What exactly is the intuition behind physical circuits being linear?
Some with a sense of humor said
&quot;On a small enough scale, all behaviors are linear.&quot;
In circuit design, we do not have exact polynomial descriptions for any component, so we go with &quot;it is linear&quot;.
And somewhat later, we learn about Taylor Series approximations to the Exponential Diode behaviors.
And we learn about 2_nd order and 3_rd order intercept points and P1 compression points, input referred and output referred.
And we learn to use spreadsheets to keep track of the distortion, and use worst case or RSS modeling.
All because our components are real structures with imperfect crystalline manufacturing, and incomplete numeric descriptions in the models.
And we get paid to release a design to the FAB or to the manufacturing floor.
So we, over years, become pragmatic, becoming engineers, accepting the wonderful variability of life, and highly reliable systems become available to customers.
It all works.
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Then we get paid to convert all the systems_on_PCB to systems_on_silicon, and the fun learning starts all over again, not forgetting the &quot;ground&quot; is outside the Integrated Circuit, several millimeters away. Thus vast differential circuits become our tools. And wide substrate/well rings, to minimize gradients on silicon surface, become a tool.
Then, with everything located only 100 microns from any other circuit (well, maybe 1,000 micron or 5,000 microns), we get to rethink Heavyside and Maxwell, and realize magnetic fields are just a result of slight delays in the Efields, thus we can SHIELD magnetic fields using the SKIN EFFECT.
Thus circuit design and system design require constant digging down into the fundamentals, to rethink what we have been taught. There is a need to detect &quot;folklore&quot;, and understand why the folklore exists, to explore that particular design space and find exceptions to the rules, and exploit them. Folklore about substrate noise control is plentious; challenge them.
Also we might ponder &quot;harmonics&quot;. Harmonics are merely an expression of the correlation between a non-linear behavior and various linearly_spaced sinusoids.
A step function correlates with ANYTHING, to some degree. We happily indicate the peaks and nulls in the amount of correlation, because of lossless energy storage(infinite Q); this realization lets us ponder FINITE_Q systems, and realize harmonics do not exist; harmonics are just the result of &quot;correlation&quot;.
Get thee to the lab, with a Spectrum Analyzer and Pulse Generator. And play with pulse_frequency and pulse_width and pulse_risetime, and learn about &quot;harmonics&quot;. Respect the input power limit of the SA.
Most importantly, alter the Resolution Bandwidth and Video Bandwidth of the SA, which lets you in essence alter_the_Q of the system; this may be the crucial takeaway thought from your lab tinkering.