**ENE 429Antenna and Transmission lines Theory ** Lecture 14Antenna problems and Radar

**Review (1)** • Small loop antenna (magnetic dipole) • Dipole antenna generates high radiation resistance and efficiency For far field region, where

**Review (2)** • Half-wave dipole p = 7.658, Dmax = 1.64, Rrad = 73.2

**Monopole antenna** • Image theory is employed to build a quarter-wave monopole antenna.

**Mirrored image charge of opposite polarity**

**Monopole antenna properties** • Monopole antenna is excited by a current source at its base. • Directivity is doubled and radiation resistance is half of that of dipole antenna.

**Practical considerations** • The best operation: ground is highly conductive (or use counterpoise in case of remote antenna) • Shorter than /4 antenna arises highly capacitive input impedances, thus efficiency decreases. • Solution: inductive coil or top-hat capacitor Inductive coil Top-hat capacitor

**Antenna arrays** • A group of several antenna elements in various configurations (straight lines, circles, triangles, etc.) with proper amplitude and phase relations, main beam direction can be controlled. • Improvement of the radiation characteristic can be done over a single-element antenna (broad beam, low directivity)

**Two-element arrays (1)** To simplify, • All antennas are identical. • Current amplitude is the same. • The radiation pattern lies in x-y plane From Consider ,

**Two-element arrays (2)** Let I1 = I0, I2= I0ej, since r1and r2 >> d/2 for far field, we can assume 1 2 and r1 r2 r.

**Two-element arrays (3)** But the exponential terms cannot be approximated, then

**Principle of pattern multiplication** We can write this as Funit = a unit factor or the maximum time-averaged power density for an individual element at Farray = array factor = where This depends only on distance d and relative current phase, . We can conclude that the pattern function of an array of identical elements is described by the product of the element factor and the array factor.

**N-element linear arrays** We will simplify assumptions as follows: • The array is linear, evenly spaced along the line. • The array is uniform, driven by the same magnitude current source with constant phase difference between adjacent elements. (Farray)max = N2

**Parasitic arrays** • Yagiuda (rooftop antenna) Parasitic elements are indirectly driven by current induced in them from the driven element.

**Friis transmission equation (1)** • Consider power transmission relation between transmitting and receiving antennas where particular antennas are aligned with same polarization. Let Prad1be Ptotal radiated by antenna 1 have a directivity Dmax1, With reciprocal property, Therefore, we have

**Friis transmission equation (2)** Each variable is independent of one another, so each term has to be constant, we found that

**Friis transmission equation (3)** • Effective area (Ae)is much larger than the physical cross section. • More general expressions We can also write

**Friis transmission equation (4)** Finally, consider Prad = etPin, Pout = erPrec, and Gt = etDt, Gr = erDr Friis transmission equation Note: Assume - matched impedance condition between the transmitter circuitry/antenna and receiver - antenna polarizations are the same.

**Receiver matching (1)** • Additional impedance matching network improves receiver performances

**Receiver matching (2)** • Since the receiver is matched, half the received power is dissipated in the load, therefore • Without the matching network,

**Radar (Radio detection and ranging)** • A monostatic radar system • Some of energy is scattered by target so called ‘the echo signal’ received at the radar antenna.

**Radiated power** Let Prad be the radiated power transmitted by the radar antenna, then the radiated power density P1(r, , ) at the target at the distance r away is The power scattered by the target is then s = radar cross section (m2)

**Radar equation** This scattered power results in a radiated power density at the radar antenna of Then By manipulation of these equations, we have or

**More on antennas** • Radiation patterns for dipole antenna http://www.amanogawa.com/archive/DipoleAnt/DipoleAnt-2.html

**More examples** Ex1 Suppose a 0.5 dipole transmitting antenna’s power source is 12-V amplitude voltage in series with a 25 source resistance as shown. What is the total power radiated from the antenna with and without an insertion of a matching network? 0.5

**Ex2 Determine the array factor and normalized power function** for five antenna elements spaced /4 apart with progressive phase steps of 30. The antennas are assumed to be a linear array of z-oriented dipole on the x-axis.

**Ex3 Consider a pair of half-wavelength dipole antennas,** separated by 1 km and aligned for maximum power transfer as shown. This transmission antenna is driven by 1 kW of power at 1 GHz. Assuming the antennas are 100% efficient, what is the receiving antenna’s output power Pout?