OT REPORT 77-131 

 

DESIGN OF A VAN-TOP 

LOW-PROFILE HF ANTENNA 

M.T. MA 

R.G. FITZGERRELL 

U.S. DEPARTMENT OF COMMERCE 

Juanita M. Kreps, Secretary 

Jordan J. Baruch, Assistant Secretary 

for Science and Technology 

OFFICE OF TELECOMMUNICATIONS 

John M. Richardson, Director 

October 1977 

iii 

TABLE OF CONTENTS 

Page 

LIST OF FIGURES iv 

LIST OF TABLES vi 

ABSTRACT 1 

1. INTRODUCTION 1 

2. INCREASING RADIATION RESISTANCE BY TOP-LOADING 2 

3. ANTENNA CAPACITANCES 4 

4. REQUIRED COIL AND RADIATION EFFICIENCY 10 

5. MEASURED RESULTS 17 

 5.1 Radiation Efficiency 17 

 5.2 Power Gain 24 

6. CONCLUSIONS 37 

7. ACKNOWLEDGEMENTS 37 

8. REFERENCES 38 
iv 

LIST OF FIGURES 

Page 

Figure 1. A base-fed short monopole. 2 

Figure 2. A top-loaded short monopole. 3 

Figure 3. A schematic diagram showing the antenna arrangement. 5 

Figure 4. Van-top antenna circuit. 6 

Figure 5. Equivalent circuit for a top-loaded short monopole. 9 

Figure 6. Radiation efficiency versus frequency for h = 12 in. 

 and N = 2. 13 

Figure 7. Radiation efficiency versus frequency for h = 15 in. 

 and N = 2. 14 

Figure 8. Radiation efficiency versus frequency for h = 18 in. 

 and N = 2. 15 

Figure 9. Full-scale simulation model for the Van-top antenna. 18 

Figure 10. Antenna reactance (per element) for h = 18 in. and 

 N = 2. 19 

Figure 11. Required Q for 16% radiation efficiency. 20 

Figure 12. Van-top model range instrumentation. 22 

Figure 13. Power measurements. 23 

Figure 14. Measurement system schematic. 25 

Figure 15. Test antenna 46 cm (18 in.) above top of vehicle. 

 Vehicle is on turntable with reference antenna 

 suspended between poles in background. 26 

Figure 16. Power gain versus elevation angle. 28 

Figure 17. Power gain versus elevation angle. 29 

Figure 18. Power gain versus elevation angle. 30 

Figure 19. Power gain versus elevation angle. 31 
v 

LIST OF FIGURES (cont.) 

Page 

Figure 20. Power gain versus elevation angle. 32 

Figure 21. Power gain versus elevation angle. 33 

Figure 22. Power gain versus elevation angle. 34 

Figure 23. Power gain versus elevation angle. 35 

Figure 24. Power gain versus elevation angle. 36 
vi 

LIST OF TABLES 

Page 

Table 1. Plate capacitance as a function of antenna height. 7 

Table 2. Monopole capacitance as a function of frequency and 

 antenna height. 8 

Table 3. Line capacitance as a function of antenna height. 9 

Table 4. Required inductance of the tuning coil. 10 

Table 5. Computed radiation efficiency. 11 
DESIGN OF A VAN-TOP LOW-PROFILE HF ANTENNA 

M. T. Ma and R. G. FitzGerrell∗

An electrically small antenna is one whose physical 

size is a small fraction of the operating wavelength. It has 

been known that it is rather difficult to design such an 

antenna. One of the most challenging problems associated with this antenna is the realization of a respectable 

radiation efficiency and bandwidth. A special low-profile 

antenna whose height is in the order of 12 to 18 inches 

(30 to 46 cm) has been designed for mobile communications within the frequency range of 3 to 12 MHz. The 

antenna is to be installed on the top of a vehicle. The 

design principle and the measured radiation characteristics in terms of power gain and radiation efficiency for a 

full-scale model are given. 

Key Words: Electrically-small antenna, gain measurement, high-frequency, low-profile, mobile 

communication, radiation efficiency. 

