R&S
®
ZVL
System Overview
Basic Concepts
Quick Start Guide 1303.6538.62-01
86
Inverted Smith chart construction
The inverted Smith chart is point-symmetric to the Smith chart:
The basic properties of the inverted Smith chart follow from this construction:
E
The central horizontal axis corresponds to zero susceptance (real admittance). The
center of the diagram represents Y/Y
0
= 1, where Y
0
is the reference admittance of
the system (zero reflection). At the left and right intersection points between the
horizontal axis and the outer circle, the admittance is infinity (short) and zero
(open).
E
The outer circle corresponds to zero conductance (purely imaginary admittance).
Points outside the outer circle indicate an active component.
E
The upper and lower half of the diagram correspond to negative (inductive) and
positive (capacitive) susceptive components of the admittance, respectively.
Example: Reflection coefficients in the inverted Smith chart
If the measured quantity is a complex reflection coefficient (e.g. S
11
, S
22
), then the
unit inverted Smith chart can be used to read the normalized admittance of the DUT.
The coordinates in the normalized admittance plane and in the reflection coefficient
plane are related as follows (see also: definition of matched-circuit (converted)
admittances):
Y / Y
0
= (1 - ) / (1 + )
From this equation it is easy to relate the real and imaginary components of the
complex admittance to the real and imaginary parts of
[
]
,
)
Im(
)
Re(
1
)
Im(
)
Re(
1
)
/
Re(
2
2
2
2
0
+
+
=
=
Y
Y
G
[
]
,
)
Im(
)
Re(
1
)
Im(
2
)
/
Im(
2
2
0
+
+
=
=
Y
Y
B
in order to deduce the following properties of the graphical representation in an
inverted Smith chart:
E
Real reflection coefficients are mapped to real admittances (conductances).
E
The center of the plane ( = 0) is mapped to the reference admittance Y
0
,
whereas the circle with | | = 1 is mapped to the imaginary axis of the Y plane.
E
The circles for the points of equal conductance are centered on the real axis and
intersect at Y = infinity. The arcs for the points of equal susceptance also belong to
circles intersecting at Y = infinity (short circuit point (–1,0)), centered on a straight
vertical line.
