1 / 18

Prof. David R. Jackson Dept. of ECE

ECE 5317-6351 Microwave Engineering. Fall 2011. Prof. David R. Jackson Dept. of ECE. Notes 2. Smith Charts. Generalized Reflection Coefficient . Recall,. Generalized reflection Coefficient:. Generalized Reflection Coefficient (cont.) . For. Proof:.

shlomo
Download Presentation

Prof. David R. Jackson Dept. of ECE

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ECE 5317-6351 Microwave Engineering Fall 2011 Prof. David R. Jackson Dept. of ECE Notes 2 Smith Charts

  2. Generalized Reflection Coefficient Recall, Generalized reflection Coefficient:

  3. Generalized Reflection Coefficient (cont.) For Proof: Lossless transmission line ( = 0)

  4. Decreasing l (toward load) l Increasing l (toward generator) Complex  Plane Lossless line

  5. Impedance (Z) Chart Define Substitute into above expression for Zn(-l ): Next, multiply both sides by the RHS denominator term and equate real and imaginary parts. Then solve the resulting equations for R and Iin terms of Rn and Xn. This gives two equations.

  6. Impedance (Z) Chart (cont.) 1) Equation #1: I Equation for a circle in the  plane R

  7. Impedance (Z) Chart (cont.) 2) Equation #2: I Equation for a circle in the  plane: R

  8. Impedance (Z) Chart (cont.) Short-hand version Xn= 1 Rn= 1 Xn= -1

  9. Impedance (Z) Chart (cont.) Xn= 1  plane Rn= 1 Xn= -1

  10. Admittance (Y) Calculations Note: Define: Conclusion: The same Smith chart can be used as an admittance calculator. Same mathematical form as for Zn:

  11. Admittance (Y) Calculations (cont.) Bn= 1 plane Gn= 1 Bn= -1

  12. Impedance or Admittance (Z or Y) Calculations The Smith chart can be used for either impedance or admittance calculations, as long as we are consistent.

  13. Admittance (Y) Chart As an alternative, we can continue to use the original  plane, and add admittance curves to the chart. Compare with previous Smith chart derivation, which started with this equation: If (RnXn) = (a, b) is some point on the Smith chart corresponding to  = 0, Then (GnBn) = (a, b) corresponds to a point located at  = - 0(180o rotation). • Rn= acircle, rotated 180o, becomes Gn= acircle. • and Xn= bcircle, rotated 180o, becomes Bn= bcircle. Side note: A 180o rotation on a Smith chart makes a normalized impedance become its reciprocal.

  14. Admittance (Y) Chart (cont.)  plane

  15. Admittance (Y) Chart (cont.) Short-hand version Bn= -1 Gn= 1 Bn= 1  plane

  16. Impedance and Admittance(ZY) Chart Short-hand version Bn= -1 Xn= 1 Gn= 1 Rn= 1 Xn= -1 Bn= 1  plane

  17. Standing Wave Ratio The SWR is given by the value of Rn on the positive real axis of the Smith chart. Proof:

  18. Electronic Smith Chart At this link http://www.sss-mag.com/topten5.html Download the following .zip file smith_v191.zip Extract the following files smith.exe smith.hlp smith.pdf This is the application file

More Related