Rohde & Schwarz 1145.1010.04/05/06, Operating Manual

Page: 131 / 813

R&S
®
ZVA/ZVB/ZVT Screen Elements
1145.1084.12 3.21 E-1
0
0
180 0
90 0
-90 0
Circles of equal
magnitude
Radial lines of
equal phase angle
Voltage reflection:
Open-circuited
load (Z = infinity)
Voltage reflection:
Short-circuited
load (Z = 0)
Matching
impedance (Z = Z
0
)
Examples for definite magnitudes and phase angles:
•
The magnitude of the reflection coefficient of an open circuit (Z = infinity, I = 0) is one, its phase
is zero.
•
The magnitude of the reflection coefficient of a short circuit (Z = 0, U = 0) is one, its phase is
–180
0
.
Smith Chart
The Smith chart is a circular diagram that maps the complex reflection coefficients S
ii
to normalized
impedance values. In contrast to the polar diagram, the scaling of the diagram is not linear. The grid
lines correspond to points of constant resistance and reactance.
•
Points with the same resistance are located on circles.
•
Points with the same reactance produce arcs.
The following example shows a Smith chart with a marker used to display the stimulus value, the
complex impedance Z = R + j X and the equivalent inductance L (see marker format description in the
help system).
A comparison of the Smith chart, the inverted Smith chart and the polar diagram reveals many
similarities between the two representations. In fact the shape of a trace does not change at all if the
display format is switched from
Polar to Smith or Inverted Smith – the analyzer simply replaces the
underlying grid and the default marker format.
Smith chart construction
In a Smith chart, the impedance plane is reshaped so that the area with positive resistance is mapped
into a unit circle.