lecture33 - Lecture 33 Antenna Arrays and Phase Arrays In...

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1 ECE 303 – Fall 2007 – Farhan Rana – Cornell University Lecture 33 Antenna Arrays and Phase Arrays In this lecture you will learn: • Antenna arrays • Gain and radiation pattern for antenna arrays • Antenna beam steering with phase array antennas ECE 303 – Fall 2007 – Farhan Rana – Cornell University Two Hertzian Dipoles – A Two Element Array y z ( ) ( ) 0 3 0 0 ˆ h r d I z r J r r r r = δ x 0 h r 1 h r 0 J r 1 J r ( ) ( ) 1 3 1 1 ˆ h r d I z r J r r r r = δ ( ) ( ) [ ] ( ) ( ) ( ) φ θ φ θ θ π η θ θ π η θ , , , sin 4 ˆ sin 4 ˆ 1 0 1 0 . ˆ 0 1 . ˆ 0 0 0 . ˆ 1 . ˆ 0 F r e I I e I I e r d I k j e I e I e r kd j r E h r k j h r k j r k j o h r k j h r k j r k j o ff Ε = + = + = r r r r r r r One can write the E-field in the far-field as a superposition of the E-fields produced by all the elements in the array: Consider first an array of just two Hertzian dipoles: Element Factor Array Factor Each antenna in the array is an “element” of the array • The “element factor” is just the E-field produced by the first element if it were sitting at the origin • The “array factor” captures all the interference effects
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2 ECE 303 – Fall 2007 – Farhan Rana – Cornell University An N-Element Antenna Array - I Consider an N-element antenna array where the elements are: - all identical (all loops, or all Hertzian dipoles, or all Half-wave dipoles, etc) - all oriented in the same way - but with possibly different current phasors Let the current phasor of the m -th antenna be I m Let the position vector of the m -th antenna be m h r y x m h r z m I 0 I 1 I 1 N I z One can write the E-field in the far-field as a superposition of the E-fields produced by all the elements in the array: ( ) ( ) ( ) ( ) φ θ φ θ φ θ , , , , , 1 0 . ˆ 0 F r e I I r r E N m h r k j m ff m Ε = Ε = = r r r r r ECE 303 – Fall 2007 – Farhan Rana – Cornell University An N-Element Antenna Array - II ( ) ( ) ( ) ( ) φ θ φ θ , , , 1 0 .
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