Originally Posted by

**ZartPARZ** Hi, everyone on MHF.

I did an experiment about current transformer and find that if I keep the current on primary coil constant, the current on secondary coil will decay and can fit by function

I = A1*exp(-t/t1) + A2*exp(-t/t2)

where A1,A2,t1 and t2 are constants.

My question is if I know the value of I, how can I solve for t?

I try all analytic way I know but failed.

Thanks in advance.

ZartPARZ.

As I(t) is a monotonicaly decreasing function of t if 0<I<A1+A2 there is a

unique solution.

I would set the problem up as: find the zero of g(t) where:

g(t) = I - A1*exp(-t/t1) - A2*exp(-t/t2)

Then use Newton-Raphson to find the root. This uses the itteration:

t_{n+1} = t_n - g(t_n)/g'(t_n)

which should converge if we set t_0=1.

Below is a demonstartion:

Code:

>t1=10;t2=3;
>I=0.7;
>A1=1;A2=0.3;
>
>function g(t)
$ global t1,t2,A1,A2,I;
$ rv=I-A1*exp(-t/t1)-A2*exp(-t/t2);
$ return rv
$endfunction
>
>function dg(t)
$ global t1,t2,A1,A2;
$ rv=A1/t1*exp(-t/t1)+A2/t2*exp(-t/t2);
$ return rv
$endfunction
>
>tn=1
1
>tnp1=tn - g(tn)/dg(tn)
3.58915
>tn=tnp1;tnp1=tn - g(tn)/dg(tn)
4.4797
>tn=tnp1;tnp1=tn - g(tn)/dg(tn)
4.55285
>tn=tnp1;tnp1=tn - g(tn)/dg(tn)
4.55329
>tn=tnp1;tnp1=tn - g(tn)/dg(tn)
4.55329
>tn=tnp1;tnp1=tn - g(tn)/dg(tn)
4.55329
>tn=tnp1;tnp1=tn - g(tn)/dg(tn)
4.55329
>

RonL