Combination resonant V-antenna and traveling-wave dipole antenn

Iizuka, K.

King, R. W. P.

English

NASA Technical Reports Server

7 -  
THE TRAVELING-WAVE V-ANTENNA 
Scient i f  ic Report No. 4 
GPO PRICE $y 
CFSTI PRICE(S) $- 
ff 653 July 65 
BY 
Keigo lizuka and Ronold W.f? King 
March 1965 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
Prepared under Grant No. NsG 579 
Gordon McKay laboratory, Harvard University 
Cambridge, Massachusetts 
(ACCESSION NUM 1 9f7 I 
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I 
. 
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https://ntrs.nasa.gov/search.jsp?R=19670006193 2020-03-16T18:46:33+00:00Z
/ .. - I .  
THE TRAVELING-WAVE V-ANTENNA 
By Keigo Iizuka and Ronold W .  P. King 
Scientific Report No. 4 
March 1965 
Prepared under Grant No. NsG 579 at 
Gordon Mc Kay Laboratory, Harvard University 
Cambridge, Massachusetts 
for 
. 
I 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
I . .  
THE TRAVELLNG-WAVE V-ANTENNA 
By Keigo Iizuka and Ronold W. P. King 
Gordon Mc Kay Laboratory, Harvard University 
Cambridge, Massachusetts 
SUMMARY 
An antenna which is a combination of the resonant V-antenna and the 
traveling-wave dipole antenna was studied both theoretically and experimentally. 
The universal curves which a r e  useful for determining the values of the length 
of the antenna a rms ,  apex angle, and loading resistors a r e  presented. The 
theoretical curves for the radiation pattern agree in a general sense with those 
of experiments. 
wavelength long traveling-wave V-antenna has a gain 10. 5 times as large as 
that of a half-wave dipole. 
The antenna has a pencibbeam radiation pattern. The two- 
INTRODUCTION 
A traveling-wave V-antenna is a V-antenna with a set  of terminating 
The traveling-wave V-antenna is a combination of the resonant V-antenna 
resis tors  near its endsof such value that the current is substantially a traveling 
wave. 
described by P . S .  Carter (ref. l), et al., in 1931 and in recent books 
(ref,  2, 3,4), and the traveling-wave dipole antenna studied by Hall& (refs.5), 
Altshuler (ref. 6), and quite recently by Wu and King (ref. 7). 
A linear dipole antenna is characterized principally by a standing wave 
of current resulting from reflections a t  the ends. 
frequency sensitive. 
waves by gradually increasing the surface impedance of the wire as the ends were 
approached. 
surface impedance of the antenna. 
maximum nearest the ends of the antenna for the same purpose. 
Its impedance is highly 
Halle/n, and Wu and King suppressed the reflected current 
It was achieved either by ohmic or  purely reactive changes of the 
Altshuler placed resistors a t  the current 
A traveling-wave V-antenna combines the advantages of a V-antenna 
It is characterized by simplicity in structure, a and a traveling-wave dipole. 
broad frequency band, and high directivity, but also by a loss of power in the 
terminating impedances. 
complications in the analysis. 
design procedures. 
The absence of cylindrical symmetry leads to 
This report includes a discussion of theory and 
-1- 
-2 -  
VALUES OF THE LOADING RESETORS FOR TRAVELING-WAVE EXCITATION 
Strictly speaking, a pure traveling wave of current can exist only on 
nonradiating transmission lines that are terminated in their characteristic 
impedances. However, the current in a properly loaded V-antenna with apex 
angle A, shown in Fig. 1, can be resolved into a large component which is a 
pure traveling wave, and a relatively small correction term. 
traveling-wave part of the current must behave just as i f  i t  were maintained on 
a tapered transmission line with a spacing d that is proportional to the distance 
from the driving point. 
(or hT away from the end). 
