C. O. A. Ugwumba

Department of Agricultural Economics and Extension, Anambra State University, Igbariam,Nigeria


R. N. Okoh

Department of Agricultural Economics and Extension, Delta State University, Asaba Campus, Nigeria




The study compared the profitability and returns to scale of African Clariid catfish farming using concrete and earthen ponds in Anambra State, Nigeria. Primary data were obtained from useful copies of questionnaire returned by 204 out of the 256 respondents interviewed for the study. Data were analyzed by means of budgetary method, translog stochastic frontier models and a 4-point Likert scale. Mean net farm income and net return on investment values were N593,314 and 0.56 for the concrete pond farms and N1,122,586 and 0.75 for the earthen pond farms. This implies that catfish production using either the concrete or earthen pond type of production unit is profitable. Returns to scale values were 2.46 and 0.69 for the concrete and earthen ponds respectively, an indication of increasing and decreasing returns to scale. Catfish production was seriously constrained by high cost of feeds, lack of capital and scarcity of seeds. The earthen ponds were more profitable than the concrete ponds, however, the concrete ponds were in the majority (77%; n = 158). Policy must be channeled towards measures that would ameliorate production problems and encourage the setting up of concrete ponds. Such measures include the establishment of modern feed mill and hatcheries; the broadening of extension services and the provision of credit facilities.


Keywords: Comparative profitability; Budgetary technique; Econometrics;                                               Concrete and earthen ponds.



 Aquaculture is the production of animals such as fish, turtle, shrimps, lobsters, crabs and crops such as rice and seaweeds (Nwuba and Onuoha, 2006). It is therefore the culture of aquatic plants and animals (F.A.O., 2003). Fish farming is part of aquaculture but sometimes the two words are used interchangeably because majority of output from aquacultural production comes from fish farming. Fish farming/culture is the growing of fish in a controlled environment which could be ponds (concrete or earthen), vats (wooden or fibre glass) and plastics (Osawe, 2004; Nwokoye, Afuluenu and Effiong, 2007).

According to Olagunju, Adesiyan and Ezekiel (2007), fish farming started in Nigeria about 50 years ago with the establishment of a small experimental station at Onikan, Lagos State and an industrial farm about 20 hectares at Panyam in Plateau State by the Federal Government of Nigeria. Presently, the culture of fish has spread to all States of the Federation. Fish culture has been established as the best alternative to bridging the widening gap between the demand for and supply of food fish in the country. This will save the country huge foreign exchange of about N50 billion expended to import close to 700,000 metric tonnes of food fish annually to cushon the effect of inadequate local supply. Among the culturable species of food fish in Nigeria (carp, tilapia and catfish), catfish is the most sought after specie, very popular with fish farmers and commands a very good commercial value in Nigerian markets (Samson,1997). Consequently, the catfish is very important to the sustainability of the aquaculture industry in  the country having possessed the following good qualities identified by Adediran (2002); Osawe (2004); as hardy; survives in different culture systems and diverse environments; grows very fast; has higher fecundity; improved survival of the fry and adaptation to supplemental feed.

 Studies conducted by Olagunju et al (2007); Kudi, Bako and Atala (2008), and a few others have attested to the profitability of catfish production. However, this profitability is still being weighed down by constraints such as the use of poor quality catfish seeds, inadequate information, high cost of feeds, traditional techniques, small size of holdings, poor infrastructural facilities and low capital investment ( Adeogun, 2007; Ugwumba and Nnabuife, 2008). The study specifically examined the profitability of catfish production using concrete and earthen ponds, elasticity and returns to scale and constraints to production in the study area.


Anambra State is one of the 36 States of the Federal Republic of Nigeria. It is composed of 21 Local Government Areas (L.G.A.s) and 4 Agricultural Zones. The population stands at over 4 million as at 2006 national population census (Federal Republic of Nigeria (FGN), 2006). It occupies an area of 4,416 km2, 70% of which is arable land. The State is situated on a fairly flat land with tropical vegetation. The climate is humid with substantial rainfall and mean temperature of 87OF. It has a weak soil that is easily eroded, thus accounting for over 500 erosion sites of varying depth and length. Agriculture is the predominant occupation in the rural areas engaging more than 70% of the rural population. Crop and livestock farming are traditional while fish farming is gaining grounds (Ugwumba, 2005).

