Finding input impedance with smith chart

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Discussion Overview

The discussion revolves around finding the input impedance of a 50 Ω transmission line that is 3λ/8 long and terminated with a 10 Ω load, utilizing a Smith chart for analysis. The scope includes homework-related problem-solving and technical reasoning regarding the use of the Smith chart.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant presents a homework problem involving the calculation of input impedance using a Smith chart and provides relevant equations.
  • Another participant questions the placement of the imaginary part on the Smith chart, indicating confusion about the chart's layout.
  • A different participant suggests that the input impedance should be found directly on the Smith chart rather than through numerical computation, implying a preference for graphical analysis.
  • Further, a participant offers guidance on how to proceed with the Smith chart, detailing the process of entering the chart at the normalized load impedance and rotating to account for the transmission line length.
  • There is an acknowledgment that explaining the Smith chart process through text can be challenging, suggesting that visual aids may be more effective.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the use of the Smith chart, with some confusion evident. There is no consensus on the best approach to find the input impedance, as different methods and interpretations are discussed.

Contextual Notes

Participants have not fully resolved the confusion regarding the graphical representation of the Smith chart and the specific steps for finding the input impedance. The discussion reflects differing levels of familiarity with the Smith chart methodology.

Who May Find This Useful

Students and individuals interested in electrical engineering, particularly those learning about transmission lines and impedance matching using Smith charts.

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Homework Statement


Find an input impedance of a 50 Ω transmission line of length transmission line of length 3λ/8
terminated with a load of 10 Ω.


Homework Equations


Zl'=(Zl/Zc)
Zin(L)=(Zl-jtan(kL))/(1+jZltan(kL))


The Attempt at a Solution


I have uploaded my attempt how far off am I?
 

Attachments

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Ok so 0 on the smith chart is the line which goes down the middle and R=0 is at the final outer 0 but where is the imaginary part 0.02?
 
Look at the values on the outer ring. The imaginary lines will extend from there. Why are you looking for the input impedance on the smith chart after computing it? Normally if you are asked to find the input impedance using the smith chart you do not actually compute the input impedance numerically, you actually do the entire analysis on the smith chart.
 
Last edited:
Ok so how should I proceed? I am confused do you have any more hints
 
To find the input impedance using the smith chart you want to enter the smith chart at the normalized load impedance. You then rotate about the point where the reflection coefficient is zero clockwise until your starting length is increased by 3λ/8. The starting length will be the outer point that is associated with a straight line segment extending from the centre of the smith chart (zero reflection) and passing through your normalized load impedance.

It is rather tedious to try and explain this process via words. Graphical demonstrations are much easier to get the point across.
 

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