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EE 4002
RF Circuit Design
Chapter 3
Smith Charts
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View Full Document History of the Smith Chart
•
Developed in 1930’s by P.H. Smith as a way to plot the
reflection coefficient and line impedances.
•
Today it is widely used to describe passive and active
RF/MW components and systems.
•
Network Analyzers have the option to show
measurements in a smith chart format. CAD Programs
use smith charts for many purposes:
–
Display measured circuit impedance
–
Design matching networks
–
Real time CAD tuning
–
Computation of noise figures
–
Gain
–
Plot stability circles
Example 32:
Finding the input impedance of a terminated TL
using derived equations
is connected to a 50 Ω transmission
line of 2 cm length, operated at 2 GHz.
Find
assuming
the phase velocity to be 50% of the speed of light
30
60
L
Z
j
=
+
Ω
in
Z
71.56
0
0
0
30
60
50
0.2
0.6
2 5
30
60
50
j
L
L
Z
Z
j
j
e
Z
Z
j

+

Γ =
=
=
+
=
+
+
+
o
2
0
( )
L
j
j
d
d
e
e
θ
β

Γ
= Γ
o
2
2
2
(.02)
0.5
3.35 rad
191.99
f
d
c
π
=
=
=
71.56
191.99
120.43
( )
2 5
2 5
j
j
j
d
e
e
e


Γ
=
=
o
o
o
Notice
only the angle changes
as we move down the TL.
The amount it
changes is
twice the electrical length
of the
line, or
0
( )
d
Γ
= Γ
0
1
( )
1 0.32
0.55
( )
50
14.7
26.7
1
( )
1
0.32
.55
in
d
j
Z
d
Z
j
d
j
+ Γ


=
=
=

Ω
 Γ
+
+
2
d
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0
0
0
0
0
0
L
j
L
r
i
L
Z
Z
j
e
Z
Z
θ

Γ =
= Γ + Γ = Γ
+
The reflection coefficient is a complex number, which can be plotted in a
polar coordinate system:
(a)
0 (short circuit)
(b)
(open circuit)
(c)
50
(d)
16.67
16.67
(e)
50
150
L
L
L
L
L
Z
Z
Z
Z
j
Z
j
=
=
Ω
=

Ω
=
+
Ω
For a transmission line with a line
impedance of
, we can plot the
Reflection coefficient.
0
50
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This note was uploaded on 01/31/2012 for the course EE 4002 taught by Professor Scalzo during the Fall '06 term at LSU.
 Fall '06
 Scalzo
 Impedance

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