1. INTRODUCTION 

When the size of an antenna is comparatively small with respect to the 

operating wavelength, the antenna is known as electrically small (Schelkunoff 

and Friis, 1952). Such an antenna is attractive because of its low visibility, 

modest height, and relatively light weiqht. However, the radiation resistance of 

such antenna is also small compared with the total loss resistance of various 

components making up the entire system, thus resulting in poor radiation 

efficiency. In addition. the input impedance of this antenna has a large reactive 

component, requiring a reactance of opposite kind for tuning the antenna to 

resonance. This requirement is equivalent to demanding a high Q of the tuning 

circuit with a sacrifice in bandwidth (Wheeler, 1975). Successful design of an 

electrically small antenna is, therefore, guided by consideration of appropriate 

selections from among these non-compatible factors. 

 

∗ The authors are with the Institute for Telecommunication Sciences, 

Office of Telecommunications, U. S. Department of Commerce, Boulder, 

Colorado, 80302. 
2

 There are two basic types of electrically small antenna: the electrical 

element such as a short monopole, which couples to the electric field and is 

commonly referred to as a capacitive antenna, and the magnetic element such 

as a small loop, which couples the magnetic field and is commonly referred to 

as an inductive antenna. The antenna design described in this report belongs 

to the former type. The antenna to be installed on the top of a vehicle is used 

for both transmitting and receiving. The space allowed for this installation is 

limited to a maximum of 18 inches (46 cm). The vehicle is constantly on the 

road, and the driver is required to maintain voice contacts, via the sky-wave 

mode, with one of several base stations. The distance between the vehicle and 

the nearest base station may be as far as 1,000 miles (1600 km). The 

frequency allocated for this mobile communication is the lower end of highfrequency band, 3 to 12 MHz. 

2. INCREASING RADIATION RESISTANCE BY TOP-LOADING 

 The radiation resistance of an ordinary base-fed short monopole shown 

in Figure 1, with an assumption of triangular current distribution on the antenna, 

may be given approximately by (Jordan, 1950): 

2 2 R 40 π (h / λ) r ≅ ohms, (1) 

where h is the monopole height expressed in the same unit as that for the 

operating wavelength λ. For example, an antenna height of 18 inches (46 cm) 

operated at 6 MHz gives only 0.033 ohm for Rr, which is indeed very small. 

Figure 1. A base-fed short monopole.
3

 One way of improving the radiation efficiency is to increase the radiation 

resistance which may be achieved by compelling a more even current 

distribution over the antenna. A conventional technique of accomplishing this is 

to apply the top-loading principle (Wait and Surtees, 1954). This principle and 

the associated approximate current distribution on the monopole itself may be 

shown as in Figure 2. Under this condition, the radiation resistance may be 

obtained as (Martin and Carter, 1961): 

( ) 2 2 Rr

′ =160π h / λ ohms, (2) 

which is four times as large as that in (1) for an unloaded monopole. 

Figure 2. A top-loaded short monopole. 

 This top-load technique not only enhances the current distribution, 

but also increases the antenna capacitance, thus reducing the capacitive 

reactance for a given monopole size and frequency and demanding less 

inductance for tuning. The required tuning coil is normally connected just 

outside the top-load plate. Since there is no room for connecting this 

tuning coil in our case, we reverse the role played respectively by the 

loading plate and metal top of the vehicle, such that the tuning coil and 

transmitting/receiving components are connected to the antenna 
4

from inside of the vehicle to avoid exterior visibility. In addition, the total 

antenna capacitance and supporting weight of the loading plate may be shared 

by more than one monopole. A schematic diagram for both of these 

considerations is given in Figure 3. 

 For the case involving multi-monopoles, the total radiation resistance per 

element, in view of the close coupling with other elements, becomes 

Rr NRr ′′ = ′ ohms, (3) 

where N is the number of monopoles and Rr’ is given in (2). 

