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4.5: DeterminarZ0 of a Line from the Smith Chart

( \newcommand{\kernel}{\mathrm{null}\,}\)

Se demostró en la Sección 3.5.2 que el locus del coeficiente de reflexión con respecto a la frecuencia de una línea terminada es un círculo en el gráfico de Smith aunque la impedancia característica de la línea no sea la misma que la impedancia de referencia del gráfico Smith. La única advertencia aquí es que el coeficiente de reflexión de la terminación debe ser independiente de la frecuencia por lo que una terminación resistiva es suficiente. Si la impedancia característica de la línea esZ01 y se hace referencia a la gráfica SmithZ02, que suele ser la misma que la impedancia del sistema de medición, entonces seZ01 puede determinar desde el centroCZ02, y el radio,RZ02, del círculo del coeficiente de reflexión. Así, las mediciones pueden ser utilizadas para determinar la impedancia desconocidaZ01. Otra situación en la que esto es útil es en el diseño donde se puede dibujar un círculo de línea de transmisión para completar un problema de diseño y a partir de esto la impedancia característica de la línea encontrada. En ambas situacionesCZ02,RZ02, yZ02 son conocidas yZ01 deben ser determinadas.

No seZ01 puede obtener una solución simple de forma cerrada para la impedancia característica desconocida a partir de las ecuaciones (3.5.14) y (3.5.15). Sin embargo, sustituyendo la Ecuación (3.5.15) en la Ecuación (3.5.14),Z01 y si yZ02 están cerca (así queB es pequeña), entonces

CZ2B1B+1BB

La aproximación es mejor para los más pequeños|ΓL,Z01|. También

RZ02|ΓL,Z01|

Entonces siempre que la impedancia característica de la línea,Z01, esté cerca de la impedancia de referencia del sistemaZ02,

Z01Z02=1+B1B1+CZ021CZ02

y esto es solo la lectura de impedancia normalizada en el centro del círculo. Por ejemplo, si una línea con una impedancia característica(Z01) de55Ω se termina en una45Ω carga, entonces en un(Z02=)50Ω sistema,CZ02=0.0939 yRZ02=0.0996. Usando Ecuación(???) la derivadaZ01=54.7Ω y, usando Ecuación(???),ΓL,Z01=0.0996 comparada con la ideal0.1000.

La tabla4.5.1 presenta la impedancia característica real de la línea como la relaciónZZ01/ZZ02 para valores particulares de centro y radio medidos en la gráfica polar a la que se hace referenciaZ02. El valor real de impedancia se compara con el valor aproximado paraZZ01/ZZ021+CZ02/1CZ02. Se observa que la aproximación en Ecuación(???) proporciona una buena estimación de la impedancia característica desconocida(Z01) mejorando ya que el centro del locus está más cerca del origen.

