lecture20 - Lecture 20 Transmission Lines The Basics In...

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1 ECE 303 – Fall 2006 – Farhan Rana – Cornell University Lecture 20 Transmission Lines: The Basics In this lecture you will learn: • Transmission lines • Different types of transmission line structures • Transmission line equations • Power flow in transmission lines • Appendix ECE 303 – Fall 2006 – Farhan Rana – Cornell University Guided Waves • So far in the course you have been dealing with waves that propagated in infinite size media • For many applications it is desirable to have electromagnetic energy be guided in much the same way as water flow is guided by having it flow in pipes Transmission lines are the simplest structures that guide electromagnetic waves Transmission line: In this course a transmission line would be any two arbitrary shaped metal conductors that are very long and uniform in at least one dimension x y A transmission line made up of two metal conductors that are very long and uniform in the z -direction
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2 ECE 303 – Fall 2006 – Farhan Rana – Cornell University Common Transmission Line Structures - I Co-axial Cable Parallel-Plate Transmission Line d W ε a b ε d W C ε = W d L o µ = = a b C log 2 ε π = a b L o log 2 π µ Capacitance and Inductance per unit length for each structure are shown ε µ o LC = ε µ o LC = ECE 303 – Fall 2006 – Farhan Rana – Cornell University Common Transmission Line Structures - II Parallel Metal Wires Metal Wire Over a Ground Plane d/2 radius a d o ε = a d C o log ε π = a d L o log π µ Capacitance and Inductance per unit length for each structure are shown = a d C o log 2 ε π = a d L o log 2 π µ radius a For d >> a : For d >> a : o o LC ε µ = o o LC ε µ =
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3 ECE 303 – Fall 2006 – Farhan Rana – Cornell University y z z 2 z 1 V ( z 1 ) V ( z 2 ) Transmission Line Voltages x y • Suppose the potential difference between the two conductors of a transmission line at location z is V ( z ) then E-field line integral in a plane parallel to the x - y plane at the location z is independent of the contour taken , and is related to the potential difference V ( z ) as: C 1 C 2 ( ) = = 2 1 . . c c s d E s d E z V r r r r Two points with different z -values can have different potentials: ( ) ( ) 2 1 2 1 . . z V s d E s d E z V c c = = r r r r The conductors are no longer equi- potentials ( ) ( ) z V C z Q = Capacitance per unit length C 1 C 2 • The charge per unit length Q ( z ) on the transmission line at location z is: ECE 303 – Fall 2006 – Farhan Rana – Cornell University Transmission Line Currents x y • Suppose the total current in the upper conductor in the + z -direction at location z is I ( z ) and in the lower conductor is – I ( z ) • The H-field flux per unit length λ ( z ) enclosed between the two conductors at the location z is related to the current I ( z ) as: ( ) ( ) z I L z = λ H y z z 2 z 1 Two points with different z -values can have different currents ( ) ( ) 2 1 z I z I I ( z 1 ) I ( z 2 )
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