The TE10 mode in a rectangular waveguide using rotational 3D wireframe diagrams

Background

 

RECTANGULAR WAVEGUIDE

Useful bandwidth is defined as the case when only a single mode can propagate. This means that only the dominant mode can propagate. It has been found that one of the widest single-mode-propagating waveguide cross sections is NOT the cylindrical waveguide cross section but the RECTANGULAR waveguide cross section, in which the second higher-order mode cut-in frequency would be higher than in other structures. The figure below shows such a rectangular waveguide in a left-handed rectangular coordinate system, where 'a' is the wider dimension and 'b' is the narrower inside dimension.

The rectangular waveguide, being a waveguide and a one-conductor propagating transmission line, can propagate only at higher-order modes. The modes of transmission can consequently be only in TE and TM modes. Subscripts are used to describe the electric and magnetic field configurations. The general symbols of TE or TM are used to describe transverse electric or transverse magnetic waves. The subscript 'm' indicates the number of HALF-WAVE variations of the electric field along the WIDE dimension of the waveguide, and 'n' indicates the number of HALF-WAVE variations of electric or magnetic field in the NARROW dimension of the guide (n for "narrow"). The TE mode, which has the longest operating wavelength, is designated as the DOMINANT mode. This is the mode for the lowest frequency that will propagate in the waveguide. If 'a' (the wide dimension of the waveguide) is less than half a wavelength (< l /2), NO PROPAGATION WILL OCCUR. Therefore, the waveguide acts as a high pass filter. For a rectangular waveguide, the cutoff frequency can be found from:

where : = c = 3 x 108 m/s (speed of light), m and n = the subscripts of the particular TE or TM mode, a and b = the wide and narrow dimensions of the rectangular guide.

The cutoff wavelength is then given by:

The cutoff for the dominant mode can easily be calculated. The dominant mode being the TE10. Substituting 1 for 'm' and 0 for 'n',

That is,

The field configuration in a rectangular waveguide propagating the commonly used TE10 mode is shown in the applet below.

Rectangular waveguides were originally chosen so that the dominant mode would exist over a certain frequency range. This frequency range determines the 'a' dimension. The 'b' dimension is chosen on the basis of the following criteria:

- the attenuation loss is greater as the 'b' dimension is made smaller

- the 'b' dimension determines the voltage breakdown characteristics and therefore determines the maximum power handling capacity.

For larger power handling capacity, 'a' and 'b' should be made as large as possible. In practice, 'b' is made about half of the 'a' dimension. It is desirable in all types of transmission systems to select sizes so that only one mode of propagation is possible. In other words, the physical size of the guide is related to the frequency band under consideration. Because of the possibility of higher-order modes, it has become common to operate waveguides over an approximately 50% frequency band. By properly selecting this frequency range, it is possible to operate far enough from cutoff so that the guide parameters do not vary too rapidly and to avoid also the frequency region where other modes are possible. The figure below shows the field configurations of some of the other higher-order modes.


 
 

The Applet

 In this applet are shown two fields for the TE10 mode; the magnetic field and the electric field. The magnetic field is that field which forms rectangular rings and the electric field is that field shown by a sine wave strip. One full cycle of the electric field is shown and its intensity is at a maximum in the centre of the sine wave strip. Color coding and mesh density has been used to indicate the sinusoidal variation of electric field strength across the strip of the peak electric field. The peak electric field variation with time, always alternates from bottom to top of the waveguide (or vice-versa), and the sinusoidal field strength or intensity increases from the edges of the field or waveguide to the centre of the guide. The magnetic field is keyed to the peak electric field, so that the centre-most ring of the magnetic field indicates a zero value of the peak electric field, and the position where two sets of magnetic field rings edge on each other, the peak electric field reaches a maximum value. The waveguide walls confine the side-ways, top and bottom of each of these fields, whereas the direction of motion of the field is along the waveguide itself. For simplicity only a snapshot of the fields is shown. It can be imagined that both fields travel along the waveguide in time keeping their same spacial form. The applet has been designed so that the fields can be viewed from different angles, indicating how the fields would look if they could be seen.
 
 

The source.

Tony Townsend tonyart@ieee.org