A multistage random sampling technique was used to select 256 catfish farmers for the study, however, 204 of them returned useful copies of questionnaire. The multistage random sampling method involved sampling 8 L.G.A.s out of the remaining 15 L.G.A.s, 4 communities from each of the 8 L.G.A.s and then 8 farmers from each of the 4 communities to arrive at the 256 respondents. Data collection was through primary sources using interview instruments, observations and respondent’s memory recall. Data collection was for a production period of 12 months and in this case January to December, 2009.

Data were collected on input and output variables, their prices and constraints to production. Data were analyzed by means of enterprise budgeting technique, translog stochastic frontier production function and a 4-point Likert scale. The enterprise budgeting technique used to assess the profitability of the catfish farming enterprise is given as:


NFI  =  GM –TFC  OR  TR – TC



GM  =  Gross margin.    TR   =  Total revenue.   TVC  =  Total variable cost

NFI  =  Net farm income.   TC  =  Total cost.   TFC  =  Total fixed cost.

NROI  =  Net return on investment.

The output elasticities with respect to the inputs, Xi, for the translog production function was calculated by mean differencing all the variables (output and inputs variables) before estimation (Coelli, Prasada and Battese, 1998). With this, the elasticities for the four inputs were the coefficients of the direct Cobb-Douglas terms, X1, X2, X3, and X4 (i.e. farm size, labour, capital, and feeds respectively) in the mean differenced translog equation and the returns to scale coefficient was the sum of the elasticities of the inputs. The respective output elasticity equations for the four inputs are given as:

Where, ξQfs, ξQl, ξQc, and ξQf are the elasticities of output with respect to farm size, labour, capital and feed respectively. Returns to scale (RTS), is the sum of individual elasticity values of the independent variables and it is represented as:


A 4-point Likert scale was deployed in determining the degree of seriousness of production constraints. The scale employs an ordinal level of measurement. The responses from the respondents were ranked in a sort of dimension or disaggregated along a continuum. The response indicating the most serious constrain was given the highest score. Responses on constraints to catfish production were disaggregated as follows:


Very serious =       4

Serious = 3

Moderately serious = 2

Not serious = 1

Determination of cut-off point,


= critical mean score

  f = total scale score (i.e. 4,3,2,1)

 n = scale points


To make inferential statement, the mean score is compared with the critical mean, 2.50. If the calculated mean of a problem is greater than the standard critical value, then that problem is regarded as very serious. The equation used to determine variable mean score is given as:


   variable mean score

   i =  variables (e.g. problems 1, 2, ……….,11 of catfish production)

 total scores of all the respondents on a variable

  n  = number of respondents




Results and Discussion

Profitability of catfish production in concrete and earthen ponds

The estimated profitability of catfish production in concrete and earthen ponds in the study area using enterprise budgetary technique and net return on investment is as presented in Table II. Results of the analysis showed that the respective mean net farm income (MNFI) and net return on investment (NROI) figures were  N594,314 and 0.56 for the concrete pond farms and N1,122,586 and 0.75 for the earthen pond farms. This implies that the earthen ponds returned on the average 19 kobo higher than the concrete ponds for every 100 kobo investment. By these results, catfish production in the study area using either the concrete or earthen pond production unit is a profitable venture. However, it could be observed that the earthen ponds were more profitable than their concrete pond mates going by higher values of MNFI and NROI recorded by them. The outcome of this analysis is surprising because the concrete ponds were preferred by majority of the farmers (77%; n = 158) contrary to the 23% of the farmers who used the earthen ponds (n = 46). The reason could be that some of the concrete pond farms performed poorly to have impacted negatively on profit. On the other hand, better performance of the earthen ponds could be attributed to the reasons reported by (Nwuba and Onuoha, 2006; Ugwumba, 2010) that the earthen ponds provide catfish with natural environment devoid of noise, and endowed with natural water filtering agents and natural feed items (such as phytoplanktons, zooplanktons, snails, worms, clay for calcium, e.t.c.) which encourage faster growth of fish. This situation, in addition to proportionately lower stocking density, bigger water volume and larger farm size, opined by Ugwumba, 2010 might have contributed to better performance of the earthen ponds.


