RigExpert products measure the complex reflection coefficient?Gamma and from that Return Loss, VSWR and Complex Impedance?(R+/-jX)?can be calculated and plotted on the screen.??
Gamma?(¦£) is a complex number expressed in the form a +/-jb? or?as Magnitude @ an angle.??The Magnitude is = sqrt(a^2+b^2) and the angle is the arctan (b/a). The angle is often referred to as the S11 phase angle and this is the angle plotted on the RigExpert.? The relationship between Gamma and the complex impedance is given by this equation:? Gamma ¦£ = (Z - Zo) / (Z + Zo) with Z being a complex number and Zo typically set at 50 or 75.? ??
The S11 phase angle is NOT the same as the impedance phase angle of what we are measuring.? An antenna, for example will have a complex impedance Z = R+/- jX where R is resistance and X is reactance.? ?The impedance phase angle? is the artctan (X/R) which is not the same as the arctan (b/a) of Gamma.? The RigExpert only calculates the S11 phase angle and if you want impedance phase angle you have to export the data and derive it externally in a spreadsheet or other program.??
Hopefully an? example will illustrate the concepts.? Let us say our antenna has a complex impedance R+jX is 50+j50.. For the case of 50+j50 the impedance phase angle is arctan (1) or 45 degrees.? If we calculate Gamma ¦£ = (Z - Zo) / (Z + Zo) = (50+j50-50)/(50+j50+50)? =?j50/(100+j50) the result? after some complex division is 0.2 +.4j.? The magnitude is sqrt (0.2^2 +0.4^2) = .45 at a phase angle of arctan (.4/.2) = 63.4 degrees.? ?If we do the same calculations with an impedance of 50 +j200 we get also get different numbers for S11 phase angle and impedance phase angle as shown below.
? ? ? ? ? ? ? ? ? Impedance phase? ? ? ? ? ? ?reflection coefficient phase
50+j50? ? ? ? ? ? ? ? 45? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?63.4
50+j200? ? ? ? ? ? ? 76? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?26.6
