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Jan 21st, 2018
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  1. S := 299792458;
  2. Rem := 1;
  3. Imm := 0;
  4. c1 = 7.1966584528920068;
  5. c2 = -2.8612955354362528*10^(-2);
  6. c3 = 4.9904748273007211;
  7. c4 = 1.1557482550800184;
  8. c5 = 1.4462311508982122*10^4;
  9. Of = 2.9899879533823599;
  10. a0 = -4.0196213710349726*10^-1;
  11. a1 = 9.9011244036818056;
  12. a2 = 2.0237033052953829*10^-1;
  13. a3 = 4.6135432671114094;
  14. a4 = 3.3240796293189689*10^-1;
  15. a5 = -2.6267966826701428*10^-1;
  16.  
  17. Ree[f_, wt_] =
  18. c5/((1.0 + Exp[c1 - c2*f])*(1.0 + Exp[c3 - c4*wt])) + Of;
  19.  
  20. Ime[f_, wt_] = a0 + (a1/(1.0 + Exp[a2*(f + a3 + a4*wt + a5*f*wt)]));
  21.  
  22. El[f_, wt_] := Ree[f, wt] - I*Ime[f, wt];
  23. Ma := Rem - I*Imm;
  24.  
  25. Z[wt_, f_, d_] :=
  26. Sqrt[Ma/El[f, wt]]*
  27. Tanh[I*2*Pi*f*10^9*d*(10^-3) *Sqrt[Ma*El[f, wt]]/S];
  28. R[wt_, f_, d_] := (Z[wt, f, d] - 1)/(Z[wt, f, d] + 1);
  29. RL[wt_, f_, d_] := 20*Log10[Abs[R[wt, f, d]]];
  30.  
  31. In[1024]:=
  32. FindRoot[RL[wt, 10, d] == -10 &&
  33. RL[wt, 11, d] == -10, {{wt, 5, 0, 10}, {d, 5, 0, 10}}]
  34.  
  35. During evaluation of In[1024]:= FindRoot::lstol: The line search decreased the step size to within tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the merit function. You may need more than MachinePrecision digits of working precision to meet these tolerances.
  36.  
  37. Out[1024]= {wt -> 2.99549, d -> 7.00699}
  38.  
  39. In[1025]:= RL[2.9954853391692704`, 10, 7.006986346111831`]
  40.  
  41. Out[1025]= -3.4359
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