According to Zen, Abdullahi and Yew (2002), technical efficiency of production is sometimes better explained by output elasticities of  production inputs and returns to scale. The result of analysis of output elasticities of catfish production inputs (i.e. farm size, lab our, capital and feed) is shown in Table III. The result indicated returns to scale  










Table II: Estimated profit for catfish production in concrete and earthen                     ponds (N)                                                                                                                  

Variable                              Concrete pond farms       Earthen pond farms   

                                                     (n = 158)                          (n = 46)             

 Total Revenue:                        260,997,850                       120,815,500

TVC:                                        183,803,675                       68,100,195

GM:                                          77,194,175                         52,715,305

TFC:                                         3,450,515                           1,076,347

TC (TVC+TFC):                      167,254,190                       69,176,542

NFI(GM-TFC) :                       93,743,660                         51,638,958

Mean NFI:                                593,314                              1,122,586

NROI(NFI/TC):                        0.56                                    0.75

Source: Field survey, 2009


Values of 2.46 and 0.69 for the concrete and earthen ponds respectively. This means that the concrete ponds were operating at increasing returns to scale and the earthen ponds at decreasing returns to scale. It also implies that the concrete and earthen pond farms are at Stages I and III of the traditional production function respectively. The concrete pond farms should continue to increase their output by employing more inputs while holding the fixed input level steady. However, caution must be exercised with the use of the labour input which had negative sign and was being over utilized. This result corroborates Zen et al (2002) who reported over utilization of the labour input in their study on technical efficiency of driftnet and payang seine fisheries in West Sumatra, Indonesia.


On the contrary, the earthen pond farms having decreasing returns to scale should scale down their operations in order to maintain their profit status. They should do so by reducing their inputs’ use especially the feed input with negatively signed coefficient, an indication of over utilization. The earthen pond farmers over utilized their feed input probably because of the earlier reported reason of their being richly endowed with natural feed items above the farmers’ expectations and calculations.


Table III: Estimated translog output elasticities and returns to scale for concrete                    and earthen ponds                                     

Farm groups              Variable                 Coefficient                T-statistic      

Concrete                   Blnfarm size                0.28                         0.28 ns             

Ponds                        Blnlabour                     0.55                         0.54 ns          

                                  Blincapital                  -0.03                         0.02 ns          

                                  Blinfeed                       1.66                         1.66*        

                                  RTS                             2.46 increasing                                    


Earthen                    Blnfarm size                 0.55                          0.55 ns              

Ponds                      Blnlabour                      0.68                          0.68 ns                  

                                Blncapital                     0.26                          0.26 ns           

                                Blnfeed                       -0.81                          0.81 ns         

                                RTS                              0.69 decreasing   

Source: Field survey, 2009.   RTS: Returns to Scale.  NS: not significant.  *: Significant at 10% level of probability.                           




Constraints to catfish production

The productivity of catfish farmers in the study area was constrained by several factors. The top in rank among these problems as shown in Table IV was high cost of feed (3.85), followed by lack of capital (3.18) and scarcity of seed (2.95). Other constraints not asterisked which were below the critical mean of 2.50, that is – lack of modern technology (2.25), high cost of transportation (2.11), high cost of labour (2.06), lack of land (1.94), poaching (1.90), inadequate water supply (1.764), mortality of fish (1.759), were perceived as moderately serious problems. However, poor storage facilities (1.33) posed no problem to catfish farming.


Table IV: Problems of catfish production.


Problem                                                        Calculated Mean                            Rank

High cost of feed                                                   3.85*                                       1st

Lack of capital                                                       3.18*                                       2nd

Scarcity of seeds                                                    2.95*                                       3rd

Lack of modern technologies                                2.25                                         4th

High cost of transportation                                    2.11                                         5th

High cost of labour                                                2.06                                         6th

Lack of land                                                          1.94                                         7th

Poaching                                                                1.190                                       8th

Inadequate water supply                                        1.764                                       9th

Mortality of fish                                                    1.759                                       10th

Poor storage facilities                                             1.33                                         11th

Source: Field survey, 2009.


