Linear and non-linear attenuator

Question

[edit 3/2/18] There are problems with the title and wording of this question. I would edit, but to do so would alter the relationship between the question and the answer that I accepted. So, I have re-asked the question in a way that better describes what I was trying to learn. You can find the new version of this question here.

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This is a newbie question. The manufacturer's data sheet for a material shows its attenuation curve over a range of frequencies. Does that curve represent the material's linearity of its attenuation? Or, does linearity mean that if the input waveform is sinusoidal, the attenuated signal will also be sinusoidal? Or, does it mean something else?

My understanding from the answer to a previous question is that high field strength can cause an attenuator to become non-linear, so that it attenuates more or less at a particular frequency, depending on the detail of the non-linearity. What does this mean? Is it that 1) the manufacturer's attenuation curve is altered, so that attenuation is enhanced or diminished at certain frequencies relative to when it's operating linearly, or 2) e.g., an input sine wave is output as a square wave, or 3) an input signal at one frequency is output at a different frequency, or 4) something else?

Answer 1

You are mistaking "linear" with "flat over frequency". The "attenuation vs frequency" curve has nothing to do with linearity.

Mathematically, "linearity" means that when if input signal A produces output signal B, then n x A produces n x B. That is, the output is proportional to the input.

Linearity DOES mean that if the input signal is sinusoidal, the output signal will also be sinusoidal. But it also means more than than - if the input signal is a superposition of sinusoidal components (which any periodic signal is), then the output signal will be a superposition of sinusoidal components at the same frequencies. A linear circuit will never output a signal component at a frequency which was not present at the input.

However, linearity does NOT imply that each frequency will be affected the same. For example, an attenuator could reduce the 1GHz component by 3dB and the 2GHz component by 4dB, and still be linear.

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So, what happens when your material gets hit with a high enough power wave that it goes nonlinear? Depends on the material and how it's being used, but in general, the attenuation curves (which are presumably listed in dB) will change. Without knowing the specific material properties, I can't say for sure whether the attenuation will increase or decrease.

In a nonlinear mode, it is possible for an input signal at one frequency to produce output signals at other frequencies - specifically, integer multiples of the original frequency. In some circuits, it is possible this will mean a sinusoidal input producing a square wave output.

If the input signal is composed of two or more frequencies (f1 and f2), then the output signal of a nonlinear circuit can include any frequency of the form (n x f1) +/- (m x f2) (for integer m and n). Researching "mixing products" for more info.

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P.S. - the amount of power required to make a bulk material go nonlinear is probably pretty high. Typically, for most every day applications it's safe to assume materials are linear - although of course every project is different and I have no idea what either your material or your application is.