Array and Phased Array Antenna Basics / Edition 1

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Reflecting a growing interest in phased array antenna systems, stemming from radar, radio astronomy, mobile communications and satellite broadcasting, Array and Phased Array Antenna Basics introduces the principles of array and phased array antennas. Packed with first-hand practical experience and worked-out examples, this is a valuable learning tool and reference source for those wishing to improve their understanding of basic array antenna systems without relying heavily on a thorough knowledge of electromagnetics or antenna theory.

  • Features a general introduction to antennas and explains the array antenna principle through discussion of the physical characteristics rather than the theory
  • Explores topics often not covered in antenna textbooks, such as active element pattern, array feeding, means of phase changing, array antenna characterisation, sequential rotation techniques and reactively loaded arrays
  • Guides the reader through the necessary mathematics, allowing them to move onto specialist books on array and phased array antennas with a greater understanding of the topic
  • Supported by a companion website on which instructors and lecturers can find electronic versions of the figures

An ideal introduction for those without a background in antennas, this clear, concise volume will appeal to technicians, researchers and managers working in academia, government, telecommunications and radio astronomy. It will also be a valuable resource for professionals and postgraduates with some antenna knowledge.

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Product Details

  • ISBN-13: 9780470871171
  • Publisher: Wiley
  • Publication date: 8/12/2005
  • Edition number: 1
  • Pages: 376
  • Product dimensions: 6.93 (w) x 9.96 (h) x 1.09 (d)

Meet the Author

Hubregt J. Visser is a Principal Antenna Engineer at TNO Industrial Technology in The Netherlands and has more than 12 years experience in this field.  He has co-chaired and been a member of the organizing panel for a number of antennas and propagation conferences and is a member of the IEE Antennas and Propagation Technical Advisory Panel.
Huib also teaches at Eindhoven University of Technology in Electromagnetics and Antenna Technology and won the 2002 Students Award for Best Lecture Material.

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Read an Excerpt

Array and Phased Array Antenna Basics

By Hubregt J. Visser

John Wiley & Sons

Copyright © 2005 John Wiley & Sons, Ltd
All right reserved.

ISBN: 0-470-87117-2

Chapter One


The key to understanding phased array antennas is to understand antennas and the key to understanding antennas is to understand electromagnetic radiation. In contrast to what is widely believed, one does not need to be a specialist in integro-differential equations and vector mathematics to grasp the mechanism of electromagnetic radiation. As in Faraday's time, a vast majority of educators prefers the rigor of a mathematical description to the insight of a physical understanding for explaining the mechanism of radiation. It is the author's belief though that the latter is needed first to form the basic understanding and once this understanding has been accomplished, the former may be used to develop this understanding and put it to practical use. For the basic understanding of electromagnetic radiation one only needs an understanding of electricity and magnetism at a level as educated in secondary school. By following the historical developments in the field of electricity and magnetism, the interaction between the two - electromagnetism - and electromagnetic radiation follows naturally.


Research in the field of electricity and magnetism goes back a long way. Hundreds of years BC, experiments dealing with these two phenomena have been described. However, for nearly two thousand years experiments have been concentrated mainly on static electricity. The absence of a source of continuous electrical energy posed a severe limitation in the progress of understanding the underlying physics of the observed electrical and magnetic phenomena. It lasted until the invention of the electric battery in 1800 by Alessandro Volta (1745-1827) - a logical next step to the famous 'frog-experiments' of Aloys Galvani (1737-1798) nine years earlier - before research could be conducted in a reproducible way.

In 1819, the Danish professor Johannis Orsted (1777-1851) observed the change in position of a compass needle, when brought into the vicinity of a current carrying wire, see figure 1.1.

This current originated from a voltaic pile. Although Orsted did not fully understand that the compass needle was not directly influenced by the electric current, but rather indirectly through the induced magnetic field around the current, he did notice the importance of his observation. It opened up the possibility to find a relation between electricity and magnetism. A few months after the publication of his experiences, Orsted introduced the term electromagnetism.

In that same year (1819), the French professor Andre-Marie Ampere (1775-1836) observed a reproduction of the Orsted experiment at the Parisian Academy. Only a week afterwards he produced a document, giving a theoretical explanation of the experiment. He assumed - correctly - that an electrical current is capable of inducing a magnetic field, see figure 1.2.

It is this magnetic field that explains why parallel currents attract and anti-parallel currents repel. For two parallel currents, the compass needles, indicating the direction of the magnetic induction, are positioned such that they will attract one another, see figure 1.3. For two anti-parallel currents, the compass needles are positioned such that they will repel one another (opposite poles attract, equal poles repel), see figure 1.4.

