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In Keysight's popular AN 150 there is a plot of noise and harmonics amplitudes versus the level of the input signal at the mixer (page 57).

It's stated there that the maximum n-th dynamic range is given at the intersection of the noise and n-th harmonic lines (i.e. when both noise and the n-th harmonic are of the same amplitude).

I'm having a hard time understanding why this is so. As I see it, one can change then level of the mixer's input to perform some kind of trade-off between SNR and harmonic distortion. So what criteria is followed to state that when both effects are equally relevant the dynamic range is maximum?

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  • \$\begingroup\$ The mixer level is the result of the input signal and attenuator and Filter BW. The attenuator ensures the Pmax input is not exceeded. Then the selection of Resolution BW determines this maximum Dynamic Range. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Jul 16 '18 at 16:52
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Signal to noise ratio gets worse as signal level falls.

Signal to distortion ratio get worse as signal level rises.

Dynamic range is the ratio of the signal level to any unwanted signal, noise or distortion.

Therefore there is a signal level where these two unwanted signals are equal. At either side of that level, one or the other unwanted signal gets worse and dominates. At that level, dynamic range is best.

Note that the noise level depends on the resolution bandwidth, whereas the distortion level doesn't. The optimum dynamic range level therefore changes with bandwidth.

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  • \$\begingroup\$ For second-order distortion, the improvement is one half the change in the noise floor; for third-order distortion, two-thirds the change in the noise floor. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Jul 16 '18 at 16:39
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    \$\begingroup\$ ... when the distortion is adequately modelled by an order, which is true often enough to lull people into a false sense of security for when it isn't. \$\endgroup\$ – Neil_UK Jul 16 '18 at 18:16
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Your spectrum analyzer cannot discern between signal, noise and distortion components--it just measures power. If you try to reduce the signal to reduce the distortion, the noise dominates, and your SNR drops (as the noise stays the same but the signal is weaker). If you increase the signal, you have more SNR at the input, but the nonlinearity of the mixer results in larger output spurs, and as these components increase more rapidly than the signal (if you double the signal power the power in the distortion increases more than double) your SNR still decreases (here the noise-component represents the distortion too, and hence is often called "SINAD" for signal-to-noise-and-distortion.

Again, as I said, your spectrum analyzer cannot tell the difference between noise and distortion, reducing one to improve the other is pointless (as in the end you still have the same amount of undesired power).

In other words, your statement

As I see it, one can change then level of the mixer's input to perform some kind of trade-off between SNR and harmonic distortion.

Is false - the mixer is at it's optimum power level there, and thus going higher will not result in increased performance.

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