What are the equations that relate Real and Imaginary data pairs to Log Magnitude, Polar, Phase, and Smith Chart formats?
Equations Relating Network Analyzer Real and Imaginary Data Points to the Various Formatted Displays (and the associated Marker Readings)
Desired | Mathematical Equation | Microsoft Excel Command See Note 1 |
|---|---|---|
| Log Magnitude | 20*Log10((Re2 + Im2))1/2 | =20*LOG10(SQRT((SUMSQ(ReCell1,ImCell1))))(dB) |
| Phase | Case of Re>0 and IM>0, tan-1(Im/Re) or arctan (Im/Re) Case of Re>0 and IM<0, tan-1(Im/Re) or arctan (Im/Re) Case of Re<0 and IM>0, tan-1(Im/Re)+180 or arctan (Im/Re)+180 Case of Re<0 and IM<0, tan-1(Im/Re)-180 or arctan (Im/Re)-180 | ATAN2(ReCell1,ImCell1)*180/PI() (Degree) |
| Polar | Magnitude = ((Re2 + Im2)) 1/2 Phase = tan-1(Im/Re) or Phase = arctan (Im/Re) | Magnitude = (SQRT((SUMSQ(ReCell 1,ImCell 1))) Phase = ATAN2(ReCell 1, ImCell 1)*180/PI() |
| Smith Chart (Marker) | Resistance = R = ((1-Re2-Im2) /((1-Re) 2+Im2)) * Z0 Reactance = X = ((2*Im) /((1-Re)2+Im2)) * Z0 | Resistance =((1-POWER(ReCell 1,2)-POWER(ImCell 1,2)) / (POWER((1-ReCell 1),2)+POWER(ImCell 1,2)))*ZCell 1 Reactance = (2*Im Cell 1) / (POWER((1-ReCell 1),2)+POWER(ImCell 1,2)))*ZCell 1 |
| Smith Chart (Marker) Inductance (L) Capacitance (C) | X > 0, L = X/(2*pi*f) X < 0, C = 1/(2*pi*f*X) |   |
Note 1 The references to ReCell 1, ImCell 1, and Cell 1 refer to the real and imaginary data pair numeric values that have been entered into specific cells in the Microsoft Excel data sheet!
The following is an example of data stored to a disk for a three-point trace:
