GATE 2017 EC – Question 34
The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $V(l) = e^{-\gamma l + j\omega t}$ Volts, where $l$ is the distance along the length of the cable in metres, $\gamma = (0.1 + j40)$ m$^{-1}$ is the complex propagation constant, and $\omega = 2\pi \times 10^9$ rad/s is the angular frequency. The absolute value of the attenuation in the cable in dB/metre is ________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.86 to 0.88
Explanation
The attenuation constant is the real part of $\gamma$, which is $\alpha = 0.1$ Np/m. To convert to decibels, multiply by $20\log_{10} e = 8.686$, which gives $0.8686$ dB/m.