CZ02 Z01/Z02
(1+CZ02)(1CZ02)
RZ02=0.2 RZ02=0.3 RZ02=0.4 RZ02=0.5 RZ02=0.6 RZ02=0.7
error Z01/Z02 error Z01/Z02 error Z01/Z02 error Z01/Z02 error Z01/Z02 error
\ (C_ {Z02}\) ">0.00 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.000 \ (R_ {Z02} =0.2\) ">1.000 \ (R_ {Z02} =0.2\) error">0% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.000 \ (R_ {Z02} =0.3\) error">0% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.000 \ (R_ {Z02} =0.4\) error">0% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.000 \ (R_ {Z02} =0.5\) error">0% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.000 \ (R_ {Z02} =0.6\) error">0% \ (R_ {Z02} =0.7\)Z01/Z02 “>1.000 \ (R_ {Z02} =0.7\) error">0%
\ (C_ {Z02}\) ">0.02 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.041 \ (R_ {Z02} =0.2\) ">1.043 \ (R_ {Z02} =0.2\) error"><1% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.045 \ (R_ {Z02} =0.3\) error"><1% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.050 \ (R_ {Z02} =0.4\) error">1% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.050 \ (R_ {Z02} =0.5\) error">1% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.065 \ (R_ {Z02} =0.6\) error">2% \ (R_ {Z02} =0.7\)Z01/Z02 “>1.080 \ (R_ {Z02} =0.7\) error">4%
\ (C_ {Z02}\) ">0.04 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.083 \ (R_ {Z02} =0.2\) ">1.088 \ (R_ {Z02} =0.2\) error"><1% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.093 \ (R_ {Z02} =0.3\) error">1% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.100 \ (R_ {Z02} =0.4\) error">2% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.113 \ (R_ {Z02} =0.5\) error">3% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.135 \ (R_ {Z02} =0.6\) error">5% \ (R_ {Z02} =0.7\)Z01/Z02 “>1.170 \ (R_ {Z02} =0.7\) error">7%
\ (C_ {Z02}\) ">0.06 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.128 \ (R_ {Z02} =0.2\) ">1.130 \ (R_ {Z02} =0.2\) error"><1% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.140 \ (R_ {Z02} =0.3\) error">1% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.155 \ (R_ {Z02} =0.4\) error">2% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.175 \ (R_ {Z02} =0.5\) error">4% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.208 \ (R_ {Z02} =0.6\) error">7% \ (R_ {Z02} =0.7\)Z01/Z02 “>1.265 \ (R_ {Z02} =0.7\) error">11%
\ (C_ {Z02}\) ">0.08 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.174 \ (R_ {Z02} =0.2\) ">1.183 \ (R_ {Z02} =0.2\) error"><1% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.193 \ (R_ {Z02} =0.3\) error">2% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.210 \ (R_ {Z02} =0.4\) error">3% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.250 \ (R_ {Z02} =0.5\) error">6% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.285 \ (R_ {Z02} =0.6\) error">9% \ (R_ {Z02} =0.7\)Z01/Z02 “>1.375 \ (R_ {Z02} =0.7\) error">15%
\ (C_ {Z02}\) ">0.10 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.222 \ (R_ {Z02} =0.2\) ">1.230 \ (R_ {Z02} =0.2\) error"><1% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.245 \ (R_ {Z02} =0.3\) error">2% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.270 \ (R_ {Z02} =0.4\) error">4% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.310 \ (R_ {Z02} =0.5\) error">7% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.370 \ (R_ {Z02} =0.6\) error">11% \ (R_ {Z02} =0.7\)Z01/Z02 “>1.500 \ (R_ {Z02} =0.7\) error">19%