If we bend a current-carrying wire into a loop as shown in figure 1.5, the magnetic inductions of all parts of the wire add up to form distinct poles at the top and bottom of the loop.

Ampere (rightfully) assumed that in solid matter, microscopic parts contain a circulating current and that in a magnet (like a piece of magnetised iron) all these microscopic current loops are lined up in the same direction, resulting in the forming of distinct macroscopic magnetic poles. This process is schematically depicted in figure 1.6.

While Orsted was conducting his experiments in Denmark, Michael Faraday (1791-1867) worked at the Royal Institution in London. Faraday was a remarkable 'self-made' man. With nothing more than a primary school education, he has become famous for his pioneering work in electromagnetism. Faraday is seen as one of the world's greatest experimenters. He succeeded in turning his limited knowledge of mathematics into an advantage, by deducing concepts directly from observations.

In 1831, Faraday observed that a changing electrical current in a coil, induced an electrical current into another coil. He had discovered electromagnetic induction. This was an important discovery. Faraday's ideas concerning conservation of energy had convinced him that, while a (changing) electrical current can create a (changing) magnetic field, the opposite must also be true: 'a changing magnetic field must be able to produce an electric field'. One of his experiments, following the discovery of the electromagnetic induction, showed that a moving magnet induced an electrical current, see figure 1.7.

The direction of the current in the loop is such that it opposes the change in magnetic induction. If the north pole of the magnet is approaching the loop, the current in the loop will be directed such that a north pole is formed in the direction of the magnet to repel this magnet. If the north pole of the magnet is moving away from the loop, the current in the loop will be directed such that a south pole is formed in the direction of the magnet to attract the magnet. If the magnet remains static, there will be no current in the loop.

To understand how a magnet influences a wire from some distance, Faraday visualised a 'magnetic field'. He saw this 'magnetic field' as magnetic force lines, laying closer together at places where the field is stronger. These magnetic field lines can be shown by placing compass needles in the vicinity of the magnet, as we have done thus far. These compass needles will direct themselves tangential to the magnetic field lines. More detail can be obtained by using iron filings that may be regarded as very small compass needles. In fact, this is how Faraday constructed his magnetic field lines. In his 1831 notes he wrote,

By magnetic curves I mean lines of magnetic forces which would be depicted by iron filings.

So, instead of visualising the magnetic field by placing compass needles, as we did in figure 1.2 for a current-carrying wire, we may now draw the magnetic field lines as shown in figure 1.8.

The electrical current, induced in a loop or a (piece of) wire at some distance from the 'source', Faraday expressed in terms of the number of magnetic field lines cut by the loop or wire (flux).

Now, let's have a closer look at the first electromagnetic induction experiment of Faraday, see figure 1.9.

Obviously, we can transport the changing electric field in one coil to an isolated second coil. So, the question arises does this mean that we are dealing with electromagnetic radiation? The answer to that question is: 'No'!

If we take away the changing electric field in the bottom coil, by keeping the switch open or closed, the changing magnetic field vanishes everywhere and no current flows in the top coil. If we had had an electromagnetic radiating system, the changing magnetic field would have induced a changing electric field, regardless of the presence of the top coil. How the radiation mechanism works will be explained further on.

For the moment we will dwell on the bottom coil of figure 1.9 only. If we connect an alternating current (AC) source to the coil, the current through the coil changes continuously and because of that, the magnetic field lines change continuously too. Because of these changing field lines, a current is recreated in this coil. Energy is thus delivered to a magnetic field and this energy is returned to the circuit.

When the magnetic field is increasing, due to the current flowing through the coil, a voltage over the coil is being created. When the current has reached its maximum value and starts to decrease, the magnetic field strength decreases. The coil, however, opposes this change and therefore tries to maintain a voltage over the coil, such that the field remains static. Therefore the current flowing through a coil lags the voltage over it.

Thus, because of this energy cycling, the current and voltage of the coil are out of phase. For a radiating electromagnetic field to exist, the electric and magnetic field need to be in phase. The field now is purely a storage field; the energy is stored in the magnetic field surrounding the inductor. If we place a second coil in the vicinity of the first coil, see figure 1.9, we can intercept some of the changing magnetic field lines and thereby create an electric current in the second coil. With the second coil we can thus take energy from the storage field of the first coil.

