1 EE 543 Theory and Principles of Remote Sensing Antenna Systems
O. Kilic EE Outline Introduction Overview of antenna terminology and antenna parameters –Radiation Pattern Isotropic, omni-directional, directional Principal planes HPBW Sidelobes –Power Density –Radiation Intensity –Directivity –Beam Solid Angle –Gain and Efficiency –Polarization and Polarization Loss Factor (PLF) –Bandwidth Antennas as Receivers Circuit representation of an antenna Reciprocity Friis transmission equation
O. Kilic EE Outline Radiation from currents and apertures –Sources of radiation –Current (wire) antennas Vector and scalar potentail Short (Hertzian) dipole Linear antennas –Aperture fields (e.g. horn antennas) Kirchoff’s scalar diffraction theory Vector diffraction theory –Array Antennas Array Factor Main beam scanning Endfire antennas Pattern Multiplication Directivity calculations
O. Kilic EE Summary So far we have discussed how waves interact with their surrounding in various ways: –Wave equation –Lossy medium –Plane waves, propagation –Reflection and transmission In this topic we discuss how waves are generated and received by antennas.
O. Kilic EE What is an antenna? Antenna is a device capable of transmitting power in free space along a desired direction and vice versa. An antenna acts like a transducer between a guided em wave and a free space wave.
O. Kilic EE What is an antenna Any conductor or dielectric could serve this function but an antenna is designed to radiate (or receive) em energy with directional and polarization properties suitable for the intended application. An antenna designer is concerned with making this transition as efficient as possible, ensuring as much power as possible is radiated in the desired direction.
O. Kilic EE Transmission Mode generator Guided em wave Transition region Waves launched into free space Horn antenna
O. Kilic EE Reception Mode detector Guided em wave Transition region Incident wave Receiver
O. Kilic EE Antenna Types Antennas come in various shapes and sizes. Key parameters of an antenna are its size, shape and the material it is made of. The dimensions of an antenna is typically in wavelength, , of the wave it launches.
O. Kilic EE Some examples Thin dipole Biconal dipole loop Parabolic reflector microstrip
O. Kilic EE Examples: Wire Antennas Wire antennas are used as extensions of ordinary circuits & are most often found in “Lower” frequency applications. They can operate with two terminals in a Balanced configuration like the dipole or with an Unbalanced configuration using a Ground Plane for the other half of the structure.
O. Kilic EE Examples: Aperture Antennas Aperture antennas radiate from an opening or from a surface rather than a line and are found at Higher frequencies where wavelengths are Shorter. Aperture antennas often have handfuls of sq. wavelengths of area & are very seldom fractions of a wavelength.
O. Kilic EE Examples: Reflector Antennas Reflector antennas collect or transmit (focus) energy by using a large (many wavelength) dish (or parabolic mirror). These are very high gain (directional) antennas used to communicate with or detect objects in space.
O. Kilic EE How do these structures launch em energy? EM energy can be radiated by two types of sources: –Currents: (e.g. dipole, loop antennas. Time varying currents flowing in the conducting wires radiate em energy.) –Aperture fields: (e.g. horn antenna. E and H fields across the aperture serve as the source of the radiated fields.) Ultimately ALL radiation is due to time varying currents. (E and H fields across the horn aperture is created by the time varying currents on the walls of the horn.)
O. Kilic EE Fundamental Concept of Maxwell’s Equations A current at a point in space induces potential, hence currents at another point far away. J E, H vv Charge distribution R RiRi R’ (0,0,0) V(R)
O. Kilic EE Overview of Antenna Parameters –Radiation Pattern –Radiation Power Density –Radiation Intensity –Directivity –Gain and Efficiency –HPBW –Polarization and Polarization Loss Factor (PLF) –Bandwidth –Beam Solid Angle
O. Kilic EE Radiation Pattern (Antenna Pattern) An antenna pattern describes the directional properties of an antenna at a far away distance from it. In general the antenna pattern is a plot that displays the strength of the radiated field or power density as a function of direction; i.e. , angles.
