Inter Modulation in Active Array Receive Antennas

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Intermodulation in Active Array Receive Antennas

Klaus Solbach,Universitt Duisburg, Hochfrequenztechnik, 47048 Duisburg, Tel. 0203-379-3286,

Fax -3498, Email: [email protected]

Markus Bck,Antenna Technology ASE 71,European Aeronautic Defence and Space Company

89070 Ulm, Tel. 0731-392-5650, Fax -5810E-Mail: [email protected]

I. Introduction

Large signals incident to the RF amplifier of a Radar receiver have been known to produceseveral deliterious effects, like compression of wanted signals, production of crossmodulations and harmonics and most problematic, the production of intermodulationsignals. Intermodulation responses (third-order-products), in particular, can appear as falsetargets in the Radar signal processor, and thus degrade the Radar performance considerably.Such large signals may come from several sources, among them ground clutter, large targets,near-in targets and interfering radar systems and jammers. Modern solid state Radar systemsare more prone to the appearance of large-signal effects from clutter returns etc., due to theuse of relatively long pulses ( with overlapping of pulses from, e.g., clutter and targets)compared to high-peak power/ low-duty cycle and short-pulse tube systems. With the adventof active array technology in Radar antennas the additional problem appears of a multitude of RF amplifiers distributed across the array as compared with a single amplifier behind apassive antenna, Fig.1.Several questions arise from this situation: What are the effects of a low gain and wide

beamwidth element pattern compared to the high gain and narrow beam antenna pattern afterbeam forming in conventional array systems and what are the effects of the beam formingnetwork behind the amplifiers on the generated spurious signals? At a fist glance, it seemsobvious that the conventional system performs better due to the spatial filtering afforded bythe antenna directivity pattern in front of the receiver and because of coherent combination of spurious signals in the combiner network of the active array. In the literature, active arrayversus passive array system aspects have been limited to Gain, ERP and G/T-figures, e.g. /1/,and large-signal intermodulation effects have been inspected for transmit active arrayantennas /2/. In /3/, the problem of spectral spreading of clutter responses due to third orderintermodulation effects is discussed for active array Radar systems, however, assumptionsconcerning the beam former signal combining are over-pessimistic and no comparison is

made between conventional and active array system.

II. Array Model

The investigation of above questions starts from a simple model of a two-element array, withdistributed amplification (active array), Fig.2. Two waves are assumed incident to the antennafrom different directions and at different frequencies, producing phase increments of and

of the received signals due to the spacing d of the elements. The amplifiers nonlinearity of the output / input relation is represented as a power series, which is truncated after the thirdorder term. The beam forming network is assumed to perform ideal power combinationwithout frequency dependence. A description both by algebraic equation is used and by the

resulting antenna directivity pattern, which relates the angles of incidence (and thus the phaseincrements between the element signals) to the sum signal level at the output port.


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II.1 Array Directivity

Considering the plane wave signals incident to the two antenna elements, it is found that thetwo signals are combined in the beam forming network corresponding to their angle of incidence, i.e. corresponding to the phase increment between the elements; this means that the

array directivity pattern may introduce different gains in the directions of the signals, as iswell known from array theory. This result is no longer true for the third-order-products, theintermodulation signals, which are generated in the distributed amplifiers in front of the beamforming network: Here, the third order means the third power of the sum of the two signals ateach amplifier with the well known creation of new frequencies (2 21 ) and (2 12 ).However, the complete arguments incorporate also the phase increments of the constituentsignals, so that new increments 2 and 2 are created. Thus, the third-order sumsignals after the beam forming network are attenuated as if received from totally differentdirections than the original signal directions. In other words, the beam forming network provides power combining also of the intermodulation signals, yet with different gain thaneffective for the received signals, depending on angles of incidence.

II.2 Intermodulation Ratio

The second major result concerns the resulting linear signal and intermodulation signalstrengths for the worst case of broadside incidence for both signals ( 0== ):All signals behind the amplifiers are combined with the broadside directivity factor, since allphase increments are zero (two equal signals combine with a factor of 2 ). Assumingidentical amplifiers and equal amplitudes of both incident waves, A=B , it can be shown thatthe ratio of intermodulation signal amplitude and original signal amplitude is independent of the number of elements

IM 3(active) = 1

23

1

33

43

4232

a Aa

Aa Aa = . (1)

The passive 2-element array with a single amplifier for the sum-signal (increased by a factorof 2 ) would produce

IM 3(passive) =1

23

33

43

224

)2(3a Aa

Aa

Aa= , (2)

while for an array of N -elements the factor of 2 is replaced by the array directivity D=N, sothat:

IM 3(active) / IM 3(passive) = N = (20logN) dB (3)

It is clear from these results that the active array has an advantage over the passive arraysystem with respect to the third-order intermodulation ratio, which improves as N , the numberof elements / array directivity, e.g. by 10 dB for a 10-element array or 30 dB for a 1000-element array. Note that the same improvement could only be achieved by inserting anattenuator of power loss equal to N in front of the amplifier in the passive array system, e.g. a10 dB-attenuator for a 10-element array!Keeping in mind that the noise level in both active and passive array variants will be thesame, e.g. /1/ and /4/, the advantage of the active array architecture vs. passive arrayarchitecture extends equally to the spurious free dynamic range (SFDR).

