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# Transmission lines

Antennas

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### Transmission lines

1. 1. Transmission Lines and Equivalent Circuits By Maryam Liaqat Federal University of Pernambuc(UFPE), Recife, Brazil
2. 2. Contornos  Elemento Teoria do Circuito  Regra Kirchoff  Circuito Equivalente para linhas de trasmissão  Análisa linhas de Transmissão  Linhas de transmissão sem perdas plano paralales  Reflxão sobre a perda menos linhas encerrada  Casos especiais denúncia
3. 3. Elementos Agrupados  Resistancia  Capacitor  Indutor Elemento Teoria do Circuito • Electric effect happens instantaniously throughout the Circuit • Net Charge of Circuit is null • Megnatic Coupling among lumped components is negligible
4. 4. Kirchhoff’s Rule  Kirchhoff’s Voltage Rule  Kirchhoff’s Current Rule
5. 5. Equivalent Circuit for Transmission Lines The lumped circuit elements are much smaller than the characteristic wavelength . Transmission circuit has greater transportation of voltage and current than wavelength.  R and G are dissipative loss.  L and C are Stored Energy. Transmission Lines Electrical circuit Federal University of Pernambuc(UFPE), Recife, Brazil
6. 6. Analysis of Transmission lines Segments by Kirchhoff’s Rules  From Voltage Rule
7. 7.  From Current Rule
8. 8. Lossless Plane-Parallel Transmission Line Inductance per unit length can be calculated by Faraday’s Law and current through a conductor plate can be calculated by Maxwell-Ampere’s Law
9. 9. Reflection on Lossless Terminated Line  ZL is the load impedance across the line conductors  At Z=0,
10. 10. Transmission line impedance Zline (-d) with line terminated by load ZL≠Z0.
11. 11. Special Termination Cases  Shorted Transmission Line ( ZL=0)  Open Circuit Transmission Line (Zl= infinit)  Line Impedance at d=-lamb/2  Line Impedance at d=lamb./4
12. 12. Shorted Transmission Line ( ZL=0) At ZL=0 , the reflection coefficient is unity therefore the Zline is dependent only on the distance and characteristic impedance. The Current is maximum in this case but voltage is nullify.
13. 13. Open Circuit Transmission Line (Zl= infinit) In open circuit the load is completely removed and therefore reflection coefficient is -1 and the Zline is exactly opposite to the shorted terminated lines. Voltage is maximum at the point of load and current is null
14. 14. Line Impedance at d=lamb/2 and at d=lamb./4  At half-wave point, Zline is equal to ZL and independent of transmission line characteristics  Quarter-wave transformation can be used for the length of the line ( lamb/4) with impedance Z1 (quarter-wave transformer) to match the input transmission line of Impedance Z0 to the given load ZL. Here reflaction co-efficient is zero therefore