Refelction from an open ended coaxial cable

A. Mostacci, S. Pisa

October 2015

General Constants

Ci=299792458; (* Speed of Light, m/s *)

LL=8;(* Cable Length, m *)

n= (Sqrt[2]);(* Refraction Index *)

AlphaPrimeValue=8.450 (10^(-4))*(10^(-3)); (* Cable attenuation, 1/(m (Hz^(1/2))) *)

Z0=50; (* Reference Impedance, Ohm *)

Scattering Parameters with/without a mismatch

S11[f_,L_,AlphaPrime_]:=Exp[-AlphaPrime 2L (Sqrt[2π f])-I n((2π f)/Ci)2L]

Z[f_,L_,AlphaPrime_]:=Z0 ((1+S11[f,L,AlphaPrime])/(1-S11[f,L,AlphaPrime]))

FullS11[f_,L_,AlphaPrime_,Zg_]:=((Z[f,L,AlphaPrime]-Zg)/(Z[f,L,AlphaPrime]+Zg))

Test Plots

20 Log10[Abs[S11[3 (10^9),LL,AlphaPrimeValue]]];

Reflection coefficient of the open ended cable

Plot[20 Log10[Abs[S11[frequency,LL (10^(-3)),AlphaPrimeValue]]],{frequency,(10^3),3*(10^9)}]

Reflection coefficient of the open ended cable with a mismatch on the connector

Plot[20 Log10[Abs[FullS11[frequency,LL/2,AlphaPrimeValue,55]]],{frequency,(10^3),1 (10^9)}]

Show[Plot[20 Log10[Abs[FullS11[frequency,LL/6,2*AlphaPrimeValue,55]]],{frequency,(10^3),1 (10^9)},PlotStyle->{Thickness[0.005]},PlotRange-> {Automatic,Automatic}],Frame->True,FrameLabel->{Hz,dB},FrameStyle-> Thick,LabelStyle->Directive[Large,Black,FontFamily->"Helvetica"],PlotRange-> {{0,Automatic},{-4,0}},ImageSize->700,LabelStyle->Directive[Large,Black,FontFamily->"Helvetica"]]

Effects of the connector imperfecation in the reflection measurument of an open ended coaxial cable

Manipulate[Show[Plot[20 Log10[Abs[FullS11[frequency,CableLength,AlphaPrime,SourceImpedance]]],{frequency,(10^3),1 (10^9)},PlotStyle->{Thickness[0.005]},PlotRange-> {Automatic,Automatic}],Plot[20 Log10[Abs[FullS11[frequency,CableLength,AlphaPrime,Z0]]],{frequency,(10^3),1 (10^9)},PlotStyle->{RGBColor[1,0,0],Thickness[0.007], Dashing[Large]},PlotRange-> {Automatic,Automatic}],Frame->True,FrameLabel->{Hz,dB},FrameStyle-> Thick,LabelStyle->Directive[Large,Black,FontFamily->"Helvetica"],PlotRange-> {{0,Automatic},{-15,0}},ImageSize->700],{{CableLength,LL},0,14},{{AlphaPrime,AlphaPrimeValue},AlphaPrimeValue/2,AlphaPrimeValue*2},{{SourceImpedance,50},40,60},LabelStyle->Directive[Large,Black,FontFamily->"Helvetica"]];