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SOLUTION OF BASIC EQUATIONS OF ELECTRODYNAMICS 185

A circular loop antenna shown in Figure 4.3.3a is considered being electrically small if its
diameter 2 < /30 (i.e. its circumference L < /10). The circular, square, triangle or elliptical
loops are often used in portable mainly receiving communication systems and as a sensor for
in the loop is set up by
the EM fields intensity measurement. The RF conductivity current
the RF generator with the displayed polarity and direction at some moment of time. Due to the
short loop circumference we can assume that the current magnitude over the loop is uniform.
Meanwhile, some phase variation of current ∆ = = (2 )( 10) = 0.628 [rad] aka 36°
⁄
⁄
can be expected. As a matter of fact, such short phase delay does not alter noticeably the far-
field radiation and can be neglected. Taking into account that the currents are oppositely
directed along the parallel dipoles (see Figure 4.3.3b) their radiated fields are completely
canceled in z-direction. Therefore, the vanishingly small loop has a sharp and deep radiation
null in the direction normal to its plane. That is why loop antennas of a variety of forms are
broadly used in radio direction finding systems. The precise line-of-direction to the source of
radiation can be found by simple rotation of the loop shown in Figure 4.3.4a and its pattern in
7
Figure 4.3.4b until the received by the loop signal reaches its minimum (along the z-axis).
Another application is to null out one of strong uninvited or jamming signal coming to a receiver
from some direction different from the main.

The rigorous analysis of a circle loop radiation is cumbersome and required the acquaintance
with the integral presentation of Bessel functions. To overcome it and simplify the far-field
analysis let us replace the circle with inscribed square as shown in Figure 4.3.3a. We preferred
the inscribed square to external one because of smaller error in the circumference: 11% for
inscribed and 27% for outer. A quick look at Figure 4.3.3b reveals that the fields radiated by

Rectangular Loop

Z

a) b) X

Figure 4.3.4 a) RF amplifier connected to loop antenna, b) Radiation pattern

square loop antenna may be viewed as the superposition of fields radiated by four electric
dipoles located in XY-plane. The two of them, say 1 and 3 , are oriented along their -axis
while the two others, say 2 and 4 , are perpendicular and oriented along the -axis. Let us
first compute the fields emitted by the aligned dipoles 1 and 3 at the observation point

7 Public Domain Image, source: http://www.nationalrf.com/type_hfdf_vector.htm