Rohde & Schwarz 1145.1010.04/05/06, Operating Manual

Page: 134 / 813

Screen Elements R&S
®
ZVA/ZVB/ZVT
1145.1084.12 3.24 E-1
The basic properties of the inverted Smith chart follow from this construction:
•
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).
•
The outer circle corresponds to zero conductance (purely imaginary admittance). Points outside
the outer circle indicate an active component.
•
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
Γ
(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 -
Γ
) / (1 +
Γ
)
From this equation it is easy to relate the real and imaginary components of the complex admittance to
the real and imaginary parts of
Γ
[ ]
,
) Im( ) Re( 1
) Im( ) Re( 1
) / Re(
2
2
2 2
0
Γ + Γ +
Γ − Γ −
= =
Y Y G
[ ]
,
) Im( ) Re( 1
) Im( 2
) / Im(
2
2
0 Γ + Γ +
Γ ⋅ −
= =
Y Y B
in order to deduce the following properties of the graphical representation in an inverted Smith chart:
•
Real reflection coefficients are mapped to real admittances (conductances).
•
The center of the
Γ
plane (
Γ
= 0) is mapped to the reference admittance Y
0
, whereas the circle
with |
Γ
| = 1 is mapped to the imaginary axis of the Y plane.
•
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.
Circles of equal
conductance
Arcs of equal
susceptance
Open-circuited
load (Y = 0)
Short-circuited
load (Y = infinity)
Matching
admittance (Y = Y
0
)