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From: JM <sunaecoNoSpam@gmail.com>
Newsgroups: sci.electronics.design
Subject: Re: A collection of monographs on high accuracy electronics
Date: Wed, 12 Jun 2024 02:50:19 +0100
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On Mon, 10 Jun 2024 15:14:40 -0400, Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> wrote:

>On 2024-06-09 21:43, Phil Hobbs wrote:
>> On 2024-06-09 20:55, JM wrote:
>>> On Mon, 10 Jun 2024 00:29:17 -0000 (UTC), Phil Hobbs 
>>> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>>>
>>>> JM <sunaecoNoSpam@gmail.com> wrote:
>>>>> On Sun, 9 Jun 2024 18:09:24 -0000 (UTC), Phil Hobbs
>>>>> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>>>>>
>>>>>> Jeroen Belleman <jeroen@nospam.please> wrote:
>>>>>>> On 6/9/24 19:02, ehsjr wrote:
>>>>>>>> On 6/7/2024 9:14 PM, JM wrote:
>>>>>>>>> A collection of monographs on high accuracy electronics written 
>>>>>>>>> by Mr.
>>>>>>>>> Chris Daykin, following his career predominantly in metrology.
>>>>>>>>>
>>>>>>>>> Unfortunately Chris will be unable to complete the unfinished
>>>>>>>>> monographs (having started end of life care) but there is plenty of
>>>>>>>>> interest to any analogue engineer.
>>>>>>>>>
>>>>>>>>> https://1drv.ms/b/c/1af24d72a509cd48/EZhO_rP5-glDmxtc4ZHycvYBhrsqmyC5tuZjt2NFFsS0gQ?e=Wq2Yj0 
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Thanks!
>>>>>>>> Ed
>>>>>>>
>>>>>>> I have an issue with his definition of resistor noise power
>>>>>>> as the product of open-circuit noise voltage and short-circuit
>>>>>>> current. That makes no sense.
>>>>>>>
>>>>>>> There's more than that, probably, but that just jumped out at
>>>>>>> me.
>>>>>>>
>>>>>>> Jeroen Belleman
>>>>>>>
>>>>>>
>>>>>> It?s four times too high, for a start.
>>>>>>
>>>>>> Cheers
>>>>>>
>>>>>> Phil Hobbs
>>>>>
>>>>> "It is shown elsewhere [1] that the noise power is four times the heat
>>>>> energy which would flow down the conductors
>>>>> from a warm source resistor to a matching cold resistor."
>>>>>
>>>>
>>>> Which, if true, would solve all our energy problems, except that
>>>> thermodynamic systems would all be unstable.
>>>>
>>>> The thermal noise power produced by a resistor into a matched load is kT
>>>> per hertz.
>> 
>>>
>>> Sure, which is what he states.  By mentioning a hot and cold resistor 
>>> he makes it clear that net energy flow is from hot to cold, and that 
>>> the T refers to the hot source.
>>>
>> But apparently he says that it's four times larger than that.
>> 
>> I'm not making a microsoft account just to download the PDF, so if you 
>> want to discuss it further, you could email it to me.
>> 
>> Cheers
>> 
>> Phil Hobbs
>> 
>> 
>> 
>Bill was kind enough to send me a copy (thanks again, Bill), and right 
>there on P. 374, the author says,
>
>Pn = 4kTB
>
>which is a factor of four too high.
>

No it isn't. He is calculating the thermal noise power dissipated in an unloaded resistor - something (or at least the related noise voltage) which is actually required in the design process of a transducer/amplifier low S/N system.  No engineer outwith some RF/microwave areas (such are specifing antenna noise temperature) is remotely interested in your definition of noise power as the maximum power which can be extracted from a thermal source (ie by a conjugate source match).  The vast majority of engineers (if asked to specify resistor noise power) would present exactly the same equation as Daykin, because they are interested in noise voltage (or current) only.  

>Twenty years ago I posted a brief derivation of the Johnson noise 
>formula in the thread "thermal noise in resistors - Baffled!", as 
>follows (with a couple of typos fixed).
>
>> One good way of deriving the Johnson noise formula (the sqrt(4kT) thing)
>> is from classical equipartition of energy. The stored energy in a
>> capacitor is a single classical degree of freedom, and hence (when
>> connected to a thermal reservoir, e.g. connected in parallel with a
>> resistor at temperature T) has a mean energy of kT/2, and since the
>> energy is CV**2/2, its rms noise voltage is sqrt(kT/C).
>> 
>> The noise bandwidth of a one-pole RC lowpass is (pi/2)*(3 dB BW) =
>> 1/(4RC). Therefore, the noise power spectral density in the flatband is
>> 
>> p_N=(kT/2C)*(4RC) per hertz,
>> 
>> so setting p_N=C(e_N)**2/2, we get
>> 
>> (e_N)**2 = kT*4R
>> 
>> and
>> 
>> e_N = sqrt(4kTR) per root hertz.
>> 
>> This is the same noise that correlated double sampling in CCDs was
>> designed to deal with. The advantage of this way of looking at it is
>> that the resistor doesn't have to be linear--CMOS reset switches behave
>> the same way.
>> 
>Cheers
>
>Phil Hobbs