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An aluminum waveguide with a=4.2 cm,b=1.5 cm,σc=3.5×107mhos/m, filled with telfon..

An aluminum waveguide with a=4.2 cm,b=1.5 cm,σc=3.5×107mhos/m, filled with telfon (μr=1,ϵr=2.6,σ=1015mhos/m) operates at 4GHz. Determine,

(a) αc and αd for TE10 mode

(b) The waveguide loss in dB over a distance of 1.5 m.

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Solution:

Cut off frequency for TE10 mode is,

fc10=12aμϵ=12x0.042μo2.6ϵ=2.213GHzδs=1πfμσc=1.35×106 mRs=1σδs=13.5×107×1.35×106=0.02110hms1(fcf)2=1(2.2134)2=0.6939η=η0μrεr=233.8ohms

αc=2Rsbη×[{1+ba}(fcf)2+{1(fcf)2}]=0.0133 Np/m

αd=σdηo21(fcf)2=1015×3772×1.66=1.4×1013 Np/m

αcαd,αd can be neglected The wave propagating in the +z direction in the rectangular waveguide vary as eαcz=e(0.0133)(1.5)=0.9802 Np or =20log10(0.9868)=0.1737 dB

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