Antenna Basics & Parameters

Antenna Basics

Basic Antenna Parameters

• Patterns:

  • Radiation pattern is a graph showing the variation of actual field strength at different points from transmitter to receiver.

  • Two types:

    • Field radiation pattern: Radiation represented as field strength.

    • Power radiation pattern: Radiation represented as power per unit solid angle.

  • Types of radiation patterns:

    • Omnidirectional pattern

    • Pencil beam pattern

    • Fan beam pattern

    • Shaped beam pattern

    • Non-uniform pattern

• Beam Area ($\Omega_A$):

  • Solid angle through which all power is radiated by the antenna.

  • Also known as beam solid angle.

  • Expressed as: $\Omega<em>A = \int</em>0^{2\pi} \int<em>0^{\pi} B(\theta, \phi) d\Omega = \int</em>0^{2\pi} \int_0^{\pi} B(\theta, \phi) \sin(\theta) d\theta d\phi$

• Radiation Intensity (U):

  • Signal strength in a particular direction, eliminating side and back radiation.

  • Expressed as: $U = r^2 \frac{P<em>{rad}}{\Omega}$, where $P</em>{rad}$ is radiation power and r is radial distance.

Beam Efficiency

• Ratio of main beam area to total beam area radiated.

• Denoted as $\eta_B$

• Formula: $\eta<em>B = \frac{\Omega</em>{MB}}{\Omega<em>A}$, where $\Omega</em>{MB}$ is the main beam area and $\Omega_A$ is the total beam area.

Directivity (D)

• Ratio of maximum radiation intensity of the main antenna to the radiation intensity of a reference antenna.

• Expressed as: $D = \frac{U<em>{max}}{U</em>{reference}}$, where $U<em>{max}$ is the max radiation intensity and $U</em>{reference}$ is the radiation intensity of reference antenna

• $D = D(\theta, \phi)$, where $\theta$ and $\phi$ are angular positions.

Gain (G)

• Describes how much power is radiated in the peak direction versus an isotropic source.

• Denoted as G.

• Expressed as: $G = \eta<em>e D$, where $\eta</em>e$ is antenna efficiency and D is directivity.

Antenna Aperture

• Ratio between effective radiation and physical radiation.

• An antenna aperture radiates power with minimal losses.

• $A<em>e = \frac{A</em>{effective}}{A_{physical}}$

Effective Height ($l_e$)

• Also known as effective length.

• Ratio between induced voltage and electric field strength.

• Expressed as: $l<em>e = \frac{V</em>0}{E<em>i}$, where $V</em>0$ is induced voltage and $E_i$ is field strength.

Radiation

Retarded Potential

• Electromagnetic potentials generated by changing electric fields with respect to time.

• Changes in the electric field due to antenna movement do not have an immediate effect; there is a time delay.

• This delay is the retarded potential.

• In retarded potential, the field propagates at the speed of light.

• $\phi(r, t) = \frac{1}{4 \pi \epsilon<em>0} \int \frac{\rho(r', t</em>r)}{|r - r'|} dv'$, where $t_r$ is the retarded time.

Field from Oscillating Dipole

• Explains radiation pattern changes based on charge particle movement in oscillating dipoles (+/- poles).

• Considers time period (T), acceleration (a), current (I), and distance (D).

• Cases:

  • Case (i): T=0, a=max, I=0, D=far: Charge particles are far, acceleration is max, current is zero.

  • Case (ii): T=$\frac{T}{4}$ , a=min, I=max, D=little close: Charge particles are moving towards each other, acceleration is min, current is max.

  • Case (iii): T=$\frac{T}{2}$ : Charge particles are very close, acceleration is zero, current is max.

  • Case (iv): T=$\frac{3T}{4}$ : Charge particles interchange, acceleration is min, current slightly decreases.

  • Case (v): T=T: Charge particles move far away, acceleration is max, current is zero.

• Summary table:

Field Zones

• Radiated field divided into two types:

  • Near Field

  • Far Field

Near Field

• Also known as the inductive field.

• Close to the transmitting antenna.

• Subdivided into:

  • Reactive Near Field: Very close to the transmitting antenna; expressed as: R << 0.62$\sqrt{\frac{D^3}{\lambda}}$

  • Radiating Near Field: Farther from the transmitting antenna; expressed as: R >> 0.62$\sqrt{\frac{D^3}{\lambda}}$

Far Field

• Zonal area very far from the transmitting antenna but close to the receiving antenna.

Front to Back Ratio (FBR)

• Power transmission in the forward direction divided by power radiation in the backward direction.

• $FBR = \frac{Forward Power}{Backward Power}$

• Using gain value: $G<em>{dB} = 10 \cdot log</em>{10} [\frac{P<em>{front}}{P</em>{back}}]$

Antenna Theorem (Reciprocity Theorem)

• Any antenna can be used as a transmitting or receiving antenna.

• Radiation patterns should be the same.

• Directivity and input impedance should be the same.

• Antennas operate with mutual inductance.

• According to the reciprocity theorem:

  • Induced current from antenna A1 to A2 is equal to the induced current from antenna A2 to A1.

• Circuit diagram of antenna theorem includes loops with self-impedances ($Z<em>{11}$, $Z</em>{22}$) and mutual impedance ($Z_m$).

