ENE 429 Antenna and Transmission lines Theory DATE: 11/09/06 15/09/06 ENE 429 Antenna and Transmission lines Theory Lecture 9 Antennas

Review (1) Optical fibers Step-index fiber Single-mode fiber Multi-mode fiber wave travels using total internal reflection at the core-cladding boundary. Numerical aperture defines a cone of acceptance over which light will propagate along the fiber.

Review (2) Signal degradation Intermodal dispersion Chromatic dispersion Power attenuation Fiber optic communication systems Optical sources Fiber Optical detectors connectors Optical link design Power budget Rise-time budget

Outline General properties Radiation fields and patterns Antenna performance

What is antenna? A structure designed for radiating and receiving EM energy in a prescribed manner The importance of the shape and size of the structure the efficiency of the radiation the preferential direction of the radiation

Generic Antenna network Complex antenna impedance Zant needs to be matched to the system impedance.

Radiated power (1) Far field region ( the distance where the receiving antenna is located far enough for the transmitter to appear as a point source) In the far field where 0 = 120 . Time-averaged power density: or W/m2.

Radiated power (2) Total power radiated by the antenna can be expressed as W

Radiation patterns The shape or pattern of the radiated field is independent of r in the far field. Radiation patterns usually indicate either electric field intensity or power intensity. A transmit-receive pair of antennas must share the same polarization for the most efficient communication. Normalized power function or normalized radiation intensity

Isotropic antenna The isotropic antenna radiates EM waves equally in all directions so that

Directional antenna (1) The directional antenna radiates and receives EM waves preferentially in some directions. Normalized electric field pattern:

Directional antenna (2) E-field pattern is plotted as a function of  for constant . H-field pattern is plotted as a function of  for  = /2. In decibels, E-field pattern and Power pattern are similar. and

Directivity (1) The overall ability of an antenna to direct radiated power in a given direction. Pattern solid angle: A steradian (sr) is defined by an area r2 at the surface. A differential solid angle d, in sr, is defined as

Directivity (2) The solid angle of a sphere is found by integrating d such that An antenna’s pattern solid angle: Comparing p for two Radiation patterns.

Directive gain D(,) (1) Normalized power’s average value: Directivity gain D(,) is defined as The maximum directive gain is called Directivity Dmax:

Directive gain D(,) (2) therefore we have Total radiated power can be written as or

Ex1 Suppose Pn(,)= 1 for 0 <  < /3 and Pn(,)= 0 otherwise Ex1 Suppose Pn(,)= 1 for 0 <  < /3 and Pn(,)= 0 otherwise. Calculate the pattern solid angle, and directivity.

Impedance and efficiency (1) The antenna resistance Rant consists of the radiation resistance Rrad and a dissipative resistance Rdiss that arises from ohmic losses in the metal conductor. Assume so we can write For maximum radiated power, Rrad must be as large as possible but still easy to match with the feed line.

Impedance and efficiency (2) Dissipated power Pdiss can be written as Antenna efficiency e is measured as The power gain can then be expressed 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

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 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 Rrad to I, or m.

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