NNLecture23

# NNLecture23 - ECE 454 Antennas Lecture 23 Antenna Impedance...

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Created by Per-Simon Kildal, November 1999 ECE 454 Antennas Lecture 23 Antenna Impedance, Efficiency, and Fields Eric Michielssen www.ece.uiuc.edu/ece454

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Created by Per-Simon Kildal, November 1999 8. Reflector Antennas Applications: Radio astronomy, radar, communications For pencil beams, multiple beams, contoured beams Terms: Main reflector, subreflector, focal point, feed
Created by Per-Simon Kildal, November 1999 Reflector antennas: Content General theory (illustrated for arbitrary single metal reflector) Geometrical optics (GO) PO integration aperture integration Paraboloidal reflector Cassegrain antenna

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Created by Per-Simon Kildal, November 1999 Feed and arbitrary reflector with their coordinate systems.
Created by Per-Simon Kildal, November 1999

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Created by Per-Simon Kildal, November 1999 General description of reflector Reflector description: r s u v x s u v x ˆ y s u v y ˆ z s u v z ˆ + + = Example: Rotationally symmetric reflector: r s   x ˆ cos y ˆ sin z z ˆ for 0 D 2 + + = Two tangent vectors: t u u r s u v x ˆ u x s u v y ˆ u y s u v z ˆ u z s u v + + = = t v v r s u v x ˆ v x s u v y ˆ v y s u v z ˆ v z s u v + + = = Surface normal: n ˆ t u t v t u t v = Check direction!
Created by Per-Simon Kildal, November 1999

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Created by Per-Simon Kildal, November 1999 Incident field on reflector Radiation field of the feed E f r   1 r f ---e jkr f G f r ˆ f = r f is phase reference point. The incident field on the reflector is E i r s E f r s = r f r s u v r f = r ˆ f r s u v r f r f = The incident H-field H i 1 --- r ˆ f E i =
Created by Per-Simon Kildal, November 1999 GO reflection Geometrical optics (GO) is asymptotically correct for large frequencies. Propagation along straight rays. Incident field is spherical wave, i.e. field propagating along a GO ray defined by: r s   r f s s ˆ i ; + = s ˆ i r ˆ f = Reflection law in vector form: s ˆ r s ˆ i 2 n ˆ s ˆ i n ˆ = Corresponds to: n ˆ s ˆ r n ˆ s ˆ i = r cos i cos = r i =

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Created by Per-Simon Kildal, November 1999
Created by Per-Simon Kildal, November 1999

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Created by Per-Simon Kildal, November 1999 Reflected GO field Reflected E-field: (orthogonal to s ˆ r E tot n ˆ 0 = & gives) E r E i 2 E i n ˆ n ˆ + = Reflected H-field: H r H i 2 H i n ˆ n ˆ 1 --- s ˆ r E r = = Reflected ray: r s   r s u r v r s s ˆ r + =
Created by Per-Simon Kildal, November 1999 General GO transmission formula will not be needed in this

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## This note was uploaded on 04/11/2010 for the course EECS 531 taught by Professor Staff during the Winter '08 term at University of Michigan.

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NNLecture23 - ECE 454 Antennas Lecture 23 Antenna Impedance...

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