J. J. Biebuma and  O.B. Omijeh

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


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          



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 12.50 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


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.

HG = ------------------1.2

HD = 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




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 a1), 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,a1, and an axial dimension  zA .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 a1and pitch angle  shown in Figure 2. Furthermore, we use two sets of coordinates: namely the primed Cartesian coordinates x1,y1,z1 and cylindrical coordinates

  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






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 z1 -axis assumes a helical shape of radius (a+a1).  The parametric equations of the helically-shaped z1 -axis, in analogy with (2b), are expressed as






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+a1) according to the following relationship


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


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:')


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


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:');


    clear;     helixant;



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;




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

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

for i=1:m




title('The Shape of The Helix Antenna')

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


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');


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  200        (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 x3x108/1500 x106 = 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  Hhh    Gain G =

G =

G  = 10.8+10log10(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 200 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 +2a1) 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  100 to 120 shown in figure 5 (c) .The maximum gain, however, occurs when = 12.50.  (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.



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.



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.