Antenna Synthesis and Continuous Sources

Prepared by:• Fathi Elnour Hamed B.Sc. Communication• Omer Adam Hassan B.Sc. Electrical Engineer• Shady Abdalla Elyas B.Sc. Computer Engineer

May 2011

Antenna Synthesis and Continuous Sources

1. Introduction.2. Continuous Sources.3. Schelkunoff Polynomial Method.4. Fourier Transform Method.5. Woodward-Lawson Method.6. Taylor Line-Source (Tschebyscheff-Error).7. Taylor Line-Source (One-Parameter).

Introduction

A chosen antenna model analyzed for itsradiation characteristics (patterns, directivity,impedance, beamwidth, efficiency, polarization andbandwidth), all of those usually accomplished byinitially specifying the current distribution of theantenna and then analyzing it by using standardprocedures. The antenna current can usually bedetermined from integral equation.

Introduction

In practice, it often necessary to design anantenna system for example:1-Whose far-field pattern possesses nulls in certaindirection.2- For pattern to exhibit a desired distribution, narrowbeamwidth and low side lobes.The task is not only to find the antenna configuration,but also its geometrical dimensions and excitationdistribution because the designed system should yieldan acceptable radiation patterns and it should satisfy

Introduction

other system constraints, this is Antenna Synthesisor The Antenna Pattern Synthesis.Synthesis of Antenna Pattern requires:1- accurate or approximate analytical model ischosen to represent the desired pattern.2- match analytical model to a physical antennamodel.As general we can classified antenna patternsynthesis into three groups:

Introduction

• First group, requires that antenna patternspossess nulls in desired directions.

• Second group, requires that the pattern exhibita desired distribution in the entire visibleregion.

• Third group, techniques that produce patternswith narrow beams and low side lobes.

Continuous Source

Arrays of discrete elements are more difficultto implement, more costly and have narrowerbandwidth. Avery long wire and a large reflectorrepresent antennas with continuous line andaperture, these continuous antennas have a largerside lobes, are more difficult to scan and they arenot versatile as arrays of discrete elements.The characteristics of continuously distributedsources can be discrete-element arrays.

Line Source

Line source

Line Source

Line Source

Line Source

It relates the angular spectrum of wave to theexcitation distribution of the source.For the continuous source distribution, the totalfield is given by the product of elements andspace factors in the analogous to the patternmultiplication for arrays.The type of current and its direction of flow onsource determine the element factor.

Discretization of Continuous Source

The radiation characteristics of continuoussource can be approximated by discrete elementarrays, and vice-versa. Whereby discrete elementswith spacing (d) between them are planed along thelength (l). Smaller spacing between the elementsyield better approximation and they can evencapture the fine details of the continuousdistribution relation characteristics.The accuracy increases as the element spacingdecreases. For large element spacing the patterns ofthe two antennas will not match.

Discretization of Continuous Source

To avoid this, another method known as Root-Matching can be used instead of sampling thecontinuous current distribution to determined theelement excitation coefficients.The Root-Matching method requires that the nullsof the continuous distribution patterns also appearin the initial pattern of the discrete element arrays.

Continuous and discrete linear sourcesFig.(1)

SCHELKUNOFF POLYNOMIAL METHOD

Array factor roots within and outside unit circle, and visible and invisible regions.

Fourier Transform Method

WOODWARD-LAWSON METHOD

The formation of the overall pattern using theWoodward-Lawson method is accomplished asfollows. The first composing function produces apattern whose main beam placement isdetermined by the value of its uniform progressivephase while its innermost side lobe level is about−13.5 dB; the level of the remaining side lobesmonotonically decreases. The second composingfunction has also a similar pattern except that itsuniform progressive phase is adjusted so that itsmain lobe maximum coincides with the innermostnull of the first composing function.

This results in the filling-in of the innermost null ofthe pattern of the first composing function; theamount of filling-in is controlled by the amplitudeexcitation of the second composing function.Similarly, the uniform progressive phase of the thirdcomposing function is adjusted so that themaximum of its main lobe occurs at the secondinnermost null of the first composing function; italso results in filling-in of the second innermost nullof the first composing function. This processcontinues with the remaining finite number ofcomposing functions.

Line-Source

TAYLOR LINE-SOURCE

The Taylor design yields a pattern that is anoptimum compromise between beamwidth andside lobe level. In an ideal design, the minor lobesare maintained at an equal and specific level. Sincethe minor lobes are of equal ripple and extend toinfinity, this implies an infinite power. Morerealistically, however, the technique as introducedby Taylor leads to a pattern whose first few minorlobes (closest to the main lobe) are maintained atan equal and specified level; the remaining lobesdecay monotonically.

Design Procedure

TAYLOR LINE-SOURCE (ONE-PARAMETER)

Side lobe level (dB) -10 -15 -20 -25 -30 -35 -40

B J0.4597 0.3558 0.7386 1.0229 1.2761 1.5136 1.7415