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have phase difference of 90°.
Design of a Quadrifilar helix antenna tuned to
7 MHz
Vempati Sai Ram Anand

Abstract—This paper describes the analysis of the right handed
circularly polarized quadrifilar helix with an operational
frequency of 7 MHz. The antenna system was simulated using
FEKO software in a free space environment with a base reference
chosen as a finite ground plane coated with a sand dielectric of
thickness 0.01m. The necessary conditions that were ensured
during the simulation were that the antenna gain should be as
high as possible and the dimensions of the antenna including the
ground plane were as small as possible. The effect of the arm
length and the diameter on the performance of the antenna is also
discussed. The practical considerations for setting up the
quadrifilar helix antenna and the impact of the various real
grounds on its performance will also be stated. Finally, a
theoretical approach is used to determine the maximum realizable
bandwidth within a tunable frequency range of 2-7 MHz.
Index Terms— FEKO,Resonance,QHA,Bandwidth
I. INTRODUCTION
The quadrifilar helical antenna(QHA) is a four-wire helical
antenna that is used in most of the satellite and mobile related
applications. In [1] the Quadrifilar helix antenna (QHA) is
stated to have many attractive features such as light weight,
circularly polarized radiation and a high gain with a wide
beamwidth. Fig 1 shows the structure of a right hand circularly
polarized quadrifilar helix antenna placed on a finite ground
plane made up of sand material.
Fig.1. A Right handed circularly polarized QHA constructed
using CADFEKO
The geometry of the quadrifilar helix antenna is similar to the
geometry of the helix antenna with its performance
characterized by the number of turns of the helix(N), height of
the helix(H), pitch angle(α), spacing(S),helix radius(R) and the
arm length(L). The relations between the various geometric
parameters of the helix are given in (1)-(3).
H = N*S
(1)
2
2
L=√𝑆 + (2𝜋𝑅) (2)
tan(𝛼) = 𝑆/(2𝜋𝑅) (3)
The right handed circular polarization of a quadrifilar helix
antenna can be obtained by setting the phases of the four
excitations in such a manner that the consecutive port voltages
The organization of the paper is as follows:
In Section II, the construction and performance simulation of
the QHA using FEKO software will be stated in detail. The
effect of the various structural parameters of the antenna on its
performance will also be described.
In Section III, the practical realization of the antenna will be
explained. The mounting of the quadrifilar antenna on a
practical ground will be discussed in detail. The impact of
various kinds of real ground on the performance of the antenna
will also be depicted.
In Section IV, the theoretical approach to achieving the
maximum realizable VSWR bandwidth of an antenna tunable
in the 2-7 MHz frequency range will be stated.
Finally in Section V, the construction and performance of the
QHA will be summarized with respect to the practical
considerations and the practical VSWR bandwidth will be
related to the theoretically calculated bandwidth in Section IV.
II. CONSTRUCTION AND SIMULATION OF QHAUSING
FEKO SOFTWARE
A. Construction of QHA using CADFEKO
The initial procedure involves the construction of quadrifilar
helix antenna using the CADFEKO software.The frequency of
operation is specified as 7 MHz. Hence the wavelength of
operation will be 42.857 m. The geometric parameters of the
QHA must be chosen such that it operates in the axial or
end-fire mode where the Cλ(circumference normalized with
respect to the wavelength) must be approximately between 0.4
and 2.0 as stated in [2]. The approximate value of the helix
radius(R) which satisfies this condition is 6.82 m. The number
of turns(N) of the antenna is chosen as 0.75 so as to ensure
minimum weight of the helix antenna excluding the ground
plane and the feed network. The optimum height of the helix
antenna that satisfies the condition of 0.75 turns is found to be
7.18 m .The pitch angle α is then calculated using (1) and (3)
and its value is found to be equal to 12.81°. The material that is
used as the core medium for the wire is copper. The quadrifilar
helix antenna is placed over a finite circular ground plane as
described in [1]. The finite ground plane consists of PEC
material that is coated with a sand dielectric. [3] states that the
sand dielectric has a relative permittivity of 10 and a
conductivity of 0.02.
The observation range for the far field radiation pattern for this
antenna was set with the elevation angle (𝜃) chosen between 0°
and 90° and the azimuth angle(ϕ) chosen between 0° and 360°
so as to observe the radiation pattern only above the ground
plane. The radius of the finite circular ground plane is 15m so
as to obtain the given condition of the VSWR less than 2.
The surrounding environment medium is air media having an
approximate relative permittivity of 1 and a loss tangent of 0.
Once the QHA model is meshed with a given mesh segment
radius, the simulation of the results will be performed using
POSTFEKO which will be described next.
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B. Simulation of the QHA using POSTFEKO
Once the QHA is built in CADFEKO with the appropriate
dimensions, the next step is to simulate the performance of this
QHA using POSTFEKO.
Since the design constraint is that the QHA must be right
circularly polarized it must have a very RHC(right handed
circularly polarized) gain and a very low LHC(left handed
circularly polarized) gain.