3. ANTENNA CAPACITANCES 

 The capacitances associated with each element antenna may be 

calculated by referring to the simplified configuration shown in Figure 4. In this 

figure, C1 is the capacitance between two parallel plates, which may be 

obtained simply by 

C1 = ε o A/ h farads, (4) 

where A is the area of the top plate in square meters, h is the antenna height in 

meters and εo = (1/36π) 10-9 in farads/meter is the permittivity of free space. 

 From (4) we see that, in order to increase C1 and reduce the required 

inductance for tuning, we can use a larger plate and/or a shorter antenna. 

However, decreasing h also decreases the radiation resistance in accordance 

with (2). Thus, we should not try to reduce the antenna height for the purpose 

of increasing C1. The only other means left is to choose a larger plate within the 

limitations of space and weight. In view of the size of the vehicle on which the 

antenna is installed, the maximum possible space available is 8.5 X 6.0 ft2 (4.74 

m2). With this area A, we obtain values for C1 as shown in Table 1.
5
6
7

Table 1. Plate capacitance as a function of antenna height. 

h (inches) C1 (picofarads) 

12 137 

15 110 

18 92 

 The value of C1 obtained from (4) is, of course, approximate in the sense 

that fringing effects at the edge of the plates have been ignored. Even though 

the exact capacitance including the fringing effects is unknown, we do know, 

however, that the actual capacitance should be higher than that obtained from 

the above simple formula (Harrington, 1958). The fact that the area of the 

bottom plate (the vehicle top) is larger will probably make C1 even larger. 

 Since capacitance C1 is shared by many monopoles, the plate capacitance per monopole should then be C1/N. 

 The capacitance C2 in Figure 4 is the one associated with the short 

unloaded monopole. This capacitance may be derived from the approximate 

reactance formula (Jordan, 1950): 

2 2 X = Zo cot kh = 1/ωC ohms, (5) 

where = 60[log ( / ) −1] Zo e h ao ohms (6) 

is referred to as the characteristic impedance, ao is the outer radius of the 

monopole, and w is the angular frequency in radians. 

 From (5), we have 

( ) Zo C tan kh / 2πf 2 = farads, (7) 

with f as the operating frequency in hertz. 

 In our design, ao = 2 inches (5 cm). The calculated values for C2 may be 

summarized in Table 2. 
8

 Table 2. Monopole capacitance as a function of frequency and 

 antenna height. 

C2 (picofarads) f (MHz) 

h = 12 inches h = 15 inches h = 18 inches 

3 21.4 20.9 21.2 

4 21.4 20.9 21.2 

5 21.4 20.9 21.2 

6 21.4 20.9 21.2 

7 21.4 20.9 21.2 

8 21.4 20.9 21.2 

9 21.4 20.9 21.2 

10 21.4 20.9 21.2 

11 21.4 20.9 21.2 

12 21.4 20.9 21.2 

 From the above table, we see that C2 remains approximately 21 pF for 

three different antenna heights. Since C2 is already the capacitance per 

element, there is no need to divide it again by the number of monopoles as we 

did for C1. 

 The capacitance C3 in Figure 4 represents that contributed by the coaxial 

line (Ramo and Whinnery, 1959): 

 C3 = 2πεo h/loge(ao/ai) farads 

 = 40.07 h picofarads, (8) 

where h is in meters.
9

 In (8), we have used ao = 2 inches (5 cm) and ai = 0.5 inch (1.27 cm). 

The values for C3 with three different antenna heights are as follows. 

Table 3. Line capacitance as a function of antenna height. 

h (inches) C3 (picofarads) 

12 12.2 

15 15.3 

18 18.3 

Note also that C3 has been considered on a per-element basis. 

 After considering the important capacitances in Figure 4, we may 

represent the entire system by the equivalent circuit as shown in Figure 5, 

where C4 = C2 + (C1/N) farads, R2 = R”r ohms [See (3)], X1 = ωL ohms with L 

representing the required inductance in henrys, and R1 is the loss resistance in 

ohms of the coil. 

Figure 5. Equivalent circuit for a top-loaded short monopole. 

 Evaluation of the capacitances as outlined above serves only the 

purpose of selecting an appropriate coil for tuning. In reality when 

there is difficulty in making an accurate evaluation, the designer can
10

just make a direct measurement of the total reactance and determine the coil 

size experimentally. 

