Radiation from a simple wire antenna, such as a dipole, is a topic discussed in many courses on electromagnetism. These discussions are almost always restricted to harmonic time dependence. A time-harmonic current distribution is assumed on the wire, and the time-harmonic radiated field is determined. The purpose of this paper is to show that simple wire antennas with a general excitation, e.g., a pulse in time, can be analyzed easily using approximations no worse than those used with time-harmonic excitation, viz. an assumed current distribution. Expressions are obtained for the electromagnetic field of the current that apply at any point in space (in the near zone as well as in the far zone). The analysis in the time domain provides physical understanding not readily available from the time-harmonic analysis. In addition, an interesting analogy can be drawn between the radiation from these antennas when excited by a short pulse of current and the radiation from a moving point charge.
REFERENCES
1.
G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge U.P., Cambridge, 1997), Chap. 6, Sec. 6.1.2, pp. 364–371.
2.
Some of the textbooks that follow this approach are: J. B. Marion and M. A. Heald, Classical Electromagnetic Radiation (Academic, New York, 1980), 2nd ed., pp. 247–257;
J. R. Reitz, F. J. Milford, and R. W. Christy, Foundations of Electromagnetic Theory (Addison–Wesley, Reading, MA, 1993), 3rd ed., pp. 529–531;
J. Schwinger, L. L. DeRaad, Jr., K. A. Milton, and W. Tsai, Classical Electrodynamics (Perseus, Reading, MA, 1998), pp. 367–374;
J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999), 3rd ed., pp. 416–417.
3.
The superscript r is used to indicate the radiated field.
4.
See Ref. 1, Chap. 8, pp. 546–607;
G. S.
Smith
, “On the interpretation for radiation from simple current distributions
,” IEEE Antennas and Propagat. Mag.
40
, 39
–44
(August 1998
).5.
This is actually the current distribution for a section of ideal transmission line of length h terminated with a reflectionless load. Here we are assuming the current on the antenna is similar to that on the transmission line. This assumption is good whenever the wire forming the antenna is infinitesimally thin, see for example, S. A. Schelkunoff, Advanced Antenna Theory (Wiley, New York, 1952), pp. 102–110;
A. Sommerfeld, Electrodynamics (Academic, New York, 1952), pp. 177–186.
6.
There is a long history associated with the derivation and physical interpretation of formulas similar to the ones presented here for the electromagnetic field of an assumed filamentary current distribution. In 1899 Heaviside discussed the reflection of an impulsive electromagnetic wave at the free ends of a wire and made sketches of the electromagnetic field surrounding the wire that are similar to those in Fig. 9: O. Heaviside, Electromagnetic Theory (The Electrician Printing and Publishing Co., London, 1899;
Republication, Chelsea, New York, 1971), Vol. II, pp. 367–372. In 1923 Manneback analyzed the radiation from a parallel-wire transmission line:
C.
Manneback
, “Radiation from transmission lines
,” J. Am. Inst. Electr. Eng.
42
,95
–105
(1923
);C.
Manneback
, J. Am. Inst. Electr. Eng.
42
, 1362
–1365
(1923
). And later Schelkunoff extended Manneback’s treatment and applied it to thin-wire antennas;S. A.
Schelkunoff
, Advanced Antenna Theory (Wiley, New York, 1952), pp. 102–109. More recently, formulas similar to those presented here for the electromagnetic field have been obtained by a number of authors. The reader is cautioned that some of the earlier papers contain errors and inconsistencies that are pointed out in the later papers. Z. Q.
Chen
, “Theoretical solutions of transient radiation from traveling-wave linear antennas
,” IEEE Trans. Electromagn. Compat.
30
, 80
–83
(1988
);J.
Zhan
and Q. L.
Qin
, “Analytic solutions of traveling-wave antennas excited by nonsinusoidal currents
,” IEEE Trans. Electromagn. Compat.
31
, 328
–330
(1989
);L.
Fang
and W.
Wenbing
, “An analysis of the transient fields of linear antennas
,” IEEE Trans. Electromagn. Compat.
31
, 404
–409
(1989
);E. J.
Rothwell
and M. J.
Cloud
, “Transient field produced by a traveling-wave wire antenna
,” IEEE Trans. Electromagn. Compat.
33
, 172
–178
(1991
);S. A.
Podosenov
, Y. G.
Svekis
, and A. A.
Sokolov
, “Transient radiation of traveling waves by wire antennas
,” IEEE Trans. Electromagn. Compat.
37
, 367
–383
(1995
);G.
Wang
and W. B.
Wang
, “Comments on transient radiation of traveling waves by wire antennas
,” IEEE Trans. Electromagn. Compat.
39
, 265
(1997
);D.
Wu
and C.
Ruan
, “Transient radiation of traveling-wave wire antennas
,” IEEE Trans. Electromagn. Compat.
41
, 120
–123
(1999
). Results for the radiated field or far-zone field are given in several places, for example, D. L. Sengupta and C.-T. Tai, “Radiation and reception of transients by linear antennas,” in Transient Electromagnetic Fields, edited by L. B. Felsen (Springer, New York, 1976), Chap. 4;R. G.
Martin
, J. A.
Morente
, and A. R.
Bretones
, “An approximate analysis of transient radiation from linear antennas
,” Int. J. Electron.
61
, 343
–353
(1986
).7.
The electric field at the element is infinite. Thus, for these plots, the field must be clipped when it is above a reference value When the Gaussian pulse is out along the element, the peak value of the electric field (in time) in the region of the element containing the pulse is where ρ is the radial distance from the element. This relation can be used to choose a value for
8.
In this graph and in similar graphs that follow, the electric field for each plot is positive in the clockwise direction measured from the time axis. For the time axis at the angle in Fig. 5(b), this direction is indicated by an arrow.
9.
For the numerical evaluation of (10) and (11), it is sometimes useful to make the substitution
10.
Here, we are assuming that the wave is not reflected as it travels along the loop, and that there is no accumulation of charge on the loop.
11.
Current is taken to be positive when it is in the direction of increasing ψ. Thus, a pulse of positive charge traveling in the clockwise direction is a positive current (30), and a pulse of negative charge traveling in the counterclockwise direction is also a positive current (34).
12.
R. W. P. King and G. S. Smith, Antennas in Matter: Fundamentals, Theory, and Applications (MIT, Cambridge, MA, 1981), Chap. 9, pp. 527–570;
G.
Zhou
and G. S.
Smith
, “An accurate theoretical model for the thin-wire circular half-loop antenna
,” IEEE Trans. Antennas Propag.
39
, 1167
–1177
(1991
).13.
The good agreement is partly the result of choosing the wire of the loop to be very thin. For thicker wire, there will be noticeable differences;
for example, for the actual antenna, the pulses will decrease in amplitude more rapidly with increasing than for the simple model.
14.
See Ref. 1, pp. 579–583;
T. W.
Hertel
and G. S.
Smith
, “Pulse radiation from an insulated antenna: An analog of Cherenkov radiation from a moving charged particle
,” IEEE Trans. Antennas Propag.
48
, 165
–172
(2000
).15.
See Ref. 1, pp. 341–347.
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© 2001 American Association of Physics Teachers.
2001
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