\ (C_ {Z02}\) ">0.12 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.273 \ (R_ {Z02} =0.2\) ">1.285 \ (R_ {Z02} =0.2\) error">1% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.305 \ (R_ {Z02} =0.3\) error">2% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.335 \ (R_ {Z02} =0.4\) error">5% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.385 \ (R_ {Z02} =0.5\) error">8% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.465 \ (R_ {Z02} =0.6\) error">13% \ (R_ {Z02} =0.7\)Z01/Z02 “>1.640 \ (R_ {Z02} =0.7\) error">22%
\ (C_ {Z02}\) ">0.14 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.326 \ (R_ {Z02} =0.2\) ">1.340 \ (R_ {Z02} =0.2\) error">1% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.365 \ (R_ {Z02} =0.3\) error">3% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.408 \ (R_ {Z02} =0.4\) error">6% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.465 \ (R_ {Z02} =0.5\) error">10% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.565 \ (R_ {Z02} =0.6\) error">15% \ (R_ {Z02} =0.7\)Z01/Z02 “>1.800 \ (R_ {Z02} =0.7\) error">26%
\ (C_ {Z02}\) ">0.16 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.381 \ (R_ {Z02} =0.2\) ">1.400 \ (R_ {Z02} =0.2\) error">1% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.428 \ (R_ {Z02} =0.3\) error">3% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.475 \ (R_ {Z02} =0.4\) error">6% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.550 \ (R_ {Z02} =0.5\) error">11% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.685 \ (R_ {Z02} =0.6\) error">18% \ (R_ {Z02} =0.7\)Z01/Z02 “>1.990 \ (R_ {Z02} =0.7\) error">31%
\ (C_ {Z02}\) ">0.18 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.439 \ (R_ {Z02} =0.2\) ">1.460 \ (R_ {Z02} =0.2\) error">1% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.495 \ (R_ {Z02} =0.3\) error">4% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.550 \ (R_ {Z02} =0.4\) error">7% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.645 \ (R_ {Z02} =0.5\) error">13% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.820 \ (R_ {Z02} =0.6\) error">21% \ (R_ {Z02} =0.7\)Z01/Z02 “>2.230 \ (R_ {Z02} =0.7\) error">35%
\ (C_ {Z02}\) ">0.20 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.500 \ (R_ {Z02} =0.2\) ">1.528 \ (R_ {Z02} =0.2\) error">2% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.565 \ (R_ {Z02} =0.3\) error">4% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.635 \ (R_ {Z02} =0.4\) error">8% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.745 \ (R_ {Z02} =0.5\) error">14% \ (R_ {Z02} =0.6\)Z01/Z02 “>1.965 \ (R_ {Z02} =0.6\) error">24% \ (R_ {Z02} =0.7\)Z01/Z02 “>2.515 \ (R_ {Z02} =0.7\) error">40%
\ (C_ {Z02}\) ">0.22 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.564 \ (R_ {Z02} =0.2\) ">1.595 \ (R_ {Z02} =0.2\) error">2% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.645 \ (R_ {Z02} =0.3\) error">5% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.720 \ (R_ {Z02} =0.4\) error">9% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.860 \ (R_ {Z02} =0.5\) error">16% \ (R_ {Z02} =0.6\)Z01/Z02 “>2.130 \ (R_ {Z02} =0.6\) error">27% \ (R_ {Z02} =0.7\)Z01/Z02 “>2.915 \ (R_ {Z02} =0.7\) error">46%