4. REQUIRED COIL AND RADIATION EFFICIENCY 

 The inductance for the required tuning coil may be determined by setting 

(See Figure 5) 

 L = 1/[ω2 (C3 + C4)] henrys, (9) 

since the capacitive reactances X3 = 1/ωC3 and X4 = 1/ωC4 are numerically 

much greater than the radiation resistance R2. For example, with h = 12 inches 

(30 cm) and N = 2, C1 = 137 pF, C2 = 21 pF, C4 = 90 pF, C3 = 12 pF, R2 = 

0.0293 ohm, we have: 

 X3 = 4345 ohms and X4 = 589 ohms at f = 3 MHz, 

which are indeed much greater than R2. 

 The required largest inductances at 3 MHz from (9) for three different 

antenna heights are summarized as follows. 

Table 4. Required inductance of the tuning coil. 

h (inches) Lmax (microhenrys) 

12 28 

15 31 

18 44 

 Since those capacitances due to fringing effects are not included in (9), 

the maximum inductances obtained above are certainly the upper limits. A coil 

made of the 3/8 in. conductor, 8 in. long, 7 in. diameter, and 14 turns yielding 

approximately L = 30 μh (Ramo and Whinnery, 1959) is definitely sufficient for 

the frequency coverage in this design with h = 12 or 15 inches, and may be 

enough even for h = 18 inches. 
11

 The radiation efficiency for the equivalent circuit in Figure 5 may be 

defined as 

η = 

power radiated power lost

power radiated

+

 = 

1

2

2

2

2

2

I R I R

I R

′′ +

′′

 = 

1

2

4

3 4

2

2

R

C

C C R

R

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ +

+

 (10) 

 The above set of equations constitute the complete design guideline. 

With a practical coil of high Q (Q = ωL/R1), a respectable radiation efficiency 

may still be realized. For example, if h = 12 in. and N = 2, we have C1 = 137 pF, 

C2 = 21 pF, C3 = 12 pF, and C4 = 90 pF. When Q = 600, the radiation efficiency 

for the antenna being considered can be easily computed in Table 5 below. 

Table 5. Computed radiation efficiency. 

f (MHz) X1 (Ohms) R1 (Ohms) R2 (Ohms) Efficiency (%) 

3 518.39 0.8640 0.0293 2.56 

4 388.79 0.6480 0.0522 5.88 

5 311 .03 0.5184 0.0815 10.87 

6 259. 19 0.4320 0.1174 17.41 

7 222. 16 0.3703 O. 1597 25.07 

8 194.39 0.3240 0.2086 33.31 

9 172.79 0.2880 0.2641 41.56 

10 1 55. 52 0.2592 0.3260 49.38 

11 141 . 38 0.2356 0.3945 56.49 

12 129.60 0.2160 0.4695 62.77 
12

 The above numerical result may be presented as in Figure 6. Corresponding curves for other values of the coil Q are also included. Clearly, the 

radiation efficiency for this electrically small antenna is still reasonable for 

frequencies above 6 MHz. At lower end of the frequency band (3 to 5 MHz), a 

radiation efficiency of only 10% or less is probably all we can achieve. This 

rather poor result is actually expected because the antenna height in this 

example amounts to only 0.00305λ at 3 MHz. 

 Similar results for h = 15 in. and h = 18 in. are given respectively in 

Figure 7 and 8. 

 From these figures we see that the radiation efficiency is generally higher 

for a larger antenna height with the same coil Q. This is true at least for the 

three antenna heights considered. Of course, increasing the antenna height 

decreases the total capacitance, thus demanding a larger coil for tuning. With a 

fixed coil Q, this means a larger loss resistance. Since the radiation resistance 

increases with the antenna height at a faster rate than the loss resistance, a 

higher radiation efficiency therefore results. It is suspected, however, that if the 

antenna height is too large, the current distribution on the antenna may differ 

substantially from that displayed in Figure 2, causing the formula in (2) to be 

invalid. In that case, the radiation resistance may not behave the same. If the 

rate of increase in radiation resistance with respect to the antenna height 

becomes slower than that for the required reactance, a decrease in radiation 

efficiency is possible. Thus, as far as maximizing the radiation efficiency is 

concerned, there may exist an optimum height if the space in which the antenna 

is installed is not restricted. Since we do have a space limitation in our design, 

the antenna heights of 15 in. and 18 in. may offer the best choice available. 

