# Find the first-order transfer function from a measured step response data

In a school experiment, we had to measure an output voltage from an IC. We gathered the data with respect to time. Now we have to find the transfer function given the output data.

I think the whole experiment was treated as a first order open loop system. Now we have to find the transfer function that drove this step response output.

I searched around to find a few equations but still finding that this is a bit hard and requires estimation? Any hints onto how I can do this?

• One intermediate step is to find the "time constant" or RC product. You can get at that from the time domain measurements using formulae related to "exponential decay".
– user16324
Commented Oct 2, 2015 at 14:46
• @ Brian The thing is this isn't a circuit with a known R and C. So, I'd probably be estimating 5 time constants when the output reaches steady state. Is this right? Commented Oct 2, 2015 at 14:50
• Roughly right. You ought to have an initial slope of V vs T, and you maybe able to measure the 50% point (see "half life"), and/or the 63% point Marko mentions. These all have relationships to RC you can find. If they all agree on what RC is, you're doing well...
– user16324
Commented Oct 2, 2015 at 14:57