I have a varying source voltage for maximum of 15 V and am using an error amplifier to maintain it using an integrator. Reference voltage is of 5V. I want a time constant of 100 msec with a capacitor of 1 uF, so I'll need a resistance of 100 kOhms. What combination of resistors would equal that resistance?
Neglecting the problem about whether the time constant of 100 ms can be achieved with what you have shown and what you propose to add to the circuit (hint, the integrator you have drawn will simply ramp indefinitely), it's possible to answer the question of what combination of R1, R2 and R3 will yield an effective output resistance of 100 kΩ, and a voltage division of 3:1.
The effective output resistance of the R1/R2 voltage divider is their parallel combination. If this is not 100 kΩ, then R3 can be used to increase the output resistance.
The simplest solution is R1 = 300 kΩ, R2 = 150 kΩ, with R3 = 0.
There is an infinity of other solutions with a finite R3, as long as R3 < 100 kΩ
- R1 = 3 x (100k-R3)
- R2 = 1.5 x (100k-R3)
We normally describe a pure integrator as having a gain, rather than a time constant. With an input resistance of 100 kΩ, the gain is 10 V/s per V, or 10/s. When the integrator is used in a feedback loop, it's usually more useful to express the gain as the frequency at which it has unity gain, which is 10 rad/s, or roughly 1.6 Hz.