 Another important point we should note from Figure 6 through 8 is that 

the radiation efficiency increases with frequency for a fixed antenna dimension 

and coil Q. This is true because the capacitive reactance decreases with 

frequency, implying a smaller coil and loss resistance. 
13
14
15
16

At the same time, the radiation resistance increases with frequency. However, 

this conclusion is valid only when the assumption made in (3) remains good. 

Strictly speaking, for a system of coupled multiple elements such as the one 

being investigated, the following expression for the radiation resistance per 

element should be used to replace that in (3): 

 Rr” = Real part of (Z11 + Z12 + ... + Z1N) , (11 ) 

where Z11 is the open-circuit self impedance of the element under consideration, and Z1i, i = 2, 3, ..., N is the open circuit mutual impedance between this 

element and the ith element in the system. Obviously, Re(Z11) = Rr’, the 

radiation resistance of a single top-loaded monopole. The real part of Z1i (i ≠ 1) 

depends on kd1i, where d1i is the distance separation between the two elements 

of concern. For low frequencies making kd1i very small, we certainly have: 

Re(Z1i) = Rr’, i ≠ 1, thus yielding the approximate expression in (3). For higher 

frequencies, kd1i may not be too small. Then, we have from (11) that Rr” < NRr’, 

thereby reducing the overall radiation efficiency. Quantitative changes in Rr” 

versus kd1i can only be determined if an expression for Z1i is available. 

 Note that the curves presented in Figures 6 through 8 only represent the 

ideal theoretical condition assumed in the formulation. In reality, there may be 

other various losses in the connecting components. The actual radiation 

efficiency is more likely lower than that given in these figures. 

 Before concluding this section, we note that the bandwidth in kilohertz for 

the antenna system may be defined as 

 BW = 1,000 fMHz/Q , (12 ) 

where fMHz is the operating frequency in megahertz. 
17

 Clearly, even at the lowest frequency of interest (i .e. 3 MHz), we should 

not encounter any difficulty in achieving the minimum bandwidth of 3 kHz 

required for voice communications with a practical value for Q. 

5. MEASURED RESULTS 

5.1. Radiation Efficiency 

 In view of the general belief that it is not easy to realize a respectable 

radiation efficiency in practice for any electrically small antenna, we cannot rely 

totally on the simple formulation outlined above. To verify the result, a full-scale 

model of the size 8.5 ft. X 6 ft. X 18 in. was built on a simulated vehicle as 

shown in Figure 9. The measured reactance of the system is given in Figure 

10, where the computed values are also included for comparison purposes. As 

it was expected, the actual reactance at a given frequency is always lower than 

the computed one, implying that the actual total capacitance is indeed much 

higher than the theoretical value when taking fringing effects into accounts. 

 The required theoretical Q for achieving 16% radiation efficiency for this 

simulated model is presented in Figure 11. The measured Q values for the two 

coils used are also included in this figure. These measured values were 

obtained directly from a Q-meter. The dimensions of these coils are as follows: 

 Diameter 7 inches (18 cm) 

 Spacing 0.83 inch (2 cm, center to center) 

 Conductor 0.5 inch (1.3 cm) diameter, silver plated 

 copper tube 

 Length 10.5 inches (26 cm) 

 Number of turns 10 

 From Figure 11 we see that, for frequencies higher than approximately 

4.8 MHz, the measured Q values are larger than the required Q for achieving 

16% radiation efficiency. In other words, for the frequency band 4.8 to 

12 MHz, the loss resistances associated with the coil, R1, are smaller 
18
19
20
21

than those required for the specific radiation efficiency being considered. This 

implies that the realized radiation efficiency of the simulated model is higher 

than 16% for frequencies above 4.8 MHz. 

