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MathGroup Archive 2006

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NonlinearFit problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66500] NonlinearFit problem
  • From: Oliver Friedrich <frixoli at qarcor.de>
  • Date: Wed, 17 May 2006 03:29:39 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hallo,

I want to use the NonlinearFit algorithm to obtain the parameters of a 
lossy line. There is a model

Cell[BoxData[
    RowBox[{
      SqrtBox[
        FractionBox[
          RowBox[{
            RowBox[{"2", " ", "\[ImaginaryI]", " ", "f", " ", "L", " ", 
"\[Pi]"}], "+", 
            RowBox[{
              SqrtBox["f"], " ", 
              SqrtBox[
                RowBox[{"2", " ", "\[Pi]"}]], " ", 
              SubscriptBox["R", "skin"]}]}], 
          RowBox[{"G", "+", 
            RowBox[{"2", " ", "\[ImaginaryI]", " ", "C", " ", "f", " ", 
"\[Pi]"}]}]]], " ", 
      RowBox[{"Tanh", "[", 
        RowBox[{"1.`", " ", 
          SqrtBox[
            RowBox[{
              RowBox[{"(", 
                RowBox[{"G", "+", 
                  RowBox[{"2", " ", "\[ImaginaryI]", " ", "C", " ", "f", 
" ", "\[Pi]"}]}], ")"}], " ", 
              RowBox[{"(", 
                RowBox[{
                  RowBox[{"2", " ", "\[ImaginaryI]", " ", "f", " ", "L", 
" ", "\[Pi]"}], "+", 
                  RowBox[{
                    SqrtBox["f"], " ", 
                    SqrtBox[
                      RowBox[{"2", " ", "\[Pi]"}]], " ", 
                    SubscriptBox["R", "skin"]}]}], ")"}]}]]}], "]"}]}]], 
"Output",
  CellLabel->"Out[166]="]

that describes the input impedance of a lossy line when shorted at the 
end. The line parameters to obtain are Rskin,L,G and C. f is the 
independant variable. I have data of the line of the form {{f1,Z1},
{f2,Z2},...} where Z is of course complex.
Unfortunately NonlinearFit seems to have problems with complex numbers 
since it returns with messages saying "Objective function isn't real 
at...".
Does anyone knows how to fix NonlinearFit for complex numbers or any 
other numerical method that could solve my problem?.

Thank you
Oliver


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