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Parameter Equations and Smith Chart Applications in Circuit Theory

Lecture 9 of course 16.360 explores parameter equations, focusing on input impedance and the application of Smith charts in circuit analysis. Key concepts such as SWR (standing wave ratio), voltage maxima and minima, and impedance to admittance transformations are discussed. An example is provided where a 50-Ω lossless line terminated with a load impedance of (Z_L = 25 + j50 , Omega) is analyzed. The lecture further delves into the calculation of voltage reflection coefficients, SWR, and distances from voltage maxima and minima, enhancing comprehension of transmission line theory.

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Parameter Equations and Smith Chart Applications in Circuit Theory

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  1. 16.360 Lecture 9 • Last lecture • Parameter equations • input impedance

  2. 16.360 Lecture 9 Parameter equations Unit circuit . Short Circuit load B Open Circuit load

  3. 16.360 Lecture 9 Parameter equations

  4. 16.360 Lecture 9 An example Smith Chart Input impedance Wavelength toward generator (WTG) Smith Chart

  5. 16.360 Lecture 9 An example find Zin (-0.1) Smith Chart Constant || circle, SWR Circle

  6. 16.360 Lecture 9 Today: • SWR, Voltage maxima and minima • Impedance to Admittance transformations

  7. + + |V(z)| |V(z)| |V0| [1+ | |], |V0| [1 - | |], = = max min 16.360 Lecture 9 SWR, voltage maximum and minimum If Smith Chart Recall: when 2z + r = 2n. when 2z + r = (2n+1).

  8. 16.360 Lecture 9 An example Smith Chart Impedance to Admittance transformations G: conductance, B, susceptance

  9. 16.360 Lecture 9 Normalized admittance z and y are directly opposite each other on Smith Chart

  10. 16.360 Lecture 9 An example A 50- lossless line is terminated in a load ZL = (25+j50). Use the smith chart to find a) voltage reflection coefficient, b) the voltage standing-wave ratio, c) the distances of the first voltage maximum and first voltage minimum from the load, d) the input impedance of the line, given the line is 3.3, and e) the input admittance of the line. Smith Chart

  11. 16.360 Lecture 9 Next lecture • Impedance matching

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