The loads are now matched and the matching network is displayed.
The corresponding series capacitor value will be displayed in the lower right. Meet the characteristic impedance of the source Z 0 of 50Ω and stop. You will notice that the dot that now follows a different trajectory (the constant resistance circle) in the counter-clockwise direction. The corresponding inductor value will be displayed in the Network Schematic.Ĭlick to select the series capacitor from the palette. Move up to the contant resistance cycle and click to stop.
You will notice a dot that moves counter-clockwise on the smith chart. Start from the load of 100Ω and move the cursor up from the diamond marker. This inductor will appear in the Network Schematic. Instead, we need to use lossless components in the matching network.Ĭlick to select the shunt inductor from the palette on the left. We do not want to use a simple 100Ω resistor in parallel with the load to do this matching because then half the source power would be dissipated by the matching network. You will see the source and load impedances appear on the smith chart as a circle and diamond marker respectively. Similarly, select the source and enter the value of 50+j*0. Select the load in the lower-right Network Schematic area and enter the value of 100+j*0. Let characteristic impedance Z 0 stay at 50Ω. Match a source with a characteristic impedance of 50Ω to a 100Ω load at 100MHz.Įnter the frequency of 100MHz in the box at the top-left. Therefore there are no voltage peaks on the transmission line.Using Agilent ADS Smith Utility for Impedance Matching Therefore, the input impedance is independent of the length of transmission line.ģ. The input impedance remains constant at the value Z0. This corresponds to the left-most point in the Smith chart. Voltage minima occur when the angle of the relfection coefficient (()) = -2(n+1) (n = 0, 1, 2, ). This corresponds to the right-most point in the Smith chart. Voltage maxima occur when the angle of therelfection coefficient (()) = -2n (n = 0, 1, 2, ). See animation Transmission Line Impedance Calculation Because:( ) ( ) ( )Īny point reflected through the centre point converts an impedance to an admittance and vice versa.īottom Half: capacitive reactance, XC = 1/CorĮxample 2Use Smith chart to find the input impedance Zin looking at the input of a transmission line. Note also that a complete turn around the Smithchart corresponds to a total length of /2.
Two scales on the periphery (in wavelengths):-Wavelengths towards generator (WTG scale),Ĭlockwise sense-Wavelengths towards load (WTL scale), Some Smith charts have a number of scales at the bottom of the chart for measuring the reflection coefficient magnitude and others. Several scales around the outside of the Smith chart are used to determine the distance along the line. All the points on this circle has the same S and same ||. This circle is also known as the constant VSWR circle.
Hence, can be obtained from L by moving clockwise along a constant circle on the Smith chart with a radius |L| through an angle -2k which is equivalent to / wavelengths measured towards the generator on the periphery of the Smith chart. This circle is known as the constant VSWR circle.Īll points on this circle have a S = r =3Įxample 1Plot the following impedances on to the Smith chart. Since all points on the dotted black circle have the same ||, they must also have the same S. Thus, the value of S is same as r when the angle of is zero and can be read out directly from the Smith chart by noting the r value (S = r). When the angle of is zero, is real and =||.
Ī point in the Smith chart gives the values of the normalized impedance z and the complex reflection coefficient at the same point on a transmission line. The Smith char is the superposition of these two families of circles together in the complex plane of reflection coefficient. The last two equations of r and x define two families of circles in the complex plane of reflection coefficient.
In terms of the normalized impedance z (drop the dependence), we can write: It is also a useful tool in impedance matching circuit design. Smith chart is convenient for transmission line and circuit calculations. It is a graph showing both the normalized impedance and the reflection coefficient. Smith chart is a graphical plot of the normalized resistance and reactance functions in the complex reflection-coefficient plane. Transmission Lines Smith Chart & Impedance Matching Hon Tat Hui Transmission Lines Smith Chart & Impedance Matching