Page 295 - Maxwell House

FEED LINE BASICS 275

Introduction
Roughly speaking, a feed aka a transmission line can be defined as any physical structure that
is capable of transporting the EM energy from some designated space area named a
source/generator to another distant one called a load. To make such wide-ranging
characterization practicable, we will assume that this energy is carried by EM waves
localized/confined in space along some path (not required to be straight and shortest) from the
generator to load. The methods of EM energy confinements are the main topic of the following
discussion. Note only that independent on confinement tactic the speed of energy

transportation is restricted by the speed of light and EM waves come to destination point with
finite delay ∆ = .
⁄

Regardless of frequency band, a feed line or feed in short must meet the multiple and often
conflicting requirements of their efficiency, power handling, noise temperature, distortions of
guided by line signals, sizes, cost, weight, producibility, strong resistance to fluctuating
environmental conditions like temperature, vibration and humidity, and so on. It is worthy to
point out that single and perfect feed for all applications continues to be a deceptive dream. In
other words, until today a plenty of different feeds and broad area of trade-off exists making
engineering work challenging and excited. We are not going to exercise the detailed
mathematical analysis of EM wave propagation in feeds thereby restricting ourselves with just
common ideas and facts to help to make the correct choice. Note that any of widely available
commercial EM simulation tools is capable of providing highly accurate data for almost any
line in seconds while the same level of rigorous analysis is mostly cobblestone and can be done
for “counted on the fingers of one hand” set of lines like classical coax, rectangular, circular
and elliptic waveguide, and maybe couple others.

To simplify the subsequent consideration, we make several assumptions:
1. Our area of analysis is the space-frequency domain.
2. EM waves can propagate only straightforward over the longitudinal axis which we will
take as the z-axis while x, y (Cartesian coordinates) or r, (polar coordinates) are the
transverse coordinates.
3. The feed line is uniform. It means that line dimensions and all thinkable material
inclusions, as well as their electrical properties, are identical at all planes transverse to the
direction of propagation is independent on the z-coordinate.
4. All field sources such as charges or currents are located outside the area where the EM
wave propagation is analyzed.
The first three assumptions let suggest the uniformity in the transverse electric and magnetic
field distribution meaning that at some frequency

(, , , ) = (, ) (∓) � (6.1)
(, , , ) = (, ) (∓)
Here the exponential factor describes the phenomenon of wave propagation over the z-
coordinate while = ∓ + is the complex propagation constant, ≥ 0 [1/m] is called the
attenuation constant, and [rad/m] is called the phase constant. The negative sign in the
exponent of (6.1) corresponds to the forward wave propagating along ≥ 0 while the positive
one belongs to a wave moving backward, i.e. ≤ 0. If both electric and magnetic vectors in