How to compute Cutoff-Frequencies

There are at least two ways to compute cutoff-frequencies with GdfidL. The easiest way is to compute resonant fields in a short section of the waveguide. When the proper boundary conditions are applied, the resulting fields and frequencies are the resonant fields at cutoff and their cutoff-frequencies.

Computation of resonant fields

The fields at cutoff can be found as resonant fields in a short section of the waveguide. Since the fields are at cutoff, they do not vary in the direction of the waveguide. The boundary conditions therefore are electric walls for TM-modes, magnetic walls for TE-modes, or periodic boundary conditions with phase shift zero for both kinds of modes.

The easiest is just to apply periodic boundary conditions with a phase shift of zero, although this is not the most computational efficient. While we are at waisting CPU-cycles, we do not even consider symmetries in the geometry of the waveguide. The computation of the cutoff-frequencies in an elliptical waveguide then is:

    gd1 < waveguide.gdf | tee out


After some seconds we get a list of frequencies like:

    i   freq(i)       acc(i)         cont(i)
1  122.4760e+6   1.2263639315  0.4112620337       # "grep" for me
2    2.2297e+9   0.0000035244  0.0000021997       # "grep" for me
3    4.0480e+9   0.0000000681  0.0000000812       # "grep" for me
4    4.4089e+9   0.0000015489  0.0000098211       # "grep" for me
5    4.7150e+9   0.0000012703  0.0000029069       # "grep" for me
6    5.7555e+9   0.0000000273  0.0000000753       # "grep" for me
7    5.8907e+9   0.0000003628  0.0000035260       # "grep" for me
8    6.1920e+9   0.0000000138  0.0000000484       # "grep" for me
9    7.0729e+9   0.0000002350  0.0000009870       # "grep" for me
10    7.6704e+9   0.0000000257  0.0000001639       # "grep" for me
11    7.7208e+9   0.0000001496  0.0000008549       # "grep" for me
12    8.4049e+9   0.0000000052  0.0000000316       # "grep" for me
13    8.5090e+9   0.0000000066  0.0000002716       # "grep" for me
14    8.5653e+9   0.0000000160  0.0000000900       # "grep" for me
15    9.3371e+9   0.0000000107  0.0000000643       # "grep" for me
16    9.3944e+9   0.0000000482  0.0000005784       # "grep" for me
17    9.7872e+9   0.0000000188  0.0000002359       # "grep" for me
18    9.9837e+9   0.0000000028  0.0000000718       # "grep" for me
19   10.0480e+9   0.0000000123  0.0000000657       # "grep" for me
20   11.0034e+9   0.0000000107  0.0000000613       # "grep" for me
21   11.0735e+9   0.0000000032  0.0000002290       # "grep" for me
22   11.1497e+9   0.0000000023  0.0000000642       # "grep" for me
23   11.3516e+9   0.0000000020  0.0000000512       # "grep" for me
24   11.5672e+9   0.0000000006  0.0000000049       # "grep" for me
25   12.2768e+9   0.0000000036  0.0000000307       # "grep" for me
26   12.4153e+9   0.0000000038  0.0000001697       # "grep" for me
27   12.4677e+9   0.0000000004  0.0000000200       # "grep" for me
28   12.5967e+9   0.0000000024  0.0000001197       # "grep" for me
29   12.6975e+9   0.0000000010  0.0000000626       # "grep" for me
30   12.7606e+9   0.0000000009  0.0000000088       # "grep" for me
31   13.3912e+9   0.0000000012  0.0000000132       # "grep" for me
32   13.6535e+9   0.0000000003  0.0000000085       # "grep" for me
33   13.8491e+9   0.0000000030  0.0000001071       # "grep" for me
34   13.9047e+9   0.0000000011  0.0000000236       # "grep" for me
35   14.2239e+9   0.0000000031  0.0000000697       # "grep" for me
36   14.4204e+9   0.0000000076  0.0000002782       # "grep" for me
37   14.5021e+9   0.0000000142  0.0000004646       # "grep" for me
38   14.7227e+9   0.0000000058  0.0000001524       # "grep" for me
39   15.0025e+9   0.0000000064  0.0000001735       # "grep" for me
40   15.1974e+9   0.0000000197  0.0000007736       # "grep" for me
41   15.3650e+9   0.0000000651  0.0000015631       # "grep" for me
42   15.6836e+9   0.0000005207  0.0000117680       # "grep" for me
43   16.0273e+9   0.0046087858  0.1073045033       # "grep" for me
44   16.0768e+9   0.0039905447  0.6498775793       # "grep" for me
45   16.1235e+9   0.0047293597  0.3225176260       # "grep" for me
46   16.2417e+9   0.0027525493  0.0795671401       # "grep" for me
47   16.5221e+9   0.0069169406  0.2046412339       # "grep" for me
48   16.6937e+9   0.0606064395  0.9964082399       # "grep" for me
49   17.2006e+9   0.0274154940  0.4583279318       # "grep" for me

The inputfile for this cavity is waveguide.gdf

Looking at the results

We use the postprocessor to look at the electric or magnetic fields at cutoff.

We start the postprocessor, gd1.pp, and use him interactively:
Input for gd1.pp:

     -general, infile= @last

-3darrow
fcolour= 7, eyeposition= ( 1, 2.3, 3 ), scale= 5
quantity= ere
solution= 2
doit

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Thats it.