ERROR ESTIMATIONS IN CYLINDRICAL NEAR FIELD SYSTEM FOR LARGE RADAR ANTENNAS S. Bugos (), F. Matín (), M. Siea-Castañe () and J.L.Besada () () Gupo de Radiación. Dpto. de Señales, Sistemas y Radiocomunicaciones. Univ. Politécnica de Madid. E.T.S.I. de Telecomunicación. Ciudad Univesitaia. 8040 Madid. Spain Tel.. +3493367366 ext. 4053 Fax.. +34954300 Email:saab@g.ss.upm.es, fmatin@g.ss.upm.es, m.siea.castane@g.ss.upm.es, besada@g.ss.upm.es ABSTRACT Cylindical nea field systems ae appopiate measuement systems fo huge L-band RADAR antennas, because the antenna can be measued on its aimuthal positione and the pobe can be easily tanslated though a vetical linea slide. So fo lage antennas the mechanical aspects of the antenna measuement systems ae impotant and the eos in this mechanical pat can affect to the fa field adiation patten. This pape pesents an eo estimation tool to analye the most impotant eos in one cylindical acquisition system and the effect of these eos in the calculation of the fa field adiation patten. This study has been pefomed to impove the cylindical system and to evaluate the eo budget of the Antenna Unde Test (AUT). The simulato calculates the fa field fom an aay of dipoles ove a gound plane (Antenna Unde Test model) and compaes the ideal esult with the electic field obtained using the cylindical nea to fa field tansfomation algoithms. The esults achieved ae the vaiation in the pincipal pattens of the fa field, RMS eos in side lobes and imum eos in side lobes. Random and deteministic souce of eos have been consideed.. INTRODUCTION Lage antennas need special measuement system. This pape pesents a measuement system fo lage L- band RADAR antennas. These antennas have the possibility of opeating with a sum o a diffeence patten. The imum length of the aay antennas (up to metes) equies an especially long antenna measuement system. The designed system is a cylindical nea field ange, whee the RADAR antennas otates on its own positione, and the pobe (double-polaied pobe) moves along a 5.5 metes linea slide, stopping in each of the defined position to acquie the nea field. Besides, the antenna can wok in eception and tansmission. To ealie how big the measuement system has to be, the following pictue (Fig.) epesents one possible Antenna Unde Test to evaluate. The acquied field is then pocessed, employing cylindical nea to fa field tansfomation techniques, to obtain the fa field adiation patten and the gain. Aftewads a post pocessing is pefomed to ecove the adiation patten main paametes. This pape is focused on the evaluation of the main eos that affect the adiation patten. The eos ae due to mechanical misalignment of the system, to phase eos caused by tempeatue vaiations and eos due to the S/N in the eceive. Figue. Example of an Antenna Unde Test This pape is divided in following pats. Fist, section descibes the main chaacteistics and specifications of the measuement system. Afte that, section 3 explains the cylindical nea to fa field tansfomation softwae. Next, section 4 validates the method applied. Aftewad, section 5 exposes the main souce of eos to analye and the solutions implemented to educe them. Then, section 6 comments the eo simulato designed and the esults. And finally, section 7 mentions the conclusions. Poc. EuCAP 006, Nice, Fance 6 0 Novembe 006 (ESA SP-66, Octobe 006)
. MAIN SPECIFICATIONS OF THE MEASUREMENT SYSTEM The main specifications of the measuement system evaluated ae: Maximum sie of the Antenna unde Test (AUT): length = metes and height = 7.5 metes. Fequency ange: L band, 5 400 MH. Maximum length of the linea slide: 5.5 metes. Distance fom AUT to Pobe: between 4 and 7 metes. Aimuth angula ange: 0º φ 360º. Elevation angula ange: depends on geomety of the system and antenna. Antenna unde Test: aays of dipoles with unifom, Taylo o Bailyss amplitude distibution in both vetical and hoiontal planes, and diffeent in eception o tansmission pefomance. Minimum Rotation velocity