**3.1 Important features on a Smith chart**

On a Smith chart there are some important points, lines and contours that should be mentioned. In Figure 3 some of these important features are indicated. The outer circle is the locus of the pure reactive impedances, that is, those with zero resistance. The horizontal axis is the locus of the real impedances. The left radius is the locus of the resistances less than *Z*<sup>0</sup> for which the reflection coefficient has a phase of 180º. The left extreme of this radius is the zero resistance and zero reactance point, that is, the short circuit point (SC). The right radius is the locus of the resistances greater than *Z*0 for which the reflection coefficient has a phase of 0º. The right extreme of this radius is the infinite resistance and infinite reactance point, that is, the open circuit point (OC).

For a lossless transmission line terminated in a load with a reflection coefficient *<sup>L</sup>* , the circle with radius *<sup>L</sup>* (known as the circle or S circle), is the locus of all impedances appearing along the line, normalized to the characteristic impedance *Z*0 of the line. These impedances can be obtained moving along the line either toward the load (counter

Using the Smith Chart in an E-Learning Approach 105

Fig. 4. Typical Smith chart. With permission of Spread Spectrum Scene, http://www.sss-

The Smith chart simplifies transmission line analysis, and is still used today in most modern textbooks and courses in electrical engineering. It promotes a better understanding of the problem being solved. And such an understanding might be relevant for the interpretation

mag.com/pdf/smithchart.pdf.

clockwise) or toward the generator (clockwise). When moving along the circle, every crossing of the left horizontal radius corresponds to a voltage minimum (therefore a current maximum) in the line and to a real impedance less than *Z*<sup>0</sup> . Similarly, every crossing of the right horizontal radius corresponds to a voltage maximum (therefore a current minimum) in the line and to a real impedance greater than *Z*<sup>0</sup> .

In Figure 3a) some important features of when the Smith chart is used as an impedance chart are pointed out.

In the resolution of some problems, it is more convenient to work with admittances than with impedances. In these cases the Smith chart can be effectively used as an admittance chart. In this case the *r* circles and the *x* curves should be seen as *g* circles and *b* curves respectively. Also the upper half of the chart now corresponds to capacitive susceptances given by positive values of *b* and, the lower half of the chart corresponds to inductive susceptances given by negative values of *b*. In Figure 3b) some important features are indicated when the Smith chart is used as an admittance chart.

It is easy to transform a normalized impedance *z* in the corresponding admittance *y*. It will be located on the circle in the opposite side of the diameter that passes through *z*.

Fig. 3. Some important features of a Smith chart. a)- When used as an impedance chart. b)- When used as an admittance chart.

Nowadays, the Smith chart appears in several different types. One of them is shown in Figure 4. The main difference between this chart and the basic Smith chart shown in figure 2 is the existence of three scales around the periphery.

The outermost scale is used to determine distances in wavelengths toward the generator and the next scale is used to determine distances in wavelengths toward the load. The innermost scale is a protractor (in degrees) and is primarily used to determine the phase of the reflection coefficient and the phase of the transmission coefficient. It can also be used to determine distances, toward the load or toward the generator, expressed in degrees bearing in mind that a distance of /2 corresponds to 360°.

The Smith chart illustrated in figure 4 has also other auxiliary scales useful for the determination of some parameters like for example, the VSWR, the amplitudes of the reflection and transmission coefficients, the return loss in dB etc.

clockwise) or toward the generator (clockwise). When moving along the circle, every crossing of the left horizontal radius corresponds to a voltage minimum (therefore a current maximum) in the line and to a real impedance less than *Z*<sup>0</sup> . Similarly, every crossing of the right horizontal radius corresponds to a voltage maximum (therefore a current minimum) in

In Figure 3a) some important features of when the Smith chart is used as an impedance

In the resolution of some problems, it is more convenient to work with admittances than with impedances. In these cases the Smith chart can be effectively used as an admittance chart. In this case the *r* circles and the *x* curves should be seen as *g* circles and *b* curves respectively. Also the upper half of the chart now corresponds to capacitive susceptances given by positive values of *b* and, the lower half of the chart corresponds to inductive susceptances given by negative values of *b*. In Figure 3b) some important features are

It is easy to transform a normalized impedance *z* in the corresponding admittance *y*. It will

a) b)

Fig. 3. Some important features of a Smith chart. a)- When used as an impedance chart. b)-

Nowadays, the Smith chart appears in several different types. One of them is shown in Figure 4. The main difference between this chart and the basic Smith chart shown in figure 2

The outermost scale is used to determine distances in wavelengths toward the generator and the next scale is used to determine distances in wavelengths toward the load. The innermost scale is a protractor (in degrees) and is primarily used to determine the phase of the reflection coefficient and the phase of the transmission coefficient. It can also be used to determine distances, toward the load or toward the generator, expressed in degrees bearing

The Smith chart illustrated in figure 4 has also other auxiliary scales useful for the determination of some parameters like for example, the VSWR, the amplitudes of the

be located on the circle in the opposite side of the diameter that passes through *z*.

the line and to a real impedance greater than *Z*<sup>0</sup> .

indicated when the Smith chart is used as an admittance chart.

chart are pointed out.

When used as an admittance chart.

is the existence of three scales around the periphery.

in mind that a distance of /2 corresponds to 360°.

reflection and transmission coefficients, the return loss in dB etc.

Fig. 4. Typical Smith chart. With permission of Spread Spectrum Scene, http://www.sssmag.com/pdf/smithchart.pdf.

The Smith chart simplifies transmission line analysis, and is still used today in most modern textbooks and courses in electrical engineering. It promotes a better understanding of the problem being solved. And such an understanding might be relevant for the interpretation

Using the Smith Chart in an E-Learning Approach 107

a)

b)

Fig. 5. Inputting a reflection coefficient. Display given by *SmithChart\_InputRho\_Eng\_FV.m*.

of the simulation results given by commercial software about antennas and microwave devices. Most modern computer based automatic network analyzers rely on the Smith chart for data display.

This chart is a unique diagram which has been used nearly for ninety years and we believe that it will be in use for many years to come not only as a pedagogically perfect analogue display, but also as an aid to professionals in obtaining quick answers to many line problems which they meet.
