{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

329lect36 - 36 Smith Chart and VSWR Consider the general...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
36 Smith Chart and VSWR Consider the general phasor expressions V ( d ) = V + e j β d (1 + Γ L e - j 2 β d ) and I ( d ) = V + e j β d (1 - Γ L e - j 2 β d ) Z o describing the voltage and current variations on TL’s in sinusoidal steady-state. + - Wire 2 Wire 1 + - 0 F = V g Z g Z L I ( d ) V ( d ) l Transmission line Load Z o Generator d d max | V ( d ) | d min | V ( d ) | min | V ( d ) | max .2 .5 1 2 r 5 x 5 2 1 .5 .2 x 5 2 1 .5 .2 0 VSWR SmithChart 1 Γ ( d ) 1 + Γ ( d ) | 1 + Γ ( d ) | maximizes for d = d max Γ ( d max ) = | Γ L | | 1 + Γ ( d ) | minimizes for d = d min such that Γ ( d min ) = - Γ ( d max ) Complex addition displayed graphically superposed on a Smith Chart z ( d max ) =VSWR Unless Γ L = 0 , these phasors contain reflected components, which means that voltage and current variations on the line “contain” standing waves. In that case the phasors go through cycles of magnitude variations as a function of d , and in the voltage magnitude in particular (see margin) varying as | V ( d ) | = | V + || 1 + Γ L e - j 2 β d | = | V + || 1 + Γ ( d ) | takes maximum and minimum values of | V ( d ) | max = | V + | (1 + | Γ L | ) and | V ( d ) | min = | V + | (1 - | Γ L | ) at locations d = d max and d min such that Γ ( d max ) = Γ L e - j 2 β d max = | Γ L | and Γ ( d min ) = Γ L e - j 2 β d min = - | Γ L | , and d max - d min is an odd multiple of λ 4 . 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
These results can be most easily understood and verified graphi- cally on a SC as shown in the margin. + - Wire 2 Wire 1 + - 0 F = V g Z g Z L I ( d ) V ( d ) l Transmission line Load Z o Generator d d max | V ( d ) | d min | V ( d ) | min | V ( d ) | max .2 .5 1 2 r 5 x 5 2 1 .5 .2 x 5 2 1 .5 .2 0 VSWR SmithChart 1 Γ ( d ) 1 + Γ ( d ) | 1 + Γ ( d ) | maximizes for d = d max Γ ( d max ) = | Γ L | | 1 + Γ ( d ) | minimizes for d = d min such that Γ ( d min ) = - Γ ( d max ) Complex addition displayed graphically superposed on a Smith Chart z ( d max ) =VSWR
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}