Flicker noise model.

[Fred Bartoli]

This has low impact on the global result, but my expressions have to be
correct, so...

Is the 1/f noise better modeled as :

In(F) = Io sqrt(1 + Fc/F)

or

In(F) = Io sqrt(|1 + j Fc/F|)

 

[Allan Herriman]

This has low impact on the global result, but my expressions have to be
correct, so...

Is the 1/f noise better modeled as :

In(F) = Io sqrt(1 + Fc/F)

or

In(F) = Io sqrt(|1 + j Fc/F|)

How about

In(F) = Io (|1 + j sqrt(Fc/F)|)

?

Regards,
Allan

 

[Fred Bartoli]

How about

In(F) = Io (|1 + j sqrt(Fc/F)|)

Hey this is the same as
but I didn't think of that one :

In(F) = Io (1 + sqrt(Fc/F))

So, which one ?

 

[Fred Bartoli]

"Fred Bartoli"

Hey this is the same as

Oops...

this is the same as the first one :

 

[Allan Herriman]

Hey this is the same as

but I didn't think of that one :

In(F) = Io (1 + sqrt(Fc/F))

So, which one ?

You are adding two independent noise sources, one with a white PSD,
the other with a pink PSD.

Of the four candidates, only

In(F) = Io (|1 + j sqrt(Fc/F)|)

models the shape correctly.

Regards,
Allan

 

[Allan Herriman]

You are adding two independent noise sources, one with a white PSD,
the other with a pink PSD.

Of the four candidates, only

In(F) = Io (|1 + j sqrt(Fc/F)|)

models the shape correctly.

Regards,
Allan

Aargh. My apologies to Fred. The correct answer is

In(F) = Io sqrt(1 + Fc/F), and this of course is the same as

In(F) = Io (|1 + j sqrt(Fc/F)|)

Regards,
Allan

 

[Fred Bartoli]

Aargh. My apologies to Fred. The correct answer is

In(F) = Io sqrt(1 + Fc/F), and this of course is the same as

In(F) = Io (|1 + j sqrt(Fc/F)|)

Thanks Allan.
I've corrected the mistakes once I've understood that the "tricky" part was
summing of 2 PSDs. Shame on me...

What's a bit depressing is to notice that I couldn't figure such an obvious
thing even in the morning.
Maybe I should retire.

 

[Mikko Kiviranta]

So, which one ?

I'm not certain where your model will be used and
in which manner, but it looks like your In(F) is
square root of the power spectral density, and you
are modelling a sum of white noise and 1/f noise.
Because uncorrelated noise sources add quadratically,
In(F) = Io sqrt(1 + f/fc) would be a correct expression.

I don't understand what role the phase factors such as
j or -1 could possibly play in the model, because all
relative phase information between two uncorrelated
sources is meaningless; so I may be misintepreting what
your model is aiming to.

Regards,
Mikko

 

[Kevin Aylward]

I'm not certain where your model will be used and
in which manner, but it looks like your In(F) is
square root of the power spectral density, and you
are modelling a sum of white noise and 1/f noise.
Because uncorrelated noise sources add quadratically,
In(F) = Io sqrt(1 + f/fc) would be a correct expression.

I don't understand what role the phase factors such as
j or -1 could possibly play in the model, because all
relative phase information between two uncorrelated
sources is meaningless; so I may be misintepreting what
your model is aiming to.

They dont play any part in the model at all. Its just a mathematical
(in)convenience.

The j is only to tell you that one adds up the sums of the squares and
takes the root of. It has nothing to do with any phase interpretation of
j. Personally, in this instance, I don't like the notation.

Kevin Aylward
[email protected]
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Roy McCammon]

They dont play any part in the model at all. Its just a mathematical
(in)convenience.

The j is only to tell you that one adds up the sums of the squares and
takes the root of. It has nothing to do with any phase interpretation of
j. Personally, in this instance, I don't like the notation.

I'm in complete agreement.