Conclusion and recommendation

Catfish production in the study area using either the concrete or earthen pond production unit is a profitable enterprise. The use of any of the pond types yielded positive mean net farm income and net return on investment. However, the earthen pond farmers realized higher profit than their concrete pond counterparts and therefore returned 19 kobo higher on every 100 kobo invested in the business. The concrete pond farms were operating at increasing returns to scale and are at Stage I of the traditional production function, while the earthen pond farms were at Stage III having exhibited attributes of decreasing returns to scale. The earthen pond farmers should reduce their inputs usage especially the feeds input in order to earn better profit.


The concrete pond farms were equally profitable and in the majority. This is an evidence that they can be established on any size and type of land. Catfish production was seriously constrained by high cost of feed, lack of capital and scarcity of quality seeds. Policy must be directed toward measures that would ensure amelioration of the production problems and the establishment of concrete ponds to create more employment opportunities. Such measures should include the setting up of modern feed mills, hatcheries and the broadening of extension services and access to credits.



Adediran, I. A. (2002) Super-Intensive Fish Culture Using Water Re-circulating

System. Proceedings of Seminar on Fish Farming, Success Attitude Development Centre (SADC), Lagos, Nigeria. Pp 1- 4.


Adeogun, O. A.; H. K. Ogunbadejo; O. A. Ayinla; A. Oresegun; O. R. Oguntade;

Alhaji Tanko and S. B. William[2007].Urban Aquaculture: Producer perceptions and practice in Lagos State, Nigeria. Middle-East Journal of Scientific Research. 2(1): 21 – 27.


Coelli, T. J., R. Prasada and G. Battese (1998). An Introduction to Efficiency

and Productivity Analysis. Boston:Kluwer Academic Press.


Federal Republic of Nigeria (FGN) (2006). Nigeria-Country Overview, Location

and Size, Population, Inland Water Ways, Ports, Air transport, in Nations Encyclopedia:: Africa. Retrieved from:http://www.


Food and Agricultural Organisation (FAO) (2003). Coastal and Marine Ecosystems – Nigeria. Earth Trends, 2003. Retieved from: http://earth library/country profiles/ coa cou 566 pdf.


Kudi, T. M., F. P. Bako and T. K. Atala (2008). Economics of Fish Production in Kaduna State, Nigeria. ARPN Journal of Agricultural and Biological Science, 3 (5 & 6): 17-21.


Nwokoye, C. O., N. L. Afuluenu and E. J. Effiong (2007). Induced Propagation of African Clarrid Catfish, Hetero`branchus Bidorsalis, using synthetic and homoplastic hormones. African Journal of Biotechnology, 6(23): 2687 – 2693.


Nwuba, L. A. and E. Onuoha (2006). Fish Farming in the Tropics: a functional                                     

approach. Maxiprints, Awka, Nigeria.


Olagunju, F. I., I. O. Adesiyan, and A. A. Ezekiel (2007). Economic

Viability of Catfish Production in Oyo State, Nigeria. J. Hum. Ecol. 21(2): 121 – 124.


Osawe, M. (2004). Catfish Fingerlings  Production and Hatchery Management

Techniques. Success Attitude Development Center, (SADC) Lagos, Nigeria. Workshop Paper, Pp 32.


Samson, Y. A. (1997). Introduction to Aquaculture and Fisheries Management

in Nigeria. Goal Education Publishing, Abeokuta, Nigeria.



Ugwumba, C. O. A. (2005). The Economics of Homestead Concrete Fish Pond

in Anambra State, Nigeria. African Journal of Fisheries  and Aquaculture, 4 (2005): 28-32.


Ugwumba, C. O. A. and E. L. C. Nnabuife (2008). Comparative Study on the

Utilization of Commertial Feed and Home-made Feed in Catfish Production for Sustainable Aquaculture. Multidisciplinary Journal of Research Development (MULJORED), 10 (6): 164-169.


Ugwumba, C. O. A. (2010). Profitability and Technical Efficiency of Catfish Production in Anambra State, Nigeria. Ph.D Dissertation, Department of Agricultural Economics and Extension, Delta State University, Abraka, Nigeria.


Zen, L. W.,  N. M. R. Abdullah and T. S. Yew (2002). Technical Efficiency of the Driftnet and Payang Seine (Lampara) Fisheries in West Sumatra, Indonesia. Asian Fisheries Science, 15 (2002): 97-106.




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: A typical 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 = ="_x0000_i1064" width="333" />

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.