System Overview
R&S
®
ZVA
71
Getting 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
2
2
0
Z
Z
R
2
2
0
)
Im(
)
Re(
1
)
Im(
2
)
/
Im(
Z
Z
X
Screen Elements