\ (C_ {Z02}\) ">0.24 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.632 \ (R_ {Z02} =0.2\) ">1.670 \ (R_ {Z02} =0.2\) error">2% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.725 \ (R_ {Z02} =0.3\) error">5% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.815 \ (R_ {Z02} =0.4\) error">10% \ (R_ {Z02} =0.5\)Z01/Z02 “>1.980 \ (R_ {Z02} =0.5\) error">18% \ (R_ {Z02} =0.6\)Z01/Z02 “>2.330 \ (R_ {Z02} =0.6\) error">30% \ (R_ {Z02} =0.7\)Z01/Z02 “>3.440 \ (R_ {Z02} =0.7\) error">53%
\ (C_ {Z02}\) ">0.26 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.703 \ (R_ {Z02} =0.2\) ">1.745 \ (R_ {Z02} =0.2\) error">2% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.810 \ (R_ {Z02} =0.3\) error">6% \ (R_ {Z02} =0.4\)Z01/Z02 “>1.920 \ (R_ {Z02} =0.4\) error">11% \ (R_ {Z02} =0.5\)Z01/Z02 “>2.120 \ (R_ {Z02} =0.5\) error">20% \ (R_ {Z02} =0.6\)Z01/Z02 “>2.555 \ (R_ {Z02} =0.6\) error">33% \ (R_ {Z02} =0.7\)Z01/Z02 “>4.380 \ (R_ {Z02} =0.7\) error">61%
\ (C_ {Z02}\) ">0.28 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.778 \ (R_ {Z02} =0.2\) ">1.830 \ (R_ {Z02} =0.2\) error">3% \ (R_ {Z02} =0.3\)Z01/Z02 “>1.905 \ (R_ {Z02} =0.3\) error">7% \ (R_ {Z02} =0.4\)Z01/Z02 “>2.030 \ (R_ {Z02} =0.4\) error">12% \ (R_ {Z02} =0.5\)Z01/Z02 “>2.270 \ (R_ {Z02} =0.5\) error">22% \ (R_ {Z02} =0.6\)Z01/Z02 “>2.830 \ (R_ {Z02} =0.6\) error">37% \ (R_ {Z02} =0.7\)Z01/Z02 “> \ (R_ {Z02} =0.7\) error">
\ (C_ {Z02}\) ">0.30 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.857 \ (R_ {Z02} =0.2\) ">1.915 \ (R_ {Z02} =0.2\) error">3% \ (R_ {Z02} =0.3\)Z01/Z02 “>2.005 \ (R_ {Z02} =0.3\) error">7% \ (R_ {Z02} =0.4\)Z01/Z02 “>2.150 \ (R_ {Z02} =0.4\) error">14% \ (R_ {Z02} =0.5\)Z01/Z02 “>2.450 \ (R_ {Z02} =0.5\) error">24% \ (R_ {Z02} =0.6\)Z01/Z02 “>3.205 \ (R_ {Z02} =0.6\) error">42% \ (R_ {Z02} =0.7\)Z01/Z02 “> \ (R_ {Z02} =0.7\) error">
\ (C_ {Z02}\) ">0.32 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>1.941 \ (R_ {Z02} =0.2\) ">2.008 \ (R_ {Z02} =0.2\) error">3% \ (R_ {Z02} =0.3\)Z01/Z02 “>2.110 \ (R_ {Z02} =0.3\) error">8% \ (R_ {Z02} =0.4\)Z01/Z02 “>2.285 \ (R_ {Z02} =0.4\) error">15% \ (R_ {Z02} =0.5\)Z01/Z02 “>2.655 \ (R_ {Z02} =0.5\) error">27% \ (R_ {Z02} =0.6\)Z01/Z02 “> \ (R_ {Z02} =0.6\) error"> \ (R_ {Z02} =0.7\)Z01/Z02 “> \ (R_ {Z02} =0.7\) error">
\ (C_ {Z02}\) ">0.34 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>2.030 \ (R_ {Z02} =0.2\) ">2.105 \ (R_ {Z02} =0.2\) error">4% \ (R_ {Z02} =0.3\)Z01/Z02 “>2.225 \ (R_ {Z02} =0.3\) error">9% \ (R_ {Z02} =0.4\)Z01/Z02 “>2.435 \ (R_ {Z02} =0.4\) error">16% \ (R_ {Z02} =0.5\)Z01/Z02 “>2.885 \ (R_ {Z02} =0.5\) error">30% \ (R_ {Z02} =0.6\)Z01/Z02 “> \ (R_ {Z02} =0.6\) error"> \ (R_ {Z02} =0.7\)Z01/Z02 “> \ (R_ {Z02} =0.7\) error">
\ (C_ {Z02}\) ">0.36 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>2.125 \ (R_ {Z02} =0.2\) ">2.215 \ (R_ {Z02} =0.2\) error">4% \ (R_ {Z02} =0.3\)Z01/Z02 “>2.350 \ (R_ {Z02} =0.3\) error">10% \ (R_ {Z02} =0.4\)Z01/Z02 “>2.600 \ (R_ {Z02} =0.4\) error">18% \ (R_ {Z02} =0.5\)Z01/Z02 “>3.125 \ (R_ {Z02} =0.5\) error">32% \ (R_ {Z02} =0.6\)Z01/Z02 “> \ (R_ {Z02} =0.6\) error"> \ (R_ {Z02} =0.7\)Z01/Z02 “> \ (R_ {Z02} =0.7\) error">
