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Calculate the cut off wavelength, guide wavelength, characteristic wave impedance of a wave guide whose internal diameter is 4 cm for a 12 GHz signal propagated in it in the TE111 mode.
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λ=vcf=3×101010×109=3cm λc=2πr(kr)=2π×4/21.84=4π1.84=6.83cm  λp=λ1(λ/λ0)2=31(3/6.83)2=310.193=3.34cm Z0=x1(λλ0)2=120π0.898=420Ω

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