| |
Cut-off Frequency of a Mode |
|
The propagation constant of the modal fields in the  -direction is given as |
|
 |
---------- (6.17) |
| |
| ---------- (6.18) |
| |
|
|
|
If the propagation constant  is real the mode will be at travelling mode whereas, if becomes imaginary the wave exponentially decays in the -direction and the fields do not represent a wave. These fields are then called 'EVANASENT FIELDS' . The evanasent fields do not carry any power. The power is carried only by the travelling modes. |
|
|
|
For the travelling mode therefore we need to be real which implies |
| |
|
---------- (6.19) |
|
Since |
|
 |
---------- (6.20) |
|
where  is the velocity of the uniform plane wave in medium 1, we get |
|
 |
|
| ---------- (6.21) |
| ---------- (6.22) |
| |
|
|
We can note the following important things at this stage: |
|
|
(1) |
For a given waveguide height  , the frequency has to be higher than certain threshold frequency for propagation of a particular mode. The threshold frequency is called CUT-OFF freuquency at the mode and given by |
|
|
|
|
---------- (6.23) |
| |
|
The corresponding cut-off wavelength is |
|
 |
---------- (6.24) |
|
|
(2) |
For a given waveguide height,  , and frequency,  , only those modes propagate for which  . |
|
This means inside a wave guide there is a possibility of only finite number of modes at a given frequency. |
|
|
(3) |
As the mode number (  ) increases and the cut-off frequency also increases meaning higher order mode get excited only at higher frequencies. |
|
|
|
The cut-off frequencies for different modes are shown in the following figure: |
|
|
|
|
If a mode has the cut-off frequency less than the frequency of operation the mode propagates otherwise it does not propagate. |
|
|
NOTE : |
|
The  mode which is also the TEM mode has no cut-off frequency. This is the mode which can propagate at any frequencies starting from  . |
|
.jpg)
