Subject: Re: Audio noise in diff amps
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Date: Thu, 19 Dec 2002 15:40:59 GMT
NNTP-Posting-Date: Thu, 19 Dec 2002 10:40:59 EST
Organization: Cox Communications
"Don Pearce" wrote in message
> On Thu, 19 Dec 2002 06:00:15 GMT, "Mike" wrote:
> >"Don Pearce" wrote in message
> >> On Wed, 18 Dec 2002 18:42:26 GMT, "Mike" wrote:
> >> >"Don Pearce" wrote in message
> >> >news:firstname.lastname@example.org...
> >> >
> >> >> Power is v squared / r.
> >> >>
> >> >> 2.4 uV in 22k ohms is -126dBm = (10 log((2.4e-6)^2 / 22000 + 30), or
> >> >> -125.8dBm.
> >> >
> >> >But 2.4uV was obtained by taking sqrt(4kTRB).
> >> >
> >> >What you've done is calculate 10*log(4kTRB/R) + 30 = 10*log(4kTB) +
> >> >equation is missing a right parenthesis: it should have been written:
> >> >log((2.4e-6)^2 / 22000) + 30).
> >> >
> >> >Assuming B = 16kHz, this is indeed -125.8, but you've removed R from
> >> >equation. Given any resistor value, the noise power you calculate will
> >> >always be the same. While that would simplify the meter design - it
> >> >read the same even if the probes weren't connected - I'm not sure it's
> >> >useful.
> >> >
> >> >I'm quite sure the meter is measuring something different...
> >> >
> >> >-- Mike --
> >> You're right - I did bungle my parentheses - I should have omitted the
> >> first one. But R is in there - 22000 is near the end of the equation.
> >> I didn't put in a bandwidth, because that was already implicit in the
> >> given voltage figure of 2.4 microvolts. I didn't calculate that 2.4 uV
> >> figure, you understand.
> >Well, gosh, Don, if you look closely, you'll notice that R is also in my
> >equation. It's in the numerator and the denominator, just like it's in
> >yours. Even if you didn't calculate the 2.4uV number, you know where it
> >from, and that it contains R.
> >-- Mike --
> Oops - just seen that last phrase. There is no reason at all to
> suppose that the 2.4uV figure contains R - indeed if you do the maths,
> it can't. If it did, how would you then use R to calculate the power?
> No, that 2.4uV can only contain B, which is what I have assumed
This _is_ getting pointless, isn't it?
The math in this case was first derived experimentally by Johnson, and
mathematically by Nyquist, in a pair of articles in the July, 1928 issue of
Physical Review. I think Mike Monett has a copy of Nyquist's paper on his
web page. The thing is, everyone since Johnson and Nyquist has been doing
the math with R. Nyquist's derivation is remarkably short and elegant - you
can write the math in just a few lines. Perhaps you'd care to show us your
math, and point out where Nyquist went wrong?
> And of course if it did contain R, what value would you use? Phil told
> us 22000 ohms, but then used 600 ohms for his calculation (inherent in
> the adoption of 0.775 volts as a voltage level for 0dBm). So what
> would you say is the correct way to interpret this?
The same way RF engineers have been interpreting dBm measurements for years
and years: as a relative value.
-- Mike --