It follows that the 
This line is terminated in a set  of resistors at r = h 
In order to answer the question, what lumped resiptance should be 
selected to minimize the wave reflected from the end, i t  is & satisfactory 
approximation to consider only the large traveling-wave component of the current 
which may be determined by transmission-line theory. For  this purpose, it  is 
convenient to introduce a characteristic impedance, Zc , that varies with the 
distance from the feeding point. 
difference between the two arms of the V to the current in a wire - a quasi- 
stationary approximation. Alternatively, it is defined as the ratio &- (refs.3, 
4, 18) where the distributed parameters L and C vary with distance and are 
calculated in a quasi-stationary manner. 
case -- = 90°, this approximation is in general agreement with the more precise 
analysis by Hallen (ref. 5) (see F ig .  2). 
(ref.  9) show that the reflected current wave is always minimum when the loading 
resistance i s  near the values obtained with this approximation. 
of ref. 9.) 
It i s  defined as the ratio of the scalar potential 
It is readily shown that in the special 
A 
2 
Moreover, measurements by Duff 
(See Fig.  3 
The resistors a r e  located where the current amplitude is a maximum 
The value of the current a t  this position is in the absence of the resistors.  
twice the incident wave, 210. When the resistors a r e  inserted, the potential 
drop Ih. R is established across  each. By the compensation theorem this 
drop may be replaced by a generator with a voltage -Ih' R where Ih is the 
total current in the resistor a t  z = h. The two generators - one in each 
arm of the V -are in ser ies  with the transmission-line impedances looking 
toward and away from the apex. 
the length hT- (2n+l) X/4 such that the input impedance is zero, the 
equivalent transmission-line circuit consist6 of a length of line h with a 
generator V at  z = 0 and a generator -21h' R at z = h. The total current is 
If the length hT toward the open end bas 
0 
FIG. 1 GEOMETRIC CONFIGURATION OF A 
TRAVEL1 NG -WAVE V-ANTENNA 
. -  
I 
I I I I I I 
9- - 
I 
10 I 
8- 
RESISTANCE R 
FOR VARIOUS D BY ALTSH U LER 
FOR fi =14 
'\i40 
~ 
c 
W z 
- I  
I 
0 
E 
w 
- 0  z 
U c 
a 
w 
- c T  
W z 
a 
E 
- 
- 0  
-1 
x 
r' / 
BY H A L L C N  - x 
THICKNESS ANTENNA FOR Till,OOO 
- 1 -  
0 I I 1 1 I I I 
FI 
200 
100 
'ANCE 
Z A 
FIG. 3 GEOMETRIC CONFIGURATION OF A SINGLE 
WIRE EXCITED BY A TRAVELING CURRENT 
WAVE. 
C 
- 3- 
cos kz - 2 IhR cos kh J -  1 I ( 2 )  = j ZCtankh 
If k is determined with z = h, the result is 
zC cos kh t j 2 ~ s i f ; l k h  
2Rcoskh t jZCs inkh  
I 
cos kz - j s in I ( z )  = 
It follows at once that a traveling wave 
V -jkz ze I ( 2 )  = c, 
is obtained when 
zC R = - .  
2 
An expression for the characteristic impedance of a tapered two-wire-line 
has been obtained by Schelkunoff (ref. 8). 
(3)  
where 
The values of 
from Eq. (4) and Eq. 
A -€or various values t 
A 
2 2h sin - 
a 
(4) 
load resistance for a traveling wave were calculated 
(5) and plotted in Fig. 2 as a function of the apex angle 
of the thickness parameter, 52 = 21n - of the wi re  where 2h a 
P a is the radius of the wi re .  
increase of R with an  increase in ) when is small, but quite insensitive 
b to changes in - when 2 
because the two wi re s  of finite radius either overlap o r  touch each other, 
and the meaning is lost. 
R is rather sensitive to changes in - (a rapid 2 A A 
A A ' t i s  larger. The range near = 0 was avoided 
When 7 -  - 7 ,  ' the V becomes a dipole antenna, and for this 
particular case, detailed discussions made by Hallek (ref. 5), Altshuler 
(ref. 6), and Wu and King (ref. 7) are available. 
