The Smith Chart is drawn by superimposing these two types of circles. The circles with centers at and radii = 1/(r+1) are known as constant resistance circles as shown in following fig.The circles with centers at (1, 1/x) and radii = 1/x are known as constant reactance circles as shown in following fig. Separating the real and imaginary part, we getįurher simplifying the above two equations, we can re-write them in standard circle equation form asĢ + (v - 0)2 = 2 with center at and radius = 1/(r+1) and Therefore, the possible values of Γ will remain within the unit circle. Γ = u + jv = Rejθ, where R is the radius and θ is the angle of incidence.įrom the last two equation, we can see that there is one-to-one correspondence and for every Z we can obtain a unique Γ. 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.
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