O. Kilic EE Coordinate System
O. Kilic EE Solid Angle Solid angle defines a subtended area over a spherical surface divided by R 2. Units: Steradians (Sr) For unit angle: For unit solid angle:
O. Kilic EE Solid Angle
O. Kilic EE Types of Radiation Patterns Idealized Point Radiator Vertical DipoleRadar Dish Isotropic Omni-directionalDirectional
O. Kilic EE Isotropic Antenna Isotropic radiator is a hypothetical lossless antenna with equal radiation in ALL directions. Although it is not realizable, it is used to define other antenna parameters, such as directivity. It is represented by a sphere whose center coincides with the location of the isotropic radiator. Isotropic pattern Polar plot Rectangular plot
O. Kilic EE Directional Antenna Directional antennas radiate (or receive) em waves more efficiently in some directions than others. Usually, this term is applied to antennas whose directivity is much higher than that of a half- wavelength dipole.
O. Kilic EE Omni-directional Antenna Omni-directional antennas are special kind of directional antennas having non- directional properties in one plane (e.g. single wire antennas).
O. Kilic EE Principal Planes E and H planes Antenna performance is often described in terms of its principal E and H plane patterns. E-plane – the plane containing the electric field vector and the direction of maximum radiation. H-plane – the plane containing the magnetic field vector and the direction of maximum radiation. Note that it is usual practice to orient most antennas so that at least one of the principal plane patterns coincide with one of the geometrical planes
O. Kilic EE Principal Planes Another definition for principal planes is elevation ( ) and azimuth ( ) plane.
O. Kilic EE Antenna Pattern Lobes Full Null Beamwidth Between 1st NULLS Main lobe Side lobes Back lobes A pattern lobe is a portion of the radiation pattern bounded by regions of relatively weak radiation intensity. nulls Half power beamwidth
O. Kilic EE HPBW, FNBW
O. Kilic EE Field Regions Close to the antenna, the field patterns change rapidly with distance, and include both radiating energy and reactive energy energy oscillates toward and away from the antenna. In the near field region non-radiating energy dominates. Further away, the reactive fields are negligible and only the radiating energy is present. Sufficiently far away; i.e. far field (Fraunhofer) region field components are orthogonal. The angular distribution of fields and power density are independent of distance. Equipartition between electric and magnetic stored energy. In between is the transitional, radiating near field region also known as Fresnel region. The angular field distribution is dependent on the distance. Note that there is no abrupt change in the fields as the boundary between these regions is crossed.
O. Kilic EE Field Regions D R1R1 R2R2 Reactive near-field region Radiating near-field (Fresnel) region Far-field (Fraunhofer) Region R>>R 2 These regions can be categorized as a function of distance R from the antenna. R < R < R 1 <
O. Kilic EE Radiation Power Density The time average Poynting vector of the radiated wave is known as the power density of the antenna. Function of and . Function of 1/r in the far field
O. Kilic EE Example on Power Density (1) Calculate the total radiated power from an isotropic source. An isotropic source radiates equal power in all directions: The radiated power is the sum of the power density in all directions: SoSo Increasing power with distance???
O. Kilic EE Reiterate isotropic source An isotropic source radiates equal power in all directions at a given distance form the source. The distance is in the far field, and the power density is a function of 1/r 2 The power density of an isotropic source is
O. Kilic EE Example on Power Density (2) The radiated power density of an antenna is given by Calculate the total radiated power. Solution: 1/2
O. Kilic EE Radiation Intensity Power radiated from an antenna per solid angle is defined as radiation intensity. It is a function of , only. decays as 1/r 2 in the far field Sincewill be independent of r
O. Kilic EE Power Pattern & Radiation Intensity Decays as {1/r 2 )
O. Kilic EE Example on Radiation Intensity (1) Show that the radiation intensity is constant for an isotropic source. Proof:
O. Kilic EE Example on Radiation Intensity (2) For an antenna with average power density given by calculate the power density of an equivalent isotropic radiator, which radiates the same amount of power. Solution: From previous example, the total radiated power for this antenna is given as For an isotropic source to radiate the same power as this antenna: SoSo S av
O. Kilic EE Example on Radiation Intensity (3) Calculate the radiation intensity for a Hertzian dipole.
O. Kilic EE Beam Solid Angle The solid angle, A, required to radiate all the power of the antenna if the radiation intensity U were uniform and equal to its maximum value within the beam and zero elsewhere. AA AA U max. A = P tot
O. Kilic EE Beam Solid Angle Thus the total radiated power is given by P rad = U max A Normalized radiation intensity
O. Kilic EE Directivity Directivity is the ratio of the radiation intensity of an antenna in a given direction to the radiation intensity of an equivalent isotropic antenna.
