Passive Integrator and Differentiator Circuits

Design a passive integrator circuit using a resistor and inductor rather than a resistor and capacitor:

In addition to completing the inductor circuit schematic, qualitatively state the preferred values of L and R to achieve an output waveform most resembling a true triangle wave. In other words, are we looking for a large or small inductor; a large or small resistor?

When you look at the schematic diagram for a passive integrator circuit, it ought to remind you of another type of circuit you’ve seen before: a passive filter circuit:

What specific type of passive filter does a passive integrator circuit resemble? Is the resemblance the same for LR integrators as well, or just RC integrators? What does this resemblance tell you about the frequency response of a passive integrator circuit?

A “cheap” way to electronically produce waveforms resembling sine waves is to use a pair of passive integrator circuits, one to convert square waves into pseudo-triangle waves, and the next to convert pseudo-triangle waves into pseudo-sine waves:

From Fourier’s theory, we know that a square wave is nothing more than a series of sinusoidal waveforms: the fundamental frequency plus all odd harmonics at diminishing amplitudes. Looking at the two integrators as passive filter circuits, explain how it is possible to get a pseudo-sine wave from a square wave input as shown in the above diagram. Also, explain why the final output is not a true sine wave, but only resembles a sine wave.