TE mode in circular wave-guide
If the frequency is very close to the cutoff frequency, the field amplitude is not accurate because \(\sqrt{1-(\frac{f_c}{f})^2}\) tends to be zero.
constants:c mu0
Azimuth mode number
Radial mode number
Radius of the wave guide
Frequency
Power
\(\chi_{mn}'\)
\(J'_m(\chi)=0\)
cutoff wave number
\(k_c=\chi_{mn}/a\)
cutoff frequency
\(k_c=k=\frac{\omega}{c}=\frac{2 \pi f_c}{c}\)
cutoff wave length
\(c=\lambda_c k_c\)
wave number for f0
\(k=\frac{\omega}{c}=\frac{2 \pi f_0}{c}\)
axial wave number
\(k^2=k_c^2+k_z^2\)
waveguide wavelength
\(\lambda_g k_z=2\pi\)
wave impendance
\(Z_{mn}=\frac{\omega \mu}{k_z}=\frac{120\pi}{\sqrt{1-(f_c/f)^2}} \)
Hz0
\(P=H_{z0}^2 \frac{Z_0}{2}(\frac{f}{f_c})^2\sqrt{1-(\frac{f_c}{f})^2} \pi \frac{1}{2} a^2[J_m(\chi_{mn}')^2-J_{m-1}(\chi_{mn}')J_{m+1}(\chi_{mn}')]\)
\(E_{\phi0}\)
\(E_{\phi}=j(\frac{\omega\mu_0 H_{z0}}{k_c})J'_m(k_c r) cos(m\phi) e^{-j k_z z}\)
\(E_{r0}\)
\(E_{r}=j(\frac{\omega \mu_0 m H_{z0}}{k_c^2}) \frac{J_m(k_c r)}{ r} sin(m\phi)e^{-j k_z z}\)
\(C_{mn}\)
\( \frac{1}{\sqrt{\pi(\chi_{mn}^{'2}-m^2)J_m^2(\chi_{mn}')}}\)