The field line concept may also be applied to electric fields. Electric field lines are then imaginary lines for which the tangent vector at a given point is directed such as to coincide with the direction in which a positively charged unit charge would accelerate. As with magnetic field lines, the separation between adjacent field lines is inversely proportional to the magnitude of the field. Tightly packed electric field lines indicate a strong field; sparsely packed electric field lines a weak one.

Faraday observed that magnetic field lines (made visible by employing iron filings) originate from one pole of a magnet and terminate on the other. So he imagined that the lines of force of an electrical field would originate on a positive charge and end on a negative charge. It appears that this is not completely true. Magnetised objects always form poles in pairs. Magnetic field lines originate from the north pole of the object and terminate on the south pole of the object. Electrically charged objects however may exist as monopole (positively charged or negatively charged). The field lines are always directed perpendicular to the surface of the charged object. The electric field lines of an isolated, positively charged monopole, start on the monopole and extend radially to infinity, those of an isolated, negatively charged monopole, start at infinity and convert radially on the monopole, see figure 1.10.

It was Faraday's belief that the physical lines of force he envisaged were really present everywhere in space, i.e. were an attribute of this space. Even though we know now that this is not true, we do understand that a magnet or electric charge brought into empty space, modifies this space. It is this understanding that formed a breakthrough in the nineteenth century in explaining the action-at-a-distance which occurs between (magnetic, electrically charged or gravitational) objects. It was Faraday's genius that perceived the concept of a field to explain how e.g. a charged object affects the surrounding space. When another charged object is brought into this space, it becomes affected by the field of the object already present as opposed to the object itself.


In the year that Michael Faraday discovered electromagnetic induction (1831), James Clerk Maxwell (1831-1879) was born in Edinburgh, Scotland. In contrast to Faraday, Maxwell received an academic education and evolved not into a experimental scientist but a brilliant thinker and mathematician.

Although Maxwell has performed monumental scientific work, like for example proving that the rings of Saturn are made up of dense particles (1859) and demonstrating the first ever colour photograph (1860), he is best known for what are currently called the Maxwell equations (1873).

The remarkable thing about the Maxwell equations is that he did not derive all of them, but rather saw the connection between Ampere's, Faraday's and Gauss's law. By extending Ampere's law with what he called a displacement current term, electricity and magnetism became united into electromagnetism. With this displacement current term added, the equations governing electricity and magnetism allow electromagnetic waves to exist, light being one out of a spectrum of waves. Maxwell predicted the existence of electromagnetic waves tens of years before he was proven right by the generation and reception of radio waves.

Before we move on to the mechanism of electromagnetic radiation, we will first pay some attention to electromagnetic waves. Therefore we will have to dwell a bit longer on the displacement current.

The equations governing electricity and magnetism before Maxwell were incomplete. This was evident in analysing a capacitor in a circuit supporting a changing current, see figure 1.11.

Although the capacitor prevents a physical current flowing through the plates, the circuit still supports a current. The explanation for this effect, Maxwell attributed to what he called the displacement current, which turns out to be the time rate of change of the electric field between the capacitor plates.

Let's assume that we look at the capacitor in figure 1.11 at the moment that the capacitor is fully charged. The charge on the right plate is Q, the charge on the opposite plate is the negative of that, -Q. Because of these charges, the current in the circuit will start flowing to the right. The electric field between the plates is directed to the left. Since a current is flowing to the right, the strength of the electric field is decreasing, so the direction of change of the electric field is to the right. Attached to this changing electric field is a surrounding magnetic field, its direction connected to the direction of change like a right-hand screw. Since this magnetic field could have been due to a physical current - one cannot tell the source from the magnetic field alone - Maxwell named the source, the changing electric field: displacement current.

It is this specialty - that a changing electric field creates a (changing) magnetic field - that makes the existence of electromagnetic waves possible. It means that once you create the 'correct' changing electric field, this field will create a changing magnetic field that in turn will create a changing electric field and so on. This expansion of the disturbance in space will continue, even when the source has ceased to exist. This is what we call wave propagation. This process is depicted in figure 1.12.

We have seen that a coil (an inductor), when connected to an AC current source, produces an electromagnetic field. Energy is delivered to a magnetic field and this energy is returned to the circuit. The field is purely a storage field; the energy is stored in the magnetic field surrounding the inductor. In a similar way a capacitor, when connected to an AC voltage source, produces an electromagnetic field. Energy is delivered to an electric field and this energy is returned to the circuit. When the AC cycle starts on its down slope, the charge in the capacitor holds the voltage (opposing the change) until the current leaves and then it starts to discharge, causing the voltage to lag the current. Also for a capacitor the current and voltage are out of phase. Again the field is purely a storage field; the energy is stored in the electric field surrounding the capacitor.

