The Smith Chart
-
Upload
beatrice-owens -
Category
Documents
-
view
162 -
download
15
description
Transcript of The Smith Chart
![Page 1: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/1.jpg)
The Smith Chart
• Developed in 1939 by P. W. Smith as a graphical tool to analyze and design transmission-line circuits
• Today, it is used to characterize the performance of microwave circuits
![Page 2: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/2.jpg)
Complex Plane
![Page 3: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/3.jpg)
Smith Chart Parametric Equations
Equation for a circle
![Page 4: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/4.jpg)
Smith Chart Parametric Equations
rL circles
xL circles
rL circles are contained inside the unit circle
Only parts of the xL circles are contained within the unit circle
![Page 5: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/5.jpg)
Complete Smith Chart
rL Circles
Positive xL Circles
Negative xL Circles
![Page 6: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/6.jpg)
Reflection coefficient at the load
![Page 7: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/7.jpg)
Input ImpedanceConstant SWR circle (standing-wave ratio)
![Page 8: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/8.jpg)
S: standing-wave ratio
11
0
0
rr
r
0iFor
11
SS
![Page 9: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/9.jpg)
Maxima and Minima
![Page 10: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/10.jpg)
Impedance to Admittance Transformation
![Page 11: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/11.jpg)
(a)
(b)
(c)
(d)
![Page 12: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/12.jpg)
Given: S = 3Z0 = 50 Ωfirst voltage min @ 5 cm from loadDistance between adjacent minima = 20 cm
Determine: ZL
λ/2 = 20
![Page 13: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/13.jpg)
Matching Networks
![Page 14: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/14.jpg)
Examples of Matching Networks
![Page 15: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/15.jpg)
Lumped-Element MatchingChoose d and Ys to achieve a match at MM’
![Page 16: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/16.jpg)
![Page 17: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/17.jpg)
Cont.
![Page 18: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/18.jpg)
Transients
Rectangular pulse is equivalent to the sum of two step functions
![Page 19: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/19.jpg)
Transient Response
Initial current and voltage
Reflection at the load
Second transient
Load reflection coefficient
Generator reflection coefficient
![Page 20: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/20.jpg)
T = l/up is the time it takes the wave to travel the full length of the line
Voltage Wave
![Page 21: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/21.jpg)
Current WaveReflection coefficient for current is the negative of that for voltage
![Page 22: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/22.jpg)
Steady State Response
![Page 23: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/23.jpg)
Bounce Diagrams
![Page 24: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/24.jpg)
![Page 25: The Smith Chart](https://reader035.fdocuments.us/reader035/viewer/2022081417/56813325550346895d9a0a52/html5/thumbnails/25.jpg)
Summary