 The radiation efficiency can also be determined by comparing the 

measured power radiated from the simulated model with that from a 30 ft. 

reference antenna. The measuring configuration is shown in Figure 12. The 

measurement procedures are as follows: 

a) Set both coils in the model antenna to the same number of turns. 

b) Feed tap at one turn for the model antenna and two turns for the 

reference vertical antenna. 

c) Measure input resistance Rin at the resonant frequency (zero reactance). 

d) Set generator at the same resonant frequency and apply 2 volts to the 

antenna. 

e) Calculate power input: P = 4/Rin. Note that the power input should be 

0.08 watt if Rin = 50 ohms. 

f) Normalize to 0.08 watt and calculate the power difference in dB: PD = 10 

log (P/0.08). 

g) Read radiated power at the measuring site after calibrating at 25 dB. 

h) Add PD obtained in Step (f) to power readings and plot. 

Results from this measurement are presented in Figure 13. Again, we see that 

the radiation efficiency of the model antenna should be higher than 16% for 

frequencies above 4.12 MHz. 

 Note that the distance between the antenna location and measurement 

site is only 200 feet or 61 meters, as indicated in Figure 12. By the 

common criterion, the measuring receiver is probably considered within 

the near-field zone of the transmitting antenna. However, with practical 

experience gained by frequent measurements for the short antenna, the 

measuring receiver at a distance of approximately 3h (h = antenna height) 
22
23
24

away from the transmitting antenna can readily be considered in the far-field 

zone (private communication with Mr. H. A. Ray, Continental Electronics, 

Dallas, Texas). This fact is also supported by the actual readings of E and,H 

fields with an approximate ratio of 377 ohms. In any case, since both of the 

model and reference antennas are treated in the same manner, the relative 

results should give a clear indication on radiation efficiency of the model 

antenna. 

5.2. Power Gain 

 Figure 14 is a schematic diagram of the antenna test site instrumentation, and examination of this figure should help clarify the measurement 

technique. The test antenna power gains are determined from a measurement 

of relative gain using the half-wave dipole as a reference, or standard gain, 

antenna (IEEE, 1965). It is common to use a horizontal dipole as a reference 

antenna in the HF band, but this is the first time we have ever used the 

horizontal dipole as a vertically polarized reference. This is done by placing the 

vertically polarized source of test site illumination on a helicopter and flying in 

the vertical E-plane of the reference antenna. This technique is feasible for 

hemispherical pattern measurements only if the test antenna is rotating 

(constantly changing its azimuthal orientation) during measurement. For these 

measurements, the test antenna was mounted on a large turntable, as shown in 

Figure 15, and rotated at about 3 rpm. 

 A phase-lock signal generator and amplifier are carried aboard the 

helicopter to supply rf power to the illuminating antenna. Because of 

congestion in the HF band and the narrow bandwidth operation of our 

receiver to eliminate the effect of this congestion on the measured data, 

a very stable rf source is definitely required. The narrow bandwidth capability 

and the ability to display the received signal in the scan mode of operation 

makes the spectrum analyzer the heart of our measurement system. 

Use of the fast switch rate (≈5/s) between test and reference antennas 

and of the relative gain measurement technique minimizes any power 

output stability limitation of the airborne equipment. More importantly, but 
25
26
27

perhaps not so obvious, the relative gain technique utilizing a known reference 

antenna power-gain pattern eliminates the need for range data and the 

accompanying path loss correction to the measured data. 

 The spectrum analyzer is the receiver as well as the source of the 

measurement system master timing signal. As the spectrum analyzer scans 

the frequency band containing the test signal, its vertical amplitude output, 

proportional to the received signal level in decibels, is fed to the sample-andhold circuit. This circuit transfers the maximum level observed during the scan 

to a digital voltmeter during scan retrace. Since the rf switch is synchronized 

with the spectrum analyzer scan, the signal levels from the test and reference 

antennas are received alternately, five times each second. 

 The CRT display stores the helicopter flight path in an elevation angle 

over azimuth angle format relative to the test antenna. Measurements cease 

when the hemisphere has been uniformly traversed by the helicopter. 

