Use the expression for the gain of an integrator to determine the relationship between the slope of the output (the output is linear in time for a constant input) and the time constant of the integrator.
Hint for P14-6
Use an inverting configuration; the low frequency gain of -30 dictates the feedback resistance (since the input resistance is specified to be 10k).
To get a low-pass response, a capacitor should also be used to feed the output back to the inverting terminal. The feedback network will thus be a resistance Rf in parallel with a capacitor. Examine the resulting expression for the gain and set the breakpoint frequency to 3 kHz to determine the appropriate value of the capacitance.
Hint for P14-9
There is no real need to find the full analytical expression for the gain in this exercise. You may approximate the behavior by determining the gain at low frequency and at high frequency and the breakpoint frequencies that connect the two regions.
That is, at a frequency sufficiently low that XC is infinity, Zf approaches 5 Mohm. At frequencies high enough that XC becomes a short, Zf will reduce to the parallel combination of 5 Mohm and 555 kohm.
Hint for P14-10
The figure shows that the output voltage should be 0.5 V when the input waveform has a slope of 0.2 V/ms. What value should R have?
Determine the desired breakpoint frequency by determining the intersection (on a Bode plot) of the gain of the differentiator (2 pi f Rf C) with the overall op-amp rolloff expression: 1.0 MHz/f. Set the value of the stabilizing resistance accordingly.