The question that remains is how to create the correct changing electric field, i.e. how to create the source of electromagnetic wave propagation; how to get changing electric and magnetic fields to be in phase. The Maxwell equations reveal that the source of electromagnetic radiation is accelerated charge. Rather than elaborating on the Maxwell equations, we will discard the mathematics and explain the radiation of accelerated charge by physical reasoning.


When looking at an electric charge, either positively or negatively charged, the electric field lines extend radially from this charge to infinity, see figure 1.13a.

The electric field lines for a slowly moving charge, i.e. having a velocity well below that of light, behave identical to that of a non-moving or static charge, figure 1.13a. This is a consequence of the principle of relativity in the restricted sense,

If, relative to K, K' is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to K' according to exactly the same general laws as with respect to K.

In other words: 'An observer moving at the same speed as the charge still sees only static fields.'


Excerpted from Array and Phased Array Antenna Basics by Hubregt J. Visser Copyright © 2005 by John Wiley & Sons, Ltd. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents





1 Radiation.

1.1 The Early History of Electricity and Magnetism.

1.2 James Clerk Maxwell, The Union of Electricity and Magnetism.

1.3 Radiation by Accelerated Charge.

1.4 Reactive and Radiating Electromagnetic Fields.

2 Antennas.

2.1 The Early History of Antennas.

2.2 Antenna Developments During the First World War.

2.3 Antenna Developments in Between the Wars.

2.4 Antenna Developments During the Second World War.

2.5 Post-War Antenna Developments.

3 Antenna Parameters.

3.1 Radiation Pattern.

3.2 Antenna Impedance and Bandwidth.

3.3 Polarisation.

3.4 Antenna Effective Area and Vector Effective Length.

3.5 Radio Equation.

3.6 Radar Equation.

4 The Linear Broadside Array Antenna.

4.1 A Linear Array of Non-Isotropic Point-Source Radiators.

4.2 Plane Waves.

4.3 Received Signal.

4.4 Array Factor.

4.5 Side Lobes and Grating Lobes.

4.6 Amplitude Taper.

5 Design of a 4-Element, Linear, Broadside, Microstrip Patch Array Antenna.

5.1 Introduction.

5.2 Rectangular Microstrip Patch Antenna.

5.3 Split-T Power Divider.

5.4 Transmission and Reflection Coefficients for a Corporate Fed Array Antenna.

5.5 Simulation, Realisation and Measurement.

6 The Linear Endfire Array Antenna.

6.1 Introduction.

6.2 Phase Differences.

6.3 Hansen–Woodyard Endfire Array Antenna.

6.4 Mutual Coupling.

6.5 Yagi–Uda Array Antenna.

7 The Linear Phased Array Antenna.

7.1 Linear Phase Taper.

7.2 Beam Broadening.

7.3 Grating Lobes and Visible Space.

7.4 Means of Phase Shifting.

8 A Frequency Scanned Slotted Waveguide Array Antenna.

8.1 Slotted Waveguide Array Antenna.

8.2 Antenna Design.

8.3 Validation.

9 The Planar Array and Phased Array Antenna.

9.1 Geometry.

9.2 Planar Array Antenna.

9.3 Planar Phased Array Antenna.

10 Special Array Antenna Configurations.

10.1 Conformal Array and Phased Array Antennas.

10.2 Volume Array and Phased Array Antennas.

10.3 Sequential Rotation and Phasing.

10.4 Reactive Loading.

11 Array and Phased Array Antenna Measurement.

11.1 Input Impedance, Self-Coupling and Mutual Coupling.

11.2 Radiation Pattern Measurement.

11.3 Scan Element Pattern.

11.4 Waveguide Simulator.

Appendix A: Complex Analysis.

A.1 Complex Numbers.

A.2 Use of Complex Variables.

Appendix B: Vector Analysis.

B.1 Notation.

B.2 Addition and Subtraction.

B.3 Products.

B.4 Derivatives.

Appendix C: Effective Aperture and Directivity.

Appendix D: Transmission Line Theory.

D.1 Distributed Parameters.

D.2 Guided Waves.

D.3 Input Impedance of a Transmission Line.

D.4 Terminated Lossless Transmission Lines.

D.5 Quarter Wavelength Impedance Transformer.

Appendix E: Scattering Matrix.

E.1 Normalised Scattering Matrix.

E.2 Unnormalised Scattering Matrix.

Appendix F: Voltage Incident at a Transmission Line.

Appendix :G Cascaded Scattering Matrices.


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