III. Experiment


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Both above results were demonstrated in an experiment using power dividers/combiners tosimulate radiator elements and feeding signals from two RF sources to simulate incidentwaves. In order to afford a good match and tracking of all components and to allow the lossesin the cables and in the power dividers/combiners to be negligible, the experiment was carriedout at a frequency of 1 GHz. Wilkinson power dividers were used for power division,

combining and beam forming and amplifiers based on the MiniCircuits series GAL wereused.Fig.3(a) shows the setup representing a passive 2-element array with two waves incident frombroadside and a single amplifier following the beam former-combiner. Amplitudes of linearand intermodulation components were measured using a spectrum analyzer.The active array representation is shown in Fig.3(b), where the sequence of beam former andamplifier is reversed with respect to Fig.3(a) and we use an extra amplifier which is adjustedto track the intermodulation level of the first amplifier to an accuracy better than 1 dB.Comparing the measured signal levels of both setups we find the IM-ratio of the active arraymodel superior by about 6.5 dB. Since eq.(3) expected 6 dB improvement, this result providessatisfactory proof, considering the nonideal tracking of the two amplifiers.A third setup, Fig.3(c), was used to test the dependence of the intermodulation products w.r.t.the angle of incidence of the waves. In the measurement setup, the signal of frequency f 1 isdistributed to the two antenna ports in-phase ( =0), while the second signal of frequency f 2 issplit using one variable length cable, producing a phase shift between the two antennaports for this signal. From the observation of the two signals at the output of the active arraymodel we find that the level of the first signal ( f 1) does not vary with while the secondsignal ( f

2) is attenuated as a function of its phase shift. In Fig. 4, bold symbols are entered formeasured relative amplitudes of this signal as a function of phase shifts of 90, -45, 45,and 90, with 0 as a reference. It is seen that the attenuation is in approximate agreementwith the beam former response (antenna pattern) which can be described by the cos( /2)-function. In each case the two intermodulation products at frequencies below and above thetwo principal carriers are also observed. Normalized levels of these products are entered intothe diagram above their respective phase angles of 2 and - . Again, the measured data fitapproximately the beam former response; this result clearly demonstrates that theintermodulation products in an active array behave like signals incident from different anglescompared to the actual signals.

IV. Conclusion

As a consequence of both above mentioned results, for most practical situations encounteredin Radar system operation the active array antenna will not degrade the large signal handling

of the system but, rather, it allows the use of amplifier circuits of inferior linearity, which cansave power consumption and circuit complexity / cost.

Literature /1/ Kraft, U.R., Gain and G/T of Multielement Receive Antennas with Active Beamforming Networks, IEEETrans. AP, vol.48, no.12, Dec.2000, 1818-1829

/2/ W.A. Sandrin,Spatial Distribution of Intermodulation Products in Active Phased Array Antennas, IEEETrans. AP, Nov. 1973, 864-867

/3/ K.M.Harrington, Active Array Radar Nonlinearity Requirements-Spectral Analysis of Third OrderIntermodulation Clutter, 1996 IEEE Intern.Symp. on Phased Array Systems and Technology,15-18 October1996, Boston, Massachusetts, ISBN 0-7803-3232-6, 313-317

/4/ Solbach, K., Noise Signal Decorrelation in Broad-Band Active Array Systems, Frequenz, Band 55,Heft 11-12, 2001, 317-322


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RadiatorArray

Beam FormingNetworkB F N

B F NAmplifier

Fig. 1 Principle concept of (a) passive array with single amplifier after beam forming and(b) active array with receive-amplification before beam forming

Uniform Plane Wave

Isotropic Radiator Elements

Phase Increments:

Amplifier

B F N

d

D

D

max D D

1

0-90 90

0

( )t y2 ( )t y1

{ } ( )t Aa 1cosRe =

{ } ( )t Bb 2cosRe =

{ }( )t x

ebea

2

j jRe

=

+

{ }( )t x

ba

1

Re

=

+

( ) ( ) ( ) ( )t xat xat xaat y 332210 +++=

sin2

= d

sin2

= d

( ) ( ) ( )( )t yt yt s 2121

+=

AntennaPattern

Fig. 2 Two-element antenna concept of an active array

(a)


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(b)

(c)

Fig. 3 Measurement setup to model 2-element array(a) passive array with broadside incident waves(b) active array with broadside incident waves(c) active array with one wave incident from broadside and one tilted incident wave

Fig. 4 Measured response of linear and intermodulation signals in active array model withtwo incident signals as a function of phase shift

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Inter Modulation in Active Array Receive Antennas