Fundamental Antenna Parameters Radiation Pattern An antenna radiation pattern is defined as “a graphical representation of the radiation properties of the antenna as a function of space coordinates. In most cases, the radiation pattern is determined in the far-field region. Radiation properties include radiation intensity, field strength, phase or polarization.

Coordinate System

Types of Radiation Patterns Idealized Point Radiator Vertical Dipole Radar Dish Isotropic Omnidirectional Directional

Radiation Pattern Lobes Half-Power BEAMWIDTH 0dB -3dB Main lobe Full Null Beamwidth Between 1st NULLS Side lobes Back lobes PEAK SIDE LOBE LEVEL ( SLL ) ~ -20dB

Radiation Pattern Lobes

Field Regions Reactive near-field region Far-field (Fraunhofer) region Radiating near-field (Fresnel) region R2

Radiation Intensity Aside on Solid Angles infinitesimal area of surface of sphere

Radiation Intensity since decays as 1/r2 in the far field will be independent of r

Radiation Intensity

Radiation Intensity Examples 1. Isotropic radiator 2. Hertzian Dipole

Directive Gain

Directivity Examples 1. Isotropic radiator 2. Hertzian Dipole

=> => Antenna Gain POWER DENSITY IN A CERTAIN DIRECTION DIRECTIVITY => DIVIDED BY THE TOTAL POWER RADIATED GAIN => POWER DENSITY IN A CERTAIN DIRECTION DIVIDED BY THE TOTAL INPUT POWER TO THE ANTENNA TERMINALS (FEED POINTS) IF ANTENNA HAS OHMIC LOSS… THEN, GAIN < DIRECTIVITY

Antenna Gain Sources of Antenna System Loss losses due to impedance mismatches losses due to the transmission line conductive and dielectric losses in the antenna losses due to polarization mismatches According to IEEE standards the antenna gain does not include losses due to impedance or polarization mismatches. Therefore the antenna gain only accounts for dielectric and conductive losses found in the antenna itself. However Balanis and others have included impedance mismatch as part of the antenna gain. The antenna gain relates to the directivity through a coefficient called the radiation efficiency (et) impedance mismatch conduction losses dielectric losses

Overall Antenna Efficiency The overall antenna efficiency is a coefficient that accounts for all the different losses present in an antenna system.

Reflection Efficiency The reflection efficiency through a reflection coefficient (G) at the input (or feed) to the antenna.

Radiation Resistance The radiation resistance is one of the few parameters that is relatively straight forward to calculate. Example: Hertzian Dipole

Radiation Resistance Example: Hertzian Dipole (continued)

Antenna Radiation Efficiency Conduction and dielectric losses of an antenna are very difficult to separate and are usually lumped together to form the ecd efficiency. Let Rcd 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 Rcd 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

Example Problem: A half-wavelength dipole antenna, with an input impedance of 73W is to be connected to a generator and transmission line with an output impedance of 50W. Assume the antenna is made of copper wire 2.0 mm in diameter and the operating frequency is 10.0 GHz. Assume the radiation pattern of the antenna is Find the overall gain of this antenna SOLUTION First determine the directivity of the antenna.

Example Problem: Continued SOLUTION Next step is to determine the efficiencies

Example Problem: Continued SOLUTION Next step is to determine the gain

Antenna Type Gain (dBi) Gain over Isotropic Power Levels Half Wavelength Dipole 1.76 1.5x Cell Phone Antenna (PIFA) 3.0 2.0x 0.6 Watts Standard Gain Horn 15 31x Cell phone tower antenna 6 4x Large Reflecting Dish 50 100,000x Small Reflecting Dish 40 10,000x

Effective Aperture plane wave Aphysical Pload incident Question: Answer: Usually NOT

Directivity and Maximum Effective Aperture (no losses) Antenna #2 transmit receiver R Direction of wave propagation Antenna #1 Atm, Dt Arm, Dr

Directivity and Maximum Effective Aperture (include losses) Antenna #2 transmit receiver R Direction of wave propagation Antenna #1 Atm, Dt Arm, Dr conductor and dielectric losses reflection losses (impedance mismatch) polarization mismatch

