Introduction to smith Chart
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The document is a presentation on the Smith Chart, a graphical tool for electrical engineers specializing in radio frequency engineering. It details concepts such as normalized impedance, constant resistance circles, and single and double stub tuners, along with practical applications involving impedance calculations. Additionally, it compares single and double stub matching techniques, emphasizing the importance of the Smith Chart in transmission line and matching network design.
Introduction to smith Chart
- 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