Understanding Radio Waves: NORCAL Antenna's Radiation Resistance and Uniform Plane Waves -, Study notes of Electrical and Electronics Engineering

Download Understanding Radio Waves: NORCAL Antenna's Radiation Resistance and Uniform Plane Waves - and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! Radio Waves, Transmitting and Receiving Antennas EE521 pg. 1 The NORCAL Antenna Up until now, the antenna of the NORCAL40A has been treated as a 50 ohm load. Antenna is the dipole antenna in the back of the lab The antenna appears as a 50 ohm load Note that the input impedance at 7 MHz of the antenna alone is not 50 ohms There is a matching network (a balun) used to transform the actual antenna impedance to 50 ohms 50 ohm coax cables connect the matched 50 ohm antenna to the antenna jack. Therefore, we can assume that around 7 MHz: • 50 0ant ant antZ R jX j= + ≈ + Ω Note: The antenna is not a resistor that dissipates power The antenna is a radiator. Antenna radiates electromagnetic fields that carry power away from the antenna. By power conservation, the electrical real power delivered to the antenna is equal to: • The power radiated by the antenna, plus • Any power dissipated by the antenna due to conduction losses. Radio Waves, Transmitting and Receiving Antennas EE521 pg. 2 Radiated Power and Radiation Resistance AC power delivered from the NORCAL to the antenna: { } { }* *1 1Re Re2 2t antP VI I Z I= = ⋅ ⋅ , or 21 2t ant P R I= antR can be expressed via the superposition: ant rR R R= + R = ohmic resistance of the antenna (due to conduction losses) rR = the “radiation resistance” • Effective resistance representing power radiated by the antenna Note that in general: rR R>> • The efficiency of the antenna is defined as: /rR Rη = By power conservation: 21 2r t P P R I= − Neglecting ohmic losses: r tP P= . Therefore: ant rR R= Radio Waves, Transmitting and Receiving Antennas EE521 pg. 5 Transmitting Antennas Antenna Coordinate System: The antenna does not radiate with equal power density in all directions. Some antennas are designed to radiate equally along one angular direction (typically azimuthal). Omni-directional Antennas Other antennas are designed to focus radiation in specification directions Directional antennas Let: ( ) 2, W/mP θ φ represent the power density at a given angle ( ),θ φ Define the gain of the transmitting antenna as: ( ) ( ), , / rG P Pθ φ θ φ= Radio Waves, Transmitting and Receiving Antennas EE521 pg. 6 rP = the maximum power density from a reference antenna The reference antenna is typically a fictitious “isotropic radiator” An isotropic radiator radiates power uniformly in all directions Approximated by: • 24 t i r PP P rπ = = ♦ tP = total power delivered to the antenna (W) ♦ 24 rπ = the surface area of a sphere of radius r (m2) The gain is thus written as: ( ) ( )2, 4 , / tG r P Pθ φ π θ φ= Gain is typically expressed in dBi dB’s relative to the isotropic radiator Half-wave dipole: (Max radiation at 90oθ = , ( ) max90 , 2 dBiG Gφ° = = ) Radio Waves, Transmitting and Receiving Antennas EE521 pg. 7 Receiving Antenna An antenna acts as transmitter and a receiver Receiving antenna “collects” electromagnetic signals Produces a current on the antenna, and induces a voltage across the antenna terminals Translates to real power collected from the illuminating EM wave Due to a principal known as “reciprocity”, the receiving pattern characteristics of an antenna are equal to its transmitting pattern. An antenna has an “effective area” The “effective area” is specifically, the effective area of the incident EM that is essentially collected by the receiving antenna. Complicated expression to derive. By reciprocity: ( ) ( ) 2 , , 4 A Gλθ φ θ φ π = • Antenna formula Radio Waves, Transmitting and Receiving Antennas EE521 pg. 10 Friis-Formula We have now been given: ( ) ( ), ,rP A Pθ φ θ φ= ( ) ( ) 2 , , 4 A Gλθ φ θ φ π = Also, from the equivalent circuit: 2 2 2 2 8 8 8 o r ant ant ant V hE h E P R R R = = = Assuming the incident field has the power density of a UPW, then: ( ) 2 1, 2 o o E P θ φ η = , or ( )2 2 ,o oE Pη θ φ= Therefore: ( ) ( ) 2 22 , , 8 4 o o r ant ant h P h P P R R η θ φ η θ φ = = Finally, since ( ) ( ), ,rP A Pθ φ θ φ= , then: ( ) 2 , 4 o ant h A R η θ φ = Radio Waves, Transmitting and Receiving Antennas EE521 pg. 11 For the transmitting antenna, we can derive: ( ) ( )2 , , 4 tP GP r θ φ θ φ π ⋅ = Thus, for the receiving antenna: ( ) ( ) ( ) ( )2 , , , , 4 t r P G P A P A r θ φ θ φ θ φ θ φ π ⋅ = = - Friis Formula Also, given that ( ) ( ) 2 , , 4 A Gλθ φ θ φ π = ( ) ( ) 2 , , 4r t r r r t t t P P G G r λθ φ θ φ π ⎛ ⎞= ⋅ ⋅ ⎜ ⎟ ⎝ ⎠