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I have an electrical circuit as shown below:

Circuit Diagram

I would like to formulate an equation for the settling time for the voltage on the capacitor node given a change in resistance on R2. I have calculated the transfer function to be

$$ \frac{V_{cap}}{V_s} = \frac{R2/(R1+R2)}{1+S\frac{CR1R2}{R1+R2}}$$

i.e

$$ K = R2/(R1+R2) $$

and

$$ \tau = \frac{CR1R2}{R1+R2} $$

There is lots of information online about settling time for a step in source voltage; however, I can't find anything for changes to the plant system.

toolic
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Rob Robinson
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1 Answers1

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Your voltage source followed by R1+R2 forms a new effective voltage source of V.R2/(R1+R2), with an output resistance of R1.R2/(R1+R2). This is the standard Thevenin expression.

Therefore calculate the settling to a new final voltage of V.R2/(R1+R2), with a time constant of C1.R1.R2/(R1+R2).

Neil_UK
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