Fig 2 gives a comparison between the RHC gain and LHC gain
at the operational frequency of 7 MHz.
Fig4. VSWR bandwidth of the QHA
Fig2. Two-dimensional RHC and LHC gain of the QHA
From Fig2, it is observed that RHC gain has a high value of
7.38 dBi, where dBi is the gain with respect to an isotropic
antenna and the LHC gain has a very low value of -28.4 dBi at
the operational frequency of 7 MHz thereby proving the right
handed circularly polarized nature of the antenna.
Another plot in Fig 3 shows the VSWR of the QHA antenna
at 7 MHz is found to be l.76 which is less than the design
VSWR constraint of 2. Fig 4 shows that the VSWR bandwidth
of the QHA is approximately equal to about 69.1 KHz which
can be considered to be a narrow bandwidth. In Fig5, it can be
observed that the real part of the impedance of the QHA
antenna at 6.99 MHz is equal to around 28.4 ohms and the
imaginary part of the impedance at 6.99 MHz to be equal to
around 0.8 ohms which can be considered almost equal to zero.
Hence, the resonant frequency of the QHA is equal to 6.99
MHz which can be approximated to a value of about 7 MHz,
the operational frequency of the QHA.
Fig3. VSWR of the QHA at 7 MHz
Fig5. Real and imaginary part of the impedance at 6.99 MHz
[4] states that the ideal value of the half power beamwidth is
in the range of 75° to 100°. Fig5. shows that the half power
beamwidth of the QHA in the ϕ=0° plane at the operational
frequency of 7 MHz is equal to 80.4641° which is well within
the beamwidth range specified.
Fig6. Half power beamwidth of the QHA at 7 MHz
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C. Impact of the structural parameters of QHA on its
performance
By performing the POSTFEKO simulation it is found out that
The structural parameters of the QHA such as its height(H),
number of turns(N), radius(R) all had an important role in
deciding the performance of the QHA especially with respect
to its VSWR.
When the height of the QHA was increased from its design
value of about 7.18 m to 8 m, there was a small increase in the
measured value of VSWR from an initial value of 1.76 to a
value of 1.9. The arm length(L), which is found to be directly
proportional to the height(H) by relating (1) and (2) thus had
the same effect as the height on the performance of the
antenna with respect to its VSWR. Fig7 depicts the VSWR of
the QHA at 7 MHz when the height of the antenna was
increased from 7.18m to 8m.
However, when the number of turns of the helix antenna is
increased from its design constraint value of 0.75 to 1 turn, it
is observed that the VSWR had the highest increase from 1.76
to a value of 39.5 with the gain increasing from its original
value of 7.38 dBi to 7.98 dBi at the operational frequency of 7
MHz. Fig7 depicts the VSWR of the QHA at 7 MHz when
the number of turns has been increased from 0.75 to 1.
Fig9.VSWR of the QHA having N=1 turn
Since the VSWR has increased to a large extent when the
number of turns was increased from 0.75 to 1 turn, it can be
concluded that the number of turns is the most important
structural parameter of the quadrifilar helix antenna.
III. PRACTICAL REALISATION OF THE QHA
Fig7. VSWR of the QHA with height H=8m
With an increase in the radius of the QHA from the initial
value of 6.82 m to about 7.5 m, it is found using POSTFEKO
that the VSWR had a fairly sharp increase from 1.76 to a
value of 13. The VSWR of the QHA when the radius is
increased to 7.5 m is shown in Fig8.
Fig8. VSWR of the QHA with radius R=7.5m
This section describes the practical requirements for actually
mounting the quadrifilar helix antenna on a real circular
ground plane of radius 15 m consisting of sand material. Also
the impact of another ground plane such as sea water will also
be discussed and compared to the performance of the QHA
mounted on a ground plane made up of sand.
A. Estimation of Antenna weight
As mentioned in [5], the quadrifilar helix antenna can be
supported using the PVC electrical pipe to make a mast with
removable support arms having a total weight of 1 kg.The
removable support arms are used for providing a structural
support to the arms of the helix.
In section II, it is mentioned that the material used for
manufacturing the helix antenna is copper having a relative
permittivity of 1 and a conductivity of 58130000. The length
of the copper wire is chosen to be slightly greater than the
height of the QHA with a value of 7.5 m(30 feet). Since four
wires are required to make a quadrifilar helix antenna, the
total length of the copper wire required will be equal to about
30 m(98 feet).The commercially available copper spool( [6])
having a total length of 100m(30.48 feet) has a weight of
about 4.1 kg.
The feed network of the antenna consists of a metallic plate
which is covered by a layer of sand dielectric. The feed
system can be realized using a Wilkinson power divider and 4
90° phase shifters so as to ensure that phase difference of 90°
is maintained between consecutive voltage sources connected
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to the four ports of the QHA. The estimated weight of this
feed network is about 0.5 kg. Hence, the total weight of the
antenna is computed as the sum of the weights of the PVC
pipe used for supporting the helical antenna, the weight of the
copper wire used for the helix, and the weight of the feed
network. Therefore, the total weight of the antenna is about
5.6 kg.
