**JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 8 NO 2, DECEMBER, 2010**

**
MODELING OF HIGH GAIN HELICAL ANTENNA FOR IMPROVED PERFORMANCE**

**
Department of Electrical and Electronic Engineering Univesity of Port
Harcourt,Port Harcourt **

**
Oweh Victor**

**
Department of Computer Engineering, Delta State Polytechnic, Otefe-Oghara, Delta
State, Nigeria**

**
E-mail:owehvicky@yahoo.com**

**
Abstract**

*The modeling of High Gain Helical Antenna structure is subdivided
into three sections : introduction
of helical structures ,Numerical analysis, modeling and simulation based on the
parameters of helical antenna. The basic foundation software for the research
paper is Matlab technical computing software, the
modeling were written in Matlab codes that will generate the structure
based on helical parameters. The helix number of turns is eleven with frequency range from 1500MHz to
2500MHz. The High Gain property was further analysed using graphical variation
of the Helical parameters. The numerical evaluation of helical parameters also
indicates that high gain is achievable. The simulation of the structure was
equally set default after extensive investigation of parameters and a novice can
do the work of simulation by inputting his values to set parameters .The
applications high gain parameters were studied. *

**
**

**
Keywords : **
Helical antenna structure, High Gain, Matlab codes, improved performance

**
**

**
Introduction**

The helical antenna, first introduced by
Kraus (1946), has been subject of extensive investigations during the past five
decades. Many modifications to the basic helix geometry have been proposed with
the aim of improving the gain, bandwidth, axial ratio, and VSWR. More recently,
the possibility of size reduction, while maintaining the radiation
characteristics, has been explored . In this paper, an improved performance
antenna with a helical geometry is
introduced.

A helical antenna is an antenna consisting of a conducting wire wound
in the form of a helix. In most cases, helical antennas are mounted over a
ground plane. Helical antennas can operate in one of two principal modes: normal
(broadside) mode or axial(or endfire) mode.The antenna then falls under the
class of waveguide antennas, and produces true circular polarization. These
antennas are best suited for space craft tracking and space communication, where
the orientation of the sender and receiver can be easily controlled.

**
Helical antenna structure **

This antenna, referred to as *Helical Antenna *is made of a primary helix
wound on a cylinder of larger diameter. An important advantage of this antenna
is that it can be conveniently constructed.

Figure 1**:Structure of helical antenna**

The helical antenna can be fully described by five parameters. The influence of
these parameters on radiation properties are examined in order to find their
optimum values.

**
Optimum parameters**

The effects of the helix parameters on radiation characteristics such as gain,
input impedance, axial ratio, and bandwidth have been studied extensively. A
brief discussion of optimum parameters is presented below. shows the effect of
circumference on gain. The influence of pitch angle on gain at different
frequencies. Clearly, a pitch angle of 12.5^{0} provides the maximum
gain . Kraus has developed empirical formulae for gain, input impedance, axial
ratio, and half power beamwidth . The empirical gain formula is given as

---------------------------------------------------------------------------------------1.1

Modification by( King and Wong,1989) expressed Gain as

Figure 2** : **Cyclical Helix

The Gain of helical Antenna can be approximated using the formula below.

G =
------------------1.2

D = diameter of helix, C =
circumference of helix =
pD

S = spacing between turns , α= pitch angle = tan-1 (S/pD)

For the half-power beamwidth, an earlier empirical expression by Kraus and, a
few decades later, a more accurate formula by** **King and Wong (1989) were
developed. The results are

---------------------------------------1.3

**
Methodology **

Computer simulation or a computer program that attempts to model a
real-life or hypothetical situation on a computer, so that it can be studied to
see how the system works. By changing the variables, predictions may be made
about the behavior of the system. A good example of the usefulness of using
computer to simulate can be found in the field of antenna simulation. In such
simulation, the model behavior will change each simulation according to the set
of initial parameters assumed for the environment. Originally, the formal
modeling of systems has been through a mathematical model which attempts to find
analytical solutions enabling the prediction of the behavior from set of
parameters and initial conditions and Matlab technical computing were used.

**
**

**
Numerical analysis of the model
**

It is now clear that a helical antenna can be fully described by five
parameters—two radii( *a and a ^{1}*), two pitch angles (
and
), and the number of larger turns (

*N*) on the cylinder of radius

*a*.

