From: Don Pearce
Subject: Re: Audio noise in diff amps
Date: Thu, 19 Dec 2002 09:37:35 +0000
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On 19 Dec 2002 09:16:20 GMT, Rick wrote:
>Don Pearce wrote:
>> On Thu, 19 Dec 2002 06:00:15 GMT, "Mike" wrote:
>>>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 came
>>>from, and that it contains R.
>> 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?
>Don - you never need to calculate the *available* power - it's always
>K * T Watts/Hz. The source and load resistances just let you determine
>how much of that power is delivered to the load.
>Consider a noisy source resistor R1 loaded by a noisless resistor R2:
>Noise generator voltage = sqrt(4*K*T*B*R1) Vrms
>The two resistors form a divider, in the ratio R2/(R1 + R2),
>so R1's noise voltage is divided down to:
>V' = sqrt(4*K*T*B*R1) * R2
>square this rms voltage (V') and divide by the load (R2):
>Noise power into load = 4*K*T*B*R1*R2
> (R1 + R2)^2
>Note that if the load (R2) is infinite or zero, no power is delivered to
>the load, which is consistent with expectations.
>Note that under maximum power transfer R1 will be equal to R2, and the
>power equation simplifies to KTB, as expected for thermal noise.
>Of course, in reality both R1 and R2 would be noisy, so there should be
>two noise equations, though you will observe that interchanging R1 and
>R2 in the noise equation yields the same result - i.e. even if R1 and
>R2 are unequal in value, they each deliver the same power to the other,
>as Phil would have us require in order to maintain thermal equilibrium!
I know, we've been through all that. But when somebody presents you
with two figures, a voltage and a resistance - there is only one
calculation you can make to work out the power. That is what I did -
and that is where all the problems started.