• Applying Kirchhoff's mesh law to loops yields:

  • $(Z<em>{22} + Z</em>m) I<em>2 = E</em>1$

  • $(Z<em>{11} + Z</em>m) I<em>1 - Z</em>m I<em>2 = E</em>1$

• Solving for $I<em>1$ and $I</em>2$ leads to.

  • $E<em>{21} = E</em>{12}$

H-Theorem (Helmholtz Theorem)

• Any smooth vector field can be used to send radio frequencies.

• Uses:

  • Divergence pattern

  • Curl pattern

Divergence Pattern

• Indicated with dot (.).

• Expressed by $\nabla \cdot F = 0$

Curl Pattern

• Indicated with cross (x).

• Expressed by $\nabla \times F = 0$

• Vector field F can be:

  • Both divergence and curl

  • Divergence but not curl

  • Curl but not divergence

  • Neither divergence nor curl

Antenna Theory Modules

• Module 1: Fundamental concepts (near field, far field, radiation pattern, beam, polarization, theorems).

• Module 2: Types of antennas (half-wave, full-wave, quarter-wave, loop, short dipole, long wire, V, helical, slot, aperture, microstrip, lens, dish, parabolic).

• Module 3: Types of antenna arrays (collinear, broadside, end-fire, parasitic, Yagi-Uda, log-periodic).

• Module 4: Wave propagation (spectrum, transmission, ionospheric, layer).

• Module 5: Waveguides.

Antenna Characteristics

• Directional: Radiates electromagnetic waves in a specific direction with focused and narrow beam; used in distance comm.

• Semi-directional: Radiates electromagnetic waves with a wider bandwidth; used in wireless and cellular comm.

• Omnidirectional: Radiates electromagnetic waves in all horizontal directions (360 degrees); used in FM radios and Wi-Fi.

Antenna Properties

• Radiation pattern, bandwidth, beam area, directivity, gain, radiation intensity, antenna aperture, effective height, and pattern.

Antenna Applications

• Satellite, wireless communication, cellular communication, distance communication, long communication, FM radios, navigation, GPS, TVs.

Antenna Functions

Transmission

• Converts electrical signals into electromagnetic waves at the transmitter.

Reception

• Converts electromagnetic signals into electrical signals at the receiver.

Antenna Frequencies

• Very low frequencies

• Low frequencies

• Medium frequencies

• High frequencies

• Very high frequencies

• Ultra-high frequencies

Antenna Dimensions

• 2-D

• 3-D

Radiation from Small Electric Dipole

• Two charge particles with equal magnitude separated by distance 'd'.

• Field generation considers:

  • Curl vector field

  • Divergence vector field

Curl Vector Field

• Flux rotating around the charge particle.

Divergence Vector Field

• Flux leaving the charge particle.

• Combination of negative and positive charges with small distance 'd' is the small electric dipole.

• Electric dipole moment: $P = qd$, where p is the moment of charge particle, q is the charge, and d is the distance.

• Small electric dipoles are used to determine antenna system properties such as surface of ground and gravity of ground.

Quarter Wave Antenna

• Type of monopole antenna.

• Driving signal connected to transmitter, resulting signal connected across the receiver.

• Antenna length calculated with wavelength ($\lambda$) and distance 'd'.

Types of Quarter Wave Antenna:

• T-antenna

• H-antenna (Helical)

• L-antenna (Linear)

• Umbrella antenna

• V-antenna

Half Wave Dipole Antenna

• Simplest antenna consisting of two conductors of equal length connected with a feed line.

• Designed by cutting and bending the monopole antenna.

• Used as feed antenna or directional antenna.

• Feeds horn, parabolic, and corner reflector antennas.

Advantages

• Good input impedance

• Perfect directivity

• Good efficiency

Applications

• TV receiver

• Radio receiver

Radiated Power

• Measures how much power is radiated from transmitter to receiver.

• Expressed as :
  $\text{TRP} = \oint<em>{\text{A}} (E \times H) \cdot d\text{A} = \int</em>0^{2\pi} \int_0^{\pi} \frac{|E|^2}{\eta} r^2 \sin(\theta) d\theta d\phi$

Radiation Resistance

• Ratio of power radiated in ohms to power radiated in watts.

• $R<em>r = \frac{P</em>{rad}}{I^2}$

Beam Width

• Range of frequencies over which the antenna can be operated perfectly without any interrupts.

Effective Area

• Also known as effective aperture: Indicates how effectively the receiving antenna receives power from the transmitter.

• $A_e = \frac{\lambda^2}{4\pi} G$, where $\lambda$ is wavelength and G is gain.

Loop Antenna

• Radiating coil with one or more turns used to carry radio frequencies.

• Shapes include circular, rectangular, and rhombus.

Types

• Small loop antenna ($\lambda$ >> circumference)

• Large loop antenna ($\lambda$ << circumference, 2$\pi$ or more)

Small Loop Antenna

• Small circumference compared to operating wavelength.

• Used for both transmission and reception.

• Radiates insufficient radiation due to small circumference.

Large Loop Antenna

• Large circumference compared to operating wavelength.

• Used for both transition and repetition.

• Radiates sufficient radiation due to large circumference.

Directivity of Loop Antenna

• Always max.

• Defined as the ratio of maximum radiation intensity of the main antenna to the radiation intensity of the reference antenna.

Natural Current Distributions

• Current is max at the center and zero at the edges.

Comparison of Small Loop and Short Dipole