From the vector potential 16, we can calculate the fields. Hertzian dipole antenna is very small length antenna and it does not exist in real life. Br ar 0 always the divergence of a curl of a vector field fr is always zero. All components of near and far electromagnetic field radiated from hertzian dipole excited by current with arbitrary time dependence are obtained in time domain by means of vector potential. Hertzian dipole antenna arrays interference and farfield radiation patterns ece 303 fall 2005 farhan rana cornell university characteristics of a single hertzian dipole antenna antenna gain. The feedpoint is usually at the center of the dipole as shown in the diagram. Dyadic greens functions for dipole excitation of homogenized. The hertzian dipole does not exists in real life, but the real antenna can be formed by taking. A hertzian dipole can be approximated by a small current source so that jr zil r 1. The hertzian dipole antenna vt the hertzian dipole is a linear d hertzian dipole 14. The retarded vector potential is for a point r directly above the x axis, a must aim in the y direction.
Hertz dipole antenna objectives in this course you will learn. Ideal hertzian dipole page 2 first, we need to derive the vector potential of the line source. The hertzian dipole does not exists in real life, but the real antenna can be formed by taking integration on hertzian dipole. Recent textbooks on electromagnetic theory rarely do more than mention the hertz vector potentials, yet many classical problems of radiation and propagation may be elegantly and concisely solved using these potentials. Hertzian dipole consider the hertzian dipole shown in the figure. An array of two hertzian dipole antennas in this lecture you will learn. The hertz vector potential notation is an efficient mathematical formalism for solving electromagnetic problems. As suggested by the cartoon on the last slide, we can assume that the current varies sinusoidally in both position and time. The potential of an isolated dipole sitting at the origin and pointing in the zdirection is. Given the vector magnetic potential solution for a hertzian dipole, derive the exact near and far field solution for e field and h field from their vector calculus definitions. We define the magnetic dipole moment to be a vector pointing out of the plane of the current loop and with a magnitude equal to the product of the current and loop area. Radiation from a hertzian dipole physics libretexts. Metrics and vector descriptions favoring simplicity bias the design accordingly.
Pdf on the alternative vector potential formulation of the. That it cannot be replaced by the magnetic field in any easy way was observed by one man after the other who tried to do so. Since the hertz dipole is small the vector potential at point p is almost same as. For cases of just electric polarization the following relations are used. Hertzian dipole antenna is discussed in this lecture. We consider a timedependent point electric dipolep p 0 e. A \displaystyle \mathbf b abla \times \mathbf a 2 considering cases of electric and magnetic polarization separately for simplicity, each can be defined in terms of the scalar and vector potentials which then allows for the electric and magnetic fields to be found. It is convenient to work in spherical polar coordinates.
Ag 0, the scalar potential isthe instantaneous coulomb potential, which for a hertzian dipole. Ag 0, the scalar potential isthe instantaneous coulomb potential, which for a hertzian dipole with arbitrary time dependence is. The vector potential a due to a hertzian dipole, after substituting 1. Retarded strengths of an instantly polarized particle 26 5. The polar axis of the dipole is a null field meaning no electric and magnetic field. Retarded potential of an instantly polarized particle 24 4. Satellite mass, m velocity, v radius, r earth mass, m eart. Electric and magnetic fields the magnetic field is given by oos ba 1 sin 4 jr os is e j rr. Zero, as potential on equatorial point, due to charges of electric dipole, are equal in magnitude but opposite in nature and hence their resultant is zero. We discuss the definition of the hertz vector potentials and demonstrate their application to the calculation of electric and magnetic dipole radiation and to the propagation. Publication of this book was made possible in part by the virginia tech university libraries open education initiative faculty grant program. The vector potential a is not unique only the curl of the vector potential is a well defined quantity i. Need software tool to compute that metric for wire antennas.
First, the expressions for the scalar potential or, t, equation 20. Thus the work we do is work we do potential energy. For the hertz dipole, the magnetic field has only component and the electric. The current along dipole arms are approximately described as proportional to sinkz where z is the distance to the end of the arm. The electromagnetic fields of a hertzian dipole can be analyzed using the electrical hertz vector.
An electromagnetic wave incident on an antenna will induce a potential at the terminals of the antenna. Dipole moments measure the electric polarity of the system of charges. Since we only have a zcomponent of current, awill only have a zcomponent as well. Using amperes law, we determine the phasor electric field. Transient near field of hertzian dipole request pdf. This result is achieved by using the concept of hertz vector potential to generate exact vector. Let me start with some general properties of the vector potential.
