4.5: Determinar $Z_{0}$ of a Line from the Smith Chart

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30 oct 2022
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- 4.4: Extracción de parámetros de línea de transmisión
- 4.6: Resumen

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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 es $Z_{01}$ y se hace referencia a la gráfica Smith $Z_{02}$ , que suele ser la misma que la impedancia del sistema de medición, entonces se $Z_{01}$ puede determinar desde el centro $C_{Z02}$ , y el radio, $R_{Z02}$ , del círculo del coeficiente de reflexión. Así, las mediciones pueden ser utilizadas para determinar la impedancia desconocida $Z_{01}$ . 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 situaciones $C_{Z02},\: R_{Z02}$ , y $Z_{02}$ son conocidas y $Z_{01}$ deben ser determinadas.

No se $Z_{01}$ 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), $Z_{01}$ y si y $Z_{02}$ están cerca (así que $B$ es pequeña), entonces

$\label{eq:1}C_{Z-2}\approx B-\frac{1}{B}+\frac{1}{B}\approx B$

La aproximación es mejor para los más pequeños $|\Gamma_{L,\:Z01}|$ . También

$\label{eq:2}R_{Z02}\approx |\Gamma_{L,\: Z01}|$

Entonces siempre que la impedancia característica de la línea, $Z_{01}$ , esté cerca de la impedancia de referencia del sistema $Z_{02}$ ,

$\label{eq:3}\frac{Z_{01}}{Z_{02}}=\frac{1+B}{1-B}\approx\frac{1+C_{Z02}}{1-C_{Z02}}$

y esto es solo la lectura de impedancia normalizada en el centro del círculo. Por ejemplo, si una línea con una impedancia característica $(Z_{01})$ de $55\:\Omega$ se termina en una $45\:\Omega$ carga, entonces en un $(Z_{02}\: =)\: 50\:\Omega$ sistema, $C_{Z02} = 0.0939$ y $R_{Z02} = 0.0996$ . Usando Ecuación $\eqref{eq:3}$ la derivada $Z_{01} = 54.7\:\Omega$ y, usando Ecuación $\eqref{eq:2}$ , $\Gamma_{L,\: Z01} = 0.0996$ comparada con la ideal $0.1000$ .

La tabla $\PageIndex{1}$ presenta la impedancia característica real de la línea como la relación $Z_{Z01}/Z_{Z02}$ para valores particulares de centro y radio medidos en la gráfica polar a la que se hace referencia $Z_{02}$ . El valor real de impedancia se compara con el valor aproximado para $Z_{Z01}/Z_{Z02}\approx 1 + C_{Z02}/1 − C_{Z02}$ . Se observa que la aproximación en Ecuación $\eqref{eq:3}$ proporciona una buena estimación de la impedancia característica desconocida $(Z_{01})$ mejorando ya que el centro del locus está más cerca del origen.

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

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