In order to facilitate the numerical analysis of the helical antenna, a set of
equations describing its geometry are needed. With the availability of these
equations, the coordinates of an arbitrary point on the helical structure are
readily determined in terms of the parameters *a,a ^{1},
*and an axial dimension
z

_{A .}Before embarking upon the derivation of equations for the helical geometry, we first examine the parametric equations for a simple cylindrical helix, such as the primary helix with radius

*a*and pitch angle

^{1}*shown in Figure 2. Furthermore, we use two sets of coordinates: namely the primed Cartesian coordinates*

*x*and cylindrical coordinates

^{1},y^{1},z^{1 }
for the geometry of the primary helix, and the unprimed
coordinates

*
(x , y ,z*)
and
z)for describing the geometry of the doubly helical
structure.

The parametric equations of the primary helix are expressed as

-----------------------------------------------------------------------------2.1a

-----------------------------------------------------------------------------2.1b

------------------------------------------------------------------------2.1c

Figure 3**:** coordinates for (a) primary
helix, (b) helical geometry

Once the primary helix is wound on a cylinder of radius *a *with a pitch
angle
as in

Figure 3a, the *z ^{1}* -axis assumes a helical shape of radius (

*a+a*). The parametric equations of the helically-shaped

^{1}*z*-axis, in analogy with (2b), are expressed as

^{1 }
-------------------------2.2a

-------------------------2.2b

---------------------2.2c

------------------2.3

----------------------------2.4

*
zA *
varies in the range 0 *A A
z
z *, where *
zA *max is the height of the helical antenna.

It is related to the number of turns *N *(turns with the mean radius( *
a+a*^{1}) according to the following relationship

-----------------------2.5

Equations (2.3) to (2.4) fully describe the geometry of helical antennas. These

equations are used to generate coordinates of discrete points on the antenna
which are then used as part of the input data to the Matlab software ( Balanis
,1997)

**
Designing flowchart of helical antenna**

The flow chart shows the design procedures using Rao-Wilton-Glisson (RWG)
boundary element for modeling Helical wire antenna because it has the potential
to avoid the development and programming of two separate algorithms. This
greatly simplifies the underlying mathematics and Matlab source codes for
Helical antenna. This text explains how to use the standard matlab package in
order to simulate antenna and microwave structures (Makarov ,2002 )

Figure 4 : flowchart of scattering Algorithm of Matlab directory

**
Matlab codes for structural design of helical antenna**

clear;

disp('To Run the simulation of the Helix Antenna')

meth=input('default values, type 1 and press Enter or type 2 and press enter to
specify your values : ');

if meth==1

a=30; ap=0.01;

alph=10*pi/180; alpha=2.5*pi/180;

length=500; inc=0.03; begin=1500; last=2500;

rad=0.005; intrvl=50;

elseif meth==2

a=input('Type in the Helix radius a:');

ap=input('Type in the Helix radius prime ap:');

alph=input('Type in the pitch angle 1 in degrees:')

alph*10*pi/180;

alpha=input('Type in the pitch angle 2 in degrees:')

alpha*2.5*pi/180;

length=input('Type in the length of helix:');

inc=input('Type in the increment for length:');

begin=input('Type in the beginning frequency in MHz:');

last=input('Type in the last frequency in MHz:');

rad=input('Type in the radius of the wire:');

intrvl=input('Type in the frequency interval in Hz:');

else

clear; helixant;

end

t=num2str(length/inc);

sym='_'; for freq=begin:intrvl:last

%simulation information

f= num2str(freq/10);

rad1=num2str(a); rad2=num2str(ap);

pitch1=num2str(a); pitch2=num2str(ap); radius=num2str(rad);

filename=strcat(t,sym,f,pitch1,'.dat'); fid=fopen(filename,'w');

Text2=strcat('CE',t,sym,pitch1,'.cav'); fprintf(fid,text1); fprintf(fid,'\r');
fprintf(fid,'\n');

c=1; lam=.02*(3*10^8/(freq*10^6));

x1(1)=0;
y1(1)=0;
z1(1)=lam;

end

S=11.02*lam;

