**ENE 429 Antenna and Transmission Lines Theory** Lecture 9 Types of Antenna

**Review (1)** • Antenna is a structure designed for radiating and receiving EM energy in a prescribed manner • Far field region ( the distance where the receiving antenna is located far enough for the transmitter to appear as a point source) • The shape or pattern of the radiated field is independent of r in the far field. • Normalized power function or normalized radiation intensity

**Review (2)** • Directivity is the overall ability of an antenna to direct radiated power in a given direction. • An antenna’s pattern solid angle: • Total radiated power can be written as • Antenna efficiency e is measured as

**Radiation characteristics** • If the current distribution of a radiating element is known, we can calculate radiated fields. • In general, the analysis of the radiation characteristics of an antenna follows the three steps below: • Determine the vector magnetic potential from known of assumed current on the antenna. • Find the magnetic field intensity from . • Find the electric field intensity from .

**Vector magnetic potential** From the point form of Gauss’s law for magnetic field, Define therefore we can express as where Jd= current density at the point source (driving point) R = distance from the point source to the observation point (m)

**Electric and magnetic fields can be determined.** • From here we can determine , then find in free space. • We can then find the electric field from • The time-averaged radiated power is The subscript “0” represents the observation point. W/m2.

**Types of antennas** • Hertzian dipole (electric dipole) • Small loop antenna (magnetic dipole) • Dipole antenna

**Hertzian dipole (1)** • A short line of current that is short compared to the operating wavelength. This thin, conducting wire of a length dl carries a time-harmonic current A and in a phasor form A.

**Hertzian dipole (2)** The current density at the source seen by the observation point is A differential volume of this current element is dV = Sdz.

**Hertzian dipole (3)** Therefore Then Where at the observation point. For short dipole, R r, thus we can write Conversion into the spherical coordinate gives

**Hertzian dipole (4)** Therefore We can then calculate for

**Hertzian dipole (5)** Multiply 2 to both nominator and denominator, so we have We are interested in the fields at distances very far from the antenna, which is in the region where or

**Hertzian dipole (6)** Under a far-field condition, we could neglect and Then and Finally, W/m2.

**Hertzian dipole (7)** Since the current along the short Hertzian dipole is uniform, we refer the power dissipated in the radial distance Rradto I, m. or

**Ex2 Find the radiation efficiency of an isolated Hertzian** dipole made of a metal wire of radius a, length d, and conductivity .

**Ex1 Let a Hertzian dipole of the length /100 be given the** current A, find • Pmax at r = 100 m

**b) What is the time-averaged power density at P (100, /4,** /2)? c) Radiation resistance

**The small loop antenna (magnetic dipole)** Assume a << A complicate derivation brings to If the loop contains N-loop coil then S = Na2

**Dipole antennas ** • Longer than Hertizian dipole therefore they can generate higher radiation resistance and efficiency. Divide the dipole into small elements of Hertzian dipole. Then find and . Figure of dipole

**Dipole antenna radiation regime**

**Field derivations (Far field) (1)** The current on the two halves are Symmetrical and go to zero at the ends. We can write Where Assume = 0 for simplicity.

**Field derivations (Far field) (2)** From In far field but since small differences can be critical.

**Field derivations (Far field) (3)** We can write

**Field derivations (Far field) (3)** From In our case

**Field derivations (Far field) (4)** where

**Antenna properties** • Find Pn(), calculate F() over the full range of for length L in terms of wavelength then find Fmax(this step requires Matlab) • Find p • Dmax (Directivity) 4. Rrad

**Antenna Radiation Pattern for different antenna lenghts** • Link to Matlab file

**Half-wave dipole (most popular antenna) (1)**

**Half-wave dipole (most popular antenna) (2)** Using Matlab, we get p = 7.658 Dmax = 1.64 Rrad = 73.2 This is much higher than that of the Hertzian dipole.