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Modeling >> Behavioral Models >> time constant doubt
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Message started by singh on Nov 22^nd, 2011, 7:35am

Title: time constant doubt
Post by singh on Nov 22^nd, 2011, 7:35am

i need to model an exponential signal with second order time constant tau1 and tau2
i know that general equation is f(t) = A . exp(-t/tau)
how to write it for two time constants tau1 and tau2.Is it like f(t) = exp(-t/(tau+tau2)) ?
i need to multiply the above function with second order low pass RC filter transfer function ( in which i have r1c1 = tau1 and r2c2 = tau2) to get the output.

Title: Re: time constant doubt
Post by raja.cedt on Nov 22^nd, 2011, 7:44am

hello,
could you please explain little bit.
Why you want to model like that? you can write like the following as well k1*exp(-tau1)+k2*exp(-tau2)

Thanks,
Raj.

Title: Re: time constant doubt
Post by singh on Nov 22^nd, 2011, 8:49am

i need to multiply my exponential function with the transfer function of second order RC filter ( time constant tau1 and tau2)

when it was first order RC filter (with time const tau) , i just used f(t) = A * exp(-t/tau) and multiplied it with filter transfer function TF_1 to get output = abs(f*TF_1)

But now i am using second order filter and need to do the same stuff. So what to use as my signal..i mean now there are two time constants. tau1 and tau2....how to write equation for decaying signal using both?

Title: Re: time constant doubt
Post by buddypoor on Nov 22^nd, 2011, 9:06am

Hello Singh,

from your information one can derive that your filter has two REAL poles at s1=-1/tau1 and s2=-1/tau2.

In this case, the solution of the describing diff. equation in the time domain will consist of two exponential elements: A1*exp(s1t)+A2*exp(s2t).
Thus, you have simply to add two exponential expressions.

Title: Re: time constant doubt
Post by singh on Nov 23^rd, 2011, 2:42am

thank you all for your responses