329lect37 - 37 Smith Chart and impedance matching In...

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Unformatted text preview: 37 Smith Chart and impedance matching In lossless TL circuits the average power input P in at the generator end precisely matches the average power delivered to the load, P L . In fact, P in and P L also match the average power P ( d ) transported on the line at an arbitrary d . +- +- F = V g Z g Z L I ( d ) V ( d ) l Load Z o d Power txed toward the load: | V + | 2 2 Z o . Power txed toward the gen- erator: | V- | 2 2 Z o . Power reflection coefficient: | L | 2 . Power transmission coeff.: 1-| L | 2 . We have in general P ( d ) = 1 2 Re { V ( d ) I * ( d ) } = 1 2 Re { ( V + e jd + V- e- jd )( V + e jd- V- e- jd Z o ) * } = 1 2 Re { | V + | 2 Z o- | V- | 2 Z o + V- V + * e- j 2 d- ( V- V + * e- j 2 d ) * Z o } = | V + | 2 2 Z o- | V- | 2 2 Z o . Note that P ( d ) is the difference of power transported | V + | 2 2 Z o toward the load by the forward-going wave, and | V- | 2 2 Z o toward the generator by the reflected wave. Also note that P ( d ) = | V + | 2 2 Z o- | V- | 2 2 Z o = | V + | 2 2 Z o (1-| L | 2 ) so that | L | 2 is an effective power reflection coefficient . 1 In TL circuits with load impedances Z L unmatched to the character- istic impedance Z o , the reflected power | V + | 2 2 Z o | L | 2 will be non-zero and the VSWR>1. +- +- F = V g Z g Z L I ( d ) V ( d ) l Load Z o d This a condition not favored by practical signal generators used in TL circuits....
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329lect37 - 37 Smith Chart and impedance matching In...

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