 The test antenna is tuned to resonance using a vector impedance meter. 

The resulting real input impedance and the computed conjugate mismatch loss 

are included in the figure legends on the data plots in Figure 16 to 24. The 

mismatch losses can be eliminated by proper coupling circuits. Therefore, 

these losses are used to correct antenna gain data by removing their effect 

from the power-gain plots. That is, power gain is the value realized with the use 

of a perfectly lossless tuner to eliminate mismatch loss. We add the mismatch 

loss to the measured gain data and plot the resulting power gain. 

 The gain plots consist of straight lines between the mean values of all 

data measured in the hemisphere. The horizontal bars indicate the interdecile 

range of data measured in a 1-degree wide elevation angle cell centered on the 

bar. If our sample size is sufficiently large, our equipment is stable, the flight 

paths perfect, and the airborne antennas perfectly polarized, the resulting plots 

show mean power gains, and the interdecile ranges show the pattern variability 

with azimuth. 
28
29
30
31
32
33
34
35
36
37

 As shown in the data plots, the maximum power gain is typically -3 dB at 

the two upper frequencies and 0 to +3 dB at the lower frequency. The 

variations in power gain with elevation angle are probably caused by scattering 

or reflections from the vertical coaxial line to the feedpoint of the reference 

dipole antenna. Errors in the reference dipole antenna power gain caused by 

estimating the dielectric properties of the test range ground are less than 1 dB 

for 3 ≤ εr ≤ 10 and 10 millimhos ≤ σ ≤ 30 millimhos. 

6. CONCLUSIONS 

 An electrically small antenna has been designed for HF communications. 

The specific frequency range of interest is 3 to 12 MHz. The antenna itself is 

not to exceed 18 inches in height. The top-loading plate has, however, the size 

of 8.5 ft. X 6.0 ft. Theoretical results on various capacitances, required Q for 

the tuning coil, radiation resistance, and radiation efficiency have been 

presented. Also included in this report are the actual measured results of 

power gain and relative power level for the full-scale model. It is believed that a 

radiation efficiency of 16% or better can be realized for most of the intended 

frequency band. 

 Although the results from all of the three antenna heights considered in 

this report meet the requirement, we recommend use of the height of 15 inches 

for final implementation. 

7. ACKNOWLEDGEMENTS 

 The authors would like to express their appreciation to Mr. H. A. Ray of 

Continental Electronics, Dallas, Texas, for verifying our initial design, building 

the full-scale model, and performing the reactance, coil Q, and relative power 

measurements. They would also like to thank their colleagues, R. D. Jennings, 

J. R. Juroshek and G. H. Stonehocker for helping with the gain measurements. 

Partial financial support received from the U. S. Energy Research and 

Development Administration, Albuquerque, N.M., for this project is gratefully 

acknowledged. Constant consultation with E. L. Morrison during the design 

stage is also appreciated. 
38

8. REFERENCES 

Harrington, R. F. (1958), Introduction to Electromagnetic Engineering (McGrawHill, New York, N.Y.), 234. 

IEEE (1965), IEEE test procedures for antennas, Number 149, IEEE Transactions on Antennas and Propagation, AP-13, No. 3, 437-466. 

Jordan, E. C. (1950), Electromagnetic Waves and Radiating Systems (Prentice 

Hall, Englewood Cliffs, N.J.), 312 and 512. 

Martin, C. A., and P. S. Carter (1961), Antenna Engineering Handbook 

(McGraw-Hill, New York, N.Y.; Heny Jasik, Editor), 19-6. 

Ramo, S., and J. R. Whinnery (1959), Fields and Waves in Modern Radio (John 

Wiley and Sons, New York, N.Y.). Table 9.01 and 261. 

Schelkunoff, S. A., and H. T. Friis (1952), Antennas, Theory and Practice (John 

Wiley and Sons, New York, N.Y.), 302. 

Wheeler, H. A. (1975), Small antennas, IEEE Transactions on Antennas and 

Propagation, AP-23, No. 4, 462-469.