Worked example 7.3.3: The waveguide feed of a microwave oven

$f_{co,10}=\frac{3\times 10^8}{0.1728}=1.736\mathrm{GHz}$ and $f_{co,20}=f_{co,01}=3.472\mathrm{GHz}$ ($b=a/2$): only TE${}_{10}$ at $2.45\mathrm{GHz}$.

$\lambda =12.24\mathrm{cm}$ and $s=\sqrt{1-(1.736/2.45{)}^2}=0.7056$:

$R_s=12.9\mathrm{m\Omega }$ and ${\alpha }_c=1.69\times 10^{-3}Np/m=0.0147dB/m$: $0.003\mathrm{dB}$ in $20\mathrm{cm}$, about $0.7\mathrm{W}$ of the $1\mathrm{kW}$.

$f_{co,10}=\frac{3\times 10^8}{0.12}=2.5\mathrm{GHz}>2.45\mathrm{GHz}$: the mode is evanescent, with

and $18\mathrm{dB}$ is lost in $20\mathrm{cm}$.

$E_0$ is $125$ times below the breakdown field, so the oven guide could carry $125^2\approx 16000$ times more power before arcing in clean air. In (e) the condition for propagation is $a>\lambda /2=6.12\mathrm{cm}$.