R&S ZNL4 - Page 209

VNA concepts and features
R&S
®
ZNL/ZNLE
209User Manual 1178.5966.02 ─ 20
Conversion of complex to real quantities
Among the measured quantities the VNA supports, only "Power Sensor" results
(R&S ZNL only) and "Stability" factors are real. All other measured quantities are com-
plex.
The following table shows how "real" response values are calculated from complex
measurement values z = x + j y (where x, y, z are functions of the sweep variable). The
formulas also hold for real measurement values (y = 0).
Trace Format Description Formula
"dB Mag" Magnitude of z in dB dB Mag(z) = 20 * log|z| dB
"Phase" Phase of z φ (z) = arctan (y/x)
"SWR" (Voltage) Standing Wave Ratio SWR = (1 + |z|) / (1 – |z|)
"Lin Mag" Magnitude of z, unconverted
|z| = sqrt ( x
2
+ y
2
)
"Real" Real part of z Re(z) = x
"Imag" Imaginary part of z Im(z) = y
"Delay" Group delay, neg. derivative of the
phase response
– d φ (z) / dΩ (Ω = 2π * f)
An extended range of formats and conversion formulas is available for markers. To
convert any point on a trace, create a marker and select the appropriate marker format.
Marker and trace formats can be selected independently.
9.2.3.2 Complex trace formats
Complex trace formats assign a complex response to the stimulus value, which can be
frequency, power (R&S ZNL only), or time..
In diagrams, the response values are always represented as points in the two-dimen-
sional complex plane:
●
The complex 0 is located at the center of the diagram.
●
The real part is drawn in horizontal direction, the imaginary part in vertical direction.
Result values for consecutive stimulus values are interconnected by straight lines, so
the trace is represented as a polygonal chain in the complex plane.
The stimulus axis is not visible. However, the stimulus value for a given trace point can
be displayed using a marker.
The difference between the different complex trace formats (Polar,Smith and Inv
Smith) is the coordinate system that is used for the representation of the response val-
ues and that is graphically overlaid to the formatted trace.
Polar
For "Polar" traces the complex response values are represented in polar coordinates:
magnitude and phase.
VNA screen elements