R&S
®
ZVL
System Overview
Basic Concepts
Quick Start Guide 1303.6538.62-01
84
The basic properties of the Smith chart follow from this construction:
E
The central horizontal axis corresponds to zero reactance (real impedance). The
center of the diagram represents Z/Z
0
= 1 which is the reference impedance of the
system (zero reflection). At the left and right intersection points between the
horizontal axis and the outer circle, the impedance is zero (short) and infinity
(open).
E
The outer circle corresponds to zero resistance (purely imaginary impedance).
Points outside the outer circle indicate an active component.
E
The upper and lower half of the diagram correspond to positive (inductive) and
negative (capacitive) reactive components of the impedance, respectively.
Example: Reflection coefficients in the Smith chart
If the measured quantity is a complex reflection coefficient (e.g. S
11
, S
22
), then the
unit Smith chart can be used to read the normalized impedance of the DUT. The
coordinates in the normalized impedance plane and in the reflection coefficient plane
are related as follows (see also: definition of matched-circuit (converted) impedances):
Z / Z
0
= (1 + ) / (1 – )
From this equation it is easy to relate the real and imaginary components of the
complex resistance to the real and imaginary parts of
:
[
]
,
)
Im(
)
Re(
1
)
Im(
)
Re(
1
)
/
Re(
2
2
2
2
0
+
=
=
Z
Z
R
[
]
,
)
Im(
)
Re(
1
)
Im(
2
)
/
Im(
2
2
0
+
=
=
Z
Z
X
in order to deduce the following properties of the graphical representation in a Smith
chart:
E
Real reflection coefficients are mapped to real impedances (resistances).
E
The center of the plane ( = 0) is mapped to the reference impedance Z
0
,
whereas the circle with | | = 1 is mapped to the imaginary axis of the Z plane.
E
The circles for the points of equal resistance are centered on the real axis and
intersect at Z = infinity. The arcs for the points of equal reactance also belong to
circles intersecting at Z = infinity (open circuit point (1,0)), centered on a straight
vertical line.
