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Unformatted text preview: 34 Line impedance, generalized reflection coef ficient, Smith Chart • Consider a TL of an arbitrary length l terminated by an arbitrary load Z L = R L + jX L . as depicted in the margin. l Input port Z o l z l d LOAD GENERATOR, Circuit Z L = R L + jX I ( d ) V ( d ) + Voltage and current phasors are known to vary on the line as V ( d ) = V + e jβd + V e jβd and I ( d ) = V + e jβd V e jβd Z o . In this lecture we will develop the general analysis tools needed to determine the unknowns of these phasors, namely V + and V , in terms of source circuit specifications. • Our analysis starts at the load end of the TL where V (0) and I (0) stand for the load voltage and current, obeying Ohm’s law V (0) = Z L I (0) . Hence, using V (0) and I (0) from above, we have V + + V = Z L V + V Z o ⇒ V = Z L Z o Z L + Z o V + . 1 – Define a load reflection coefficient “Load reflection coefficient” is a well justified name for Γ L since the forward travel ing wave with phasor V + e jβd gets reflected from the load. Γ L ≡ Z L Z o Z L + Z o and rewrite the voltage and current phasors as V ( d ) = V + e jβd [1+Γ L e j 2 βd ] and I ( d ) = V + e jβd [1 Γ L e j 2 βd ] Z o . – Define a generalized reflection coefficient The term “generalized reflec tion coefficient” is also well justified even if there is no reflection taking place at ar bitrary d — the reason is, if the line were cut at location d and the stub with the load were replaced by a lumped load having a reflection co efficient equal to Γ( d ) , then there would be no modifica tion of the voltage and cur rent variations on the line to wards the generator. Γ( d ) ≡ Γ L e j 2 βd and rewrite the voltage and current phasors as V ( d ) = V + e jβd [1 + Γ( d )] and I ( d ) = V + e jβd [1 Γ( d )] Z o ....
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 Summer '10
 KUDEKI
 Impedance, Volt, Complex number, Transmission line, Impedance matching, zo, Sc

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