Derivation of the output of an integrator using ideal op amp properties and capacitor current
Evaluation of capacitor voltage subject to singularity function current
Diagram for differentiator circuit, including selected resistor and capacitor values, expected input and output functions (set equal to each other as shown, assuming unit amplitude), and derivation of ideal frequency for unity gain
Measured resistance. Capacitance measurement function non-operational, though measurement of time constant subject to square wave would be a viable option
Implemented circuit
Input (blue) and output (yellow) wave forms at 234 Hz, both of
amplitude 1V. 500Hz yielded output 2.1V and 100Hz 0.4V.
Summary
Circuit behaves as expected, yielding unity gain at the expected frequency and a phase shift of pi/4 consistent with cos differentiating to sin. Higher frequencies yield higher gain and low frequencies attenuation, as expected. Curiously, Waveforms' oscilloscope function refused to align the output with time 0 under any triggering configuration. Also, matte finishes are clearly superior to gloss.
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