Power of the integrated 1/f noise of a transistor

[radiohead]

Hi,

I try to define the power of the integrated 1/f noise of a transistor.

\[P = \int\limits_{fa}^{fb} {\frac{{P_{1Hz} }}{f}} df = \left| {\ln f}\right|_{fa}^{fb} = \ln \left( {\frac{{fb}}{{fa}}} \right)\]

Now, when we choose fb the corner frequency of the 1/f noise, and fa equal to 0Hz, the integral does not converge any more. This physically is not correct, around DC there simply is no power but the 1/f formula predicts it to be infinite. Is there some low frequency corner where the noise spectrum flattens again?

PS: Damn these tex formulas. You never get them straigth from the first time

 

[ambreesh]

Re: Integrated 1/f noise

This is what I have read from razavi: (Quoting him) Chapter 7 pg:216
Extending Fa to 0 means we are intresed in arbitrarily slow noise components. A noise component at 10^-6 varies once in a week. Secondly the infinite flicker noise power means that we observe the circuit for a very long time. At such low rates, noise is indistinguishable from thermal drift or aging of devices.
Aslo the signals encountered in most applications donot contain significant low frequency component, so our observation window need not be large

 

[radiohead]

Re: Integrated 1/f noise

A noise component at 10^-6 varies once in a week. Secondly the infinite flicker noise power means that we observe the circuit for a very long time.

That is correct, but according to the model, it's power should be quite big (inversily proportional to frequency). And if the subhertz power would be that big (but it is not), it cannot be neglected even though it changes very slowly. Suppose your opamps output common mode is 2.5V today and 3.6V tomorrow, that wouldn't make you too happy no?

My guess is that the model doesn't predict behaviour at subhertz frequency too well, and that noise spectrum flattens again to white noise from a certain corner frequency fa on. Is this correct?

 

[ambreesh]

Re: Integrated 1/f noise

Dear radiohead,
Ok we should not neglect that power in sub-hertz range.
All is OK if you are doing processing in sub-herts range signals. When we are not doing that, why should we concider it.
And above that lthe logarithmic function does very good compression. For f=1nHz
your logarithm value would be -20.
And the time window to observe should be 31.79Years

 

[opamp741]

Re: Integrated 1/f noise

then wht shd be the minimum freq Fa..I was using 1Hz in my simulations..Is this wrong..
thanx