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

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)

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 it s like parallel universe 2) Waveguide 1) Signal Source 1) Control Room (source)

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 it s like parallel universe b 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.

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

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 12.4 - 18 Location of modes Some Standard Rectangular Waveguide

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

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 = 2.840 mils and b = 1.340 mils. Converting to metric units we have a = 7.214 cm and b = 3.404 cm. TE10 TE01 TE20 TE11 TM11 TE10: TE01: TE20: TE11:

Rectangular Waveguide Example:

Rectangular Waveguide Example:

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) 2.286 cm and b = 0.450 inch (or) 1.143 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!

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:

Rectangular Waveguide Let`s consider an example WR90 Standard Waveguide it s like parallel universe

Rectangular Waveguide Case 1) WR-90 (X-Band) Waveguide a=1.016 cm No Propagation, The Incomig Wave Is Reflected b=2.286 cm it s like parallel universe Incoming wave frequency (f)=5 GHz

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

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 it s like parallel universe 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

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 it s like parallel universe Incoming wave frequency (f)=18 GHz

Rectangular Waveguide Final Decision to choose the appropriate operating frequency: WR-90 (X-Band) Waveguide a=1.016 cm b=2.286 cm it s like parallel universe 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 6.5-13.1 GHz.

Rectangular Waveguide 8.2-12.4 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 8.2-12.4 GHz high loss zone low loss zone it s like parallel universe

Standard Sizes of Rectangular Waveguide

Standard Sizes of Rectangular Waveguide

Microwave Connectors it s like parallel universe It is highly recommended to visit http://www.microwaves101.com/encyclopedia/connectors.cfm for more information. Also the webpage is available in the folder)

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. http://www.learningmeasure.com/cgi- 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)