O. Kilic EE Directivity Directivity is a measure of how well antennas direct (focus) energy in one direction. For an isotropic source, the directivity is 1; i.e. exhibits no preference for a particular direction. Directivity is typically expressed in dB. If a direction is not specified, typically the maximum value is implied.
O. Kilic EE Directivity Example (1) Show that the directivity of an isotropic source is 1.
O. Kilic EE Directivity Example (2) The power density of an antenna is given by Calculate its directivity. Solution: Note that we have solved for the equivalent isotropic source in Example (2) for radiation intensity. Therefore: From the previous solution:
O. Kilic EE Directivity Example (3) Calculate the directivity of a Hertzian dipole.
O. Kilic EE Antenna Gain Gain is the ratio of the radiation intensity in a given direction to the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically. P in P rad Input terminal Output
O. Kilic EE Gain Gain is closely related to the directivity. It accounts for the antenna efficiency as well as the directional capabilities, whereas directivity is only controlled by the antenna pattern. Antenna efficiency Does not involve the input power to the antenna If the antenna has ohmic losses Gain < Directivity.
O. Kilic EE Efficiency Accounts for losses associated with the antenna Sources of Antenna System Loss 1.losses due to impedance mismatches (reflection) 2.losses due to the transmission line 3.conductive and dielectric losses in the antenna 4.losses due to polarization mismatches reflection conduction dielectric
O. Kilic EE Overall Antenna Efficiency The overall antenna efficiency is a coefficient that accounts for all the different losses present in an antenna system.
O. Kilic EE Antenna Circuit Model The Tx antenna is a region of transition from a guided wave on a transmission line to a free space wave. The Rx antenna is a region of transition from a space wave to a guided wave on a transmission line. Thus, the antenna is a transitional circuit which interfaces a circuit and space.
O. Kilic EE Antenna as a Circuit The input impedance of an antenna is the impedance presented by the antenna at its terminals. The input impedance will be affected by other antennas or objects that are nearby.
O. Kilic EE Antenna and How It Responds to the Environment TX or RX Antenna RrRr RrRr Region of space within the antenna response pattern Virtual transmission line linking the antenna with space The radiation resistance can be thought of as a “virtual” resistance that couples the transmission line terminals to distant regions of space via a virtual transmission line.
O. Kilic EE Antenna Impedance For the discussions that follow, we will assume that the antenna is in an isolated environment. The input impedance of the antenna is composed of real and imaginary parts: Z in = R in +jX in The input resistance, R in represents dissipation in the form of heating losses (Ohmic losses) or radiation. The input reactance, X in represents power stored in the near field of the antenna.
O. Kilic EE Antenna Input Impedance An antenna’s input impedance describes the terminal behavior of the antenna as seen from the source (transmit mode) or receiving amplifier (receive mode). Antenna + -
O. Kilic EE Reflection Efficiency The reflection efficiency through a reflection coefficient ( ) at the input (or feed) to the antenna.
O. Kilic EE Transmitting Antenna Circuit Model V g =generator voltage (peak) R g =generator output resistance X g =generator output reactance R g =antenna conductor loss resistance R r =antenna radiation loss resistance X A =antenna input reactance
O. Kilic EE Transmitting Antenna Circuit Model Maximum power transfer to antenna when
O. Kilic EE Receiving Antenna Circuit Model V A =antenna voltage (peak) R L =receiver load resistance X L =receiver load reactance R g =antenna conductor loss resistance R r =antenna radiation loss resistance X A =antenna input reactance
O. Kilic EE Radiation Resistance The radiation resistance is relatively straight forward to calculate. Example: Hertzian Dipole
O. Kilic EE Radiation Resistance Example: Hertzian Dipole (continued) Very low. It can be increased by increasing the antenna length.
