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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?

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  • \$\begingroup\$ 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". \$\endgroup\$
    – user16324
    Oct 2, 2015 at 14:46
  • \$\begingroup\$ @ 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? \$\endgroup\$
    – 89sam
    Oct 2, 2015 at 14:50
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    \$\begingroup\$ 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... \$\endgroup\$
    – user16324
    Oct 2, 2015 at 14:57

2 Answers 2

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Finding the coeficients of 1st order is simple:
Gain = Vout/Vin ... Vout is a steady state output
Time = when output reaches 63% of steady state output, or simply draw a tangential line to the output curve at time t=0, when this tangential line cross the stady state level thaen this is the time constant.

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  • \$\begingroup\$ Isn't 1-e^(-1) based on the system and, thus, is not for all 1st order systems? Or did I miss a concept? \$\endgroup\$
    – 89sam
    Oct 2, 2015 at 14:56
  • \$\begingroup\$ F = Vout/Vin = K*(1-exp(-t/T)) in time domain, or F(s) = K/(1+Ts) in Laplace domain, this is the transferfunction of 1st order, it can be an RC circuit (in this case T=RC, K=1) or whatever else that has similar response, only K and T are the coeficients to be estimated. \$\endgroup\$
    – Marko Buršič
    Oct 2, 2015 at 16:03
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Im not an expert but I will try to answer it. Sorry, I'd like to put this as a comment but there is no add comment button here.

Ok, now you know the output, y(t) and the input, x(t). Then from the data, you can try to find the equation y(t) = f[x(t)]. Use laplace transform and then rearrange into TF = Y(s)/X (s) to get the answer.

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