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aaron_do

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Intermodulation
Jan 22^nd, 2008, 12:15am

Hi all,

my question is about intermodulation (IM). Assume you have an output,

y(t) = a0 + a1x(t) + a2 x^2(t) + a3 x^3(t) +...

The IM3 component arises due to a3x^3(t). Suppose you are concerned with the IM3 product arising from x1 x2 and x3 which have frequencies f1, f2, and f3 respectively. Then the output IM3 component will be

IM3 = a3*x1(t)*x2(t)*x3(t)

suppose you want the IM3 product at f1+f2+f3. a3 can be a function of frequency. Therefore, my question is, to calculate IM3, at what frequency do we calculate a3? Is it at f1+f2+f3 or is it something else, for example, cube root of a3 at f1 * a3 at f2 * a3 at f3?

Lastly, when we simulate IIP3, we run a PSS analysis and a PAC analysis, where the PSS analysis is only run at one frequency. So therefore, i seems that the simulator does not calculate a3(f). So is it true to say that the IM3 calculated by spectre is less accurate as the PAC frequency becomes further away from the PSS frequency?

thanks,
Aaron

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Stefan

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Re: Intermodulation
Reply #1 - Jan 22^nd, 2008, 12:28am

I struggled also with this some weeks ago and I've found that IM3/IP3 (not comparable with NF, 1dBCP or alike) is something that is only specified for two input frequencies.

Then, it is specified as the powers at 2f1-f2 or 2f2-f1 (both are possible).

As far as I understood, there is no IM3 for more than two input signals.
Maybe you could define it the same way as above as the components at

2f1-f2
2f1-f3
2f2-f1
2f2-f3
2f3-f1
2f3-f2

but I doubt that this is very useful. Anyway, what do you want to use it for ?
IM3 is a specification for nonlinearity which is clearly implemented with the taylor series you wrote.
Components of the taylor series can be either specified via 1dBCp or via IM3/IP3 measurements.

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didac

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manresa,spain

Re: Intermodulation
Reply #2 - Jan 22^nd, 2008, 12:59am

Hi,
I agree with Stefan IIP3,IIP2 are by definition two tones test. For the PSS and PAC I thing that the problem arises more from the point of view of simulation time than anything else, if you put a pss tone of 2.45GHz and a small signal at 2.4501GHz the pss fund it's 2.45GHz, if you use the pss to provide two large signals the fundamental it's 0.01GHz so the simulation time grows up. If I remember well the use of PAC gives good results for input powers below CP1db-10dB or something like that, otherwise the large non-linearity introduces errors.
Hope it helps,

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Ken Kundert Global Moderator Offline Posts: 2386 Silicon Valley	Re: Intermodulation Reply #3 - Jan 22^nd, 2008, 1:22am Aaron, To answer your question about PAC ... No, SpectreRF does not become less accurate as the PAC frequency diverges from the PSS frequency (until the frequency increases beyond maxacfreq, but I don't think that was your concern. -Ken
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aaron_do

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Re: Intermodulation
Reply #4 - Jan 22^nd, 2008, 6:08am

Thanks for all the replies,

I chose 3 tones just to make the analysis general. If we forget about IIP3, I don't see why 3 tones can't produce IM3...

the main thing i'm trying to figure is which frequencies a3 should be evaluated at. My thinking is that if a3 should be evaluated at a frequency different from the frequency used by the PSS analysis, then the simulated IIP3 would be inaccurate.

I'm trying to come up with a simple way to evaluate out-of-band IIP3...I guess I could explain further if anyone is interested...

cheers,
Aaron

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Stefan Senior Member Offline Posts: 124	Re: Intermodulation Reply #5 - Jan 22^nd, 2008, 6:13am I don't agree with your general calculation of IM3 ... What happens if you just have x1(t) and x2(t), but x3(t)=0 ? According to your equation IM3=a3x1(t)x2(t)*x3(t) you wouldn't have any IM3 products, which is wrong since there do some exist for x1 and x2 (2f1 -f2 and 2f2-1). I think there is something fundamental wrong here ...
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aaron_do

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Re: Intermodulation
Reply #6 - Jan 22^nd, 2008, 4:44pm

Hi stefan,

I wasn't really trying to emphasize the fact that three tones can cause IM3, but since you point it out, the receiver will receive say ten different interference tones. Any combination of three of these tones will then create IM3 including 2f1-f2 or 2f10-f6 or f9-f7-f4. In the equation, I didn't discount the possibility that x3 is equal to x1. If you do the expansion, you will find that all combinations exist...

(cosw1t+cosw2t+cosw3t)^3

will result in all combinations of the three tones. It is up to the user to decide which ones are more relevant for IP3 calculation. i.e. which ones result in in-band distortion.

cheers,
Aaron

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RFICDUDE

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Re: Intermodulation
Reply #7 - Jan 27^th, 2008, 4:10pm

First, keep in mind that input and output referred intercept points are defined applying a two-tone signal to a purely third order nonlinearity. We all know that the world is not purely third order, but that is the abstraction that is used.

For a three tone signal, you could measure the slope of the intermodulation products and extrapolate the input/output intercept points, but they would not be the same as the two-tone intercept points because the amplitude modulation between two and three tone singles are different.

Now, you can extract the third order coefficient �a3� from a three tone analysis and then say what the two-tone intercept point is from knowledge of �a3.�

If define a three tone input by
X(t)= A*cos(w1*t) + B*cos(w1*t+delta) + C*cos(w1+2*delta)
then the intermodulation products on the lower side of the carrier frequency are

At (2*w1 � w2)
3/4*A^2*B+3/2*A*B*C which if A=B=C equals �*A^3 + 3/2*A^3 = 9/4*A^3

At (2*w1 � w3)
3/4*A^2*C = �*A^3

Now a3 can be determined from either of the two intermodulation products (assuming everything is purely third order).

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