of the AUT (velocity fo measuement pocess): 5 7.5 pm. Measuement eos: o Maximum eo in gain: ± 0.5 db. o Eo at 30 db SLL: ± db. o Eo at 40 db SLL: ± 3 db. o Pointing eo: ± 0.05º in both aimuth and elevation planes. The system has been designed to assue the pevious eos in the fequency band, and this study analyses the effect of the pevious eos in final esults of the adiation patten. This fist analysis has been pefomed consideing a theoetical antenna (Antenna Unde Test and pobe), whose main chaacteistics ae: - Length:.5 metes (4 columns). - Height:.08 metes (6 ows). - Radiating element: vetical λ/ dipole ove a gound plane. - Columns excitation: unifom in amplitude and phase. - Rows excitation: tapeed in amplitude and unifom in phase. - Distance fom antenna to pobe: 4 metes. - Pobe: ideal hon cos 3 θ, which can pefom a polaiation otation on its positione. - Length of the vetical slide: 5.5 metes. - Fequency: 5 MH. - Cylindical Nea field acquisition: 8 angula positions and 5 vetical positions (samples sepaated.5 cm ( λ/). In the following figues, a pactical (Fig.) illustation of the studied system is epesented: Pobe polaisations (90º otation) Vetical movement A.U.T. Aimuthal otation Figue.Pactical illustation of the system 3. CYLINDRICAL NEAR FIELD TO FAR FIELD TRANSFORMATION The method employed to detemine the antenna fa field patten fom pobe compensated nea field data measued ove the suface of a cylinde enclosing the antenna is based on the scatteing matix fomulation [], [3], whee diffeent types of scatteing matices can be used to deive the coupling equation. The matices ae used to elate the amplitudes of waveguide modes to expansion coefficients by linea matix tansfomations. These matices can be taken as definitions o deived fom Maxwell s equations. In ode to pefom a pecise measuement, it has to be consideed that the pobe employed to measue has an impact on the samples etieved. Theefoe, a pobe coection has to be caied out, so as to compensate this undesied side-effect. In any case, this adjustment can be pefomed, only once the complex amplitude weighting functions - in the cylindical wave expansion of the field adiated by the pobe - ae known. Futhemoe, these functions can be calculated fom the measued amplitude and phase of the fa field adiated by the pobe.
The nea to fa field convesion algoithm is epesented in the following diagam (Fig.3) [], [3], [4], [5], [6], [7], [8], [0] : AUT cylindical nea field acquisition AUT coupling poducts calculation [Bucci] Main Cuts of the pobe acquisition Reconstuction of the complete field of two pobes [Hansen] Pobe modal coefficients computation [Yaghjian] 4. METHOD VALIDATION In ode to validate this fomulation, a compaison between the theoetical fa field and the fa field obtained afte pocessing an ideal cylindical acquisition has been pefomed, as it is illustated in the next gaph (Fig.4): IDEAL Acquisition Nea To Fa Field TRANSFORMATION (with pobe coection) THEORETICAL FIELD: Aay Facto Dipole adiation patten in the main planes AUT modal coefficients with pobe coection estimation [Leach] Fa Field Radiation Patten Fa Field Radiation Patten AUT Fa Field evaluation [Leach] Results stoage Figue 3. Nea to fa field tansfomation algoithm So, the tansfomation pocess is divided in the following steps:. Fist, the AUT cylindical nea field is acquied and sampled.. Then, the AUT coupling poducts ae calculated: T(n,h), whee n is the numbe of modes and h is equal to k cos θ (k = π/λ). They ae calculated though a FFT in aimuthal dimension and a DFT in vetical ange (values fo a egula gid in θ angles ae obtained in the valid angula ange). 3. Afte that, the econstuction of the complete field of two othogonal linea polaied pobes, using the main cuts of the pobe, is completed. The pobes satisfy µ=±. 4. The next thing to do is the computation of the pobe modal coefficients: c (n,h), c (n,h), d (n,h), d (n,h) though an invese FFT. 5. Aftewads, with the AUT coupling poducts and the pobe coection coefficients, the AUT modal coefficients with pobe coection can be detemined: a(n,h), b(n,h). 