-4- 
Hall& defined a quantity, Go, the characteristic wave/ conductance of 
an antenna of arbitrary length in the process of solving Hallen's integral 
equation for the cylindrical transmitting antenna. His expression is 
It is noteworthy that this expression is independent of the length of the wire. 
Altshuler obtained an approximate expression for the characteristic 
impedance of the wire from a similarity of the expressions for the input 
impedance of an open-circuited transmission line and the zero-order impedance 
of a dipole antenna. The result is 
P 
P - zc - - 21i (7) 
where iP is a parameter that depends on ph and pa. An approximate value 
for short antennas is 
( 8 )  
2h 
a p = 52- 2, s1= 2h- - 
/ 
The values of the loading resistors for * = 7 * obtained using Hallen's 
They are and Altshuler's results a r e  also included in Fig. 2 for comparison. 
all in  reasonable agreement. 
The distribution of current measured by Duff (ref. 9) indicates that the 
traveling-wave V-antenna is predominantly excited by a traveling-wave when 
the relations among the apex angle, length of the antenna and the value of loading 
resis tor  are close to the ones specified by the graph in Fig.  2. 
RADIATION FROM A SINGLE WIRE EXCITED B Y  A TRAVELING WAVE 
A traveling-wave V-antenna consists of two identical arms meeting a t  
the driving-point and, except in the standing-wave section between the 
resis tor  and the end of the antenna, both a r m s  a r e  excited by a traveling 
current wave of the same amplitude but opposite in sign. 
of the arms, the radiation pattern of the traveling-wave V-antenna can be 
obtained immediately by a proper superposition if the complex field factor 
(radiation pattern) of one of the two identical arms is known. 
Due to the identity 
- 5- 
Consider a polar coordinate system with a straight wire stretched 
along the z-axis from z = 0 to z = h, as shown in Fig.  3. When the wire is 
excited solely by a traveling current wave 
where (9) 
From the general expression for the far-zone field (refs.  9 and lo) ,  the field 
intensity at P is 
where R = R - z c o s 8  . 
0 
The integration can be performed immediately; the result is 
- j PRO 
*= Ro * W )  
e 
Eo = Iobo 
where - 
- jph( 1 - cos 0) 
sin 8 1 - e  
1 - case F(6) = 
to = / %  = 1207l , 
Figure 4a ,  b, and c, respectively, shows the real part, imaginary par t ,  and 
the absolute value of the field factor (radiation pattern) calculated from 
Eq. (11) a s  a function of 8 for a range of values of ph = li, 2u, 2. 5a, and 
3. 5jr .  
by u radians. 
Note that the nurnber of lobes increases by one with an increase in ph 
It ehould also be observed that with an increase in the length of the 
wire, a quantity of practical interest, the direction 8, of the major lobe 
moves cloeer to the direction of the axis of the wire .  The values of 8, 

- 6 -  
can be found by equating the derivative of 
Calculated values of 8, a r e  shown in Fig. 2; em is along the horizontal 
axis; the length of the wire is along the vertical axis. It is seen from the 
figure that the rate of decrease in 8, with respect to an increase in ph 
becomes rapidly smaller as 8, is reduced and 6, can be zero only in the 
limit of infinite ph. The rate of decrease in 8, is extremely small when 
ph is larger  than 1 2 ~ .  
Eo with respect to 6 to zero ~ 
This information about for a single wire is important for 
determining the apex angle A of the traveling-wave V-antenna for which 
the maximum power is radiated in the direction of the y-axis (see Fig. 5). 
For  the optimum value 
since,with this apex angle, the direction of the major lobe of the one arm is  
superimposed on that of the other. 
traveling-wave V-antenna should be decreased as the length of the a r m s  is 
increased in order to maintain the maximum radiation along the y-axis. 
