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FEED LINE BASICS 277

describes a single wave mode with definite propagation constant while the actual analytical
or numerical value of is strained by the boundary and radiation conditions. If two or more
modes have the same propagation constant (called sometimes eigenvalue) but different field
patterns (called sometimes eigenvectors), they are degenerate modes. The phenomenon of
mode degeneration is quite seldom event and typically appears in feed lines of high rotation
symmetry like circular or square waveguide.
The standard classification of wave modes reflects which field components are present or
absent. For example, the modes are called
1. Transverse EM, TEM in short, if there are no longitudinal components at all, i.e. =

= 0.

2. Quasi-TEM, → 0, → 0, if the energy stored by the longitudinal components in

respect to the total energy carried by line is so insignificant that it can be neglected. The
important feature of quasi-TEM mode is that the frequency lowering makes it more and
more similar to pure TEM.
3. Transverse E, TE in short, if the longitudinal electric component = 0 while ≠ 0.

Also it is called H-modes.
4. Transverse M, TM in short, if the longitudinal electric component = 0 while ≠ 0.

Also it is called E-modes.
5. Hybrid HE if the total energy carried by H-fields of mode is dominant while ≠ 0, ≠

0.
6. Hybrid EH if the total energy carried by E-fields of mode is dominant while ≠ 0, ≠

0.
Occasionally, it is suitable to use other classification arrangements based on the presence or
absence of some transversal components [17].
Finally, note that the feed line definition we outlined at this introduction is too broad and
includes, for example, all antennas and free space as a feed line between them. To be more
specific, we add the condition that any energy loss in line (likewise heat or radiation) must be
minor, i.e. ≪ 1 in (6.1). Then formally all feed lines can be attributed to two broad classes:
open to surrounding and unlimited space and isolated from it.

6.1 FEED LINE CHARACTERISTICS

6.1.1 TEM Mode
Writing (6.1) and (6.2) we claimed without proof that EM wave could propagate over a line.
To be more specific let us start from the simplest case of TEM mode that is very similar to the
waves in free space (see Chapter 4). Let look back at the equation (6.2) and suppose now that
the line is free-of-loss ( = ) and − = 0 or = ±. The equity (6.1) tells us that, for
� 2
2
2
2
example,
(, , ) = (, ) (∓) (6.4)
A quick comparison of (6.4) and (4.52) reveals that (6.4) describes the electric vector of EM
wave that is guided along the z-axis likewise the wave propagating in source-free space. The