Properties of Smith Chart

1. Mrs.R.Chitra, AP/ECE,
Ramco Institute of Technology,
Rajapalayam

2.  It is developed by P.H.Smith of Bell Laboratory.
 Smith chart is a valuable graphical tool for solving radio
frequency transmission line problems very easily which
would be difficult to solve by analytical methods.
 Design of dissipation line can be simplified significantly
by drawing smith chart.
 It is superposition of two sets of R-circle and X-circle.
 resistive and reactive components are in circular form.

3.  Main objective is that the values of resistive and
reactive components are represented in the rectangular
form which are extended to infinity.
 But, in the smith chart, the infinite resistive and
reactive components are transferred to an area inside a
circle in circular form.
 Smith chart is basically a polar plot of reflection co-
efficient K expressed in terms of normalized
impedance.

6.  Smith chart my be used for impedances as well as
for admittances.
 It consists constant ri -circles and constant xi-circles
super positioned on one chart.
 The normalized values of ri and xi are given by
ri= R/Ro & xi=X/Ro
 Constant ri circles have their centers on the
horizontal axis (u-axis) and constant xi circles have
their centers on the vertical axis (v-axis)

7.  It is based on the assumption that,
Maximum magnitude of u+jv is the maximum
magnitude value of K (i.e. unity).
So it is possible to locate all possible values of
impedances inside the outer circle of unit
radius.
 For properly terminated and any length, the impedance
is represented by the point(1,0) as center of the smith
chart.

8. Smith chart properties

9.  Horizontal line passing through the centre of the smith chart
represents real axis or ri-axis for impedance or gi -axis for
admittance plot.
 To the extreme left of the chart, along the ri-axis, ri =0 & xi =0
(Z=0+j0) which indicates zero impedances at load point or the
short circuit condition.
 To the extreme right of the chart, along the ri -axis, ri =∞ & xi
= ∞ (Z= ∞ +j ∞) which indicates infinite impedances at load
point or the open circuit condition.
 Outer rim of the chart is scaled into either degrees or
wavelengths with an arrow which indicates the electrical
length of the line.
 Outer circle is called as βs scale which indicates the electrical
length of the line.

10.  A complete revolution of 360ᵒ represents a distance of
λ/2 on the line.
 Clockwise movements indicates the travel toward the
generator from the load along the line.
 Anticlockwise movements indicates the travel toward
the load from the generator along the line.

11.  Three scales are provided.
 Outermost scale are useful in determining the distance
from the generator in wavelengths, along the line.
 Next scale are useful in determining the distance from
the load in wavelengths, along the line.
 Innermost scale is used to determine the angle of the
reflection coefficient in degrees.

12.  For impedance purpose, the inductive reactance are
above ri -axis while the capacitive reactance are below
ri =axis
 For admittance calculations,
1) ri -axis becomes gi -axis
2) xi -axis becomes bi axis
3)extreme left of the chart represents open
circuit.
4)extreme right of the chart represents short
circuit.
 Voltage maxima occur where Zin(max) is located which
can be represented at right side of the center of the
chart.
 Voltage minima occur where Zin(min) is located which
can be represented at left side of the center of the chart.

13.  John D Ryder, “Networks, lines and fields”, 2nd
Edition, Prentice Hall India, 2010.
 E.C.Jordan and K.G. Balmain, “Electromagnetic Waves
and Radiating Systems”,Prentice Hall of India, 2006.
 G.S.N Raju "Electromagnetic Field Theory and
Transmission Lines”, Pearson Education, First edition
2005.