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Radio Wrangle So, why the convenient dB/dB slopes? They seem almost too good to be true and are reliable at low enough levels, and the factors are accurate, not just close.
Take a device and model its transfer function as a mathematical power series. The zeroeth power gives you DC output if you're bothered. The first power gives your wanted output, the square power gives you second order distortions, the cube power gives you third order, the fourth and so on
Differentiate this series to get the slopes and you see that as per normal calculus, the power of a term is multiplied into its coefficient. And there is the basis of those convenient scales for each order of product.
The bad behaviour at higher levels would be modelled properly if you took the time to make a complicated enough series to model high level behaviour in detail. No-one does, it's easy to take the simple view because we only want to use devices in their well-behaved region and aren't bothered just how bad the badly behaved region is.
So there you have it.
You need to do a full plot of the intermod product power so that you can see this in action and feel comfortable about it.
You need to do a full plot of a new device so you can check where it goes badly behaved and the small-signal assumptions and models fail.
Jeremy's mentioned the handy estimate of TOI versus 1dB compression point. It's pretty good on all well-behaved devices. On the bad guys it's an assumption that will have you.
There are other rough rules of thumb. Howard Swain was responsible for one relating relative levels to relative amounts of compression. Handy for spectrum analyser designers deciding where to pitch maximum operating levels and designing to meet an overall compression figure which is actually the budget for the total of several contributing stages. Noise figure instruments are touchier in this area than spectrum analysers so it's one reason why the purpose-designed NF instruments out perform general analysers with a software personality.
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Thank you. I think my problem is more to do with working out the origins and derivations of the linear equations from the first principles in the graphs.
I have attached 5 versions of the same graphs. Seemingly, they are the same but not quite. Some plot 1.distortion dbc, 2. signal-to-noise ratio dBc, 3 dynamic range db, 4. distortion products relative to mixer db.
It seems that
DANL = -1 x mixer level + y-intercept 1
IMD2 = 2 x mixer level + y-intercept 2
IMD3 = 3X mixer level + y-intercept 3
It will be very helpful if I can have these three equations with the unknown intercepts. None of the articles give you this information.
I can see where the straight lines for IMD2 and #IMD3 coming from. But none of the HP, Agilent and R&S articles explain why DANL is a linear function of mixer level with a negative slope of -1. It is not so obvious when i have tried to derive the proof of those straight lines and intercepts by looking at the geometries of the intersecting lines and triangles.
The maximum 2nd and 3rd order dynamic ranges are at the intercepts with the DANL line.