To simplify the derivation, we shall consider the special case of a straight thin dipole of arbitrary length that is illuminated by a plane wave. We discuss the definition of the hertz vector potentials and demonstrate their application to the calculation of electric and magnetic dipole radiation and to the propagation modes of a rectangular waveguide. Here, we follow in part holloway and kuester 15 and model a metasurface as a twodimensional 2d surface with equivalent electric. May 22, 2007 hi, in my notes for the hertzian dipole i have a derivation of the vector potential a, and the scalar potential phi. However, the potentials description of the e field involves the equation. Electric and magnetic fields the magnetic field is given by oos ba. In that process, we first compute the phasor vector magnetic potential 4 jr c ire a rdl r 1.
It is defined as a vector whose magnitude is charge times the separation between two opposite charges. In the previous lecture, we discussed the fundamental sourcefield relationship that can be used to calculate the e and h fields produced by sinusoidal steady state line currents. Potentials of hertzian dipole there is a retarded magnetic vector potential parallel to the current, which is along the direction of the dipole. As will be shown, hertz vector potential can be reduced to a set of two scalar potentials, which are solutions of helmholtzs equations, for any orthogonal curvilinear coordinate system. We assume that it is located at the origin of a coordinate system and that it carries a uniform current constant throughout the dipole, i io cos cot. An easier way of seeing this is noticing that the vector potential solution in part a is equivalent to the vector potential of a single hertzian dipole i. Therefore, this is comparable to a hertzian dipole with an effective current i h. Sources of electromagnetic radiation university of liverpool. However, im missing the derivation of the e and b fields from these potentials. The area vector, and thus the direction of the magnetic dipole moment, is given by a righthand rule using the direction of the currents. Radiation by a hertzian dipole 253 hertzian dipole. Jun 24, 2018 hertzian dipole antenna is discussed in this lecture. Formally, given a vector field v, a vector potential is a vector field a such that. An electric dipole is a pair of equal and opposite charges separated by a small distance and dipole moment measures its strength.
There is a retarded magnetic vector potential parallel to the current, which is along the direction of the dipole. Potentials in the coulomb gauge in the coulomb gauge, where. Pdf we address the nonuniqueness of the vector potential for the sommerfeld halfspace problem with a horizontal hertzian dipole. The charge qis varying in time harmonically because it is driven by the generator. Pdf the vector potential of a point magnetic dipole. This is analogous to a scalar potential, which is a scalar field whose gradient is a given vector field. It is well known that in a homogeneous space this potential does not depend on the orientation of the dipole l, 2. In the case of a short dipole, that is essentially a linear drop from at the feedpoint to zero at the end. Copper shielding integrated circuits shielded box printed circuit boards closed loop acts as an antenna sensitive to em interference. Need vector description to represent each possible antenna. An atomic unit of electric dipole moment is a0e, where a0 is the radius of the first bohr orbit for hydrogen and e is the magnitude of the electronic charge. The general retarded vector potential a for a point dipole with an arbitrary time dependence magnetic moment m has been obtained in 19 by means of the current density j and green function. The absence of magnetic field is clear enough since there is no curl in the vector potential there. In free space, a hertzian dipole located at the origin with a radiation resistance of 1 and oriented in the zdirection, is.
It is an idealized tiny segment of conductor carrying a rf current with constant amplitude and direction along its entire short length. This type of antenna is called a hertzian dipole, after the german physicist heinrich hertz. It is a continuous current distribution over its length z. In vector calculus, a vector potential is a vector field whose curl is a given vector field. The retarded potential of a dipole and the method of retarded strengths 19 1. It seems that only the theta component of the e field exists, and i have. Therefore three dipoles in unison is equivalent to a single dipole pointing along the d, d, d vector. To make the vector potential a unique, one needs to fix the value of its divergence a process that usually goes by the names gauge fixing or fixing the. At a general angle, the torque, the dipole moment p and the electric field e are related by. Now, we want to consider an application of the lienardwiechert potentials, namely, the oscillating electric dipole with the dipole moment p p t, first investigated by heinrich hertz. The field tends to pull it into alignment toward 1. Now we can find the radiated magnetic field of the dipole. It was a scalar function, related to electric eld through e rv.
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