R&S ZVB - Page 54

R&S
®
ZVA / R&S
®
ZVB / R&S
®
ZVT System Overview
Screen Elements
Operating Manual 1145.1084.12 – 30 39
Smith Chart
The Smith chart is a circular diagram that maps the complex reflection coefficients S
ii
to normalized
impedance values. In contrast to the polar diagram, the scaling of the diagram is not linear. The grid lines
correspond to points of constant resistance and reactance.
 Points with the same resistance are located on circles.
 Points with the same reactance produce arcs.
The following example shows a Smith chart with a marker used to display the stimulus value, the complex
impedance Z = R + j X and the equivalent inductance L (see marker format description in the help
system).
A comparison of the Smith chart, the inverted Smith chart and the polar diagram reveals many
similarities between the two representations. In fact the shape of a trace does not change at all if the
display format is switched from Polar to Smith or Inverted Smith – the analyzer simply replaces the
underlying grid and the default marker format.
Smith chart construction
In a Smith chart, the impedance plane is reshaped so that the area with positive resistance 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 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 negative
(capacitive) reactive components of the impedance, respectively.