System Overview
R&S
®
ZVA
71Getting Started 1145.1090.62 ─ 13
Smith chart construction
In a Smith chart, the impedance plane is reshaped so that the area with positive resist-
ance is mapped into a unit circle.
The basic properties of the Smith chart follow from this construction:
●
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 hori-
zontal axis and the outer circle, the impedance is zero (short) and infinity (open).
●
The outer circle corresponds to zero resistance (purely imaginary impedance).
Points outside the outer circle indicate an active component.
●
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 Γ (e.g. S
11
, S
22
), then the
unit Smith chart can be used to read the normalized impedance of the DUT. The coor-
dinates 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 + Γ) / (1 – Γ)
From this equation it is easy to relate the real and imaginary components of the com-
plex resistance to the real and imaginary parts of Γ:
,
)Im()Re(1
)Im()Re(1
)/Re(
2
2
22
0
ZZR
2
2
0
)Im()Re(1
)Im(2
)/Im(
ZZX
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