Presentacion Crf 2

  • November 2019
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CRF

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Parámetros de una linea de transmisión

∇ x H = σE

+

jωεE

Densidad de Densidad de corriente de corriente de conducción desplazamiento

=

σ  jω  ε − j .E ω 

Permitividad compleja

CRF

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Permitividad relativa y Tan perdidas

CRF

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Ecuaciones de una linea de Transmision v( z + ∆z , t ) = v( z , t ) +

∂v( z , t ) ∆z ∂z

∂ 2v ∂v ∂ 2v = RGv+ ( RC + LG ) + LC 2 ∂z 2 ∂t ∂t

i ( z + ∆z , t ) = i ( z , t ) +

∂i( z , t ) ∆z ∂z

∂ 2i ∂i ∂ 2i = RGi+ ( RC + LG ) + LC 2 ∂z 2 ∂t ∂t

[ ] i ( z , t ) = I ( z ) cos( wt ) = R [ I ( z ) e ]

v( z , t ) = V ( z ) cos( wt ) = Re V ( z ) e jwt jwt

e

Ecuación General V ( z ) = V+ e −γz + V− e γz

I ( z ) = I + e −γz + I − e γz

γ = ( R + jwL )(G + jwC ) ZC =

R + jwL = Zo G + jwC

γ = α + jβ

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Impedancia de entrada en la Linea Línea en corto circuito

Z L = 0 + j0

Z i ,cc

V (−l ) A(eγ l − e −γ l ) = = Zo I ( −l ) A(eγ l + e −γ l )

1 − e −2γ l = Zo = Z o tanh γl 1 + e − 2γ l

≈ Z oγl Z i ,cc = l ( R + jwL)

CRF

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Impedancia de entrada en la Linea Línea en circuito abierto

Z i ,ca

V ( −l ) A(eγ l + e −γ l ) = = Zo I (−l ) A(eγ l − e −γ l )

1 + e −2γ l = Zo = Z o coth γl − 2γ l 1− e



Z i ,ca =

Zo γl

1 l (G + jwC )

CRF

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Reactancia de entrada y equivalentes

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