Smith Chart


Dear friends, today we will discuss about the basics of Smith Chart or construction of Smith Chart. Let us understand, what is Smith Chart:

  • Smith chart is a graphical method to solve transmission line problems.
  • It is a graph between resistance component (R/Z0) (or conductance component, C/Y0) and reactance component (±iX/Z0).

Where R is normalized resistance,

Z0 is Characteristic impedance and

X is normalized reactance

  • In other words, it is a graphical plot of normalized resistance and reactance in the reflection coefficient plane. So it gives the indication of impedance at transmission line as one moves along the line.
  • We will discuss it further also.
  • Impedances are always normalized with respect to characteristic impedance, Z0 in Smith chart to avoid construction of one chart for each Z0.
  • Thus normalized load impedance is given by:
  • Zn = ZR/Z0 = R +iX

Construction of Smith chart

Smith chart consists of two types of circles:

1.) The constant R- circles:

Smith chart is basically an impedance chart containing two set of lines. The first set of lines referred to as Constant Resistance lines form circles, all tangent to each other at the right hand of horizontal diameter. These circles are known as constant resistance, R circles.

Each circle represents a fixed resistance that is all points on a particular resistance circle represent the same resistance.

The resistance values which these constant resistance circles represent are marked on the horizontal diameter at the points of intersection of these circles and the horizontal line.

The outermost resistance circle cutting the horizontal line on the extreme left represents zero resistance while the circle cutting the horizontal line on the right  extreme right represents infinite resistance.

The Constant X-circles

There is another set of lines called constant Reactance lines. These lines are arcs of circles, all tangent to each other on the right hand extreme of horizontal diameter and also tangent to this line. These circles are known as constant reactance, X circles.

The lines in the upper half represent positive reactances while those in the lower half represent negative reactances.

The reactances have also been normalized with respect to Z0.

The complete Smith chart is obtained by the superposition of the two sets of X-circles and R- circles.

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