Answer to Question #305146 in Electricity and Magnetism for Rhulani

Question

A circular copper waveguide has a radius of 0.4 cm and is filled with a dielectric material having 𝜀𝑟 = 1.5 and tan δ = 0.0002.

2.1.1. Identify the first four propagating modes and their cut-off frequencies.

2.1.2. For the dominant mode, calculate the attenuation due to dielectric loss and attenuation due to conductor loss at 20 GHz.

Answer 1

1)

$\nu_1=20~GHz,$

$\nu_2=5.0~GHz,$

$\nu_3=2.2~GHz,$

$\nu_4=1.3~GHz.$

2)

$k_d=\omega\sqrt{\mu\epsilon(1-j\tan\delta)}=0.4~GHz,$

$k_c=\beta-j\alpha=350~MHz.$