Antenna Systems: Definitions and Theory

• The unit aims to help you understand the basic theories of antenna systems and analyze how different types of antennas work

Key Definitions

• Antenna: A device that transmits and/or receives electromagnetic waves (aka radio waves)
• Beam Width: The angular separation where the radiation pattern's magnitude decreases by 50% (or -3dB) from the main beam's peak
• Wavelength: The distance between identical points on adjacent cycles of a waveform signal traveling in space or along a wire
• Frequency: The number of times a repeating event occurs per unit of time
• Directivity: A measure of how "directional" an antenna's radiation pattern is
• Antenna Gain: How much an antenna concentrates radiated power in a direction or absorbs incident power from that direction, compared to a reference antenna

Antenna System Overview

• Antennas convert electrical power into electromagnetic waves and vice versa
• They can be transmitting antennas (radiate electromagnetic waves from electrical signals) or receiving antennas (convert electromagnetic waves into electrical signals)
• In two-way communication, the same antenna can be used for both
• An antenna can also be called an aerial
• Modern antennas come in various sizes and shapes to suit different applications
• Antennas are generally metallic objects (often wires or groups of wires) that convert high-frequency signals into electromagnetic waves and vice versa
• They either radiate signal energy or collect it
• Antennas either radiate or intercept electromagnetic radiation, acting as passive reciprocal devices

Antenna System Components

• Coupler Device (Coupling Coil): Connects the transmitter to the feeder
• Feeder: A transmission line that carries energy to the antenna
• Antenna: Radiates energy into space

Basic Antenna Parameters

• Frequency: How often an event occurs; the reciprocal of the time period (T) for a periodic wave
• Wavelength: The distance between two immediate positive or negative peaks; the length of the wave
• Impedance Matching: Matching the impedance of a transmitter to a receiver (or vice versa), necessary between the transmission line and the antenna for maximum power transfer
• VSWR (Voltage Standing Wave Ratio) & Reflected Power: VSWR indicates impedance mismatch, with higher VSWR values meaning greater mismatch; the ideal VSWR is 1:1 for effective radiation; Reflected power is power wasted, and both reflected power and VSWR indicate the same thing
• Bandwidth: A range of frequencies specified for a particular communication, ensuring signals don't interfere with each other
• Percentage Bandwidth: The ratio of absolute bandwidth to the center frequency (resonant frequency)

Key formulas

• Percentage Bandwidth Formula: (fH - fL) / fc, where fH is higher frequency, fL is lower frequency, and fc is center frequency
• Radiation Intensity: Power per unit solid angle; a measure of the maximum intensity of radiation emitted by an antenna in a particular direction

More Key formulas

• Radiation Intensity (U) Formula: U = r² × Wrad, where r is the radial distance and Wrad is the power radiated

Near Field and Far Field

• Near Field (Inductive Field): The area closer to the antenna with an inductive effect
• Far Field (Radiation Field): The area far from the antenna where radiation effect is high; antenna parameters, directivity, and radiation patterns are considered in this region

Antenna Efficiency

• Antenna Efficiency: Ratio of power radiated by the antenna to power delivered to the feedpoint, or the ratio of radiation resistance to total antenna resistance
• Effective Aperture: Describes the effectiveness of an antenna in receiving mode as the ratio of power delivered to the load to incident power density

Key formulas

• Antenna Efficiency Formula : η = Prad / (Pa + Prad) = Rrad / (Rd + Rrad)
• Where: Prad = Power Radiated, Pa= Power Absorbed, Rrad = Radiation Resistance, Rd = Dissipated resistance
• Effective aperture Formula: e = Prad / Pin

Bandwidth and Beamwidth Considerations

• Bandwidth: The frequency range over which an antenna radiates effectively or satisfactorily
• Beamwidth: The width, in degrees, of the major lobe between the two directions where relative radiated power is half its peak value
• Half-Power Beamwidth (HPBW): The angle between two vectors from the pattern's origin to the points where radiation intensity is half its maximum; used to describe antenna resolution properties and is important in radar and radioastronomy
• First-Null Beamwidth (FNBW): The angle between two vectors, originating at the pattern's origin and tangent to the main beam at its base; approximately FNBW ≈ 2*HPBW

Antenna Properties and Characteristics

• Reciprocity: An antenna's ability to transfer energy from the atmosphere to its receiver with the same efficiency it transfers energy from the transmitter into the atmosphere
• Reciprocal antenna characteristics remain the same regardless of whether sending or receiving electromagnetic energy
• Properties of transmitting and receiving antennas: Equality of directional patterns, directivities, effective lengths, antenna impedances

Directional Patterns

• The radiation pattern of transmitting antenna1 to receiving antenna2 is equal to the radiation pattern of antenna2 if it transmits and antenna1 receives
• Directivity is the same for both transmitting and receiving antennas
• The maximum effective aperture is the same for both transmitting and receiving antennas, maintaining equality in lengths based on wavelength

Antenna Impedances

• The output impedance of a transmitting antenna and the input impedance of a receiving antenna are equal for effective communication

Radiation Pattern Details

• Radiation Pattern: Diagrammatical representations of the distribution of radiated energy into space as a function of direction, often shown as a polar diagram of field strength or power densities

