1 Antennas: from Theory to Practice 1. Basics of Electromagnetics Yi HUANG Department of Electrical Engineering & Electronics The University of Liverpool

Antennas: from Theory to Practice

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1. Basics of Electromagnetics

Yi HUANGDepartment of Electrical Engineering & Electronics

The University of Liverpool

Liverpool L69 3GJ

Email: [email protected]


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Objectives of this Chapter

• Review the history of RF engineering and antennas;

• Lay down the foundation of mathematics required for this course;

• Examine the basics of electromagnetics and • introduce Maxwell’s equations to establish

the link between the fields and sources.


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1. 1 The First Successful Antenna Experiment

It was conducted by Hertzin 1887

Experimental set-up


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1.2 Radio Systems

• Compared with a wired system, radio systems can offer the following advantages:– Mobility

– Good coverage over an area

– Low path-loss over a long distance

A typical radio system


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1.3 Necessary Mathematics

• Complex numbers


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• Vectors– A vector has both a magnitude and a direction


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• Vector addition and subtraction


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• Vectors multiplication: – dot product:

– cross product:

Cross product doesn’t obey the commutative law!


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An Example


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• Cartesian and spherical coordinates


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1.4 Basics of Electromagnetics

f (Hz)

(m


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Radio Frequency Bands

Frequency Band Wavelength Applications• 3-30 kHz VLF 100-10 km Navigation, sonar, fax• 30-300kHz LF 10-1 km Navigation• 0.3-3 MHz MF 1-0.1 km AM broadcasting• 3-30 MHz HF 100-10 m Tel, Fax, CB, ship

comms• 30-300MHz VHF 10-1 m TV, FM broadcasting• 0.3-3 GHz UHF 1-0.1 m TV, mobile, radar,

satellite• 3-30 GHz SHF 100-10mm Radar, microwave links• 30-300GHz EHF 10-1 mm Radar, wireless comms• 0.3-3 THz 1-0.1 mm Sub-millimetre

application


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dB

• Logarithmic scales are widely used in RF engineering and antennas community since the signals we are dealing with change significantly

but


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The Electric Field

• The electric field (in V/m) is defined as the force (in Newtons) per unit charge (in Coulombs). From this definition and Coulomb's law, the electric field E created by a single point charge Q at a distance r is

is the electric permittivity, also called dielectric constant

In free space:


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• The product of permittivity and the electric field is called the electric flex density (also called the electric displacement), D which is a measure of how much electric flux passes through a unit area, i.e.,

The complex permittivity can be written as

The ratio of the imaginary part to the real part is called the loss tangent


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Relative permittivity of some materials


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• The electric field E is related to the current density J (in A/m2), another important parameter, by Ohm’s law:

EJ

is the conductivity which is the reciprocal of resistivity. It is a measure of a material’s ability to conduct an electrical current and is expressed in Siemens per metre (S/m).


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Conductivity of some materials


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The Magnetic Field

• The magnetic field, H (in A/m), is the vector field which forms closed loops around electric currents or magnets. The magnetic field from a current vector I is given by the Biot-Savart law as

24 rrI

Hˆ


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• Like the electric field, the magnetic field exerts a force on electric charge. But unlike an electric field, it employs force only on a moving charge, and the direction of the force is orthogonal to both the magnetic field and charge's velocity


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Relative permeability of some materials


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Qv can actually be viewed as the current vector I and the product of is called the magnetic flux density B (in Tesla), the counterpart of the electric flux density.

When we combine the electric and magnetic fields, the total force:

This is called the Lorentz force. The particle will experience a force due to the electric field of QE, and the magnetic field Qv × B


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1.5 Maxwell’s Equations

Maxwell’s equations describe the interrelationship between electric fields, magnetic fields, electric charge, and electric current


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• Faraday's Law of Induction

The induced electromotive force is proportional to the rate of change of the magnetic flux through a coil. In layman's terms, moving a conductor through a magnetic field produces a voltage or a time varying magnetic field can generate an electric fields!


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• Amperes’ Circuital Law

• Gauss' Law for Electric Fields

It shows that both the current (J) and time varying electric field can generate a magnetic field.

It means that charges () can generate electric fields, andit is not possible for electric fields to form a closed loop.


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• Gauss’ Law for Magnetic Fields

• Integral form

It means that the magnetic field lines are closed loops, thus the integral of B over a closed surface is zero

The partial differential formapplies to a pointBut this is for an area/volume!


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1.6 Boundary Conditions

Tangential components of an electric field are continuous across the boundary between any two media.

The change in tangential component of the magnetic field across a boundary is equal to the surface current density.


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Applying these boundary conditions on a perfect conductor

Field distribution around a two-wire transmission line: E-field is orthogonal to the line surface and H-field (loops).

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1 Antennas: from Theory to Practice 1. Basics of Electromagnetics Yi HUANG Department of Electrical Engineering & Electronics The University of Liverpool