System Overview
R&S
®
ZVA
67
Quick Start Guide 1145.1090.62 ─ 10
3.2.4.2
Conversion of Complex into Real Quantities
The results in the "Trace – Measure" menu can be divided into two groups:
●
"S-Parameters", "Ratios", "Wave Quantities", "Impedances", "Admittances", "Z-
Parameters", and "Y-Parameters" are complex.
●
"Stability Factors" and "DC Input" values (voltages, PAE) are real.
The following table shows how the response values in the different Cartesian diagrams
are calculated from the complex measurement values z = x + jy (where x, y, z are functions
of the sweep variable). The formulas also hold for real results, which are treated as com-
plex values with zero imaginary part (y = 0).
Trace Format
Description
Formula
dB Mag
Magnitude of z in dB
|z| = sqrt ( x2 + y2 )
dB Mag(z) = 20 * log|z| dB
Lin Mag
Magnitude of z, unconverted
|z| = sqrt ( x2 + y2 )
Phase
Phase of z
φ (z) = arctan (y/x)
Real
Real part of z
Re(z) = x
Imag
Imaginary part of z
Im(z) = y
SWR
(Voltage) Standing Wave Ratio
SWR = (1 + |z|) / (1 – |z|)
Delay
Group delay, neg. derivative of the
phase response
– d φ (z) / dΩ (Ω = 2
π
* f)
An extended range of formats and conversion formulas is available for markers. To con-
vert any point on a trace, create a marker and select the appropriate marker format.
Marker and trace formats can be selected independently.
3.2.4.3
Polar Diagrams
Polar diagrams show the measured data (response values) in the complex plane with a
horizontal real axis and a vertical imaginary axis. The grid lines correspond to points of
equal magnitude and phase.
●
The magnitude of the response values corresponds to their distance from the center.
Values with the same magnitude are located on circles.
●
The phase of the response values is given by the angle from the positive horizontal
axis. Values with the same phase are on straight lines originating at the center.
The following example shows a polar diagram with a marker used to display a pair of
stimulus and response values.
Screen Elements
