INTRODUCTION TO REAL ARRAYS

Transcription

1 Aerospace Radar - Lesson 2a: INTRODUCTION TO REAL ARRAYS Hon.-Prof. Dr.-Ing. Joachim Ender Head of Fraunhoferinstitut für Hochfrequenzphysik and Radartechnik FHR Neuenahrer Str. 20, Wachtberg joachim.ender@fhr.fraunhofer.de

2 Phased array principle - 2 -

3 Phased array principle - 3 -

4 Mammut - the first phased array Germany 1942 Four Antennas Mechanical phase shifters - 4 -

5 Modern Phased Arrays COBRA DANE PAMIR - 5 -

6 Traveling distances for an impinging wave Phase front x m cos x m x - 6 -

7 DOA vector The vector received at the elements of a linear array with element positions x m : is called direction of arrival vector (DOA vector): Directional cosine Wave number - 7 -

8 Beamformer If z is the output of an array, the operation y b M z m1 is called beamforming. * * b m z m The vector b is called beamformer. z b 1 * b M * y=b * z To form a beam into direction u 0, the beamformer obtains the highest output power in direction u 0 for constant b 2 (SNR-optimum beamformer) - 8 -

9 Three dimensional array Element positions Unit vector u,v, w are the directional cosines relative to the x,y, z axis DOA vector ( ) - 9 -

10 Characteristics of an array We use a beamformer to direction u 0 A wave comes from direction u Array characteristics (output of the beamformer as a function of ) Single element characteristics Beamformer DOA vector Array factor

11 Array factor The characteristics of an array antenna with identical identically orientated single elements is the product of the array factor with the single element characteristics. We use the normalization factor d 1 jk u, x jk u, x1 ( u) e M r,, e r M t Array factor

12 The array characteristics as spatial Fourier transform Remember: Write the sum as integral: Element distribution function The array factor is the Fourier transform of the spatial element distribution

13 The array factor of an equi-spaced linear array Element positions Array factor M 1 F( u, u0) exp M m1 jk r u u 0 mx Phase increments Dirichlet-function

14 The array factor of an equi-spaced linear array The array factor is the sum of vector elements in the Gaussian plane. Since the phase is linearly growing, the end points lie on a circle. The magnitude is the distance of the resulting vector to the origin. Magnitude = 0 for one ore more closed circles. Im Re u

15 Resolution and beamwidth First zero at u=u 0 +du The beamwidth of an SNR-optimum focused linear antenna array in the directional cosine domain is given by l / l x

16 Ambiguities for an equi-spaced linear array The DOA vector exp jk rux 1 d( u) M exp jk umx r is periodical with the period u determined by k r ( u u) x k ux 2 r k r ux 2 2 ux 2 l ux l l u 2x From this follows that also the optimum beamformer and the array factor are periodical with this period

17 Ambiguity of the array factor, secondary main lobes

18 Ambiguity of the array factor, secondary main lobes Remember: u l 2x

19 Ambiguity of the array factor, secondary main lobes To avoid secondary main beams, the spatial sampling interval of a linear array has to be smaller or equal to the half wavelength, if the whole visibility area shall be scanned, and equal or smaller to l / (1 + u max ), if only the interval [-u max, u max ] has to be covered. For an infinite linear aperture, the spatial sampling interval has to be smaller or equal to l/2 to reconstruct the complex amplitudes of the impinging waves unambiguously

20 Secondary mainbeams for a planar array (rectangular grid)

21 Secondary mainbeams for a planar array (triangular grid)

22 Standard design of a phased array system Antenna Elements T/R-Modules Manifold A /D A /D A /D g* g* A /D A /D A /D g* Receivers A/D Conversion g* g* g* Algorithms Processor Steering Interface Information processing

23 Transmit-receive module T/R switch Low noise amplifier LNA T/R switch High power amplifier HPA Tunable Attenuator Phase shifter Digital Interface

24 Transmit-receive module Limiter LNA Rx Phase shifter Pol switch Balanced HPA Tx Amplifiers Tx Phase shifter A T/R module constructed at Fraunhofer FHR