Quantum explanation for Passive Intermodulation (PIM)

[ande4jo]

As I understand it PIM is always present when we have 2 or more RF signals traveling in a medium where we have dissimilar metals (like a coax cable attached to a connector). Further, it seems that the intermodulation is highest at IM2 product and weakens as the IM product increases. The most interesting part is that there appears to be no bounds to the highest IM product. That's where I wonder if there is something at the quantum fields that would account for a maximum IM product. For clarity the IM product number that I am referring to works as follows. Take 2 RF signals one at 700 Mhz and the other at 710 Mhz. One IM2 product would be 710 - 700 (10 Mhz), another IM2 product would be 710 + 700 (1410 Mhz) as well as 700 + 700 (1400 Mhz) and last 710 + 710 (1420 Mhz). This process continues for IM3 where there are variations of the 2 signals but with 3 terms added/subtracted together. I'm not sure if this is a question better suited for engineering site. THANKS

 

[Swamp Thing]

It is a quantum phenomenon only in the sense that all electronic phenomena are quantum. But it is possible to analyze passive IM by thinking of the junction as a weakly nonlinear element - i.e. a very poorly built diode that conducts just a tiny bit more current in one direction than in the other, given the same voltage.

Once you assume a nonlinearity, you can approximate it by a polynomial P(x) that connects current and voltage The polynomial could in principle be an infinite series, because many of these phenomena have exponential terms in the math. The x in P(x) would be like A1 sin (ω₁ t) + A₂ sin(ω2t) and the polynomial would expand into a series based on trig identities. If the polynomial's coefficients decrease to zero only at an infinite order, then the trig terms in the expansion would also go to zero at infinite order -- meaning that, in principle, there would be some non-zero signal at any frequency term you like to think of.

So, quantum mechanics (solid state physics) may explain why the behaviour is exponential, but it is all trig and math from that point on.

 

[ande4jo]

Thanks for the reply on this.
I am still thinking there needs to be some restriction to not allow infinite frequencies at non zero signal.
Of course this is needed for both ultimate large frequencies as well as infinitely small frequency bandwidths within a finite frequency band.
It seems to violate conservation of energy.
Also, where is this Passive Intermodulation energy expected to come from?
Can it only come from inefficient RF propagation (loss of RF signal as it traverses the junction)?
If so, it is very typical to only have ~0.2 - 0.3db of loss of RF energy due to connectors.
I am still hopeful that there is a quantum solution to resolve the apparent infinite energy required to have infinite frequencies at non-zero energy.

 

[Swamp Thing]

I am still thinking there needs to be some restriction to not allow infinite frequencies at non zero signal.

The total energy will not be infinite. The sum of an infinite series can be finite - if the terms decrease fast enough.

Also, where is this Passive Intermodulation energy expected to come from?

The passive IM products are typically like -100 dB down (or even lower) from the applied signal. If we do the maths, we find that all the passive IM products added together "steal" a very minute amount of power. Just for fun, I worked out that an PIM component of -100 dB will correspond to about -0.4E-10 dB attenuation in the transmitted signal.

 

[ande4jo]

Can you share the math please.
I don't understand how infinite frequencies all at non-zero power can add up to less than infinite power.

 

[f95toli]

Can you share the math please.
I don't understand how infinite frequencies all at non-zero power can add up to less than infinite power.

This is -if I understand your question correctly- really no different than for a normal geometric sum

http://en.wikipedia.org/wiki/Geometric_series

 

[ande4jo]

Yeah, I do understand normal geometric sums but that was a good refresher; thanks.

The way I see it though, is that we aren't talking about a diminishing series since the number of frequency terms actually increases with the higher order modulation product. For instance, using my original example, there were 2 frequencies expected to combine in a nonlinear device. I looked at the first 4 orders of modulation to show the pattern. In all of these cases I excluded frequencies of zero or less. BTW, the fact that the math can account for negative frequencies is, itself interesting to me, but we can leave that for another thread.
The first even IM product (IM2) has 4 new unique frequencies while the second even IM product ( IM4) has 5 new unique frequencies.
This process appears to coninue to grow for all higher order even products.
The same process also appears within the odd products where the first odd IM product (IM3) has 6 new uniques frequencies while the second odd IM product (IM5) has 10 new unique frequencies.
I have attached the simple algebraic sum for the fist 4 IM products that shows this pattern.
If this unbounded additional frequencies phenomenon is accurate, and if all new frequencies have non zero energy, then I expect quantum affects need to be analyzed to find the mechanism that will stop this process and keep the mathematics used here from requiring infinite energy loss.
This was the purpose for this original post; though admittedly I probably didn't put in enough detail in the original post.
I'm interested to see what anyone thinks of this.

 

[Swamp Thing]

What your procedure is doing is listing out the "labels" associated with each term of the infinite series. You are not calculating the actual value of each labeled term. If you do so, and if you add more and more values, you will see that the result will asymptotically approach a number that is not only finite but quite small compared to the applied signal (assuming that the nonlinearity is a weak one).

 

[ande4jo]

I have to respectfully disagree with what my procedure is doing.
My procedure was showing that as the order of IM product increases so to does the number of unique new frequencies.
This is not simply the labels but rather an indication that energy is spreading out over a larger and larger range of frequencies at the higher order IM products.
Does anyone else out there see it this way as well?

 

[ande4jo]

Another point that I was trying to make was that we are continually adding more new terms to the infinite series which is different than a simple Fourier series of harmonics where the terms follow a geometric pattern of frequecy multipled by increasing integer . The quantum affect that I have thought about applying to stop this affect could simply be E=fh where E is energy, f is frequency and h is plank constant. Thus, at orders of magnitude where a frequency component is high enough and the energy available for said frequency is low enough (less than plank constant), then said frequency would not exist in the order of IM products and thus a mechanism to stop the runaway condition that I envisioned. Of course all higher IM products with even higher frequency and even lower energy than previously mentioned will also not appear as well (since the would not be enough energy for even one photon at given frequency).