The above equation can also be written as Γ = / for r lies between 0 and ∞, x lies between -∞ and +∞. Γ = (ZL-1) / (ZL+1) as Zo takes constant values such as 50Ω, 100Ω, etc. Therefore, Reflection coefficient can expressed as Normalized impedance, Z = ZL/ Zo = r+ jx, where r = R / Z0 and x = X / Z0. This is because the behavior of the transmission line depends on load impedance as well as characteristic impedance. Normalized impedance is used for plotting on Smith chart.

Γ = (ZL - Zo) / ( ZL + Zo ) where, ZL is load impedance and Zo is the characteristic impedance of transmission line, a constant. Therefore, from the fig., gamma can be expressed as, The amount of reflected wave depends upon the mismatching of the source and load impedances. The ratio of the voltage of reflected wave and the voltage of incident wave is known as the reflection coefficient. If there is impedance mismatching, part of the energy in the incident wave is reflected back giving rise to a standing wave. transmitter to antenna or antenna to receiver), the impedance of source must be equal to the impedance of load. While transferring the RF waves on a finite transmission line, for maximum power transfer from source to load (i.e. These are the impedance matching circuits. Transmission lines are the circuits that deliver power from a transmitter to an antenna and from an antenna to a receiver.

Calculation of the length of a short circuited piece of transmission line to provide a required capacitive or inductive reactance.īefore plotting on a Smith Chart we need to study a few terms such as transmission line, characteristic impedance, standing wave, etc.

Impedance calculations on any transmission line, on any load.

Admittance calculations on any transmission line, on any load.The important applications of a Smith Chart are as follows: The complete circle of the Smith Chart represents a half wavelength along the straight line. The horizontal axis represents the normalized resistance and the normalized line reactance is shown on the outer edge of the circles. The figure to the right shows the Smith Chart. One is the set of complete circles whose centers lie on the straight line and the other one is the set of two arc circles which lie on the either sides of the straight line. It consists of two sets of circles for plotting various parameters of mismatched transmission lines. The Smith Chart is the most used tool for microwave engineers to visualize complex-valued quantities and calculate the mapping between them. It is the circular plot of the characteristics of microwave components. The Smith Chart is the graphical representation of a complex mathematical equation.

Use smithchart rf toolbox