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# What are the equations that relate Real and Imaginary data pairs (as read from either a disk save, the GPIB interface, or a display marker) 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
Format
Mathematical EquationMicrosoft Excel Command See Note 1
Log
Magnitude
20*Log10((Re2 + Im2))1/2=20*LOG10(SQRT((SUMSQ(ReCell1,ImCell1))))(dB)
PhaseCase 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: 