Introduction to smith Chart Introduction to smith Chart Normalized Impedance Constant Resistance Circles Constant Reactance ‘Arcs’ Plot a Complex Impedance What about Admittance? Analysis of Single stub Tuner VSWR and Transmission Lines Analysis of Single stub tuner Analysis of Double-Stub Tuner Difference between single stub matching and double stub matching A 50 ohm transmission line is terminated to load of 25+50j. The length of the transmission line is 3.3 lemda. Find: (a)Reflection coefficient (b)VSWR (c)Input impedance (d)Input admittance

1. Date: Tuesday, February 25, 2020
Jatiya Kabi Kazi Nazrul Islam University ,Department of Electrical & Electronic Engineering
Presentation on Introduction to smith Chart
(1)AL-AMIN
ID:16102904
Session:2015-16
(2) SOMAYA SOLAYMAN MITU
ID:17102932
Session:20116-17
(3) Miskatun Zinan
ID:17102944
Session:2016-17
Studying at Jatiya Kabi Kazi Nazrul
Islam University Department of
Electrical & Electronic
Engineering
Smith
Chart

2. Index
 Introduction to smith Chart
 Normalized Impedance
 Constant Resistance Circles
 Constant Reactance ‘Arcs’
 Plot a Complex Impedance
 What about Admittance?
 Analysis of Single stub Tuner
 VSWR and Transmission Lines
 Analysis of Single stub tuner
 Analysis of Double-Stub Tuner
 Difference between single stub matching and double stub matching
 A 50 ohm transmission line is terminated to load of 25+50j. The length of the transmission line is 3.3 lemda.
Find:
(a)Reflection coefficient
(b)VSWR
(c)Input impedance
(d)Input admittance
Smith-
Chart

3. Smith-chart:
Introduction to
smith Chart
The smith chart , invented by Phillip H . Smith (1905-1987) is a
graphical calculator or monogram designed for electrical and
electronics engineers specializing in radio frequency
(RF)engineering to assist in solving problems with transmission line
and matching circuit .
A graphical tool to plot and compute:
 Complex impedance
 Complex reflection coefficient
 VSWR
 Transmission line effects
 Matching Networks

4. Normalized Impedance
• Normalized Z = Actual Z/System Zo
• For Zo = 50 ohm, divide values by 50
• Example,
• Z = 37 + j55
• Z’ = 37/50 + j55/50
• Z’ = 0.74+j1.10
• Makes it usable for any system Zo
Normaliz
ed
Impedan
ce

5. Real Axis
+J Inductive part
R+jX
-J Capacitive Part
R-jX
Smith-
Chart
(Purely Resistive jx=0)

6. Key Values on the Chart
Z0
system
impedance
Open
circuit
Short
circuit
Normaliz
ed
Impedan
ce

7. Constant Resistance Circles Constant Resistance Circles

8. Constant Reactance ‘Arcs’
Constant Reactance ‘Arcs’

9. Plot a Complex Impedance
• Z = 25+j40
• Divide by 50 to Normalize
• Z’ = 0.5+j0.8
• Find intersection of R’ = 0.5
• circle and X’ = 0.8 arc
Normaliz
ed
Impedan
ce

10. Adding Series Elements
• Add Components to move around the
smith chart
• Series L & C move
• along constant R circles
• Series L move CW
• Series C move CCW
Normaliz
ed
Impedan
ce

11. What about Admittance?
• Admittance is handy when adding elements in
parallel.
• Admittance Y = 1/Z
• Conductance G = 1/R
• Susceptance B = 1/X
• Converting Impedance to Admittance is easy with
smith chart
Normaliz
ed
Impedan
ce

12. Converting to Admittance
• Draw circle centered on Zo that crosses through Z
point.
• Bisect circle
• through Z and Zo
• Y is 180 degree
• away on circle ,
• Z’ = 1+j1.1,
• Y’=0.45-j0.5
Normaliz
ed
Impedan
ce

