circular waveguide
According to the mode and frequency to calculate the waveguide radius
Parameters
frequency
f
\(Hz\)
Azimuth mode
m
\(\)
Radial mode
n
\(\)
radius
r
\(m\)
Output
Root of Bessel J Prime `chi'_{mn}`
`J'_{mn}(chi)=0`
Wave number k
`k=omega sqrt(epsilon mu)=omega/c=(2 pi f)/c`
Cutoff radius a
`k=k_c=(chi')/a`
cutoff wave number `k_c`
`k_c=(chi\')/a`
cutoff frequency `f_c`
`k_c=(2*pi*f_c)/c`
`k_z`
`k_z^2+k_c^2=k^2`
impedance `Z_{TE}`
`Z_{TE}=(omega*mu)/k_z`
TM mode
`chi_{mn}`
`J(chi_{mn})=0`
`k_c`
`k_c=chi/a`
Cutoff radius a
`k_c=chi/a`
cutoff frequency `f_c`
propagation const `k_z`
Impedance `Z_{TM}`
`Z_{TM}=E_rho/H_phi=(Z_0*k_z)/k`