Radiation Patterns

• Field Patterns: Plotted as a function of electric and magnetic fields on a logarithmic scale
• Power Patterns: Plotted as a function of the square of the magnitude of electric and magnetic fields, often on a logarithmic or dB scale

Lobes

• Maxima or lobes in radiation at various angles, separated by nulls (zero radiation angles)
• Main Lobe (Major Lobe): The portion where maximum radiated energy exists, indicating the antenna's directivity
• Side Lobes (Minor Lobes): Areas where radiation is distributed sideways, representing wasted power
• Back Lobe: Located opposite the main lobe, also a minor lobe, where significant energy is wasted

Front-to-Back Ratio

• FBR = (Radiated flux density from the center of the major lobe) / (Radiated flux density from the center of the back lobe)
• Directional Antenna: Radiates/receives much more power in certain directions

Isotropic Radiation

• Radiation from a point source radiating uniformly in all directions with the same intensity, practically impossible as every antenna radiates energy with some directivity
• The isotropic radiation is an Omni-directional radiation

Directive Gain

• Directive Gain: Ratio of power density in a particular direction of one antenna to the average power density radiated by an omnidirectional antenna

More Key formulas

• Formula for Directive Gain (D): D= Po / PDref
• Gain G: Ratio of radiated power in the maximum direction to the radiated power of an isotropic antenna; an isotropic antenna has a gain of 0 dB; gain refers to the direction of maximum radiation and is usually expressed in decibels

More Key Definitions and Facts

• Gi ("Isotropic Power Gain"): A theoretical concept where the reference antenna is isotropic
• Gd: Reference antenna is a half-wave dipole
• dBi: dB referenced to an isotropic (equal radiation in all directions) radiator
• dBd: dB referenced to a half wavelength dipole

Power Gain Calculation

• It is defined as the ratio between the power radiated by a directional antenna to the power radiated by a reference antenna, but the antenna efficiency is taken into account.

Note

• A receiving antenna absorbs some of the energy from radio waves.
• A larger antenna receives more power than a smaller antenna
• Receiving antennas have gain, just as transmitting antennas do.
• The power from a receiving antenna depends on its size and its gain

Formulas

• Formulas: G = η (PD/PDref); G = ηD

EIRP (Effective Isotropic Radiated Power)

• The power radiated by an antenna in its favored direction, referenced to an isotropic radiator
• EIRP = PG

Effective Radiated Power

• If the Radiated power is calculated by taking half wave dipole as the reference, rather than an isotropic antenna, then it can be termed as ERP (Effective Radiated Power).
• ERP(dBW) = EIRP(dBW) – 2.15dBi

Power Transfer in Free Space

• Power Density: P = PGT / 4πr²
• Effective Area: Aeff= PR / PD, Aeff= λ²GR / 4π

Friis Transmission Equation

• For Polarization matched antennas aligned for maximum directional radiation and re caption, the ratio of the transmitted and received power is:
• Free Space Attenuation: PR / PT = λ²GTGR/ 16π²r²
• Free Space Loss: Lfs = 32.44 + 20logdkm +20logfMHz - GT(dBi) - GT(dBi) - GR(dBi)

Polarization

• The orientation or direction in space of the E field part of the em wave being radiated by the transmitting system. When a wave is transmitted or received, it may be done in different directions.

Linear Polarization

• It helps in maintaining the wave in a particular direction and avoiding all the other directions Electric field vector stays in the same plane and so we use this linear polarization to improve the directivity of the antenna

Key facts regarding Polarization

• Vertical Polarization: Electric field is perpendicular to the earth's surface, the low frequency vertically polarized waves are helpful for ground wave transmission

• These are not affected by the surface reflections and so vertical polarization is used for mobile communications.

• Horizontal Polarization: Electric field is parallel to the earth's surface, makes the wave weak, as the reflections from the earth surface affect it. They are usually weak at low frequencies below 1GHz

Circular Polarization

• Electrical field vector rotates 360° as the wave moves one wavelength through space and the field strength is the same at all angles of polarization.
• Using circular polarization, the effect of multi-path gets reduced and so it is used in satellite communications such as GPS

Elliptical Polarization

• Electrical field vector of the wave rotates 360° as the wave moves one wavelength through space and the field strength varies changes in polarization

Beamwidth Details

• The angle that which main lobe falls by half on either side
• Half Power Beam Width (HPBW): The angular separation, in which the magnitude of the radiation pattern decreases by 50%
• This means that it is the area where most of the power is radiated, which is the peak power

More Beam Width facts

• First Null Beam Width (FNBW) or Beam Width between First Null (BWFN): The angular span between the first pattern nulls adjacent to the main lobe
• The mathematical expression of First Null Beam Width is FNBW is 2*HPBW
• The unit of FNBW is radians or degrees

Effective Length & Effective Area

• They are also important as these parameters help us to know about the antenna's performance

Effective Length facts

• The ratio of the magnitude of voltage at the open terminals of the receiving antenna to the magnitude of the field strength of the incident wave front, in the same direction of antenna polarization

More Key formulas

• Antenna Effective length is used to determine the polarization efficiency of the antenna
• The math Formula to calculate this: le = Voc/Ei