[X,Y]=meshgrid(linspace(-S,S,20),linspace(-S,S,20));

Z=zeros(size(X)); f= begin:intrvl:last;

f=f/10^6; m=max(size(f));

for i=1:m

end

figure(1);

plot3(x1,y1,z1,'b')

title('The Shape of The Helix Antenna')

Xlabel('X-Axis') Ylabel('Y-Axis') Zlabel('Z-Axis')

hold

q=size(z1); q1=q(1)*q(2); qx=[0,-4*x1(q1)]; qy=[0,-12*y1(q1)];

oo=[0,0] ;mesh(X,Y,Z)

plot(qx,oo,'y'); plot(oo,qy,'m');

plot3([0,0],[0,0],[0,qz],'r');

grid on.

**
Simulation results analysis
**

Modeling and simulations are better
summarized in three different perspective :

i).
The shapes modeling based on different parameters of Helical antenna.

ii). The graphical representation of High Gain
based on modeled helical antenna parameters.

iii). How to obtained high gain based on the
calculation using simulation helix parameters.

**
Helical antenna structures with varying parameters**

(a)
The true shape (1500 – 2500) MHz. (b) The shape
frequency interval to 5000 Hz.

(c)The shape freq.(15000 – 25000)MHz
(d) The shape Radius of Helix at 35 mm

(e)The shape of pitch angle of 20^{0}
(f) The shape lambda = 0.06

Figure 5:
Helical Antenna structures with varying parameters from (a – f)

**
The graphical explanation of high gain
parameters**

**
**

(a)
The graph of Gain against
(b) The graph of Gain against Number of

Circumference (mm)
Turns

(e) The graph of Gain
against frequency (f) The graph of Gain against
peak

(MHz)
Wavelength(mm)

Figure 5 (a – f)** :** The graph of High Gain parameter
of Helical Antenna

**
High**
**gain calculation using simulation parameters**

The following are simulation parameters using in obtaining the high gain of the
helical antenna.

i). Radius/Diameter (a)=31.83mm/63.66 mm .

ii). Spacing between turns(s) = S=1.102 x 40 = 44.34 mm.

iii). Wavelength (lambda) = 0.02 x3x10^{8}/1500 x10^{6}
= 0.04 m =40mm.

iv). Number of Helix turns = 11.

v). Circumference of Helix (C) = 2
a=2x3.142x31.83=200.011
mm.

vi).Pitch angle of the Helix (
=
.

vii). Axial length or Height of Helix = NS =
= NS= 11x44.34=
487.74 mm.

viii). Total length of wire used in helical coil =

= 11
mm.

xi). The
Gain G =

G =

G = 10.8+10log_{10}(25.002)(11)(1.1085)(1.658)
= 35.6 dB.

**
The effects on high gain values due to variation of parameters **

The variation on gain can be summarized by calculation of gain based on helical antenna parameters used in
the simulation.

**
(a) figure 4 a :**The
gain obtained here are basically due to the default setting ,therefore these the
following parameters are responsible for high gain of 35.6 dB which include
axial length ,frequency range, radius of helix, Number of turns ,spacing between
turns.

**
(b) figure 5 b :**With
the interval of frequency increase to 5000Hz , which changes with increase in
Number of Turns and reduction in diameter of the helix, both parameters
contribute to high gain .

**
(c) figure 5 c :**It
is believe that with increase in the radius of the helix will result to High
gain ,the high gain computation with of 35 mm is 36,46 dB. The value obtained
shows clearly that increase in the radius of helix is a great contribution of
high gain.

**
(d) figure 5 d :**Modeling
at this high frequencies between (15000 – 25000)MHz, a high value of Gain is
65.64 dB is obtained, although the number of turns of the helix is reduced.

**
(e) figure 5e :**The
variation of the pitch angle with increase to 20^{0} has a retrogressive
effects on the gain. The computed values of the gain using the simulation
parameter revealed that the gain is 32.06 dB. That at very higher pitch angle
the gain collapses.

**
(f) figure 5 f : **
The effect of peak wavelength(λ) reduces drastically the gain , when λ=0.06,the
gain is 21.32 dB, revealing that with increase in peak wavelength reduces gain.

