{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

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

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

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 8

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online