Friis Transmission Equation (no loss) Antenna #1 transmit Antenna #2 (qr,fr) receiver Arm, Dr Atm, Dt (qt,ft) R The transmitted power density supplied by Antenna #1 at a distance R and direction (qr,fr) is given by: The power collected (received) by Antenna #2 is given by:

Friis Transmission Equation (no loss) Antenna #1 transmit Antenna #2 (qr,fr) receiver Arm, Dr Atm, Dt (qt,ft) R If both antennas are pointing in the direction of their maximum radiation pattern:

Friis Transmission Equation ( loss) Antenna #1 transmit Antenna #2 (qr,fr) receiver Arm, Dr Atm, Dt (qt,ft) R conductor and dielectric losses receiving antenna reflection losses in receiving (impedance mismatch) free space loss factor conductor and dielectric losses transmitting antenna reflection losses in transmitter (impedance mismatch) polarization mismatch

Friis Transmission Equation: Example #1 A typical analog cell phone antenna has a directivity of 3 dBi at its operating frequency of 800.0 MHz. The cell tower is 1 mile away and has an antenna with a directivity of 6 dBi. Assuming that the power at the input terminals of the transmitting antenna is 0.6 W, and the antennas are aligned for maximum radiation between them and the polarizations are matched, find the power delivered to the receiver. Assume the two antennas are well matched with a negligible amount of loss. = 0 = 1 = 1 = 0 = 1

Friis Transmission Equation: Example #2 A half wavelength dipole antenna (max gain = 2.14 dBi) is used to communicate from an old satellite phone to a low orbiting Iridium communication satellite in the L band (~ 1.6 GHz). Assume the communication satellite has antenna that has a maximum directivity of 24 dBi and is orbiting at a distance of 781 km above the earth. Assuming that the power at the input terminals of the transmitting antenna is 1.0 W, and the antennas are aligned for maximum radiation between them and the polarizations are matched, find the power delivered to the receiver. Assume the two antennas are well matched with a negligible amount of loss. = 0 = 1 = 1 = 0 = 1

Friis Transmission Equation: Example #2 A roof-top dish antenna (max gain = 40.0 dBi) is used to communicate from an old satellite phone to a low orbiting Iridium communication satellite in the Ku band (~ 12 GHz). Assume the communication satellite has antenna that has a maximum directivity of 30 dBi and is orbiting at a distance of 36,000 km above the earth. How much transmitter power is required to receive 100 pW of power at your home. Assume the antennas are aligned for maximum radiation between them and the polarizations are matched, find the power delivered to the receiver. Assume the two antennas are well matched with a negligible amount of loss. = 0 = 1 = 1 = 0 = 1

Radar Range Equation Definition: Radar cross section or echo area of a target is defined as the area when intercepting the same amount of power which, when scattered isotropically, produces at the receiver the same power density as the actual target. (radar cross section) m2 R (distance from target) m Ws (scattered power density) W/m2 Winc (incident power density) W/m2

Radar Range Equation (no losses) Power density incident on the target is a function of the transmitting antenna and the distance between the target and transmitter: The amount of power density scattered by the target at the location of the receiver is then given by: The amount of power delivered by the receiver is then given by: Note that in general:

Radar Range Equation (losses)

Radar Cross Section (RCS) Definition: Radar cross section or echo area of a target is defined as the area when intercepting the same amount of power which, when scattered isotropically, produces at the receiver the same power density as the actual target. Transmitter and receiver not in the same location (bistatic RCS) Transmitter and receiver in the same location (usually the same antenna) called mono-static RCS

Radar Cross Section (RCS) RCS Customary Notation: Typical RCS values can span 10-5m2 (insect) to 106 m2 (ship). Due to the large dynamic range a logarithmic power scale is most often used. 100 m2 20 dBsm 10 m2 10 dBsm 1 m2 0 dBsm 0.1 m2 -10 dBsm 0.01 m2 -20 dBsm