\ (C_ {Z02}\) ">0.38 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>2.226 \ (R_ {Z02} =0.2\) ">2.325 \ (R_ {Z02} =0.2\) error">4% \ (R_ {Z02} =0.3\)Z01/Z02 “>2.490 \ (R_ {Z02} =0.3\) error">11% \ (R_ {Z02} =0.4\)Z01/Z02 “>2.785 \ (R_ {Z02} =0.4\) error">20% \ (R_ {Z02} =0.5\)Z01/Z02 “>3.515 \ (R_ {Z02} =0.5\) error">37% \ (R_ {Z02} =0.6\)Z01/Z02 “> \ (R_ {Z02} =0.6\) error"> \ (R_ {Z02} =0.7\)Z01/Z02 “> \ (R_ {Z02} =0.7\) error">
\ (C_ {Z02}\) ">0.40 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>2.333 \ (R_ {Z02} =0.2\) ">2.455 \ (R_ {Z02} =0.2\) error">5% \ (R_ {Z02} =0.3\)Z01/Z02 “>2.640 \ (R_ {Z02} =0.3\) error">12% \ (R_ {Z02} =0.4\)Z01/Z02 “>3.000 \ (R_ {Z02} =0.4\) error">22% \ (R_ {Z02} =0.5\)Z01/Z02 “>3.925 \ (R_ {Z02} =0.5\) error">40% \ (R_ {Z02} =0.6\)Z01/Z02 “> \ (R_ {Z02} =0.6\) error"> \ (R_ {Z02} =0.7\)Z01/Z02 “> \ (R_ {Z02} =0.7\) error">
\ (C_ {Z02}\) ">0.42 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>2.585 \ (R_ {Z02} =0.2\) ">2.585 \ (R_ {Z02} =0.2\) error">5% \ (R_ {Z02} =0.3\)Z01/Z02 “>2.805 \ (R_ {Z02} =0.3\) error">13% \ (R_ {Z02} =0.4\)Z01/Z02 “>3.240 \ (R_ {Z02} =0.4\) error">24% \ (R_ {Z02} =0.5\)Z01/Z02 “> \ (R_ {Z02} =0.5\) error"> \ (R_ {Z02} =0.6\)Z01/Z02 “> \ (R_ {Z02} =0.6\) error"> \ (R_ {Z02} =0.7\)Z01/Z02 “> \ (R_ {Z02} =0.7\) error">
\ (C_ {Z02}\) ">0.44 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>2.730 \ (R_ {Z02} =0.2\) ">2.730 \ (R_ {Z02} =0.2\) error">6% \ (R_ {Z02} =0.3\)Z01/Z02 “>2.985 \ (R_ {Z02} =0.3\) error">14% \ (R_ {Z02} =0.4\)Z01/Z02 “>3.535 \ (R_ {Z02} =0.4\) error">27% \ (R_ {Z02} =0.5\)Z01/Z02 “> \ (R_ {Z02} =0.5\) error"> \ (R_ {Z02} =0.6\)Z01/Z02 “> \ (R_ {Z02} =0.6\) error"> \ (R_ {Z02} =0.7\)Z01/Z02 “> \ (R_ {Z02} =0.7\) error">
\ (C_ {Z02}\) ">0.46 \ (Z_ {01} /Z_ {02}\ approx\)(1+CZ02)(1CZ02) “>2.704 \ (R_ {Z02} =0.2\) ">2.885 \ (R_ {Z02} =0.2\) error">6% \ (R_ {Z02} =0.3\)Z01/Z02 “>3.180 \ (R_ {Z02} =0.3\) error">15% \ (R_ {Z02} =0.4\)Z01/Z02 “>3.865 \ (R_ {Z02} =0.4\) error">30% \ (R_ {Z02} =0.5\)Z01/Z02 “> \ (R_ {Z02} =0.5\) error"> \ (R_ {Z02} =0.6\)Z01/Z02 “> \ (R_ {Z02} =0.6\) error">- \ (R_ {Z02} =0.7\)Z_{01}/Z_{02} “>- \ (R_ {Z02} =0.7\) error">-

Tabla\PageIndex{1}: Tabla de la impedancia característica normalizadaZ_{01}/Z_{02} de una línea de transmisión terminada que tiene impedancia característicaZ_{01} trazada en una gráfica de Smith con una impedancia de referenciaZ_{02} en términos del centro,C_{Z02}, del locus circular (con respecto a la longitud de línea) de la línea para diversos radios,R_{Z02}, del locus circular. C_{Z02}yR_{Z02} son en términos de coeficiente de reflexión medidos en el gráfico de Smith. También se muestra la aproximación,(1 + C_{Z02})/(1 − C_{Z02}), deZ_{01}/Z_{02} (ver Ecuación\eqref{eq:3}).


This page titled 4.5: DeterminarZ_{0} of a Line from the Smith Chart is shared under a CC BY-NC license and was authored, remixed, and/or curated by Michael Steer.

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