It follows that the apex angle of the 
Another interesting fact to be mentioned is that the narrowest beam 
width D (angle between the first  minima of the azimuthal radiation pattern) 
of the traveling-wave V-antenna obtainable by adjusting the apex angle for 
a given length and resistor is equal to the apex angle of the antenna, i. e . ,  
~ = h o p t  
2 m 
The width of the major lobe of the antenna increases with either an  
increase o r  decrease in the apex angle from its optimum value. 
In the above analysis, the attentuation of the traveling wave along the 
wire was not taken into consideration. 
antenna is very long. 
along the wi re  to be used is 
This is not necessary unless the 
When attenuation is included, the distribution of current 
The calculated results using Eq. (15) instead of Eq. (9) are compared with 
those based upon a loss-free w i r e  in Fig. 4. The attenuation.constant used 
in  the calculations is  that measured by Duff (ref. 9),viz., 0 . 6  dB per  wave- 
length independent of the apex angle. 
It is seen that the attenuation of the current has little effect on the radiation 
pattern. 
This corresponds to C L / ~  = 0.021 5. 
-Y  
FIG. 5 QUALITATIVE DISCUSSION OF THE RADIATION 
PATTERN OF A TRAVELING - WAVE V-ANTENNA 
WITH RESPECT TO THE APEX ANGLE 
-7- 
CONTRIBUTION OF THE STANDING WAVE ALONG THE END SECTION 
In the previous sections it has been assumed that the contribution of 
the standing wave along the end section (hT in Fig. 3) to the radiation pattern 
can be ignored. 
Consider the configuration of one of the two arms of the traveling-wave 
V-antenna shown in Fig. 3, again. 
position of the loading resistor z = h to the end of the antenna h t hT , which 
is predominantly excited by a standing current wave, is 
In the following, the contribution from this section is examined. 
The conkribution of the section from the 
I = I s i n p  (h t hT - z). s so 
The expression N(e)  for the far-zone field can be obtained in a similar form 
as Eq. (10) by replacing Eq. (9) by Eq. (16). 
r U 
sin ("z cos 8 )  t j [ s i n ( T  cos 8 )  - COS e)] . (18) 
e 
N(8)  = 
'R The calculated results of IN ( 8 )  I are plotted in Fig. 4 (a) for @hT = 7 . 
The magnitude of N(8)  for the standing-wave section is seen to be much 
smaller than that for the travelin -wave section, F ( 8 )  expressed by Eq. (12). 
i s 3 . 8 ,  5.7, 7.1, 8.3, 9.2, 10.3, o r l l . O f o r h / k = l ,  2, 3, 4, 5, 6, o r 7  
with constant phT = f . It m a y  be concluded that in the calculations in 
The ratio of the main lobes of F ( B ) to the maximum of the magnitude of N(e) 
Fig. 2, which were based only on the traveling-wave section, the error due 
to the exclusion of the contribution of the standing-wave section actually 
becomes insignificant at sufficiently great lengths of the antenna. 
RADIATION PATTERN FROM A TRAVELING-WAVE V-ANTENNA 
The radiation pattern of the single wi re  due to the contributions of 
both traveling wave and standingaave sections is obtained as a sum of 
Eq. (1 1) and Eq. (17) with a consideration of the continuation of the traveling 
and standing wave currents at z = h; 
-jW0 
M ( 6 )  (19) e = roto 
Etotal 4a Ro 
-8- 
Since the field of each arm is known, the field of the V-antenna with 
The E-plane pattern (in the plane of the antenna o r  jd dependence) is 
an  arbi t rary apex angle A is simply the addition of, the fields of the two 
arms. 
given by 
The negative sign indicates that the currents in the two arms are equal and 
opposite in the sense that in the one i t  is away from the apex, in the other 
toward the apex. 
experiment. The correlation is not perfect, but the expreseion of Eq. (21) 
with Eq. (20) is adequate for most uses in  design. 
