50 Radio Engineering for Wireless Communication and Sensor Applications
Table 3.2
Standard Waveguides
Abbreviation |
a [mm] |
b [mm] |
f c [GHz] |
Range [GHz] |
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WR-90 |
22.86 |
10.16 |
6.56 |
8.2–12.4 |
WR-75 |
19.05 |
9.53 |
7.87 |
10–15 |
WR-62 |
15.80 |
7.90 |
9.49 |
12.4–18 |
WR-51 |
12.95 |
6.48 |
11.6 |
15–22 |
WR-42 |
10.67 |
4.32 |
14.1 |
18–26.5 |
WR-34 |
8.64 |
4.32 |
17.4 |
22–33 |
WR-28 |
7.11 |
3.56 |
21.1 |
26.5–40 |
WR-22 |
5.69 |
2.84 |
26.3 |
33–50 |
WR-19 |
4.78 |
2.39 |
31.4 |
40–60 |
WR-15 |
3.76 |
1.88 |
39.9 |
50–75 |
WR-12 |
3.10 |
1.55 |
48.4 |
60–90 |
WR-10 |
2.54 |
1.27 |
59.0 |
75–110 |
WR-8 |
2.03 |
1.02 |
73.8 |
90–140 |
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0.1 dB/cm, the power absorbed into the walls of the waveguide is about 240 W/cm at the maximum power. If the load reflects some of the power, the maximum field strength is due to the standing wave higher than in the matched case. Then, the maximum power is lower than that calculated above.
3.4.2 TM Wave Modes in Rectangular Waveguide
TM wave modes have no longitudinal magnetic field component, Hz = 0. The solution of the longitudinal electric field has a form of
Ez = B sin (k 1 x ) sin (k 2 y )
The other field components are
Hx = |
vek |
2 |
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j |
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B sin (k 1 x ) cos (k 2 y ) |
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k 2c |
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ve k 1 |
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Hy = −j |
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B cos (k 1 x ) sin (k 2 y ) |
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k 2c |
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Ex = Z TM Hy
(3.57)
(3.58)
(3.59)
(3.60)
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Transmission Lines and Waveguides |
51 |
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Figure 3.6 Attenuation of standard waveguides.
Ey = −Z TM Hx |
(3.61) |
The wave impedance of TM modes is
Z TM = h√ |
1 − ( f c /f )2 |
(3.62) |
From boundary conditions it follows that the equations for the cutoff wavelength and cutoff frequency are the same as those for the TE wave modes. Now, both indices n and m have to be nonzero. The TM wave mode having the lowest cutoff frequency is TM11 . Although TM11 and TE11 wave modes have equal cutoff frequencies, their field distributions are different. Figure 3.7 shows transverse field distributions of some TE and TM wave modes.