1. Rectangular Waveguide
In the name of God
Antenna and Microwave Laboratory
Babol Noshirvani University of Technology, Iran
Rectangular Waveguide
Import video, voice + dipole 60cm

2. Rectangular Waveguide
In Microwave frequencies, waveguides play the same role as simple wires do in dc/low frequencies.
Cobham Company, manufacturer of waveguide components (also see Cobham Catalog in the folder)

3. Rectangular Waveguide 1) Control Room (source)
Waveguides are primarily used to transfer the signal from the source to antenna or vise-versa.
3) deliver to Antenna
3) Antenna
2) Waveguide Section
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2) Waveguide
1) Signal Source
1) Control Room (source)

4. Rectangular Waveguide
Fundamental Sweet Theory:
The Waveguide assigns a set of rules in order to allow an incoming wave to be propagated inside it.
Highway name = TE10
Highway name = TE20
Highway name = TE01
Highway name = TM11
Highway name = TE11 … a
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Rule#1) But, the Propagating wave inside the rectangular waveguide will be either TE or TM, and not TEM.
Incoming wave with frequency (f) can be TEM, TE, or TM.
Rule#2) The propagation speed in each highway is also different with the others and in not constant c=3*10^8.

5. Rectangular Waveguide
Waveguide can support TE and TM modes.
The order of the mode refers to the field configuration in the guide, and is given by m and n integer subscripts, TEmn and TMmn.
A particular mode is only supported above its cutoff frequency. The cutoff frequency is given by
Location of modes

6. Rectangular Waveguide
The cutoff frequency is given by:
Waveguide
Designation a
(in) b t
fc10
(GHz)
freq range
WR975
9.750
4.875
.125
.605
.75 – 1.12
WR650
6.500
3.250
.080
.908
1.12 – 1.70
WR430
4.300
2.150
1.375
1.70 – 2.60
WR284
2.84
1.34
2.08
2.60 – 3.95
WR187
1.872
.872
.064
3.16
3.95 – 5.85
WR137
1.372
.622
4.29
5.85 – 8.20
WR90
.900
.450
.050
6.56
8.2 – 12.4
WR62
.311
.040
9.49
Location of modes
Some Standard Rectangular Waveguide

7. Rectangular Waveguide
Waveguide Identity:
Each waveguide, based ONLY on its dimensions (a&b) has a unique identity (Set of Highway Rules): a b
fmn is the minimum required frequency (f) the incoming wave must have in order to have the permission to drive in highway #mn
umn is the allowable driving speed in highway #mn

8. Rectangular Waveguide
Example:
Let us calculate the cutoff frequency for the first four modes of WR284 waveguide. From Table 7.1 the guide dimensions are a = mils and b = mils. Converting to metric units we have a = cm and b = cm.
TE10
TE01
TE20
TE11
TM11
TE10:
TE01:
TE20:
TE11:

9. Rectangular Waveguide
Example:

10. Rectangular Waveguide
Example:

11. Rectangular Waveguide
Example:
Let’s determine the TE mode impedance looking into a 20 cm long section of shorted WR90 waveguide operating at 10 GHz.
From the Waveguide Table 7.1, a = 0.9 inch (or) cm and b = inch (or) cm.
TE10
TE20
TE01
TE11
TM11
6.56 GHz
13.12 GHz
TE02
26.25 GHz
14.67 GHz
13.13 GHz
TE10
6.56 GHz
Mode
Cutoff Frequency
TE01
13.12 GHz
TE11
14.67 GHz
TE20
13.13 GHz
TE02
26.25 GHz
At 10 GHz, only the TE10 mode is supported!

12. Rectangular Waveguide
Example:
The impedance looking into a short circuit is given by:
The TE10 mode impedance:
The TE10 mode propagation constant is given by:

13. Rectangular Waveguide Let`s consider an example
WR90 Standard Waveguide
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14. Rectangular Waveguide
Case 1)
WR-90 (X-Band) Waveguide
a=1.016 cm
No Propagation, The Incomig Wave Is Reflected
b=2.286 cm
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Incoming wave frequency (f)=5 GHz

15. Rectangular Waveguide
Case 2)
WR-90 (X-Band) Waveguide
a=1.016 cm
b=2.286 cm
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Incoming wave frequency (f)=8 GHz
Highway name = TE10 and Speed=u10

16. Rectangular Waveguide
Case 3)
WR-90 (X-Band) Waveguide
Highway name = TE10 and Speed=u10
Highway name = TE20 and Speed=u20
Highway name = TE01 and Speed=u01
a=1.016 cm
b=2.286 cm
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higher highway #s have more speed (based on umn formula)
As a result, the outcoming waves are not summed synchronously, and the dispersion happens, which is a disaster !
Incoming wave frequency (f)=15 GHz

17. Rectangular Waveguide
Case 4)
WR-90 (X-Band) Waveguide
Highway name = TE10 and Speed=u10
Highway name = TE20 and Speed=u20
Highway name = TE01 and Speed=u01
Highway name = TM11 and Speed=u11
Highway name = TE11 and Speed=u11
a=1.016 cm
b=2.286 cm
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Incoming wave frequency (f)=18 GHz

18. Rectangular Waveguide
Final Decision to choose the appropriate operating frequency:
WR-90 (X-Band) Waveguide
a=1.016 cm
b=2.286 cm
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In practical application, ONLY one propagation mode (highway) must be excited (as in case 2). Otherwise the dispersion will happen (as in case 3,4).
As a result, the operating frequency for this WR90 example is proposed between GHz.

19. Rectangular Waveguide
In the case when the loss of the conductor is accounted (not PEC), the following attenuation (α) plot must be considered.
Based on this, the frequencies so close to cutoff will result in high amount of loss which is not appropriate.
As a result, the operating frequency must have some distance from the cutoff frequency.
The proposed operating frequency for WR90 waveguide is then defined as GHz
high loss zone
low loss zone
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20. Standard Sizes of Rectangular Waveguide

21. Standard Sizes of Rectangular Waveguide

22. Microwave Connectors
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It is highly recommended to visit for more information. Also the webpage is available in the folder)

23. Frequency (GHz), Theory
Task
Please insert first 9 calculated modes of your regarded waveguide (each student one type) in the Table.
Also insert your waveguide name, dimension, frequency range, and band name in Table Caption.
Then visit this link to get your cut-off frequencies calculated in theory. Insert these frequencies in the Table as well. bin/calculators/rectwgm.pl
Mode TEmn
Frequency (GHz), CST
Frequency (GHz), Theory
TE10
TE20
TE01
TE11
TM11
TE21
TM21
TE12
TM12
Table A:
WR? (? cm × ? cm)
? -Band (?GHz- ?GHz)