O. Kilic EE Antenna Conduction and Dielectric Efficiency Conduction and dielectric losses of an antenna are very difficult to separate and are usually lumped together to form the cd efficiency. Let R cd represent the actual losses due to conduction and dielectric heating. Then the efficiency is given as For wire antennas (without insulation) there is no dielectric losses only conductor losses from the metal antenna. For those cases we can approximate R cd by: where b is the radius of the wire, w is the angular frequency, s is the conductivity of the metal and l is the antenna length
O. Kilic EE Polarization Loss Factor In general, the polarization of the receiving antenna will not be the same as the polarization of the incident wave Polarization mismatch Thus the power extracted by the antenna from the incident wave will not be maximum. Polarization loss factor The polarization loss factor: The amount of incident power lost by mismatches in polarization between the incident field and the antenna. Incoming wave: Receiving antenna polarization:
O. Kilic EE Effective Aperture plane wave incident A physical P load Question: Answer: Usually NOT How much power can we pick up with a receive antenna???
O. Kilic EE Effective Aperture under matched conditions maximum effective aperture Note that typically S inc is assumed uniform over the effective area. Measure of how effectively the antenna converts incident power density into received power.
O. Kilic EE Directivity and Maximum Effective Aperture Antenna #2 transmit receiver R Direction of wave propagation Antenna #1 A tm, D t A rm, D r The transmitted power density supplied by Antenna #1 at a distance R if Antenna #1 were isotropic would be: Since actual antennas are not isotropic the actual power density would be multiplied by the directivity in that direction:
O. Kilic EE Directivity and Maximum Effective Aperture Antenna #2 transmit receiver R Direction of wave propagation Antenna #1 A tm, D t A rm, D r The power collected (received) by Antenna #2 is given by: If Antenna #2 is now the transmitter and Antenna #1 the receiver:
O. Kilic EE Directivity and Maximum Effective Aperture (no losses) Antenna #2 transmit receiver R Direction of wave propagation Antenna #1 A tm, D t A rm, D r Assume one of the antennas (say Antenna #1) is isotropic : Equatingandgives
O. Kilic EE Maximum Directivity, Effective Aperture and Beam Solid Angle Also Therefore For a fixed wavelength A em and A are inversely proportional.
O. Kilic EE Effective Aperture (as a function of direction) Can be used for received power when the direction of incident radiation is arbitrary, not necessarily along maximum directivity. Useful when dealing with incoherent radiation form extended sources such as sky or terrain.
O. Kilic EE Directivity and Maximum Effective Aperture (include losses) Antenna #2 transmit receiver R Direction of wave propagation Antenna #1 A tm, D t A rm, D r conductor and dielectric losses reflection losses (impedance mismatch) polarization mismatch
O. Kilic EE Friis Transmission Equation (no loss) Antenna #2 Antenna #1 R transmit A tm, D t receiver A rm, D r The transmitted power density supplied by Antenna #1 at a distance R and direction (q r,f r ) is given by: t t ) r r ) The power collected (received) by Antenna #2 is given by:
O. Kilic EE Friis Transmission Equation (no loss) Antenna #2 Antenna #1 R transmit A tm, D t receiver A rm, D r t t ) r r ) If both antennas are pointing in the direction of their maximum radiation pattern:
O. Kilic EE Friis Transmission Equation ( loss) Antenna #2 Antenna #1 R transmit A tm, D t receiver A rm, D r t t ) r r ) conductor and dielectric losses transmitting antenna conductor and dielectric losses receiving antenna reflection losses in transmitter (impedance mismatch) reflection losses in receiving (impedance mismatch) polarization mismatch free space loss factor
O. Kilic EE Friis Transmission Equation: Example Two losses X-band (10.0 GHz) horns are separated by distance of 100. The reflection coefficients measured at the terminals of the transmitting and receiving antennas are 0.1 and 0.2 respectively. The directivities of the transmitting and receiving antennas are 16 dB and 20 dB respectively. Assuming that the power at the input terminals of the transmitting antenna is 3.0 W, and the antennas are aligned for maximum radiation between them and the polarizations are matched, find the power delivered to the receiver.
O. Kilic EE References Stutzman “Antenna Theory and Design” Microwave Remote Sensing, F. T. Ulaby, et.al. Addison-Wesley Kraus Balanis, “Antenna Theory”. EE 540 lectures, Prof. Mirotznik