This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ....
View
Full
Document
This note was uploaded on 07/19/2010 for the course ECE ECE329 taught by Professor Kudeki during the Summer '10 term at University of Illinois at Urbana–Champaign.
 Summer '10
 KUDEKI
 Impedance, Volt

Click to edit the document details