Concepts and Features
R&S
®
ZNC
39
User Manual 1173.9557.02 ─ 13
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 horizontal
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 neg-
ative (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 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 +
Γ
) / (1 –
Γ
)
From this equation it is easy to relate the real and imaginary components of the complex
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
According to the two equations above, the graphical representation in a Smith chart has
the following properties:
●
Real reflection coefficients are mapped to real impedances (resistances).
Screen Elements