In Fig.  6, the calculated E-plane pattern is compared with 
POWER GAIN 
The power gain in the direction of the maximum radiation of the 
traveling-wave V-antenna is defined as the ratio of the power required from 
an  isotropic radiator to produce the given intensity in the desired direction 
to that required from the actual antenna (ref. 11) 
4mR0' Pr - 4u RoL Pr 
w i R e I  g =  
0 
where Re is the external or radiation resistance of the traveling-wave 
V-antenna. 
Y-axis (in Fig. 5) is obtained from Eq. (20) and Eq. (21) with jd = r ,  and the 
radiated power in this direction is 
An approximate expression for the field in the direction of the 
1 * 1 1  * P =-EH =--EE , 
(50 
r 2  
Insertion of Eq. (23) into Eq. (22) leads to 
Note that the f i rs t  factor in Eq. (24) is in the same form as that of 
the power gain of a half-wave dipole antenna 
- 120 - 
gdipole e 
Rdipole 
8 
-5 
t (IN db) -10 
I 
C 
-5  
(IN db) 
-10 
-I 5 
-20 
. 
(IN 
FIG. 6 THEORETICAL AND EXPERIMENTAL RADIATION PATTERNS 
OF TRAVELING WAVE V-ANTENNA. E-PLANE (IN THE PLANE OF V)  
-9- 
Hence, the second factor in Eq. (25) determines how much better the 
directivity of a traveling-wave V-antenna is than that of a half-wave dipole, 
when the radiation resistances a re  the same for both antennas. Taking the 
traveling-wave V-antenna with h = 2h (whose apex angle 7 is 36O from Fig. 2)  
for example, the gain is 
A 
g = 1 0 . 5 .  g dipole * 
ACKNOWLEDGMENT 
Numerous helpful discussions with Trilochan Padhi a r e  gratefully 
acknowledged. 
some of the expressions for the field pattern. 
W e  are also indebted to Bob Duff for independently suggesting 
REFERENCES 
1. P. S.  Carter,  C. W. Hansell, and N. E. Lindenbald, "Development of 
Directive Transmitting Antennas by RCA Communications, Inc., 
Proc. IRE l9, 1773-1842 (October 1931). 
P res s ,  Cambridge, Massachusetts, 1956, pp. 381-397, 686 and 691. 
2. R. W. P. King, The Theory of Linear Antennas, Harvard University 
3. S. A. Schelkunoff, Advanced Antenna Theory, John Wiley and Sons, Inc., 
New York, 3952, pp. 97-109. 
4. S. A. Schelkunoff and H. T. Friis, Antennas, John Wiley and Sons, Inc., 
New York, 1952, pp. 109-110, 424-427, 499-502, 260 and 193. 
5. E. Hallen, Electromagnetic Theory, John Wiley and Sons, Inc., New York, 
1962, pp. 501-504, 444-456. 
6 .  E. E. APtschuler, ''The Traveling-Wave Linear Antenna, Trans. IRE on 
Antennas and Propagation - 9  AP-9 324-329 (July 1961). 
7. T. T. Wu and R. W. P. King, !'The Cylindrical Antenna with Nonreflecting 
Resistive Loading, '1 submitted to IEEE Trans. on Antennas and 
Propagation. 
8. S. A. Schelkunsff, Electromametic Waves, Van Nostrand Co., Inc., 
New York, 1943, p. 293. 
.J 
-10- 
9. B. M. Duff, "The Resistively-Loaded V-Antenna Current Distribution, 
Impedance, and Terminal- Zone Correction, Radiation Field, sf 
NASA Scientific Report No. 3, Harvard University, Cambridge, 
Massachusetts , October 1964. 
10. R. W. P. King, Electromagnetic Engineering, McGraw-Hill Book C Q . ,  
Inc., New York, 1945, pp. 268-275; the same pages of the Dover 
edition published in 1963. 
11. S. Ram0 and J. Whinnery, Field and Waves in  Modern Radio, John Wiley 
and Sone, Inc., New York, and Hall, Ltd., London, 1953, pp. 503-504. 


The traveling-wave V-antenna

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