrote: >> >> > >> >Hello All, >> > >> >I had a recent situation where I needed to write a paper explaining the >> >why's and wherefores of Johnson noise. So if you are interested, the >> >following link will take you to my paper. >> > >> >http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf >> > >> > >> >Any and all comments welcome. >> > >> >Thanks, >> > >> >Clay >> >> >> Definitely a keeper! >> >> According to the analysis and last figure the noise is reduced at >> 60GHz? Do I understand correctly that that's really just a failing >> of the approximation and the thermal noise is really independent of >> frequency? >> > >Hello Eric, > >Actually, the Johnson formula is the approximation - it assumes the >noise power is constant across all frequencies. Basically a conductor >at room temperature would have little noise power up above 60GHz. At >light frequencies (~10^14 Hz), there is almost none. Of course, just >heat up the conductor to several thousand Kelvins, and the situation >changes. > >But at room temperature and constraining one's self to frequencies < >10GHz, the Johnson formula is quite good. The exact power is given by >an integral of hf/(exp(hf/kT)-1) df over the band of interest. It is >just that this integral does not have a nice closed form solution, so >we look to approximations or numerical solutions. > >Clay > >p.s. Thanks for reading.
That's pretty cool and something that I didn't realize: the thermal noise would be less at 60GHz than at typical lower frequencies. That might be another motivator for people looking at 60GHz technology, but not one that I ever heard articulated before. Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org
Eric Jacobsen wrote:
> On 31 Dec 2006 11:24:18 -0800, "Clay" <physics@bellsouth.net> wrote: > > > > >Eric Jacobsen wrote: > >> On 30 Dec 2006 17:10:02 -0800, "Clay" <physics@bellsouth.net> wrote: > >> > >> > > >> >Hello All, > >> > > >> >I had a recent situation where I needed to write a paper explaining the > >> >why's and wherefores of Johnson noise. So if you are interested, the > >> >following link will take you to my paper. > >> > > >> >http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf > >> > > >> > > >> >Any and all comments welcome. > >> > > >> >Thanks, > >> > > >> >Clay > >> > >> > >> Definitely a keeper! > >> > >> According to the analysis and last figure the noise is reduced at > >> 60GHz? Do I understand correctly that that's really just a failing > >> of the approximation and the thermal noise is really independent of > >> frequency? > >> > > > >Hello Eric, > > > >Actually, the Johnson formula is the approximation - it assumes the > >noise power is constant across all frequencies. Basically a conductor > >at room temperature would have little noise power up above 60GHz. At > >light frequencies (~10^14 Hz), there is almost none. Of course, just > >heat up the conductor to several thousand Kelvins, and the situation > >changes. > > > >But at room temperature and constraining one's self to frequencies < > >10GHz, the Johnson formula is quite good. The exact power is given by > >an integral of hf/(exp(hf/kT)-1) df over the band of interest. It is > >just that this integral does not have a nice closed form solution, so > >we look to approximations or numerical solutions. > > > >Clay > > > >p.s. Thanks for reading. > > That's pretty cool and something that I didn't realize: the thermal > noise would be less at 60GHz than at typical lower frequencies. That > might be another motivator for people looking at 60GHz technology, but > not one that I ever heard articulated before. >
Hello Eric, My earlier statement was a bit misleading - the power density at 60GHz is reduced compared to lower freqs at room temperature, but the difference isn't worth writing home about. At T=300K, the -3 dB point for the power densitity is 5.45*10^12 Hz. So the desire to use 60GHz will be motivated by other reasons. Clay
"Clay" <physics@bellsouth.net> wrote in message 
news:1167584506.683040.232840@h40g2000cwb.googlegroups.com...
> > Martin Eisenberg wrote: >> Clay wrote: >> >> > http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf >> >> I'll keep that, thanks! Noticed a typo though -- the left equation in >> the penultimate formula on page 3 has a factor 1/2 missing. >> >> >> Martin >> >> -- >> The difference between genius and >> stupidity is that genius has limits. > > Hello Martin, > > Thanks for reading my paper. And yes I see the typo and I'm fixing it. > Again thanks,
Hi Clay - thanks - it's nice! I know it's just a matter of personal taste but I usee -228.6 dBW/K/Hz for Boltzmann's and the 0.6 makes a difference in some of my stuff.... Best of Luck - Mike
Mike Yarwood wrote:

> Hi Clay - thanks - it's nice! I know it's just a matter of personal taste > but I usee -228.6 dBW/K/Hz for Boltzmann's and the 0.6 makes a difference > in some of my stuff.... > > Best of Luck - Mike
Thanks Mike, For exactness I went ahead and reworked the numbers with the fundamental constants utilized out to their currently known limits! The paper has been updated. Clay
Clay schrieb:

> Hello All, > > I had a recent situation where I needed to write a paper explaining the > why's and wherefores of Johnson noise. So if you are interested, the > following link will take you to my paper. > > http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf
Hello Clay, thanks for your public domain work (including the other papers on your site - I especially liked the oscillator paper). I have a query with the Nyquist noise paper. You develop your formular in differential form, for example P(f) = h f / ( exp(h f / k T) - 1) df, keeping the integral operator df. Further down you integrate and get P_bar = integral_0^b P(f) df. which, when substituting the term above becomes P_bar = integral_0^b h f / ( exp(h f / k T) - 1) df^2, which is probably not what you want (note the df^2 term). Can't you just delete the differential operator in your derivation and set for example P(f) = h f / ( exp(h f / k T) - 1)? Regards, Andor