**
Graphical interpretation results**

The basic Matlab command used in plotting the graphs is” ezplot with hold on and
hold off codes” ,the fundamental information for designing the antenna is given
by Kraus , who has derived an approximate expression modified by king and Wong
.The important results of the investigation of helical antenna with respect to
High Gain are summarized below:

**
(i)**
The peak gain occurs when the outer circumference 2
(*a *+2*a ^{1}*) is about 0.96
. For a conventional helix of comparable gain, this
peak occurs at a circumference of about 1.2
; Figures 5(a) and 5(d)

**
(ii)**
High gains and wide axial-ratio based bandwidths are obtained when the pitch
angle
is about 10^{0}
to 12^{0} shown in figure 5 (c) .The maximum gain, however, occurs when
= 12.5^{0}. ** (iii)**The gain increases with the number of
turns, but the overall gain is reduced; Figure 5(b).** (vi)** The wavelength values has
great significance on the diameter of the Helix in figure 5 (a).

**
The applications of high gain on improved performance**

The modeled high gain of helical antenna has physical attributes on the antenna
in general with these simulation results were validated by comparing theoretical
and empirical formula, the following can be deducted.

**
(a) Signal to noise ratio(snr) : **
modeling at the microwave frequency
of 2.5 GHz , with such a high gain the signal to noise ratio is moderated as
such noise minimum and clear or filtered signal received or transmitted for
helical antenna.

**
(b) Sensitivity : **
sensitivity of receiving helical antenna is the ability to pick up and reproduce
weak signal . it is determined by the value of microwave frequency and because
high gain for improved performance, the higher sensitivity is achieved , thereby
reducing the order of distortion transmitting or receiving signal and reduced
interference.

**
(c) Range of reception : **
the requirement of the transmitter or receiver
helical antenna demands that the gain property is capable of being sending or
receiving signal within such range of microwave nature of frequencies and selectivity within the frequency range which may
be microwave frequency results of high gain attribute of the antenna.

**
(e) Directivity :**
is a figure of merit for an helical antenna , it’s the power density of actual
antenna radiation in the direction of its strongest emission. It also indicating
how much of the total energy from the source is radiating in a particular
direction,with high gain directivity is very efficient from modeling
characteristic and high directivity of energy high directivity of energy to a
source or from a source.

**
Conclusions**

The helix antenna has been used as an example to demonstrate the improvement
found when using the matlab code . As a secondary goal of this paper, the matlab
code is used to analyze some interesting properties of the helix..A
comprehensive numerical analysis of helical antenna has been carried out using
the Matlab codes. Gain-characteristics have been computed for numerous cases
,Several helical antennas were created. Generally.

Great advantage of model this antenna and the
accurate data. In an actual design, the helix as simulated may be
acceptable for the application; if not, one at least is aware that a redesign is
likely to be advisable, without even the need first to build a prototype.

**
References**

Balanis C. A.(1997) ,“*Antenna Theory: Analysis and Design*, 2nd ed., New
York: John Wiley

and Sons.

Barts R.M and Stutzman W. L.(1977), “ A Reduced Size Helical Antenna,” *Proc. IEEE Antennas and Propagat.
Soc. Int. Symp.*, vol. 3.

Cardoso J.C and Safaai-Jazi C.(1993),“Spherical Helical Antenna with Circular Polarization Over a Broad Beam”, *
Electronics Letters*, vol. 29, pp. 325-326.

David B. D.(2005),” *Computational
Electromagnetics for RF & Microwave Engineering”,* Cambridge University
Press.

Fox N.D.(1988) , “A detailed analysis of the helical array as a high performance
portable ground station antenna,” Master’s Thesis, Virginia Tech.

Glasser. O.J and Kraus J.D(1948) ,“Measured Impedances of Helical Antennas”,* App.Phys., *vol. 19, pp. 193-197.

*
*

King H.E. and Wong J.L.(1982) , “Empirical helix antenna design,” *Proc. IEEE
antenna Propagat. Int. Symp*., pp. 366-368.

*
*

Kraus J.D.(1988),” *Antennas for All Applications*”, 2nd ed., New York :
McGraw Hill.

Makarov n. Sergey (2002) ,”*Antenna & EM Modeling with Matlab*”
New York: John Wiley and Sons.