13. VSWR and Transmission Lines
• Constant VSWR circle
• Impedance varies
• VSWR stays same
• One trip around smith chart
• is ½ wavelength
• Impedance repeats
• Half way around is ¼ wavelength
• Open transformed to short
• Short transformed to open
• Transmission line effects
• Predict z vs line length
• Example
• Measure z at TX ,predict at antenna
Normaliz
ed
Impedan
ce

14. Analysis of Single stub tuner
Normaliz
ed
Impedan
ce

15. Single-Stub Matching: Steps (shunt version in parentheses)
• 1. Plot the normalized load impedance on the Smith Chart (and convert to admittance for shunt
stub tuning)
• 2. Draw the |Γ| circle and translate the impedance along the line to the rL=1 (gL=1) circle (2
solutions) => r’ = 1±jx’ (y’ = 1±jb’)
• 3. Determine load-section length d from angles between point representing zL (yL)and the point
on the rL=1 (gL=1) circle
• 4. Determine stub length ℓ between the open / short circuit point and the points representing ±jx’
(±jb’)
Normaliz
ed
Impedan
ce

16. • Z= 60+80j ohm
• Zo = 50 ohm
• Z’=1.2+1.6j ohm(divide by 50 ohm)
• D = 0.176 lemda – 0.436lemda= -
0.260+0.5lemda = 0.240 lemda
• jb1 = -j1.5
• Ls = 0.344lemda – 0.25lemda =0.094 lemda
Normaliz
ed
Impedan
ce

17. (Shunt) Double-Stub Tuners
• Alternative to single-stub tuner
• d0 is fixed
• lA, lB used to tune the network
• λ/8
•Z=60+40j
z=50ohom

18. • Line impedance Zo = 50 ohm
• Z = 60+40j ohm
• Z’ = 1.2+0.8j ohm
• Yl = 0.57-0.4j
• Moving on constant resistance value is
0.57+j0.06
• Jb1 = j(0.06 – (-0.4)) =
j0.46=l1=0.25lemda+0.068lemda=0.318lmda
• Move on original 1+jb circle value is 1+j0.57
• Jb2 = -j0.57=l2=0.416lmda-
0.25lmda=0.166lmda
Normaliz
ed
Impedan
ce

19. Analysis of Double-Stub Tuner
Normaliz
ed
Impedan
ce

20. Double Stub Tuner Steps
• 1. Draw the g=1 circle; this is where yB should be located.
• 2. Rotate this circle d0/λ wavelengths towards the load
(CCW); this is the circle on which yA should be located.
• 3. Plot yL on the Smith Chart.
• 4. Translate yL along a resistance/ conductance circle to get
onto the rotated g=1 circle
Normaliz
ed
Impedan
ce

21. • 5. Determine the stub length lA required to produce
the reactance/susceptance .
• 6. Rotate the modified load impedance/ admittance
onto the g=1 circle
• 7. Determine the stub length lB required to produce
the reactance/susceptance to move the rotated
impedance/admittance to the origin
Normaliz
ed
Impedan
ce

22. Single stub matching consist of the the short as well as open section
of a transmission line .This type of stub has the impedance just same
like those of the main line. Short circuited stubs are considered to be
more than the open because of its low energy radiation even at high
frequency.
Double stub matching is used as an alternative to single stub
because in single stub the stub is placed only at specific point and
that specific point may be at a wrong place where it is not needed
so the double stubs used to match the load .
Difference between single stub matching
and double stub matching

23. Summary
• The smith chart is highly useful tool:
• Complex impedance transformations
• Determining VSWR ,Rl and much more
• Transmission line impedance transformations
• Matching network design

24. Mathematical problem:
 A 50 ohm transmission line is terminated to load of
25+50j. The length of the transmission line is 3.3 lemda.
 Find:
I. Reflection coefficient
II. VSWR
III. Input impedance
IV. Input admittance

25. Normaliz
ed
Impedan
ce