Question

The characteristics impedance of a certain line is 7100Z-16when the frequency is 1kHz. At this frequency the attenuation is 0.01 neper per km and the phase function is 0.035 radian per km. Calculate the resistance, the leakage the inductance, and capacitance per km​

Answer 1

Answer:

$Z_{i n}=647.236 < -70.35^{\circ} \mathrm{ohm}$

Explanation:

Step 1: Impedance, denoted by the letter Z, is a unit of measurement for the resistance to electrical flow. Ohms are used to measure it. Resistance (R) is the same as impedance (I), which is calculated for DC systems by dividing the voltage across an element by the current (R = V/I).

Charactersfic impedance, $z_0=710 < 14^{\circ} \Omega$propagation constant, $\gamma=0.007+j 0.028 \mathrm{rad} / \mathrm{km}$

Step 2:So, phase constant$(\beta)=0.028 \mathrm{rad} / \mathrm{km}$ Load impedance$\left(I_L\right)=300 \Omega$, Line length $(l)=100 \mathrm{~km}$

$\begin{aligned}Z_{i n}^* & =Z_0\left(\frac{Z_L+j Z_0 \tan (\beta l)}{Z_0+j Z_L \tan (\beta l)}\right) \\\Rightarrow Z_{i n} & =\left(710 < 14^{\circ}\right)\left(\frac{300+j\left(710 < 14^{\circ}\right)\left(\tan \left(\begin{array}{c}0.028 \\\times 100\end{array}\right)\right.}{710 < 14^{\circ}+j 300 \tan \left(\begin{array}{c}0.028 \times \\100\end{array}\right)}\right)\end{aligned}$

$\begin{aligned}& \Rightarrow I_{i n}=\left(710 < 14^{\circ}\right)\left(\frac{300+j(-34.513-j 250)}{97.0834+j 703.33+j(-106.65)}\right) \\& \Rightarrow Z_{i n}=\left(710 < 14^{\circ}\right)\left(\frac{300-j 34.513+250}{97.0834+j 703.33-j 106.65}\right)\end{aligned}$

$\begin{aligned}& \Rightarrow Z_{i n}=\left(710 < 14^{\circ}\right)\left(\frac{5500-j 34.513}{97.0834+j 596.68}\right) \\& \Rightarrow Z_{i n}=\left(710 < 14^{\circ}\right)\left(\frac{551.08 < -3.6^{\circ}}{604.52 < 80.75}\right) \\& \Rightarrow Z_{i_n}=\left(710 < 14^{\circ}\right)\left(0.9116 < -84.35^{\circ}\right) \\& \Rightarrow Z_{i_n}=647.236 < -70.35^{\circ} \mathrm{ohm}\end{aligned}$

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