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Smith Chart Indian Institute of Technology Delhi(史密斯圆图德里印度科技学院的)
Transmission Lines
Smith Chart
The Smith chart is one of the most useful graphical tools for high
frequency circuit applications. The chart provides a clever way to
visualize complex functions and it continues to endure popularity
decades after its original conception.
From a mathematical point of view, the Smith chart is simply a
representation of all possible complex impedances with respect to
coordinates defined by the reflection coefficient.
Im(Γ )
The domain of definition of the
reflection coefficient is a circle of
1
Re(Γ ) radius 1 in the complex plane. This
is also the domain of the Smith chart.
© Amanogawa, 2000 - Digital Maestro Series 137
Transmission Lines
The goal of the Smith chart is to identify all possible impedances on
the domain of existence of the reflection coefficient. To do so, we
start from the general definition of line impedance (which is equally
applicable to the load impedance)
V( d) 1+ Γ ( d)
( ) = =
Z d Z0
I (d ) 1− Γ (d )
( ) Re , Im
This provides the complex function Z d = f { (Γ ) (Γ )} that
we want to graph. It is obvious that the result would be applicable
only to lines with exactly characteristic impedance Z0.
In order
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