In the above image, take note of the line
dV/dt being much less than dVin/dt as a condition. I once asked a question about Integrators. I understand both the above image and my earlier question on integrators well enough (I think).
A later section of the book in the frequency domain (above) references image 1.14 when it says "we can restate the earlier time domain condition for its proper operation (Vout being much less than Vin). I understand what follows when it mentions the 3dB point. My question specifically relates to finding the condition ....
Vout being much less than Vin
I do not see this in the section on differentiators. If anything, I see the condition of dV/dt being much less than dVin/dt in section 1.14. Vout as a condition, being much less than Vin was in an earlier section on integerators, not differentiators, which states their rates of change.
Can someone point out where the book finds the required conditon Vout being much less than Vin in section 1.14? I suppose that if the condition on their derivatives...dV/dt being much less than dVin/dt is met then necessarily, Vout being much less than Vin is also met, though in a differentiator, Vout can go negative while Vin remains positive. (high to low transition). Is this statement referencing magnitudes? Basically, I am trying to find how the above line on the condition for a high pass filter, which basically is an RC differentiator, is referenced in section 1.14. I am not able to find the exact wording or convert the meanings/statements properly. Can one necessarily state that a relation on the derivatives of V and Vin transfers to their functions?Thanks.