lecture32 - Lecture 32 Circuit Properties of Antennas In...

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1 ECE 303 – Fall 2006 – Farhan Rana – Cornell University Lecture 32 Circuit Properties of Antennas In this lecture you will learn: • Circuit properties of transmitting and receiving antennas • Thevenin circuit models for receiving antennas • Antenna theorem ECE 303 – Fall 2006 – Farhan Rana – Cornell University Circuit Properties of Transmitting Antennas - I How does an antenna look to a driving circuit? d Z o () () ()() y x z I z r J δ ˆ = r r x z I Z o I Z A P = Net time-average power going into the antenna Antenna appears as a load impedance Z o P Poynting theorem: () ( ) ()() t r E t r J t t r W t r S , . , , , . r r r r r r r + = Time-average form for time-harmonic signals: ( ) ( )( ) t r E t r J t r S , . , , . r r r r r r = P rad P rad P rad P rad Note the distinction between P and P inc and P rad P = P inc -P ref P = P inc ref P inc P ref
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2 ECE 303 – Fall 2006 – Farhan Rana – Cornell University Circuit Properties of Transmitting Antennas - II Z o P Time-average form for time-harmonic signals: ( ) ( )( ) dv t r E t r J a d t r S ∫∫∫ = ∫∫ , . , . , r r r r r r r Net power dissipated Z o I Z A P Net power going in diss rad R I P P 2 2 1 = P rad P rad P rad P rad But: rad rad R I P 2 2 1 = So we get: () rad diss R R I P + = 2 2 1 But from the circuit model: [] A Z I P Re 2 1 2 = diss rad A R R Z + = Re P = P inc -P ref ECE 303 – Fall 2006 – Farhan Rana – Cornell University Circuit Properties of Transmitting Antennas - III Z o I Z A P Z o I P jX A R A ( ) A diss rad A A A jX R R jX R Z + + = + = The reactive part is due to the net inductance or capacitance of the antenna structure Not all the power P going into an antenna is converted into radiated power P rad –some is dissipated due to the less-than-infinite conductivity of real metals (i.e. non-zero R diss ) Definition of Antenna Gain for real antennas: 2 4 ˆ . , , r P r t r S G π φ θ r r = ( ) 2 4 ˆ . , , r P r t r S G rad r r = NOT: The Antenna Efficiency η rad is defined as: + = = diss rad rad rad rad R R R P P () ( ) rad d d G ππ 4 sin , 2 00 = ∫∫ P = P inc ref P = P inc ref
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3 ECE 303 – Fall 2006 – Farhan Rana – Cornell University Z o P P rad P rad P rad P rad Transmitting and Receiving Antenna Systems Z o P out Need to determine the following: i) From the net power P going to the antenna how much is the total radiated power P rad ii) From the total radiated power how much power is coupled into the receiving antenna iii) From the total power coupled into the receiving antenna how much ends up as the useful power P out in the receiving circuit Transmitting antenna Receiving antenna P = P inc -P ref ECE 303 – Fall 2006 – Farhan Rana – Cornell University Transmitting Antennas: Gain and Radiated Power Z o P x z θ P
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lecture32 - Lecture 32 Circuit Properties of Antennas In...

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