Waveguide Theory

          In order to be able to use waveguides to their best impact, it is necessary to own a basic understanding of conductor theory, as well as propagation and also the propagation constant. whereas conductor theory will become significantly concerned, it is not the aim here to dig too deeply into the conductor theory arithmetic.

          Waveguide theory is predicated around radiation theory as a result of the waves propagating on waveguides square measure magnetic force waves that are forced, usually inside a hollow metal tube. The constrictive boundaries of the metal tube stop the radiation from spreading out and thereby reducing in intensity in step with the inverse sq. law. As a result, losses square measure terribly low.

Waveguide theory of propagation

            According to conductor theory there square measure variety of various kinds of radiation which will propagate inside the conductor. These differing kinds of waves correspond to the various parts inside associate degree radiation.

• TE waves: crosswise electrical waves, conjointly typically referred to as H waves, square measure characterized by the actual fact that the electrical vector (E) is often perpendicular to the direction of propagation.
• TM waves: crosswise magnetic waves, conjointly referred to as E waves square measure characterized by the actual fact that the magnetic vector (H vector) is often perpendicular to the direction of propagation.
• TEM waves:   The crosswise radiation is can not be propagated inside a conductor, however is enclosed for completeness. It is the mode that is usually used inside coaxal and open wire feeders. The TEM wave is characterized by the actual fact that each the electrical vector (E vector) and also the magnetic vector (H vector) square measure perpendicular to the direction of propagation.

          Text regarding conductor theory usually refers to the TE and metal waves with integers once them: TEm,n. The numerals M and N square measure continuously integers which will defy separate values from zero or one to eternity. These indicate the wave modes inside the conductor.

       Only a restricted range of various m, n modes may be propagated on a conductor dependent upon the conductor dimensions and format.

          For each mode there is a precise lower frequency limit. this can be called the cut-off frequency. Below this frequency no signals will propagate on the conductor. As a result the conductor may be seen as a high pass filter.

          It is attainable for several modes to propagate on a conductor. the quantity of attainable modes for a given size of conductor will increase with the frequency. It is conjointly price noting that there is only 1 attainable mode, referred to as the dominant mode for rock bottom frequency which will be transmitted. It is the dominant mode within the conductor that is ordinarily used.

          It ought to be remembered, that although conductor theory is expressed in terms of fields and waves, the wall of the conductor conducts current. for several calculations it is assumed to be an ideal conductor. actually this can be not the case, and a few losses square measure introduced as a result.

Rules of thumb 

        There square measure variety of rules of thumb and customary points which will be used once managing conductor theory. 

• For rectangular waveguides, the TE10 mode of propagation is that the lowest mode that is supported.     

• For rectangular waveguides, the width, i.e. the widest internal dimension of the cross section, determines the lower cut-off frequency and is adequate to 1/2 wavelength of the lower cut-off frequency.

• For rectangular waveguides, the TE01 mode happens once the peak equals 1/2 wavelength of the cut-off frequency. 

• For rectangular waveguides, the TE20, happens once the breadth equals one wavelength of the lower cut-off frequency.

 Waveguide propagation constant

           A amount called the propagation constant is denoted by the Greek letter gamma, γ. The conductor propagation constant defines the part and amplitude of every part of the wave because it propagates on the conductor. The issue for every part of the wave may be expressed by:

 exp[jωt - γm,n z]

Where:

    z = direction of propagation

    ω = angular frequency, i.e. two π x frequency

          It may be seen that if propagation constant, γm,n is real, the part of every part is constant, and during this case the amplitude decreases exponentially as z will increase. during this case no important propagation takes place and also the frequency used for the calculation is below the conductor cut-off frequency.

          It is truly found during this case that a little degree of propagation will occur, however because the levels of attenuation square measure terribly high, the signal solely travels for a really tiny distance. because the results square measure terribly predictable , a brief length of conductor used below its cut-off frequency may be used as associate degree attenuation with renowned attenuation.

          The alternative case happens once the propagation constant, γm,n is imagined. Here it is found that the amplitude of every part remains constant, however the part varies with the gap z. this suggests that propagation happens inside the conductor.

          The value of γm,n is contains strictly imagined once there\'s a completely loss less system. As actually some loss continuously happens, the propagation constant, γm,n can contain each real and imagined elements, αm,n and βm,n severally.

Accordingly it will be found that:

γm,n   =   αm,n + j βm,n

           This conductor theory and also the conductor equations square measure true for any conductor despite whether or not they square measure rectangular or circular.



By RR Team

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