rectangle waveguide

width

height

frequency

Mode

Power

Break Electric Field

Phase

wavelength `lambda`

`lambda f=c`

angular frequency `omega`

`omega=2 pi f`

Wave number k

`k=omega sqrt(epsilon mu)=omega/c`

 `k_x`

`k_x=(m pi)/a`

 `k_y`

`k_y=(n pi)/b`

cutoff wavenumber `k_c`

`k_c^2=k_x^2+k_y^2`

cutoff frequency `f_c`

`k_c=omega/c=(2 pi f)/c`

 `k_z`

`k^2=k_x^2+k_y^2+k_z^2`

horizontal angle  `theta`

`tan(theta)=k_x/k_z`

vertical angle `phi`

`tan phi=k_y/k_z`

cutoff angle `theta_c`

`sin theta_c=k_c/k`

waveguide wavelength `lambda_g`

`lambda_g=(2 pi)/k_z`

Wave Impendance `Z`

`Z=E_x/H_y=(omega mu)/k_z`

 `H_0`

`P=(Z k_z^2 a b H_0^2)/(8|4 k_c^2)`

 `E_{y0}`

`H_0 (Z k_z m pi)/(a k_c^2)`

 `E_0`

`E_0=H_0 (omega mu)/k_c^2`

 `E_{x0}`

`E_{x0}/E_(y0)=n/m a/b`

 `H_{zmax}`

`H_{zmax}=E_b/sqrt(1+(n/m a/b)^2) (a k_c^2)/(Z k_z m pi)`

Break Power `P_b`

`P_b=(Z k_z^2 a b H_{zmax}^2)/(8|4 k_c^2)`

 `phi(E_x)`

`phi+90^0`

 `phi E_y`

`phi-90^0`

express `E_x(x,y)`

`cos((m pi)/a x)sin((n pi)/b y)`

 `E_y(x,y)`

`sin((m pi)/a x)cos((n pi)/b y)`