FPGA Central

Hi,

I'm trying to get a better feel for modeling various analog
impairments. Right now, I am searching clarification for 3rd order IMD
modeling.

As I understand it, for RF 3rd order IMD, the effect would be as
follows:

EQ1: y = x - x^3*10^(-IP3/10)*1000/R,

where IP3 is in dBm and R is impedence in ohms.

Also, I think that for complex baseband, the effect would be:

EQ2: Re(y) = Re(x) - Re(x)^3*10^(-IP3/10)*1000*2/(3*R);
EQ3: Im(y) = Im(x) - Im(x)^3*10^(-IP3/10)*1000*2/(3*R).

Q1: Is this correct?
Q2: If A1 is yes for EQ2, then what do the factor of 2 and 3 represent?
Q3: if A1 is no, then what are the correct equations?

Thank you in advance for your help.

BR,
Phil

Google

"Third order intercept point"

Mark

"Phil" <[email protected]> wrote in message
news:[email protected] oups.com...
> Hi,
>
> I'm trying to get a better feel for modeling various analog
> impairments. Right now, I am searching clarification for 3rd order IMD
> modeling.
>
> As I understand it, for RF 3rd order IMD, the effect would be as
> follows:
>
> EQ1: y = x - x^3*10^(-IP3/10)*1000/R,
>
> where IP3 is in dBm and R is impedence in ohms.
>
> Also, I think that for complex baseband, the effect would be:
>
> EQ2: Re(y) = Re(x) - Re(x)^3*10^(-IP3/10)*1000*2/(3*R);
> EQ3: Im(y) = Im(x) - Im(x)^3*10^(-IP3/10)*1000*2/(3*R).
>
> Q1: Is this correct?
> Q2: If A1 is yes for EQ2, then what do the factor of 2 and 3 represent?
> Q3: if A1 is no, then what are the correct equations?
>
> Thank you in advance for your help.
>
> BR,
> Phil
>
Hi Phil , I really wouldn't recommend doing this as, in my opinion, the
innacuracies in presented IP3 make it near useless for anything other than
rough work.

Still, if you want to try to model it assuming that the IP3 you've got is
actually accurate in your situation (whatever that may be) then you could
express the complete non-linearity by
Vout(t) = A*Vin(t) +B*Vin(t)^3 similar to your first equation.
Unfortunately B is not simply related to the IP3 value and nor is A. To
measure IP3 they put two tones into the device (usually near equal power at
the input or output - hardly ever say which) they then measure the power in
either one or both tones at the output and look at the power in the third
order intermods too - if you put two tones into the cubic term above you
will get third order intermod tones and components at your original input
frequencies in antiphase with the original input so the bigger B is with
respect to A the more it cancels out A. Still , I expect you could
eventually work out what A and B actually are w.r.t IP3 if you wanted to.
Incidentally IP3 is a power measure so you can expect to use a lot of
10^(IP3/20) stuff, not 10.

I have no idea why you want to try to split the non-linearity into separate
in-phase and quadrature streams when you have complex envelope
representation - I would just put the whole thing through a complex cube
function , at least that way I wouldn't need to worry about those factors of
2/3 that have mysteriously appeared.

Whichever way you do it be very very careful that you know what your model
predicts as you get closer and closer to the IP3 point ( about 12 dB below
it on the input side you'll see what I mean) and ensure that your signal
envelope doesn't get into any regions you don't feel comfortable with.


Hoping some of this may be of some use - best of luck - Mike