It is possible to deal with such problems on an extension of the normally used Smith chart. provided that there is attenuation and the line’s γ has a real part as then tanhγℓ goes to one).Ĭan the Smith Chart be used for lossy transmission line?Ībstract: It is shown that under certain circumstances the magnitude of the voltage reflection coefficient Γ can exceed unity even for a passive load. Note that Zin is a quasi-periodic function of ℓ and approaches Z0 for a long lossy line (i.e. This equation is also known as the lossy telegrapher’s equation. What is the input impedance of a lossy line?ģ Input Impedance of a Lossy Line. Transmission Lines (4.19) (4.20) A lossless line has these properties: (a) it does not dissipate any power, (b) it is non-dispersive (i.e., the phase constant varies linearly with frequency ω, or the velocity vp = ω/β is independent of frequency), and (c) its characteristic impedance Z0 is real. How do I know if my transmission line is lossless? As such, it allows calculations of all parameters related to transmission lines as well as impedances in open space, circuits, and the like. The Smith chart is a chart of normalized impedances (or admittances) in the reflection coefficient plane. What is Smith chart in transmission lines? This is opposite to a lossless transmission line, where the speed of wave propagation is the same for all frequencies.
#Smith chart lossy line series
(Note that the lengths specified in the following table are in cm but the propagation constant is defined in per-meter units.) Name L (cm) ZR (12) Abdou Issa 43 13 + j20 Ajani 69 12.5+j30 Aliyu 42 17.5+j45 Andrews 66 20+ j37.5 Bergman 39 25+j55 Biratu 64 40 + 365 Caldwell 36 45 +90 Chaves 45 13 + 20 Colston 70 12.5+j30 Dansoko 43 17.5 +45 Field 68 20+ j37.5 Fondja Tchankou 41 25+j55 Golatt 66 40 + 365 Justice 37 45 + 290 Kenney 69 13 + 20 Krakowski 43 12.5 + 30 Morocho 68 17.5+45 Nemaga 40 20+ 137.5 Niraula 65 25+j55 Ntyame 38 40 + 365 Scott 62 45 +90 Senawo 71 13 + 20 Sethi 44 12.5+j30 Siyapbie Soh 69 17.5 + j45 Takahashi 42 20+ j37.5 Tsui 67 25 + 55 Walker 40 40 + 365 | $9582 Zinolens) Ω If it is not clear exactly how you obtained the values of Tin and Zin from the Smith Chart, you will not receive credit for those results.Lossy Transmission Lines A lossy transmission line consists of an appreciable value of series resistance and shunt conductance where different frequencies travel at different speeds.
Note - To receive credit for each part of this problem, you MUST UTILIZE a Smith Chart in order to solve each of the impedance and reflection coefficient values and, when utilizing that Smith Chart, you MUST completely LABEL every point or value that you either plot on or read from the Smith Chart and/or its accompanying scales. Zin(los), of the lossy line (in rectangular form), and c) the actual reflection coefficient, Tin(lenay), (in polar form) seen at the input (sending-end) of the lossy line. Zin(lossless), of the line (in rectangular form) if the losses are ignored. Determine (using a Smith Chart): a) the input impedance. If the line has length L and is terminated by a load having an impedance Zr, the values of which are specified in the table shown below (based on your last name).
Problem #7) Given a lossy transmission line that has the following characteristics when supplied by a 450 MHz source: Z.
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