![]() Impedance ↔ admittance z ↔ y = 1/z Any point reflected through the centre point converts an impedance to an admittance and vice versa. #Transmission line impedance matching smith chart generatorTwo scales on the periphery (in wavelengths): -Wavelengths towards generator (WTG scale), clockwise sense -Wavelengths towards load (WTL scale), anticlock sense Note also that a complete turn around the Smith chart corresponds to a total length of λ/2. Some Smith charts have a number of scales at the bottom of the chart for measuring the reflection coefficient magnitude and others. Hon Tat Huiġ.2 Reading on Smith chart 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 |Γ|. This circle is also known as the constant VSWR circle. Hence, Γ can be obtained from ΓL by moving clockwise along a constant circle on the Smith chart with a radius |ΓL| through an angle -2kℓ which is equivalent to ℓ/λ wavelengths measured towards the generator on the periphery of the Smith chart. Γ (A ) = Γ = Γ L e − j 2 kA Γ = ΓL Hon Tat Hui Hon Tat Huiįor example, All points on this circle have a S = r =3Įxample 1 Plot the following impedances on to the Smith chart.ġ.1 Smith chart and transmission lines ΓL This circle is known as the constant VSWR circle. Since all points on the dotted black circle have the same |Γ|, they must also have the same S. Then, 1+ Γ 1+ Γ =S 1− Γ 1− Γ But when the angle of Γ is zero, 1+ Γ =z=r 1− Γ Thus, the value of S is same as r when the angle of Γ is zero and can be read out directly from the Smith chart by noting the r value (S = r). When the angle of Γ is zero, Γ is real and Γ =|Γ|. Hon Tat HuiĪ point in the Smith chart gives the values of the normalized impedance z and the complex reflection coefficient Γ 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 Γ. The last two equations of r and x define two families of circles in the complex plane of reflection coefficient Γ. In terms of the normalized impedance z (drop the ℓ dependence), we can write: z −1 Γ = Γ re + jΓim z +1ġ + Γ (1 + Γ re ) + jΓim = z = r + jx = 1 − Γ (1 − Γ re ) − jΓim Transmission Lines – Smith Chart & Impedance Matching 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. Transmission Lines – Smith Chart & Impedance Matching 1 Smith Chart Smith chart is a graphical plot of the normalized resistance and reactance functions in the complex reflection-coefficient plane. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |