Antenna 1g5s30
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Antenna Lab Manual EELE5133
ﻣﺨﺘﺒﺮ اﻟﻬﻮاﺋﻴﺎت واﻟﺒﺚ اﻹذاﻋﻲ
Prepared By Dr. Mohammed Ouda Eng. Saied Emghary
2008-2009 Include CD-ROM
Table of contents Title
Page
Preface
3
Syllabus
4
Experiment 1
Antenna Parameters
5
Experiment 2
Wire Antennas
9
Experiment 3
•
Linear Arrays Introduction
23
•
Broadside Array
29
•
End-Fire Array
34
Experiment 4
Yagi-Uda antenna
39
Experiment 5
Horn antennas
50
Experiment 6
Reflector Antennas
61
2
Preface This Lab manual is prepared to help antenna course students to deal with the most popular softwares that used in the design of the antennas beside the investigation of the topics covered in the course, Some of the labs are taken from an old lab manual prepared by Eng. Mohammed Al-Absi by using a new versions of the softwares used there, some labs are prepared newly, a new multi-purpose software is used here which is 4nec2.
3
Syllabus Digital Signal Processing Laboratory (EELE 4110) Objectives: • • • • • •
To be familiar with the most popular antenna design programs To investigate the different parameters associated with the specific antenna. To deal with various wire antennas, dipole , loop, helix … etc. To get close to arrays and the different parameters that control the shape of the pattern. To design yagi antenna using design graphs and software programs. To investigate the high directional antennas such as Horn and Reflector antennas.
Course Plan 1st Week Discussion: Antenna Parameters 2nd Week Lab: Antenna Parameters 3rd Week Discussion: Wire Antennas 4th Week Lab: Wire Antennas 5th Week Discussion: Linear Arrays 6th Week Lab: Linear Arrays (Broadside Array) 7th Week Lab: Linear Arrays (End-Fire Array) 8th Week MIDTERM EXAM 9th Week Discussion: Yagi-Uda Antenna 10th Week Lab: Yagi-Uda Antenna 11th Week Discussion: Horn Antenna 12th Week Lab: Horn antenna 13th Week Discussion: Reflector antennas 14th Week Lab: Reflector Antennas 15th Week PROJECT EVALUATION 16th Week FINAL EXAM
References: • •
Class Notes Antenna Design, Balanis ,2nd Ed.
Grades: Attendance…………………….. Midterm Exam……………….... Final Exam…………………..... Reports………………………… Project………………………… Quizzes………………………...
10 15 30 15 20 10
Pts Pts Pts Pts Pts Pts
Lab Policy: • • •
No late reports or pre-labs will be accepted Reports should be done individually. Mid term Exam will be at the end of Lab(6)
Office Hours: Open-door policy, by appointment or as posted. 4
Experiment
1 Antenna Parameters Objective: • •
Studying antenna parameters, Radiation pattern, Pattern beamwidth, Radiation intensity, Directivity, Gain, radiation efficiency. Using "MATLAB" to plot radiation intensity, calculating dirctivity and halfpower beamwidths.
Theoretical Background: •
HPBW: is the angle between two vectors, originating at the pattern's origin and ing through these points of the major lobe where the radiation intensity id half its maximum
•
FNBW: is the angle between two vectors, originating at the pattern's origin and tangent to the main beam at its base. It is very often approximately true that FNBW≈ 2HPBW.
5
•
Radiation intensity U: in a given direction is the power per unit solid angle radiated in this direction by the antenna.
dΩ = sin θdθdφ There is a direct relation between the radiation intensity U and the radiation power density P (that is pointing vector magnitude of the far field) since
Wrad =
dP , W / m2 ds
ds = r 2 sin θdθdφ , m 2 Then U = r 2Wrad v v | E |= η | H | Wrad
r v 2 1 | E |2 1 = η|H| = 2 η 2
U (θ , φ ) =
•
r2 r 2 |E| 2η
Directivity:
Can be defined as the ratio of the radiation intensity of the antenna in a given direction and the radiation intensity of an isotropic radiator fed by the same amount of power. U (θ , φ ) U (θ , φ ) = 4π D(θ , φ ) = U Isotropic Prad D0 =
U max U = 4π max U Isotropic Prad
6
2π π
Prad =
∫ ∫ U (θ , φ ) sin θdθdφ 0 0
•
Gain:
The gain G of an antenna is the ratio of the radiation intensity U in a given direction and the radiation intensity that would be obtained, if the power fed to the antenna were radiated isotropically. G (θ , φ ) = 4π
U (θ , φ ) Pin
The gain is dimensionless quantity, which is very similar to the directivity D. when the antenna has no losses, i.e. when Pin=Prad, then G(θ,φ)=D(θ,φ). Thus, the gain of the antenna takes into the losses in the antenna system. It is calculated via the input power Pin, which is measurable quantity, unlike the directivity, which is calculated via the radiated power prad. The radiated power is related to the input power through a coefficient called radiation efficiency: Prad = ePin G (θ , φ ) = eD(θ , φ ) •
The beam solid angle ΩA :
Is the solid angle through which all the power of the antenna whould flow if its radiation intensity were constant and equal to the maximum radiation intensity U0 for all angles within ΩA. D0 = 4π
1 4π 4π = ≈ Ω A θ1rθ 2 r U (θ , φ ) ∫0 ∫o U max sin θdθdφ
2π π
The relation between the maximum directivity and the beam solid angle is obvious. For antennas with narrow major lobe and with negligible minor lobes, the beam solid angle ΩA is approximately equal the product of the HPBWs in two orthogonal planes. •
The effective area Ae :
The effective area Ae of an antenna is the value corresponding to the direction of maximal gain Gmax. We write in this case: Gmax =
7
4πAe
λ2
Experimental Procedure: Part I The normalized radiation intensity of a lossless antenna is given by: ⎧sin θ sin 2 φ ,0 ≤ θ ≤ π ,0 ≤ φ ≤ π F (θ , φ ) = ⎨ ⎩0, elsewhere
Using MATLAB: a) b) c) d)
Plot radiation intensity at polar coordinates on x-y, y-z planes. Find the azimuthal and elevation plane HPBWs in degrees. Find the maximum directivity (Dmax) Find the approximate directivity using results in (b)
Part II The normalized radiation intensity of a lossless antenna is given by: π π ⎧ ⎪2 sin θ sin φ | sin(φ − ) sin(φ + ) |,0 ≤ θ ≤ π ,0 ≤ φ ≤ π F (θ , φ ) = ⎨ 6 6 ⎪⎩0, elsewhere
Using MATLAB: a) b) c) d)
Plot radiation intensity at polar coordinates on x-y plane. Find the azimuthal HPBW in degrees. Find the maximum directivity (Dmax) Find the ratio of the radiation & field intensities between the main and first side lobes.
8
Experiment
2 Wire Antenna Types of wire antennas •
• • • • •
Linear 1. Dipole 2. monopole Loop 1. circular 2. rectangular Helix Yagi Arrays 1. Broadside Linear 2. End-Fire Linear …………..
Software: EMMCAP "ElectroMagnetic Modeling Computation and Analysis Program" 1. Introduction: EMMCAP is a program system for the modeling of 3D arbitrarily shaped wire structures and for the computation and analysis of their electromagnetic behavior including radiation and scattering problems. EMMCAP computes the current distribution on a thin-wire structure operating in the frequency domain. Using a Method of Moments (MoM) approach with curved segments simulates the current distribution. This means that the structure is first divided into segments which exactly follow the contour of the wires instead of the typical approximation with straight wire segments. The straight wire approximation often requires a large number of segments to adequately approximate the curved wire geometry. Because of this by using curved segments the number of unknowns and memory space can be reduced allowing for the simulation of bigger problems. Next a basis function is defined on each pair of adjacent segments representing an unknown current. Then an Electric Field Integral Equation (EFIE) is converted into a system of linear equations which has to be solved for the unknown currents. Afterwards field strengths radiated power and other parameters of interest can be computed.
9
In using the EMMCAP program system simulating a wire structure is a four-step procedure: : : : :
Defining the program's configuration. Drawing the wire geometry. Performing the computation. Visualizing the computed results.
The program's configuration refers to the definition of the operating frequency or range of frequencies of the system the permittivity and permeability of the medium and other options defining the type of simulation such as a free space computation or a simulation over a perfect electric conductor (PEC) ground plane.
2. Defining the configuration: Selecting "Computation | Configure..." in the main menu can set the program configuration. The "Configuration" dialog box has the following pages: Frequency ,Medium ,Options ,Far-Field and Incident Wave Fig. 2.1.
1. Frequency page The Frequency page has three different options: Single, List and Sweep. By choosing one option the computation can either be performed for a single frequency, for frequencies taken from a list or for a frequency sweep, Fig. 2.1. 2. Medium page The relative permittivity and permeability of the medium can be defined in this page, Fig 2.2. Two sets of values have to be defined, the medium's constants for the computation of currents and the medium's constants for the computation of far-fields. 3. Options page
10
Four options for the type of simulation are available, Fig. 2.3. If "Ground Plane" is checked an infinite PEC ground plane will be placed at the specified height from the xy-plane. Thus, the ground plane is parallel to the xy-plane. If "Height" is positive the ground plane will be over the xy-plane, if "Height" is negative the ground plane will be under the xy-plane, and if "Height" is set to zero the ground plane will be the xy-plane.
11
3. Drawing Wires 1. Attributes page EMMCAP has different types of wires. Each wire has its own input parameters and attributes that can be set in its specific dialog box. Each wire has to be divided into a given number of segments. An unknown current on each segment must be found in the simulation process. This number is set automatically by considering the wavelength and the length of the wire, but can also be set manually by the . The "Attributes" page in the "Draw" dialog box for the wire "Line" is shown in Fig. 3.1. The "Draw" dialog box for each type of wire has its own "Attributes" page with the same features described above.
2. Wire Line Wire "Line" refers to a straight wire. By clicking with the right mouse button in any part of the screen a pop-up menu where the type of wire can be chosen will be shown. Selecting "Draw | Edit " in the main menu can also choose the type of wire By selecting "Line" the "Draw" dialog box where the parameters and attributes of the wire can be set will be shown Fig. 3.2. On the "Line" page of the "Draw" dialog box there are two options available: "2 Points" and "Start - Direction - Length". The "2 Points" option allows to enter the straight wire by giving two points: "From Point" and "To Point" Fig. 3.2.
12
3. Adding sources/loads By clicking with the right mouse button in any part of a wire a pop-up menu where the "Source / Load" option can be chosen will be shown Fig. 3.4. The "Source / Load" option can also be chosen by first selecting a wire by clicking with the left mouse button on it and next selecting " Source / Load " under "Edit" in the main menu Fig. 3.5. When the "Source / Load" option has been chosen a special tool-bar at the bottom of the screen will be shown Fig. 3.6.
13
o Adding source
By clicking on the "Add Source" button a dialog box is shown Fig. 3.7. In the "Add Source" dialog box the type of source its amplitude and phase and its inner impedance can be set.
14
o Adding load
By clicking on the "Add Load" button a dialog box is shown Fig. 3.8. In the "Add Load" dialog box the type of lumped load and its resistance and inductance/capacitance can be set. By selecting the type of impedance a load element can either represent a resistance in series with an inductance or a resistance in series with a capacitance.
In the "Add Load" dialog box the type of lumped load and its resistance and inductance/capacitance can be set. By selecting the type of impedance a load element can either represent a resistance in series with an inductance or a resistance in series with a capacitance.
4. Performing computations When the configuration the geometry and the excitation are defined EMMCAP is ready to compute the currents on the segments. Pressing "Computation | Run Currents" in the main menu Fig. 4.1 can run this simulation.
Pressing "Computation | Run Far-Field" in the main menu Fig. 4.2 can run this simulation.
15
5. Visualizing computed results 1. Current plot A 2D plot of the current distribution along a particular wire can be shown by clicking on the wire with the right mouse button and selecting "Plot Current" in the pop-up menu Fig. 5.1.
Choosing this option executes the EMMPLOT program where the current is plotted in amplitude vs. position along the wire Fig 5.2. The current distribution can also be shown in phase real and imaginary parts by selecting these options under "View" in the EMMPLOT's main menu.
16
2. Radiation pattern plot The computed radiation pattern can be shown as a 2D rectangular plot by selecting "View | Plot Far-Field | 2D Plot" in the main menu Fig 5.3.
Choosing this option shows the "Radiation Pattern Cut" dialog box where two kinds of plots can be produced: conical and vertical. Conical plots are for fixed Theta with Phi varying and vertical plots are for fixed Phi with Theta varying Fig 5.4. Selecting a kind of radiation pattern cut executes the EMMPLOT program where the average Poynting vector is plotted vs. Phi if a conical plot was chosen (for fixed Theta) or vs. Theta if a vertical plot was chosen (for fixed Phi) Fig 5.5.
17
Selecting these options under "View" in the EMMPLOT's main menu can also show the total E-field the E-theta and E-phi field components and the directivity patterns. The radiation patterns can also be plotted in a 2D polar chart by pressing "Polar/Ortho" under "View" in the EMMPLOT's main menu Fig 5.6.
3. Listing results Clicking with the right mouse button on a particular wire shows a pop-up menu Fig. 5.7. Pressing "List ..." in the pop-up menu shows a tool-bar Fig.5.8.
18
The tool-bar has a "Track-Bar". Each position of the Track-Bar corresponds to the position of a segment in the selected wire. Thus this Track-Bar allows selecting a particular segment in the wire. By clicking on the "Current vs. Freq" button a dialog box with a list of the current in the selected segment is shown Fig. 5.9.
This list shows the current in the segment vs. frequency and pressing the "Plot" button in the dialog box can plot these data. If the selected segment has a source on it the "Input List" button is enabled. Choosing this option shows the list of the input impedance vs. frequency that can be plotted by pressing the "Plot" button Fig. 5.10.
19
6. procedure "Simulation of a cylindrical antenna" A straight wire with a voltage source at its center can simulate a center-fed cylindrical antenna. Following the steps listed below can perform the simulation. Step 1: Select "Computation | Configure..." in the main menu. In the "Frequency" page of the "Configuration" dialog box choose "Sweep" and fill the "Frequency Sweep" box as shown in Fig. 6.1.
Step 2: Select "Edit | Draw | Line" in the main menu. The "Draw" dialog box for the wire "Line" will be shown. Fill the pages "Line" and "Attributes" as shown in Fig. 6.2 and Fig 6.3. A straight wire with 17 segments will be drawn.
20
Step 3: Clicking with the right mouse button on the wire shows a pop-up menu where the "Source/Load" option can be selected. Put a voltage source in the segment no. 9 i.e. at the middle point of the wire. The source voltage can be 1 (0º) V. Step 4: Press "Computation | Run Currents" in the main menu. Once the simulation has finished press "Computation | Run Far-Field".
21
Step 5: Clicking on the wire with the right mouse button and selecting "Plot Current" in the pop-up menu can show a plot of the current distribution. Step 6:Plot input impedance vs. frequency Step 7:Plot Real part of the input impedance vs. frequency Step 8:Plot Imaginary part of the input impedance vs. frequency
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Experiment
3
Introduction
Linear Arrays Introduction All the individual radiators of an array are usually similar, with the most common array element being the half-wave dipole. The radiation pattern of an array in freespace depends on four factors: • • • •
The relative positions of the individual radiators with respect to each other The relative phases of the currents of fields in them The relative magnitudes of the individual radiator currents or fields The patterns of the individual radiators
The basic theory of arrays is developed in of the first three factors. The fourth factor assumes that the individual radiators are fictional isotropic point sources. An isotropic point source is one that radiates with uniform intensity in all directions and has no physical size and also no ‘electrical’ size, hence, it does not block or otherwise affect the radiation of the other elements of the array. An array radiation pattern can be calculated on the basis of these assumptions and then a correction to it can be made to take into that in reality the individual radiators do affect each other and do not radiate isotropically.
Definition of Antenna Pattern If an antenna is imagined to be located at the centre of a spherical coordinate system, its radiation pattern is determined by measuring the electric field intensity over the surface of a sphere at some fixed distance r. Since the field E is then a function of the two variables θ and φ, it is written E(θ, φ). A measurement of the electric field intensity E(θ, φ) of an electromagnetic filed in free space is equivalent to a measurement of the magnetic field intensity H(θ, φ), since the magnitudes of the two quantities are directly related by the expression E = 377H. Vectorially E and H are at right angles to each other and their phase angles are equal. Therefore, the pattern could equally well be given in of E or H. It is customary, however, to discuss patterns in of the electric field intensity E. The power density of the field P(θ, φ), can also be computed when E(θ, φ) is known. The relation being P = E2/377. Therefore a plot of the antenna pattern in of P(θ, φ) conveys the same information as a plot of the magnitude of E(θ, φ).
23
Assuming free-space propagation, a pattern that represents field strength as a function of angular direction at a fixed distance from the antenna is identical to a plot of distance for constant field strength. Therefore, a field-strength pattern can be interpreted in either of these ways, by simply changing the labelling of the radial coordinate scale. A similar statement, however, is not true for power-density patterns.
Relative pattern Often the pattern is plotted in relative , that is, the field strength or power density is represented in of its ratio to some reference value. The reference usually chosen is the field level in the maximum-field-strength direction. The field strength or power density is given the value unity in this direction and fractional values in other directions. This relative pattern provides as much information about the antenna as does an absolute pattern and therefore relative patterns are usually plotted when it is desired to describe only the properties of the antenna, without reference to an associated transmitter or receiver.
Two-Isotropic-element Array The simplest array comprises two isotropic point-source radiators. It is discussed here because it covers most of the principles of multi radiator arrays. The meaning of the term phase as applied to the radiating elements of an array is illustrated by considering the following; At some distant point the fields of the two radiating elements are examined and are found to be in phase with each other. If then the phase of the current in Radiator 2 is changed by an amount α radians and the phase of the current in Radiator 1 is left unchanged, it will be observed that the two fields at the distant point are now out-of-phase by the amount α radians. The phase of a radiating element in an array is always discussed in relation to the phases of the other elements. If the phases of the two radiators in a two-element array are changed by the same amount, the array pattern is unaffected, but changing the phases between the two elements affects the way that the individual fields of the tow radiators add up at a specified distant point. Figure 1 shows the significant geometry of a two-element isotropic-point-source array.
Figure 1 – Array of two isotropic sources
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The coordinates of P are ‘r’ and φ are two coordinates of the spherical coordinate system. The third spherical coordinate θ, is not shown because only a plane in which θ is constant is being considered here, namely, the xy-plane in which θ = π radians. 2 The point P is the field point, that is, any point in space where the field is to be calculated. Hence, an expression of the field strength a P applies to all points and thus defines the radiation pattern of the array. Calculation of the field due to the array at an arbitrary point P is the basic problem of array theory. Because the distances r1 and r2 are much larger than the distance d, the amplitudes of the separate fields of the two radiators at point P will be very nearly the same due to the large attenuation that the radiation from each radiator experiences. On the other hand, the relative phases of the two fields at P arising from the two radiators will be dependent on δ, where δ = r2 − r1 , as shown in Figure 2.
Figure 2 – Two-element array geometry
The resulting phase difference of the fields due to δ is equal to − 2πδ
λ radians,
where Radiator 1 or R1 is taken to be the reference phase. To this difference must be added the initial phase difference α, between the two radiators themselves. The total phase difference ψ of the two fields at P is then given by 2πδ ψ =α − (1)
λ
The resultant field at P is the superposition of two fields of equal amplitude, Eo, and phase difference ψ. If two fields of the same amplitude Eo, are considered as two vectors separated by an angle ψ, then the resultant field E, can be found by using the cosine rule, as ⎛ψ ⎞ E = 2 Eo cos ⎜ ⎟ (2) ⎝2⎠ This is the first step toward finding the radiation pattern of the array, which is an expression of E as a function of φ, the angle of the direction of P from the centre of the array. To obtain the radiation pattern, it is necessary to express ψ in of φ. From figure 2, δ = d sin φ (3) On substituting equation 3 into equation 1 and the resultant back into equation 2, gives the equation for the field E(φ) at P.
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⎡ α π d sin φ ⎤ E (φ ) = 2 Eo cos ⎢ − λ ⎥⎦ ⎣2
(4)
Equation 4 is the expression for the field at P as a function of the angle φ that the direction of P makes with the line perpendicular to the line of the array. Equation 4 gives the shape of the pattern in the xy-plane or θ = π plane. The absolute-value 2 brackets are used to indicate that the field intensity being calculated is proportional to the amplitude or to the rms value and is therefore a positive number, although the expression inside the brackets may be signed. In order to obtain the relative pattern, for which the field strength in the maximumintensity direction has the value unity, equation 4 must be divided by the maximum value of E, which is usually, but not always 2E0.
Three-dimensional pattern Equation 4 describes the array pattern in the xy-plane, in which the angle θ of a threedimensional coordinate system is constant ( θ = π ). Because the angle θ is constant 2 it does not appear in equation 4. The three-dimensional pattern is obtained by revolving the xy-pattern about the yaxis, which is the line of the array. This is possible as the xy-pattern is identical in shape and size at any value of rotation in the yz-plane. The pattern in the yz-plane is expressed as a function of the angle θ instead of the angle φ. In other planes, both angles are involved. The expression for the complete three-dimensional pattern is given by, ⎡ α π d sin θ sin φ ⎤ E (θ , φ ) = 2 Eo cos ⎢ − (4a) ⎥⎦ λ ⎣2
Parallel dipole two-element array The pattern defined by equation 4 can be plotted as a function of the angle φ for different values of the parameters d and α. (Note that a parameter is defined in mathematics as a quantity that can vary but is held constant in a particular problem so that the effect of some other variable may be studied, uncontaminated by any variation of the parameter.) Although the various resulting patterns obtained are for an array of isotropic elements, they also represent the patterns of an array of two dipoles in the plane perpendicular to their axis. Providing that the dipoles are parallel to each other and perpendicular to the line ing their centres (line of the array), as shown in Figure 3. This diagram may be thought of as the horizontal-plane patterns of a pair of vertical dipoles or monopoles separated by a distance d and with currents having a phase difference α.
26
Figure 3 – Geometrical positioning of pattern for two dipoles
It should be noted that when the two elements are in phase (α = 0°), the radiation is always maximum in the direction perpendicular to the line ing the elements, that is in the x-direction in Figure 3 above. That is, because the distances from the elements to the field point P are equal in that direction (φ = 0°), the phase difference due to path difference is zero also; hence the total phase difference of the superimposed fields is ψ = 0°. Consequently, the fields add directly and the maximum possible resultant field is obtained. When α = 0° and the pattern maximum is in the direction perpendicular to the array line, as shown in Figure 3, the antenna is called a broadside array. For certain conditions the resultant field in some directions is zero, that is when the sum of the radiator phase difference α, and the phase difference due to path difference 2πδ is an odd integral multiple of π radians. The fields of the individual radiators
λ
are in this case, of equal amplitude and opposite phase, so they cancel. This occurs, for example, when α = 0° and d = λ/2, in the φ = 90° and 270° directions, since in these directions the field phase-difference is 180 degrees, whereas the phase difference due to radiator phase difference is zero. The same result occurs when the 180 degrees net phase difference is due to a combination of path difference and radiator phase difference. These directions of zero intensity in a pattern are called nulls. Certain combinations of d and α result in maximum radiation in the direction of the line ing the array elements. The array is then said to be operating as an endfire array. The radiation of an endfire array may be either bidirectional or unidirectional. A bidirectional array is where the radiation lobes are in both directions along the line of the array. Whereas, a unidirectional array has a lobe in one direction and a null in the opposite direction.
Multi-element Uniform Linear Arrays When more than two elements are used in an array, the principle of calculating the pattern (from which in turn the beamwidth and directive gain can be computed) is the same as for a two-element array. Except that the fields of all the elements must be superposed at the field point. The simplest type of multi-element array is one in which all the radiators are in a line, with equal spacing between adjacent pairs. This is shown in Figure 4 below. The method of analysis is suggested by showing a field-point P 27
ed by ray lines to each element. Such an array is called a linear array. When all the elements are radiating with equal intensity and the phase difference between adjacent elements is constant, the array is called uniform. The applet provided demonstrates a uniform linear array of up to nine elements.
Figure 4 – Linear array of four radiating elements
Radiation Pattern If the array contains n isotropic point-source elements, with equal spacing d and phase difference α between adjacent elements, the pattern in a plane containing the line of the array can be shown to be ⎡ ⎛ π d sin φ α ⎞ ⎤ − ⎟⎥ sin ⎢ n ⎜ 2 ⎠⎦ ⎝ λ ⎣ (5) Erel = ⎡ π d sin φ α ⎤ − ⎥ n sin ⎢ 2⎦ ⎣ λ
For n = 2, this expression reduces to equation 4. As in the two-element case, the three dimensional pattern is obtained simply by replacing sinφ by the product sinφ.sinθ. The factor n in the denominator of equation 5 is a normalizing factor that is used to make Erel a true relative pattern. That is, it permits Erel = 1 for the particular values of φ in the direction of maximum field intensity, in accordance with the definition of relative pattern given above. It is equation 5 that is used in the applet to determine the polar pattern of an n element array.
28
Experiment
3
PART A
Broadside Linear Arrays
When α = 0°, all the elements are in phase and pattern maxima occur at φ = 0° and φ = 180°, that is, in the directions perpendicular to the line of the array. This configuration is called a broadside array. The pattern will be maximum in these directions regardless of the element spacing, d. These will be the only primary maxima if d < λ. If d = λ, additional maxima occur at φ = 90° and φ = 270°. As d is increased still further, additional maxima occur as cones of radiation about the axis of the array. They are known as grating lobes, analogous to the lobes observed in the optical study of a diffraction or reflection grating. Ordinarily, therefore, the spacing of elements in a broadside array is kept less than a wavelength. However, there is an advantage in spacing the elements of an array by more than half a wavelength. For a two-element array the optimum spacing is about 0.7λ, for a four-element array it is about 0.8λ and for a large number of elements the optimum is about 0.95λ. The directivity increases gradually as the spacing is increased until the optimum is reached, then drops rather sharply with further increase. The advantage of the wider spacing is in the directivity obtainable with a given number of elements. In of the ratio of the directivity to the total length of the array, there is no advantage in the wider spacing. These observations can be seen in the applet. Although the above discussion is based on a uniform linear broadside array of point-source isotropic radiators, they apply also to a similar array of dipoles. These dipoles have their centres on the array line and their axes perpendicular to the array line and parallel to each other. The pattern is in the plane perpendicular to the dipole axes, that is, the xyplane as shown in Figure 3. The polarization of the array follows the direction of the dipoles. If the array line is horizontal and the dipole axes are vertical, the radiation is vertically polarized. If the array line is horizontal and the dipole axes are horizontal, as shown in Figure 5, the radiation is horizontally polarized. Figure 5 shows a broadside array and its polar pattern for n = 6, d = 0.7λ and α = 0°.
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Figure 5 – Linear broadside array of six radiating dipoles all elements in phase showing the position of the polar pattern
The in-phase currents in the individual dipoles, required for a broadside pattern, may be obtained by properly connecting a branched transmission line to the feed point of each dipole. That is, if the total line length from the transmitter to each dipole is the same the dipoles will be fed in phase. It is important to ensure that the same side of the line is connected to the same side of each dipole. Reversing this connection reverses the phase. Broadside arrays may also b e formed from other types of elements, such as horns, slots, helixes and polyrods. If the elements are unidirectional radiators, such as sectoral or pyramidal horns, waveguide slots, axial mode helixes and polyrods, a unidirectional broadside array results.
Beamwidth and Gain of Broadside Linear Arrays Isotropic elements spaced a half-wavelength For a uniform broadside linear array of n isotropic elements spaced a half-wavelength apart, the beamwidth is given by • For n = 2 60°. • For n = 3 36°. • For n >3 102/n°. The directivity of such an array is equal to n
Isotropic elements spaced other than a half-wavelength When the element spacing is not half-wavelength but is not greatly different from this value, the beamwidth formula becomes 51λ BW = (6)
nd
30
Procedure: Use 4nec2 software to implement a broadside array and its polar pattern for n = 6, d = 0.7λ and α = 0°
31
32
33
Experiment
3
PART B
Endfire Linear Arrays
If in equation 5 the phase-difference α between adjacent elements is equal to 2π d
λ
radians, the condition for a maximum of radiation is satisfied when φ = 90° and for this value only, provided that d < λ/2. The maximum field intensity is radiated in a direction along the line of the array, “off the end” rather than off the side. Hence the name endfire array. The maximum is toward only one of the ends of the array, rather than in both the endfire directions. In of Figure 4, if the progressive phase change is a retardation going in the direction of the positive y-axis by the amount α per element, the beam will be in the φ = 90° direction. If the sign of α is changed, or its amount is increased by 180 degrees without changing the element spacing, the beam will be in the direction φ = 270°. Although the condition stated above for the value of α results in an endfire array, it does not result in an endfire pattern with the maximum possible directivity and narrowest possible beam. Hansen and Woodyard showed that an endfire beam with a greater gain results if the phase change per element satisfies ⎛ 2π d π ⎞ Hansen-Woodyard condition + ⎟ radians (7) α =⎜ n⎠ ⎝ λ This condition does not necessarily result in a unidirectional pattern as does the basic endfire condition. The basic endfire analysis assumes isotropic radiators, but it applies also to other radiators that have radiation along the line of the array. Thus, parallel dipoles can be used buy not collinear dipoles. For isotropic elements the beam has three-dimensional axial symmetry where the horizontal and vertical beamwidths are the same. The case where d = λ/8 with α = 135° and d = λ/4 with α = 90° provide a complete null or zero field intensity in the back direction for a 2 element array. These patterns are advantageous in applications where a high front-to-back ratio is required. The condition for a null condition for any uniform linear endfire array with an even number of elements is given by ⎛ 2d ⎞ Condition for null in one endfire direction α = π ⎜ 1 ± radians (8) λ ⎟⎠ ⎝ A null is never absolute because of unavoidable imperfections in the spacing and phasing of the elements and many-element arrays are more susceptible to such imperfections than those of few elements. Figure 6 shows an endfire arrangement. 34
Figure 6 – Linear endfire array of six radiating dipoles all elements in phase showing the position of the polar pattern.
Parasitically Excited Endfire Arrays It is not necessary to feed each element of an endfire array by direct connection to a transmission line. If only one dipole as such an array is directly fed, or driven the field that it sets up will cause currents to flow in ading elements. This process is called parasitic excitation and the elements thus excited are parasitic elements. Endfire arrays employing this principle are known as Yagi-Uda antennas, which are often just called Yagis. (Professor Uda first described these antennas in Japanese and H. Yagi was the first to describe the antenna in English, giving full credit to Uda’s work.) The Yagi-Uda antenna can also be regarded as a surface-wave antenna. Parasitic excitation cannot be employed in broadside arrays. To produce the in-phase currents required for a broadside pattern, a full-wavelength element spacing would be required. There would then be two endfire lobes of radiation as well as the two broadside lobes. This type of pattern is not a true broadside pattern. Therefore, broadside arrays are always driven arrays rather than parasitic arrays. The phases of the currents in parasitic dipole elements are determined by their spacing from the adjacent element and also by their lengths. A parasitic dipole cut exactly a half wavelength or slightly longer will be inductive and the phase of its current will lag the induced emf. A dipole cut shorter than a half wavelength will be capacitive and the current in it will lead the induced emf. Comparatively close spacing of elements is used in parasitic arrays to obtain good excitation and the induction fields of the elements play a major role. The exact analysis is very complicated. Properly spaced dipole elements slightly shorter than a half wavelength act as directors, reinforcing the field of the driven element in the direction away from the driven element. Thus, a line of directors may be used with each one exciting the next one. On the other hand, an element one-half-wavelength long or slightly longer will act as a reflector, if correctly spaced. This reflector reinforces the field of the driven element in a direction toward the driven element from the reflector. Therefore, if a reflector element is placed adjacent to a driven element, another element placed beyond the reflector will not be appreciably excited. Although parasitic elements are usually longer or shorter than a half wavelength when used as reflectors or directors, respectively, they may also be one half-wavelength long and made to act as reflectors or directors by proper spacing.
35
For these reasons a Yagi-Uda endfire array usually consist of one driven element, one reflector on one side of it, and a number of directors on the other side of it. Antennas of this type offer the advantages of a unidirectional beam of moderate directivity with light weight, simplicity of feed design and low cost. The design becomes critical if high directivity is attempted trough the use of many elements. Up to fie or six may be used without difficulty and arrays of thirty or forty elements are possible. The input impedance of a yagi-Uday array tends ot be low and the bandwidth is limited to around 2%, typically. Directive gain of around 10 dB is readily achieved with a moderate number of elements, usually five or six. Higher gains may be achieved by making a broadside array of which the elements are Yagi-Uda arrays.
Procedure: Use 4nec2 software to implement an End-Fire array and its polar pattern for n = 6, d = 0.3λ and α = 129°
36
37
38
Experiment
4 Yagi-Uda in VHF Band
Description of The Antenna The Yagi (or Yagi-Uda) antenna is a linear array of parallel dipoles. One element is energised directly by a feed transmission line with the others acting as parasitic radiators. The function of these elements is to enhance the radiation pattern in the source direction. Generally the reflector will be 5% longer than the driven element (ie diploe)and the directors will be 5% shorter. Parameter limits are: • • • • •
Driven Element: 0.45-0.49 wavelengths. Directors: 0.4-0.45 wavelengths. Separation between Directors: 0.3-0.4 wavelengths. Radii of directors: 0.15-0.25 wavelengths. Separation between driven element an parasitics: 0.15-0.25 wavelengths.
Optimization of the Yagi-Uda Antenna can be achieved by simulating the radiation patterns for various lengths of the elemnets and the spacing between them. Other factors that effect the radiation pattern are: • • • • •
•
For an antenna with a length of 6 wavelengths or more the overall gain is independant of the director spacing. The reflector size and spacing have negligable effect on the forward gain and large effects on the backward gain and input impedance. The size and spacing of the directors has a large effect on the forward gain, backward gain and input impedance. More than one reflector provides little improvement on the directivity of the antenna. The addition of more directors will increase the gain of the antenna although after the addition of approximately 5 directors the advantages of adding more directors decreases significantly. The use of a folded dipole will increase the input impedance of the driven element. This is an advantage as the Yagi design generally has a low input impedance and the antenna impedance needs to match the transmission line impedance.
39
System Requirements It's suggested to design a yagi antenna to receive a TV channel in VHF band this channel has a bandwidth of 6MHz from 174 to 180 MHz with video carrier at 175.25MHz and DTV carrier at 174.31MHz and audio carrier at 179.75MHz. The antenna location is of about 50km from the transmitting station (20dBi) and of no landscape obstacles.
Design Curves
The following design curves enable the optimum selection of the following variables/characteristics (all as a function of boomlength) related to the design of a simple Yagi antenna: * Number of elements * Gain * Reflector length * The ratio of reflector length to director length * Bandwidth
40
Figure 1 indicates the optimum number of elements for an antenna of specific boom length
Note: This table is typical performance of Yagi's with the stated number of elements. Typically, the gain will be within 2 dB of the indicated gain. However, Front-to-back ratio can vary greatly (as much as 25 dB) from the indicated F/B. F/B is much more sensitive to adjustments to the element length and spacing.
41
The gain resulting from using the optimum number of elements is shown in figure 2 as a function of boom length.
This curve can be used to obtain the gain that will be achieved from a given boomlength in a boom length limited design, or vice versa. Figure 3 shows the reflector length required to achieve optimum gain as a function of boom length.
42
The director length can be obtained using the known reflector length, and the curve of the ratio of reflector length to director length shown in Figure 4.
Finally the bandwidth for the particular antenna can be obtained using figure 5. If a greater bandwidth is required, the reflector to director ratio can be adjusted to give an increased bandwidth as shown by the red and magenta plots.
43
Antenna special parameters Yagi-Forward gain:
The ratio of the intensity in a given direction to the radiation intensity that would be obtained if the power accepted by the antenna where radiated isotropically. Standard value: >10dBi Front to back ratio:
The ratio of the maximum intensity in the direction of maximum radiation to the radiation intensity of the back lobe in the opposite direction. Standard value: >25dB Front to rear ratio:
The ratio of the maximum intensity in the direction of maximum radiation to the maximum radiation intensity of the side lobes. Standard value: >20dB Drive impedance / SWR:
Due to the mis-match between the load and the feeding system the reflected wave together with incident wave form a standing wave the SWR is the ratio of Vmax to Vmin of this standing wave and is related to impedance of the load and the characteristic impedance if the feeder. Standard value: <2.5
44
Design Using Yagi Designer Software
Optimization Using QuickYagi Software
45
46
Simulation Using 4nec2 Software
47
48
49
Experiment
5 Horn Antennas Horn Antennas: ƒ
flared waveguides that produce a nearly uniform phase front larger than the waveguide itself
ƒ
constructed in a variety of shapes such as sectoral E-plane, sectoral H-plane, pyramidal, conical, etc.
Application Areas: ƒ ƒ ƒ ƒ
used as a feed element for large radio astronomy, satellite tracking and communication dishes A common element of phased arrays used in the calibration, other high-gain antennas used for making electromagnetic interference measurements
Horn Antenna Types: 1. E-Plane Sectoral Horn 00
60 0
Relative power (dB down)
30
0
30 0 10
20
60 0 30
30
90 0
20
1500
1500 180
E- and H-Plane Patterns
50
90 0
1200
1200
E-Plane H-Plane
10
0
2. H-Plane Sectoral Horn 00 Relative power (dB down)
30 0
60 0
30 0 10
20
60 0 30
30
90 0
20
10
90 0
1200
1200
E-Plane H-Plane 1500
1500 180
0
E- and H-Plane Patterns
3. Pyramidal Horn
30 0
60 0
Relative power (dB down)
00 30 0 10
20
60 0 30
30
90 0
20
10
90 0
1200
1200
E-Plane H-Plane
1500
1500 1800
E and H-Plane Patterns
51
4. Conical Horn Antenna
00
60 0
Relative power (dB down)
30
0
30 0 10
20
60 0 30
30
90 0
20
E-Plane H-Plane
1500
1500 1800
E- and H-Plane Patterns
Other horn antenna types: Multimode Horns Corrugated Horns Hog Horns Biconical Horns Dielectric Loaded Horns
Horn advantages: ƒ ƒ ƒ ƒ ƒ
90 0
1200
1200
ƒ ƒ ƒ ƒ ƒ
10
Frequency above 1GHz High gain Wide bandwidth Low weight Easy to construct
52
Horn Antenna Design: Design a pyramidal horn so that the gain is 17.05 dbi at f=11GHz.
53
54
55
56
Horn Antenna Analysis: Use Sabor software to analyze the designed horn above.
57
58
59
60
Experiment
6 Reflector Antennas Objective: a) The main objective is to know the main characteristics and parameters that effect on the parabolic reflector antenna. b) Plotting the radiation pattern of parabolic antenna c) See the effect of changing it's parameter on radiation pattern such as • Frequency of operation • Diameter of the dish • Focal length to diameter ration F/D
Theoretical Background: Antennas based on parabolic reflectors are most common type of directive antennas when a high gain is required. The main advantage is that they can be made to have gain and directivity as large as required . the main disadvantage is that big dishes are difficult to mount and are likely to have a large windage. The basic property of a perfect parabolic reflector is that it converts a spherical wave irradiating from a point source placed at the focus into plane waves. Conversely, all the energy received by the dish from a distant source is reflected to a single point at the focus of the dish. The position of the focus, or focal length, is given by: D2 f = 16c Where D is the dish diameter and c is the depth of the parabola at its center. The size of the dish is the most important factor since it determines the maximum gain that can be achieved at the given frequency and the resulting beamwidth. The gain and beamwidth obtained are given by:
( πD )2 G=e λ
BW =
2
70λ D
Where D is the diameter of the dish and e is the efficiency.
61
Total Efficiency
It has been fairly easy to calculate efficiency for an idealized feed horn pattern due to illumination taper and spillover but there are several other factors that can significantly reduce efficiency. Because the feed horn and its ing structures are in the beam of the dish part of the radiation is blocked or deflected. A real feed horn also has sidelobes so part of its radiation is in undesired directions and thus wasted. Finally no reflector is a perfect parabola so the focusing of the beam is not perfect. We end up with quite a list of contributions to total efficiency: • • • • • • • • •
Illumination taper Spillover loss Asymmetries in E- and H-Planes Focal point error Feedhorn sidelobes Blockage by feed horn Blockag by ing structures Imperfections in parabolic surface. Feedlineloss
Scattering
Spillover
Diffraction Each time the diameter of a dish is doubled the gain is four times or 6db greater, if both stations doubles the diameter the signal strength will be increased by 12dB, the total efficiency can be assumed 50% for hand built antenna. The ratio f/D is the fundamental factor governing the design of the feed for dish. He ratio is directly related to the beamwidth of the feed necessary to illuminate the dish effectively. Two dished of the same diameter but different focal lengths require different design of feed if both are to be illuminated efficiently. The value of .25 correspond to the common focal-plane dish in witch the focus is in the same plane as the rim of the dish.
62
Design steps:
63
64
65
Effect of changing the parabolic parameter on radiation: 4
a) Changing Frequency to 4GHz
b) Changing Diameter to 50cm
66
c) Changing F/D ratio to .3
67
68
ﻣﺨﺘﺒﺮ اﻟﻬﻮاﺋﻴﺎت واﻟﺒﺚ اﻹذاﻋﻲ
Prepared By Dr. Mohammed Ouda Eng. Saied Emghary
2008-2009 Include CD-ROM
Table of contents Title
Page
Preface
3
Syllabus
4
Experiment 1
Antenna Parameters
5
Experiment 2
Wire Antennas
9
Experiment 3
•
Linear Arrays Introduction
23
•
Broadside Array
29
•
End-Fire Array
34
Experiment 4
Yagi-Uda antenna
39
Experiment 5
Horn antennas
50
Experiment 6
Reflector Antennas
61
2
Preface This Lab manual is prepared to help antenna course students to deal with the most popular softwares that used in the design of the antennas beside the investigation of the topics covered in the course, Some of the labs are taken from an old lab manual prepared by Eng. Mohammed Al-Absi by using a new versions of the softwares used there, some labs are prepared newly, a new multi-purpose software is used here which is 4nec2.
3
Syllabus Digital Signal Processing Laboratory (EELE 4110) Objectives: • • • • • •
To be familiar with the most popular antenna design programs To investigate the different parameters associated with the specific antenna. To deal with various wire antennas, dipole , loop, helix … etc. To get close to arrays and the different parameters that control the shape of the pattern. To design yagi antenna using design graphs and software programs. To investigate the high directional antennas such as Horn and Reflector antennas.
Course Plan 1st Week Discussion: Antenna Parameters 2nd Week Lab: Antenna Parameters 3rd Week Discussion: Wire Antennas 4th Week Lab: Wire Antennas 5th Week Discussion: Linear Arrays 6th Week Lab: Linear Arrays (Broadside Array) 7th Week Lab: Linear Arrays (End-Fire Array) 8th Week MIDTERM EXAM 9th Week Discussion: Yagi-Uda Antenna 10th Week Lab: Yagi-Uda Antenna 11th Week Discussion: Horn Antenna 12th Week Lab: Horn antenna 13th Week Discussion: Reflector antennas 14th Week Lab: Reflector Antennas 15th Week PROJECT EVALUATION 16th Week FINAL EXAM
References: • •
Class Notes Antenna Design, Balanis ,2nd Ed.
Grades: Attendance…………………….. Midterm Exam……………….... Final Exam…………………..... Reports………………………… Project………………………… Quizzes………………………...
10 15 30 15 20 10
Pts Pts Pts Pts Pts Pts
Lab Policy: • • •
No late reports or pre-labs will be accepted Reports should be done individually. Mid term Exam will be at the end of Lab(6)
Office Hours: Open-door policy, by appointment or as posted. 4
Experiment
1 Antenna Parameters Objective: • •
Studying antenna parameters, Radiation pattern, Pattern beamwidth, Radiation intensity, Directivity, Gain, radiation efficiency. Using "MATLAB" to plot radiation intensity, calculating dirctivity and halfpower beamwidths.
Theoretical Background: •
HPBW: is the angle between two vectors, originating at the pattern's origin and ing through these points of the major lobe where the radiation intensity id half its maximum
•
FNBW: is the angle between two vectors, originating at the pattern's origin and tangent to the main beam at its base. It is very often approximately true that FNBW≈ 2HPBW.
5
•
Radiation intensity U: in a given direction is the power per unit solid angle radiated in this direction by the antenna.
dΩ = sin θdθdφ There is a direct relation between the radiation intensity U and the radiation power density P (that is pointing vector magnitude of the far field) since
Wrad =
dP , W / m2 ds
ds = r 2 sin θdθdφ , m 2 Then U = r 2Wrad v v | E |= η | H | Wrad
r v 2 1 | E |2 1 = η|H| = 2 η 2
U (θ , φ ) =
•
r2 r 2 |E| 2η
Directivity:
Can be defined as the ratio of the radiation intensity of the antenna in a given direction and the radiation intensity of an isotropic radiator fed by the same amount of power. U (θ , φ ) U (θ , φ ) = 4π D(θ , φ ) = U Isotropic Prad D0 =
U max U = 4π max U Isotropic Prad
6
2π π
Prad =
∫ ∫ U (θ , φ ) sin θdθdφ 0 0
•
Gain:
The gain G of an antenna is the ratio of the radiation intensity U in a given direction and the radiation intensity that would be obtained, if the power fed to the antenna were radiated isotropically. G (θ , φ ) = 4π
U (θ , φ ) Pin
The gain is dimensionless quantity, which is very similar to the directivity D. when the antenna has no losses, i.e. when Pin=Prad, then G(θ,φ)=D(θ,φ). Thus, the gain of the antenna takes into the losses in the antenna system. It is calculated via the input power Pin, which is measurable quantity, unlike the directivity, which is calculated via the radiated power prad. The radiated power is related to the input power through a coefficient called radiation efficiency: Prad = ePin G (θ , φ ) = eD(θ , φ ) •
The beam solid angle ΩA :
Is the solid angle through which all the power of the antenna whould flow if its radiation intensity were constant and equal to the maximum radiation intensity U0 for all angles within ΩA. D0 = 4π
1 4π 4π = ≈ Ω A θ1rθ 2 r U (θ , φ ) ∫0 ∫o U max sin θdθdφ
2π π
The relation between the maximum directivity and the beam solid angle is obvious. For antennas with narrow major lobe and with negligible minor lobes, the beam solid angle ΩA is approximately equal the product of the HPBWs in two orthogonal planes. •
The effective area Ae :
The effective area Ae of an antenna is the value corresponding to the direction of maximal gain Gmax. We write in this case: Gmax =
7
4πAe
λ2
Experimental Procedure: Part I The normalized radiation intensity of a lossless antenna is given by: ⎧sin θ sin 2 φ ,0 ≤ θ ≤ π ,0 ≤ φ ≤ π F (θ , φ ) = ⎨ ⎩0, elsewhere
Using MATLAB: a) b) c) d)
Plot radiation intensity at polar coordinates on x-y, y-z planes. Find the azimuthal and elevation plane HPBWs in degrees. Find the maximum directivity (Dmax) Find the approximate directivity using results in (b)
Part II The normalized radiation intensity of a lossless antenna is given by: π π ⎧ ⎪2 sin θ sin φ | sin(φ − ) sin(φ + ) |,0 ≤ θ ≤ π ,0 ≤ φ ≤ π F (θ , φ ) = ⎨ 6 6 ⎪⎩0, elsewhere
Using MATLAB: a) b) c) d)
Plot radiation intensity at polar coordinates on x-y plane. Find the azimuthal HPBW in degrees. Find the maximum directivity (Dmax) Find the ratio of the radiation & field intensities between the main and first side lobes.
8
Experiment
2 Wire Antenna Types of wire antennas •
• • • • •
Linear 1. Dipole 2. monopole Loop 1. circular 2. rectangular Helix Yagi Arrays 1. Broadside Linear 2. End-Fire Linear …………..
Software: EMMCAP "ElectroMagnetic Modeling Computation and Analysis Program" 1. Introduction: EMMCAP is a program system for the modeling of 3D arbitrarily shaped wire structures and for the computation and analysis of their electromagnetic behavior including radiation and scattering problems. EMMCAP computes the current distribution on a thin-wire structure operating in the frequency domain. Using a Method of Moments (MoM) approach with curved segments simulates the current distribution. This means that the structure is first divided into segments which exactly follow the contour of the wires instead of the typical approximation with straight wire segments. The straight wire approximation often requires a large number of segments to adequately approximate the curved wire geometry. Because of this by using curved segments the number of unknowns and memory space can be reduced allowing for the simulation of bigger problems. Next a basis function is defined on each pair of adjacent segments representing an unknown current. Then an Electric Field Integral Equation (EFIE) is converted into a system of linear equations which has to be solved for the unknown currents. Afterwards field strengths radiated power and other parameters of interest can be computed.
9
In using the EMMCAP program system simulating a wire structure is a four-step procedure: : : : :
Defining the program's configuration. Drawing the wire geometry. Performing the computation. Visualizing the computed results.
The program's configuration refers to the definition of the operating frequency or range of frequencies of the system the permittivity and permeability of the medium and other options defining the type of simulation such as a free space computation or a simulation over a perfect electric conductor (PEC) ground plane.
2. Defining the configuration: Selecting "Computation | Configure..." in the main menu can set the program configuration. The "Configuration" dialog box has the following pages: Frequency ,Medium ,Options ,Far-Field and Incident Wave Fig. 2.1.
1. Frequency page The Frequency page has three different options: Single, List and Sweep. By choosing one option the computation can either be performed for a single frequency, for frequencies taken from a list or for a frequency sweep, Fig. 2.1. 2. Medium page The relative permittivity and permeability of the medium can be defined in this page, Fig 2.2. Two sets of values have to be defined, the medium's constants for the computation of currents and the medium's constants for the computation of far-fields. 3. Options page
10
Four options for the type of simulation are available, Fig. 2.3. If "Ground Plane" is checked an infinite PEC ground plane will be placed at the specified height from the xy-plane. Thus, the ground plane is parallel to the xy-plane. If "Height" is positive the ground plane will be over the xy-plane, if "Height" is negative the ground plane will be under the xy-plane, and if "Height" is set to zero the ground plane will be the xy-plane.
11
3. Drawing Wires 1. Attributes page EMMCAP has different types of wires. Each wire has its own input parameters and attributes that can be set in its specific dialog box. Each wire has to be divided into a given number of segments. An unknown current on each segment must be found in the simulation process. This number is set automatically by considering the wavelength and the length of the wire, but can also be set manually by the . The "Attributes" page in the "Draw" dialog box for the wire "Line" is shown in Fig. 3.1. The "Draw" dialog box for each type of wire has its own "Attributes" page with the same features described above.
2. Wire Line Wire "Line" refers to a straight wire. By clicking with the right mouse button in any part of the screen a pop-up menu where the type of wire can be chosen will be shown. Selecting "Draw | Edit " in the main menu can also choose the type of wire By selecting "Line" the "Draw" dialog box where the parameters and attributes of the wire can be set will be shown Fig. 3.2. On the "Line" page of the "Draw" dialog box there are two options available: "2 Points" and "Start - Direction - Length". The "2 Points" option allows to enter the straight wire by giving two points: "From Point" and "To Point" Fig. 3.2.
12
3. Adding sources/loads By clicking with the right mouse button in any part of a wire a pop-up menu where the "Source / Load" option can be chosen will be shown Fig. 3.4. The "Source / Load" option can also be chosen by first selecting a wire by clicking with the left mouse button on it and next selecting " Source / Load " under "Edit" in the main menu Fig. 3.5. When the "Source / Load" option has been chosen a special tool-bar at the bottom of the screen will be shown Fig. 3.6.
13
o Adding source
By clicking on the "Add Source" button a dialog box is shown Fig. 3.7. In the "Add Source" dialog box the type of source its amplitude and phase and its inner impedance can be set.
14
o Adding load
By clicking on the "Add Load" button a dialog box is shown Fig. 3.8. In the "Add Load" dialog box the type of lumped load and its resistance and inductance/capacitance can be set. By selecting the type of impedance a load element can either represent a resistance in series with an inductance or a resistance in series with a capacitance.
In the "Add Load" dialog box the type of lumped load and its resistance and inductance/capacitance can be set. By selecting the type of impedance a load element can either represent a resistance in series with an inductance or a resistance in series with a capacitance.
4. Performing computations When the configuration the geometry and the excitation are defined EMMCAP is ready to compute the currents on the segments. Pressing "Computation | Run Currents" in the main menu Fig. 4.1 can run this simulation.
Pressing "Computation | Run Far-Field" in the main menu Fig. 4.2 can run this simulation.
15
5. Visualizing computed results 1. Current plot A 2D plot of the current distribution along a particular wire can be shown by clicking on the wire with the right mouse button and selecting "Plot Current" in the pop-up menu Fig. 5.1.
Choosing this option executes the EMMPLOT program where the current is plotted in amplitude vs. position along the wire Fig 5.2. The current distribution can also be shown in phase real and imaginary parts by selecting these options under "View" in the EMMPLOT's main menu.
16
2. Radiation pattern plot The computed radiation pattern can be shown as a 2D rectangular plot by selecting "View | Plot Far-Field | 2D Plot" in the main menu Fig 5.3.
Choosing this option shows the "Radiation Pattern Cut" dialog box where two kinds of plots can be produced: conical and vertical. Conical plots are for fixed Theta with Phi varying and vertical plots are for fixed Phi with Theta varying Fig 5.4. Selecting a kind of radiation pattern cut executes the EMMPLOT program where the average Poynting vector is plotted vs. Phi if a conical plot was chosen (for fixed Theta) or vs. Theta if a vertical plot was chosen (for fixed Phi) Fig 5.5.
17
Selecting these options under "View" in the EMMPLOT's main menu can also show the total E-field the E-theta and E-phi field components and the directivity patterns. The radiation patterns can also be plotted in a 2D polar chart by pressing "Polar/Ortho" under "View" in the EMMPLOT's main menu Fig 5.6.
3. Listing results Clicking with the right mouse button on a particular wire shows a pop-up menu Fig. 5.7. Pressing "List ..." in the pop-up menu shows a tool-bar Fig.5.8.
18
The tool-bar has a "Track-Bar". Each position of the Track-Bar corresponds to the position of a segment in the selected wire. Thus this Track-Bar allows selecting a particular segment in the wire. By clicking on the "Current vs. Freq" button a dialog box with a list of the current in the selected segment is shown Fig. 5.9.
This list shows the current in the segment vs. frequency and pressing the "Plot" button in the dialog box can plot these data. If the selected segment has a source on it the "Input List" button is enabled. Choosing this option shows the list of the input impedance vs. frequency that can be plotted by pressing the "Plot" button Fig. 5.10.
19
6. procedure "Simulation of a cylindrical antenna" A straight wire with a voltage source at its center can simulate a center-fed cylindrical antenna. Following the steps listed below can perform the simulation. Step 1: Select "Computation | Configure..." in the main menu. In the "Frequency" page of the "Configuration" dialog box choose "Sweep" and fill the "Frequency Sweep" box as shown in Fig. 6.1.
Step 2: Select "Edit | Draw | Line" in the main menu. The "Draw" dialog box for the wire "Line" will be shown. Fill the pages "Line" and "Attributes" as shown in Fig. 6.2 and Fig 6.3. A straight wire with 17 segments will be drawn.
20
Step 3: Clicking with the right mouse button on the wire shows a pop-up menu where the "Source/Load" option can be selected. Put a voltage source in the segment no. 9 i.e. at the middle point of the wire. The source voltage can be 1 (0º) V. Step 4: Press "Computation | Run Currents" in the main menu. Once the simulation has finished press "Computation | Run Far-Field".
21
Step 5: Clicking on the wire with the right mouse button and selecting "Plot Current" in the pop-up menu can show a plot of the current distribution. Step 6:Plot input impedance vs. frequency Step 7:Plot Real part of the input impedance vs. frequency Step 8:Plot Imaginary part of the input impedance vs. frequency
22
Experiment
3
Introduction
Linear Arrays Introduction All the individual radiators of an array are usually similar, with the most common array element being the half-wave dipole. The radiation pattern of an array in freespace depends on four factors: • • • •
The relative positions of the individual radiators with respect to each other The relative phases of the currents of fields in them The relative magnitudes of the individual radiator currents or fields The patterns of the individual radiators
The basic theory of arrays is developed in of the first three factors. The fourth factor assumes that the individual radiators are fictional isotropic point sources. An isotropic point source is one that radiates with uniform intensity in all directions and has no physical size and also no ‘electrical’ size, hence, it does not block or otherwise affect the radiation of the other elements of the array. An array radiation pattern can be calculated on the basis of these assumptions and then a correction to it can be made to take into that in reality the individual radiators do affect each other and do not radiate isotropically.
Definition of Antenna Pattern If an antenna is imagined to be located at the centre of a spherical coordinate system, its radiation pattern is determined by measuring the electric field intensity over the surface of a sphere at some fixed distance r. Since the field E is then a function of the two variables θ and φ, it is written E(θ, φ). A measurement of the electric field intensity E(θ, φ) of an electromagnetic filed in free space is equivalent to a measurement of the magnetic field intensity H(θ, φ), since the magnitudes of the two quantities are directly related by the expression E = 377H. Vectorially E and H are at right angles to each other and their phase angles are equal. Therefore, the pattern could equally well be given in of E or H. It is customary, however, to discuss patterns in of the electric field intensity E. The power density of the field P(θ, φ), can also be computed when E(θ, φ) is known. The relation being P = E2/377. Therefore a plot of the antenna pattern in of P(θ, φ) conveys the same information as a plot of the magnitude of E(θ, φ).
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Assuming free-space propagation, a pattern that represents field strength as a function of angular direction at a fixed distance from the antenna is identical to a plot of distance for constant field strength. Therefore, a field-strength pattern can be interpreted in either of these ways, by simply changing the labelling of the radial coordinate scale. A similar statement, however, is not true for power-density patterns.
Relative pattern Often the pattern is plotted in relative , that is, the field strength or power density is represented in of its ratio to some reference value. The reference usually chosen is the field level in the maximum-field-strength direction. The field strength or power density is given the value unity in this direction and fractional values in other directions. This relative pattern provides as much information about the antenna as does an absolute pattern and therefore relative patterns are usually plotted when it is desired to describe only the properties of the antenna, without reference to an associated transmitter or receiver.
Two-Isotropic-element Array The simplest array comprises two isotropic point-source radiators. It is discussed here because it covers most of the principles of multi radiator arrays. The meaning of the term phase as applied to the radiating elements of an array is illustrated by considering the following; At some distant point the fields of the two radiating elements are examined and are found to be in phase with each other. If then the phase of the current in Radiator 2 is changed by an amount α radians and the phase of the current in Radiator 1 is left unchanged, it will be observed that the two fields at the distant point are now out-of-phase by the amount α radians. The phase of a radiating element in an array is always discussed in relation to the phases of the other elements. If the phases of the two radiators in a two-element array are changed by the same amount, the array pattern is unaffected, but changing the phases between the two elements affects the way that the individual fields of the tow radiators add up at a specified distant point. Figure 1 shows the significant geometry of a two-element isotropic-point-source array.
Figure 1 – Array of two isotropic sources
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The coordinates of P are ‘r’ and φ are two coordinates of the spherical coordinate system. The third spherical coordinate θ, is not shown because only a plane in which θ is constant is being considered here, namely, the xy-plane in which θ = π radians. 2 The point P is the field point, that is, any point in space where the field is to be calculated. Hence, an expression of the field strength a P applies to all points and thus defines the radiation pattern of the array. Calculation of the field due to the array at an arbitrary point P is the basic problem of array theory. Because the distances r1 and r2 are much larger than the distance d, the amplitudes of the separate fields of the two radiators at point P will be very nearly the same due to the large attenuation that the radiation from each radiator experiences. On the other hand, the relative phases of the two fields at P arising from the two radiators will be dependent on δ, where δ = r2 − r1 , as shown in Figure 2.
Figure 2 – Two-element array geometry
The resulting phase difference of the fields due to δ is equal to − 2πδ
λ radians,
where Radiator 1 or R1 is taken to be the reference phase. To this difference must be added the initial phase difference α, between the two radiators themselves. The total phase difference ψ of the two fields at P is then given by 2πδ ψ =α − (1)
λ
The resultant field at P is the superposition of two fields of equal amplitude, Eo, and phase difference ψ. If two fields of the same amplitude Eo, are considered as two vectors separated by an angle ψ, then the resultant field E, can be found by using the cosine rule, as ⎛ψ ⎞ E = 2 Eo cos ⎜ ⎟ (2) ⎝2⎠ This is the first step toward finding the radiation pattern of the array, which is an expression of E as a function of φ, the angle of the direction of P from the centre of the array. To obtain the radiation pattern, it is necessary to express ψ in of φ. From figure 2, δ = d sin φ (3) On substituting equation 3 into equation 1 and the resultant back into equation 2, gives the equation for the field E(φ) at P.
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⎡ α π d sin φ ⎤ E (φ ) = 2 Eo cos ⎢ − λ ⎥⎦ ⎣2
(4)
Equation 4 is the expression for the field at P as a function of the angle φ that the direction of P makes with the line perpendicular to the line of the array. Equation 4 gives the shape of the pattern in the xy-plane or θ = π plane. The absolute-value 2 brackets are used to indicate that the field intensity being calculated is proportional to the amplitude or to the rms value and is therefore a positive number, although the expression inside the brackets may be signed. In order to obtain the relative pattern, for which the field strength in the maximumintensity direction has the value unity, equation 4 must be divided by the maximum value of E, which is usually, but not always 2E0.
Three-dimensional pattern Equation 4 describes the array pattern in the xy-plane, in which the angle θ of a threedimensional coordinate system is constant ( θ = π ). Because the angle θ is constant 2 it does not appear in equation 4. The three-dimensional pattern is obtained by revolving the xy-pattern about the yaxis, which is the line of the array. This is possible as the xy-pattern is identical in shape and size at any value of rotation in the yz-plane. The pattern in the yz-plane is expressed as a function of the angle θ instead of the angle φ. In other planes, both angles are involved. The expression for the complete three-dimensional pattern is given by, ⎡ α π d sin θ sin φ ⎤ E (θ , φ ) = 2 Eo cos ⎢ − (4a) ⎥⎦ λ ⎣2
Parallel dipole two-element array The pattern defined by equation 4 can be plotted as a function of the angle φ for different values of the parameters d and α. (Note that a parameter is defined in mathematics as a quantity that can vary but is held constant in a particular problem so that the effect of some other variable may be studied, uncontaminated by any variation of the parameter.) Although the various resulting patterns obtained are for an array of isotropic elements, they also represent the patterns of an array of two dipoles in the plane perpendicular to their axis. Providing that the dipoles are parallel to each other and perpendicular to the line ing their centres (line of the array), as shown in Figure 3. This diagram may be thought of as the horizontal-plane patterns of a pair of vertical dipoles or monopoles separated by a distance d and with currents having a phase difference α.
26
Figure 3 – Geometrical positioning of pattern for two dipoles
It should be noted that when the two elements are in phase (α = 0°), the radiation is always maximum in the direction perpendicular to the line ing the elements, that is in the x-direction in Figure 3 above. That is, because the distances from the elements to the field point P are equal in that direction (φ = 0°), the phase difference due to path difference is zero also; hence the total phase difference of the superimposed fields is ψ = 0°. Consequently, the fields add directly and the maximum possible resultant field is obtained. When α = 0° and the pattern maximum is in the direction perpendicular to the array line, as shown in Figure 3, the antenna is called a broadside array. For certain conditions the resultant field in some directions is zero, that is when the sum of the radiator phase difference α, and the phase difference due to path difference 2πδ is an odd integral multiple of π radians. The fields of the individual radiators
λ
are in this case, of equal amplitude and opposite phase, so they cancel. This occurs, for example, when α = 0° and d = λ/2, in the φ = 90° and 270° directions, since in these directions the field phase-difference is 180 degrees, whereas the phase difference due to radiator phase difference is zero. The same result occurs when the 180 degrees net phase difference is due to a combination of path difference and radiator phase difference. These directions of zero intensity in a pattern are called nulls. Certain combinations of d and α result in maximum radiation in the direction of the line ing the array elements. The array is then said to be operating as an endfire array. The radiation of an endfire array may be either bidirectional or unidirectional. A bidirectional array is where the radiation lobes are in both directions along the line of the array. Whereas, a unidirectional array has a lobe in one direction and a null in the opposite direction.
Multi-element Uniform Linear Arrays When more than two elements are used in an array, the principle of calculating the pattern (from which in turn the beamwidth and directive gain can be computed) is the same as for a two-element array. Except that the fields of all the elements must be superposed at the field point. The simplest type of multi-element array is one in which all the radiators are in a line, with equal spacing between adjacent pairs. This is shown in Figure 4 below. The method of analysis is suggested by showing a field-point P 27
ed by ray lines to each element. Such an array is called a linear array. When all the elements are radiating with equal intensity and the phase difference between adjacent elements is constant, the array is called uniform. The applet provided demonstrates a uniform linear array of up to nine elements.
Figure 4 – Linear array of four radiating elements
Radiation Pattern If the array contains n isotropic point-source elements, with equal spacing d and phase difference α between adjacent elements, the pattern in a plane containing the line of the array can be shown to be ⎡ ⎛ π d sin φ α ⎞ ⎤ − ⎟⎥ sin ⎢ n ⎜ 2 ⎠⎦ ⎝ λ ⎣ (5) Erel = ⎡ π d sin φ α ⎤ − ⎥ n sin ⎢ 2⎦ ⎣ λ
For n = 2, this expression reduces to equation 4. As in the two-element case, the three dimensional pattern is obtained simply by replacing sinφ by the product sinφ.sinθ. The factor n in the denominator of equation 5 is a normalizing factor that is used to make Erel a true relative pattern. That is, it permits Erel = 1 for the particular values of φ in the direction of maximum field intensity, in accordance with the definition of relative pattern given above. It is equation 5 that is used in the applet to determine the polar pattern of an n element array.
28
Experiment
3
PART A
Broadside Linear Arrays
When α = 0°, all the elements are in phase and pattern maxima occur at φ = 0° and φ = 180°, that is, in the directions perpendicular to the line of the array. This configuration is called a broadside array. The pattern will be maximum in these directions regardless of the element spacing, d. These will be the only primary maxima if d < λ. If d = λ, additional maxima occur at φ = 90° and φ = 270°. As d is increased still further, additional maxima occur as cones of radiation about the axis of the array. They are known as grating lobes, analogous to the lobes observed in the optical study of a diffraction or reflection grating. Ordinarily, therefore, the spacing of elements in a broadside array is kept less than a wavelength. However, there is an advantage in spacing the elements of an array by more than half a wavelength. For a two-element array the optimum spacing is about 0.7λ, for a four-element array it is about 0.8λ and for a large number of elements the optimum is about 0.95λ. The directivity increases gradually as the spacing is increased until the optimum is reached, then drops rather sharply with further increase. The advantage of the wider spacing is in the directivity obtainable with a given number of elements. In of the ratio of the directivity to the total length of the array, there is no advantage in the wider spacing. These observations can be seen in the applet. Although the above discussion is based on a uniform linear broadside array of point-source isotropic radiators, they apply also to a similar array of dipoles. These dipoles have their centres on the array line and their axes perpendicular to the array line and parallel to each other. The pattern is in the plane perpendicular to the dipole axes, that is, the xyplane as shown in Figure 3. The polarization of the array follows the direction of the dipoles. If the array line is horizontal and the dipole axes are vertical, the radiation is vertically polarized. If the array line is horizontal and the dipole axes are horizontal, as shown in Figure 5, the radiation is horizontally polarized. Figure 5 shows a broadside array and its polar pattern for n = 6, d = 0.7λ and α = 0°.
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Figure 5 – Linear broadside array of six radiating dipoles all elements in phase showing the position of the polar pattern
The in-phase currents in the individual dipoles, required for a broadside pattern, may be obtained by properly connecting a branched transmission line to the feed point of each dipole. That is, if the total line length from the transmitter to each dipole is the same the dipoles will be fed in phase. It is important to ensure that the same side of the line is connected to the same side of each dipole. Reversing this connection reverses the phase. Broadside arrays may also b e formed from other types of elements, such as horns, slots, helixes and polyrods. If the elements are unidirectional radiators, such as sectoral or pyramidal horns, waveguide slots, axial mode helixes and polyrods, a unidirectional broadside array results.
Beamwidth and Gain of Broadside Linear Arrays Isotropic elements spaced a half-wavelength For a uniform broadside linear array of n isotropic elements spaced a half-wavelength apart, the beamwidth is given by • For n = 2 60°. • For n = 3 36°. • For n >3 102/n°. The directivity of such an array is equal to n
Isotropic elements spaced other than a half-wavelength When the element spacing is not half-wavelength but is not greatly different from this value, the beamwidth formula becomes 51λ BW = (6)
nd
30
Procedure: Use 4nec2 software to implement a broadside array and its polar pattern for n = 6, d = 0.7λ and α = 0°
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32
33
Experiment
3
PART B
Endfire Linear Arrays
If in equation 5 the phase-difference α between adjacent elements is equal to 2π d
λ
radians, the condition for a maximum of radiation is satisfied when φ = 90° and for this value only, provided that d < λ/2. The maximum field intensity is radiated in a direction along the line of the array, “off the end” rather than off the side. Hence the name endfire array. The maximum is toward only one of the ends of the array, rather than in both the endfire directions. In of Figure 4, if the progressive phase change is a retardation going in the direction of the positive y-axis by the amount α per element, the beam will be in the φ = 90° direction. If the sign of α is changed, or its amount is increased by 180 degrees without changing the element spacing, the beam will be in the direction φ = 270°. Although the condition stated above for the value of α results in an endfire array, it does not result in an endfire pattern with the maximum possible directivity and narrowest possible beam. Hansen and Woodyard showed that an endfire beam with a greater gain results if the phase change per element satisfies ⎛ 2π d π ⎞ Hansen-Woodyard condition + ⎟ radians (7) α =⎜ n⎠ ⎝ λ This condition does not necessarily result in a unidirectional pattern as does the basic endfire condition. The basic endfire analysis assumes isotropic radiators, but it applies also to other radiators that have radiation along the line of the array. Thus, parallel dipoles can be used buy not collinear dipoles. For isotropic elements the beam has three-dimensional axial symmetry where the horizontal and vertical beamwidths are the same. The case where d = λ/8 with α = 135° and d = λ/4 with α = 90° provide a complete null or zero field intensity in the back direction for a 2 element array. These patterns are advantageous in applications where a high front-to-back ratio is required. The condition for a null condition for any uniform linear endfire array with an even number of elements is given by ⎛ 2d ⎞ Condition for null in one endfire direction α = π ⎜ 1 ± radians (8) λ ⎟⎠ ⎝ A null is never absolute because of unavoidable imperfections in the spacing and phasing of the elements and many-element arrays are more susceptible to such imperfections than those of few elements. Figure 6 shows an endfire arrangement. 34
Figure 6 – Linear endfire array of six radiating dipoles all elements in phase showing the position of the polar pattern.
Parasitically Excited Endfire Arrays It is not necessary to feed each element of an endfire array by direct connection to a transmission line. If only one dipole as such an array is directly fed, or driven the field that it sets up will cause currents to flow in ading elements. This process is called parasitic excitation and the elements thus excited are parasitic elements. Endfire arrays employing this principle are known as Yagi-Uda antennas, which are often just called Yagis. (Professor Uda first described these antennas in Japanese and H. Yagi was the first to describe the antenna in English, giving full credit to Uda’s work.) The Yagi-Uda antenna can also be regarded as a surface-wave antenna. Parasitic excitation cannot be employed in broadside arrays. To produce the in-phase currents required for a broadside pattern, a full-wavelength element spacing would be required. There would then be two endfire lobes of radiation as well as the two broadside lobes. This type of pattern is not a true broadside pattern. Therefore, broadside arrays are always driven arrays rather than parasitic arrays. The phases of the currents in parasitic dipole elements are determined by their spacing from the adjacent element and also by their lengths. A parasitic dipole cut exactly a half wavelength or slightly longer will be inductive and the phase of its current will lag the induced emf. A dipole cut shorter than a half wavelength will be capacitive and the current in it will lead the induced emf. Comparatively close spacing of elements is used in parasitic arrays to obtain good excitation and the induction fields of the elements play a major role. The exact analysis is very complicated. Properly spaced dipole elements slightly shorter than a half wavelength act as directors, reinforcing the field of the driven element in the direction away from the driven element. Thus, a line of directors may be used with each one exciting the next one. On the other hand, an element one-half-wavelength long or slightly longer will act as a reflector, if correctly spaced. This reflector reinforces the field of the driven element in a direction toward the driven element from the reflector. Therefore, if a reflector element is placed adjacent to a driven element, another element placed beyond the reflector will not be appreciably excited. Although parasitic elements are usually longer or shorter than a half wavelength when used as reflectors or directors, respectively, they may also be one half-wavelength long and made to act as reflectors or directors by proper spacing.
35
For these reasons a Yagi-Uda endfire array usually consist of one driven element, one reflector on one side of it, and a number of directors on the other side of it. Antennas of this type offer the advantages of a unidirectional beam of moderate directivity with light weight, simplicity of feed design and low cost. The design becomes critical if high directivity is attempted trough the use of many elements. Up to fie or six may be used without difficulty and arrays of thirty or forty elements are possible. The input impedance of a yagi-Uday array tends ot be low and the bandwidth is limited to around 2%, typically. Directive gain of around 10 dB is readily achieved with a moderate number of elements, usually five or six. Higher gains may be achieved by making a broadside array of which the elements are Yagi-Uda arrays.
Procedure: Use 4nec2 software to implement an End-Fire array and its polar pattern for n = 6, d = 0.3λ and α = 129°
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Experiment
4 Yagi-Uda in VHF Band
Description of The Antenna The Yagi (or Yagi-Uda) antenna is a linear array of parallel dipoles. One element is energised directly by a feed transmission line with the others acting as parasitic radiators. The function of these elements is to enhance the radiation pattern in the source direction. Generally the reflector will be 5% longer than the driven element (ie diploe)and the directors will be 5% shorter. Parameter limits are: • • • • •
Driven Element: 0.45-0.49 wavelengths. Directors: 0.4-0.45 wavelengths. Separation between Directors: 0.3-0.4 wavelengths. Radii of directors: 0.15-0.25 wavelengths. Separation between driven element an parasitics: 0.15-0.25 wavelengths.
Optimization of the Yagi-Uda Antenna can be achieved by simulating the radiation patterns for various lengths of the elemnets and the spacing between them. Other factors that effect the radiation pattern are: • • • • •
•
For an antenna with a length of 6 wavelengths or more the overall gain is independant of the director spacing. The reflector size and spacing have negligable effect on the forward gain and large effects on the backward gain and input impedance. The size and spacing of the directors has a large effect on the forward gain, backward gain and input impedance. More than one reflector provides little improvement on the directivity of the antenna. The addition of more directors will increase the gain of the antenna although after the addition of approximately 5 directors the advantages of adding more directors decreases significantly. The use of a folded dipole will increase the input impedance of the driven element. This is an advantage as the Yagi design generally has a low input impedance and the antenna impedance needs to match the transmission line impedance.
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System Requirements It's suggested to design a yagi antenna to receive a TV channel in VHF band this channel has a bandwidth of 6MHz from 174 to 180 MHz with video carrier at 175.25MHz and DTV carrier at 174.31MHz and audio carrier at 179.75MHz. The antenna location is of about 50km from the transmitting station (20dBi) and of no landscape obstacles.
Design Curves
The following design curves enable the optimum selection of the following variables/characteristics (all as a function of boomlength) related to the design of a simple Yagi antenna: * Number of elements * Gain * Reflector length * The ratio of reflector length to director length * Bandwidth
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Figure 1 indicates the optimum number of elements for an antenna of specific boom length
Note: This table is typical performance of Yagi's with the stated number of elements. Typically, the gain will be within 2 dB of the indicated gain. However, Front-to-back ratio can vary greatly (as much as 25 dB) from the indicated F/B. F/B is much more sensitive to adjustments to the element length and spacing.
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The gain resulting from using the optimum number of elements is shown in figure 2 as a function of boom length.
This curve can be used to obtain the gain that will be achieved from a given boomlength in a boom length limited design, or vice versa. Figure 3 shows the reflector length required to achieve optimum gain as a function of boom length.
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The director length can be obtained using the known reflector length, and the curve of the ratio of reflector length to director length shown in Figure 4.
Finally the bandwidth for the particular antenna can be obtained using figure 5. If a greater bandwidth is required, the reflector to director ratio can be adjusted to give an increased bandwidth as shown by the red and magenta plots.
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Antenna special parameters Yagi-Forward gain:
The ratio of the intensity in a given direction to the radiation intensity that would be obtained if the power accepted by the antenna where radiated isotropically. Standard value: >10dBi Front to back ratio:
The ratio of the maximum intensity in the direction of maximum radiation to the radiation intensity of the back lobe in the opposite direction. Standard value: >25dB Front to rear ratio:
The ratio of the maximum intensity in the direction of maximum radiation to the maximum radiation intensity of the side lobes. Standard value: >20dB Drive impedance / SWR:
Due to the mis-match between the load and the feeding system the reflected wave together with incident wave form a standing wave the SWR is the ratio of Vmax to Vmin of this standing wave and is related to impedance of the load and the characteristic impedance if the feeder. Standard value: <2.5
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Design Using Yagi Designer Software
Optimization Using QuickYagi Software
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Simulation Using 4nec2 Software
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Experiment
5 Horn Antennas Horn Antennas: ƒ
flared waveguides that produce a nearly uniform phase front larger than the waveguide itself
ƒ
constructed in a variety of shapes such as sectoral E-plane, sectoral H-plane, pyramidal, conical, etc.
Application Areas: ƒ ƒ ƒ ƒ
used as a feed element for large radio astronomy, satellite tracking and communication dishes A common element of phased arrays used in the calibration, other high-gain antennas used for making electromagnetic interference measurements
Horn Antenna Types: 1. E-Plane Sectoral Horn 00
60 0
Relative power (dB down)
30
0
30 0 10
20
60 0 30
30
90 0
20
1500
1500 180
E- and H-Plane Patterns
50
90 0
1200
1200
E-Plane H-Plane
10
0
2. H-Plane Sectoral Horn 00 Relative power (dB down)
30 0
60 0
30 0 10
20
60 0 30
30
90 0
20
10
90 0
1200
1200
E-Plane H-Plane 1500
1500 180
0
E- and H-Plane Patterns
3. Pyramidal Horn
30 0
60 0
Relative power (dB down)
00 30 0 10
20
60 0 30
30
90 0
20
10
90 0
1200
1200
E-Plane H-Plane
1500
1500 1800
E and H-Plane Patterns
51
4. Conical Horn Antenna
00
60 0
Relative power (dB down)
30
0
30 0 10
20
60 0 30
30
90 0
20
E-Plane H-Plane
1500
1500 1800
E- and H-Plane Patterns
Other horn antenna types: Multimode Horns Corrugated Horns Hog Horns Biconical Horns Dielectric Loaded Horns
Horn advantages: ƒ ƒ ƒ ƒ ƒ
90 0
1200
1200
ƒ ƒ ƒ ƒ ƒ
10
Frequency above 1GHz High gain Wide bandwidth Low weight Easy to construct
52
Horn Antenna Design: Design a pyramidal horn so that the gain is 17.05 dbi at f=11GHz.
53
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Horn Antenna Analysis: Use Sabor software to analyze the designed horn above.
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60
Experiment
6 Reflector Antennas Objective: a) The main objective is to know the main characteristics and parameters that effect on the parabolic reflector antenna. b) Plotting the radiation pattern of parabolic antenna c) See the effect of changing it's parameter on radiation pattern such as • Frequency of operation • Diameter of the dish • Focal length to diameter ration F/D
Theoretical Background: Antennas based on parabolic reflectors are most common type of directive antennas when a high gain is required. The main advantage is that they can be made to have gain and directivity as large as required . the main disadvantage is that big dishes are difficult to mount and are likely to have a large windage. The basic property of a perfect parabolic reflector is that it converts a spherical wave irradiating from a point source placed at the focus into plane waves. Conversely, all the energy received by the dish from a distant source is reflected to a single point at the focus of the dish. The position of the focus, or focal length, is given by: D2 f = 16c Where D is the dish diameter and c is the depth of the parabola at its center. The size of the dish is the most important factor since it determines the maximum gain that can be achieved at the given frequency and the resulting beamwidth. The gain and beamwidth obtained are given by:
( πD )2 G=e λ
BW =
2
70λ D
Where D is the diameter of the dish and e is the efficiency.
61
Total Efficiency
It has been fairly easy to calculate efficiency for an idealized feed horn pattern due to illumination taper and spillover but there are several other factors that can significantly reduce efficiency. Because the feed horn and its ing structures are in the beam of the dish part of the radiation is blocked or deflected. A real feed horn also has sidelobes so part of its radiation is in undesired directions and thus wasted. Finally no reflector is a perfect parabola so the focusing of the beam is not perfect. We end up with quite a list of contributions to total efficiency: • • • • • • • • •
Illumination taper Spillover loss Asymmetries in E- and H-Planes Focal point error Feedhorn sidelobes Blockage by feed horn Blockag by ing structures Imperfections in parabolic surface. Feedlineloss
Scattering
Spillover
Diffraction Each time the diameter of a dish is doubled the gain is four times or 6db greater, if both stations doubles the diameter the signal strength will be increased by 12dB, the total efficiency can be assumed 50% for hand built antenna. The ratio f/D is the fundamental factor governing the design of the feed for dish. He ratio is directly related to the beamwidth of the feed necessary to illuminate the dish effectively. Two dished of the same diameter but different focal lengths require different design of feed if both are to be illuminated efficiently. The value of .25 correspond to the common focal-plane dish in witch the focus is in the same plane as the rim of the dish.
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Design steps:
63
64
65
Effect of changing the parabolic parameter on radiation: 4
a) Changing Frequency to 4GHz
b) Changing Diameter to 50cm
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c) Changing F/D ratio to .3
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