A Brief Introduction to Antennas

& Transmission LinesSATISH KUMAR(A.P ECE)

GITAM, KABLANA

Outline of Presentation

• Maxwell’s Equations & EM Waves

• EM Spectrum

• Antenna Characterization

• Dipoles and Monopoles

• End Fires (Yagis & Log-Periodics)

• Apertures (Parabolic Reflectors)

• Patches & Arrays

• Transmission Lines

• Friis’ Equation

• I. Outline for Wire, Aperture and Patch

Antennas

• EM Spectrum

• Antenna Characterization

• Dipoles and Monopoles

• End Fires (Yagis & Log-Periodics)

• Apertures (Parabolic Reflectors)

• Patches & Arrays

EM waves in free space

• v2 = 1/(oµo) so v = 3 x 108 m/s

o = 8.855 x 10-12 Farads/m

– µo = 1.2566 x 10-6 Henrys/m

• EM waves in free space propagate freely without attenuation

• What is a plane wave?

– Example is a wave propagating along the x-direction

– Fields are constant in y and z directions, but vary with time and space along the x-direction

– Most propagating radio (EM) waves can be thought of a plane waves on the scale of the receiving antenna

E & H fields and

Poynting Vector for Power Flow

• Power flow in the EM field

– P = E x H (P is Poynting vector)

• In free space E and H are perpendicular

• P is perpendicular to both E and H

• Plane wave radiated by an antenna

– P = E x H -> Eo Ho Sin2(t-kx)

– P = [Eo2/] Sin2(t-kx)

– Pavg = (1/2) [Eo2/] in W/m2

= impedance of free space = 377

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After Kraus & Marhefka, 2003

RF Bands, Names & Users

After Kraus & Marhefka,

2003

Radiation from a Short Antenna Element or Hertzian Dipole

• Using the Electrodynamic Retarded Potential A (Vector) we can derive (see Ramo et al., 1965 or Skilling, 1948, Ulaby, 2007 or any EM theory book)

E and H fields associated with a small element of current of length l (<< ) that has the current varying as

i = I Sin (t)

• This could be a wire or charge moving in space, e.g. in the plasma of the ionosphere or a star or nebula

• E and H fields at r could be in the r, or directions

Radiation from a Short Antenna Element

• Terms that fall off as 1/r3 or 1/r2 are small at any

significant distance from an antenna

• Remaining “radiation” terms fall off only as 1/r

and thus transmit energy for long distances also

E and H fields are in phase

• When one is in the “near field” the 1/r3 or 1/r2

the other terms are important

Antenna Field Zones

• The dividing line

“Rule of Thumb” is R

= 2L2/

• The near field or

Fresnel zone is r < R

• The far field or

Fraunhofer zone is

r > R

Intuitive Picture of Radiation

Polarization of EM Waves

AR = Axial Ratio

Simple Dipole Antenna

Antenna Characterization

• Directivity

• Power Pattern

• Antenna Gain

• Effective Area

• Antenna Efficiency

Antenna Directivity

• An omnidirectional antenna radiates power into all directions (4 steradians) equally

• Typically an antenna wants to beam radiation in a particular direction

• Directivity

D = 4/, is the antenna beam solid angle

• What would be for one octant (x,y,z all > 0) ?

Antenna Gain

• Gain is like directivity, but includes losses as well

• G( ) ≈ /( ) is nondimensional° --

accounts for losses

• dB = 10 log(x/xref) -- always refers to power

• Gain for Typical Antenna with significant

directivity

• G( ) ≈ 2500/(° °), taking into account

beam shape and typical losses

Estimating Effective Antenna Area & Gain

• Definition: G = (4 Ae)/2

• Ae = A, where A is the physical area

and is the antenna efficiency

• To get the average power available at the antenna

terminals we use

• Pav,Ant = Pav,Poynting (Average Poynting Flux) Ae

• A crude estimate of G can be obtained by letting

≈ (/d), where d is the antenna dimension along the

direction of the angle -- big antenna means small

– and G( ) ≈ /( )

Radiation Resistance & Antenna Efficiency

• Radiation resistance (Rrad) is a fictitious resistance,

such that the average power flow out of the antenna is

Pav = (1/2) <I>2 Rrad

• Using the equations for our short (Hertzian) dipole we

find that

Rrad = 80 2 (l/)2 ohms

• Antenna Efficiency

= Rrad/(Rrad+ Rloss)

where Rloss = ohmic losses as heat

• Gain = x Directivity --- G = D

Antenna Family

Short Dipole Antenna Analysis

• Consider a finite, but short antenna with

l << situated in free space

• Current is charging the uniformly

distributed capacitance of the antenna

wire & so has a maximum at the middle

and tapers toward zero at the ends

• Each element dl radiates per our radiation

equations (previous slide), namely

• In the far field

E = ( I dl sin/(2 r )) cos {[t-(r/c)]}

• The direction is in the same plane as the

element dl and the radial line from

antenna center to observer and

perpendicular to r

Short Dipole Antenna Result

• The resultant field at the observer at r is the sum of the

contributions from the elemental lengths dl

– Each contribution is essentially the same except that the current I varies

– Radiation contribution to the sum is strongest from the center and

weakest at the ends

• This can be summarized as the rms field strength in volts per

meter as

E,rms = [ Io le sin/(2 r )] -- V/m

• What do you think the effective length le & current Io are?

• The radiated power is

Pav = (E,rms)2/(2)

Modifications for Half Wavelength Dipole

• For antennas comparable in size to

– Current distribution is not linear

– Phase difference between different parts of the antenna

• Current distribution on

/2 dipole

– Antenna acts like open circuit transmission line with uniformly distributed capacitance

– Sinusoidal current distribution results

Fields from /2 Dipole

• To take account of the phase differences of the contributions from all the elements dl we need to integrate over the entire length of the antenna as shown by the figure (from Skilling, 1948)

E = ∫±/4 ( Io sine/2 re ) cos kx cos [t-(re/c)] dx

– Integral is from -/4 to /4, i.e. over the antenna length

• Result of integration

E = (Io/2 r) cos [t-(r/c)] {cos [( /2) cos] / sin}

• We know that Er = E = 0 as for the Hertzian dipole

/2 and Dipole Antenna Pattern (E-field)

Monopole over a Conducting Plane -- /4 Vertical

Yagi - Uda

• Driven element induces currents in parasitic elements

• When a parasitic element is slightly longer than /2, the element acts inductively and thus as a reflector -- current phased to reinforce radiation in the maximum direction and cancel in the opposite direction

• The director element is slightly shorter than /2, the element acts inductively and thus as a director --current phased to reinforce radiation in the maximum direction and cancel in the opposite direction

• The elements are separated by ≈ 0.25

3 Element

Yagi

Antenna

Pattern

• A log periodic is an extension of the Yagi idea to a broad-band,

perhaps 4 x in wavelength, antenna with a gain of ≈ 8 dB

• Log periodics are typically used in the HF to UHF bands

Log-Periodic Antennas

Parabolic Reflectors

• A parabolic reflector operates much the same way a reflecting telescope does

• Reflections of rays from the feed point all contribute in phase to a plane wave leaving the antenna along the antenna bore sight (axis)

• Typically used at UHF and higher frequencies

Array Antennas

Very Large Array

http://www.vla.nrao.edu/

Organization:

National Radio

Astronomy

Observatory

Location:Socorro NM

Wavelength:

radio 7 mm and larger

Number & Diameter

27 x 25 m

Angular resolution:

0.05 (7mm) to 700

arcsec