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R&S ZVA Series User Manual

R&S ZVA Series
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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
Screen Elements

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R&S ZVA Series Specifications

General IconGeneral
BrandR&S
ModelZVA Series
CategoryMeasuring Instruments
LanguageEnglish

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