B. QHA mounting
The practical QHA is mounted on a finite circular ground
plane covered by a layer of sand dielectric having a relative
permittivity of 10 and a conductivity of 0.02. It will be
supported using a PVC pipe with removable support arms in
accordance with [5].
C. Effects of real ground on performance of the QHA
To consider the effects of real ground on the performance of
the QHA, the sand dielectric was replaced by sea water
having a conductivity of 5 S/m and a relative permittivity of
82.The dimensions of the antenna were kept unchanged and
the simulation was performed using POSTFEKO.
From the simulation results, it is observed that there are no
major changes in the overall antenna performance except a
slight increase in the real part of impedance from 28.36 ohms
to 28.68 ohms, and the a small reduction in the VSWR from
1.76 to 1.75. Hence, it can be concluded that there is no major
impact in changing the ground plane material on the
performance of the quadrifilar helix antenna.
IV. THEORETICAL APPROACH FOR ACHIEVING THE MAXIMUM
REALIZABLE VSWR BANDWIDTH OF AN ANTENNA TUNABLE IN
THE 2-7 MHZ FREQUENCY RANGE
In accordance with [7], the maximum realizable matched
VSWR bandwidth is defined as the difference between the
two frequency points on either side of the resonant frequency
on a plot of VSWR versus frequency where the VSWR is
equal to a constant ‘s’.
In case of the quadrifilar helix antenna, the value of ‘s’ will
be equal to 2 which is the maximum VSWR specified by the
design constraint and the tuned frequency
The approach used in [7] to calculate the matched VSWR
bandwidth involves calculating the quality factor Q from the
electric and magnetic field expressions of the quadrifilar
helix.The expression for the quality factor Q in terms of the
R(ωo) resistance at the tuned frequency ωo , the VSWR value
‘s’ and Zo’(ωo), the frequency derivative of the impedance at
the tuned frequency ωo is given in (4).
(4)
Once the quality factor at the tuned frequency ωo is estimated,
the matched VSWR bandwidth FBWv(ωo) can be calculated
from the inverse relation between them as specified in (4).
(4) holds good for all the frequencies within the resonant as
well as the antiresonant frequency ranges.
V. SUMMARY
The quadrifilar antenna was constructed on FEKO to satisfy
the requirements of VSWR less than 2, maximum gain and
minimum dimensions of the antenna including the ground
plane. From the analysis of the POSTFEKO simulation of the
helical antenna, the effect of the structural parameters such as
height(H), number of turns(N) and radius(R) on the VSWR
performance of the antenna was discussed and the most
important structural parameter of the antenna was found to be
the number of turns (N). The observed bandwidth was found
to be about 69 KHz, which is a narrow bandwidth, hence the
equation (4) is applicable for theoretically estimating the
VSWR bandwidth. The observed beamwidh is 80.4641°
which states the fact the quadrifilar helix antennas provide a
higher beamwidth as compared to one wire helix antennas.
The practical design consideration involving the estimation of
the weight of the antenna to be around 5.6kg and the mounting
of the antenna on a real ground plane with the help of PVC
pipes was also discussed. The effect of real ground such as sea
water is also analyzed and is found to have no major impact on
the VSWR performance of the antenna. Finally an expression
to theoretically estimate the VSWR of the QHA by calculating
the quality factor based on the electric and magnetic fields of
the QHA is explained.
REFERENCES
[1] Sultan Shoaib, Waqar Ali Shah, Ali Fahim Khan, Muhammad Amin
Design and Implementation of Quadrifilar Helix Antenna for Satellite
Communication, 2010 6th International Conference on Emerging
Technologies (ICET)
[2] Arlon T. Adams,K. Greenough, Robert F. Wallenberg, Ada Mendelovicz,
C. Lumjiakh, “The Quadrifilar Helix Antenna” lEEE Transactions on
Antennas and Propogation, Vol. AP-22, No. 2, March 1974
[3] Karl emil eliassen, “A survey of ground conductivity and dielectric
constant in Norway within the the frequency range 0.2-10 Mc/s”, Norwegian
Defence Research Establishment(Manuscript received October,1956)
[4] C. C. Kilgus, “Resonant quadrifilar helix”, IEEE Transactions on
Antennas and Propogation., vol. AP-17, pp. 349-351, May 1969.
[5] http://www.g4ilo.com/qfh.html,”A QFH antenna for the weather satellite
band”
[6] http://www.cablewholesale.com/products/home-theater/speaker/product10g3-291hd.,”100m Copper Spool ”
[7] A.D. Yaghjian and S.R. Best, “Impedance, Bandwidth, and Q of
Antenna,” IEEE Transactions on Antennas and Propagation., (2005).