6. Finally, the fa-field of the AUT is established, nomalied and stoed: E θ (, φ, θ), E φ (, φ, θ): k sin θ e Eφ (, φ, ) = k sin θ e Eθ (, φ, ) = jk jk n n = n n n= n n j a( n, k cos θ ) e j n+ b( n, k cos θ ) e jnφ jnφ () () 7. Once the AUT fa-field is known, the paametes of the AUT (adiated powe, diectivity, beamwidth ) can be deduced. COMPARISON Figue 4. Validation Diagam The theoetical fa field has been calculated multiplying the aay facto by the λ/ dipole adiation patten. On the othe hand, the ideal acquisition has been pefomed on a cylinde whose adius is 4 metes and whose geneatix is 5.5 metes. Besides, the eceived field in each point of the gid has been calculated, consideing the field adiated by all the dipoles modified by the pobe patten. The field fom each dipole in a point of the gid is given by the sum of 3 plane waves modified by the pobe adiation patten in the appopiate diection [9]: E = I mn e R jkr jkr jk e e f ( θ ) + f ( θ ) cos(kl ) f ( θ) (3) s R x whee the angles and distances ae shown in Fig.5, and f s is the adiation patten of the pobe: I( ) DIPOL E d = L R R θ d = -L θ θ s PROBE: P (x, y, ) Figue 5. Geomety of the dipole and pobe x
Besides, as the paamete L is equal to λ/4 (half wavelength dipole), theefoe the expession of the adiated field is simplified (4), and the pobe adiation patten is cos 3 θ: E = I mn e R jkr cos 3 e θ + R jkr cos 3 θ (4) Futhemoe, in ode to make the calculation of the field easie, the Image Theoy is applied to the paallel dipoles aay of the AUT. Fig. 6 and Fig. 7 epesent the compaison in the main planes between the theoetical fa field and the fa field obtained in two steps: fist afte an ideal acquisition and then a cylindical nea to fa field tansfomation. Figue 6.Compaison of theoetical fa field and ideal tansfomed fa field. Hoiontal plane Figue 7. Compaison of theoetical fa field and ideal tansfomed fa field. Vetical plane The slight eo obseved in the vetical plane is due to the fact that the numbe of samples evaluated in the vetical axis, -axis of the pobe, is finite. 5. SOURCES OF ERRORS ANALYSIS The main eos that affect to a nea field measuement ange ae summaied in [0],[], []. The most impotant eo souces fo ou case of study (outdoo facility) ae: - RF Measuement system: Dynamic ange and andom amplitude and phase. - Positioning system: mechanical positioning and pobe oientation/otation. - Nea field pobe: mechanical alignment and scatteing coss section. - Envionmental: Tempeatue, tempeatue spatial gadient, electomagnetic intefeence and eflections. - Measuement pocedue: limited measuement aea, sample point spacing, sampling time ate and Pobe/AUT sepaation (multiple eflections). - Computational: algoithm appoximations. In section 4 the computational eos and the eos due to limited measuement aea and sample point spacing ae obseved in the compaison between the theoetical fa field and the ideal tansfomation fom nea to fa field. These eos ae negligible in the hoiontal plane. Howeve, in vetical plane some eos ae obseved in the exteme angles. This pape analyses the eos in the beamwidth, diectivity, SLL and pointing diection fo the souces of eos shown in Tab. (notice that thee ae some impotant eos as the eflections that ae not analysed). The type of eo is R (andom) o D (deteministic). The 3 last columns show the methods employed to evaluate the eos: NO means that the eo is not impotant, Theo indicates that the effect of the eo can be estimated theoetically and Sim denotes the effect of the eo is evaluated by simulation. Souce of eos Type Pointing SLL BW Axes paallelism D Theo NO NO Eo in aimuthal oigin D Theo NO NO Positioning eos in x/y R Sim Sim Sim Positioning eos in R Sim Sim Sim Tempeatue vaiations D/R Sim Sim Sim S/N of the eceive R NO Sim NO Random amplitude and phase R Sim Sim Sim Table. Souces of eos and Method of evaluation The axes paallelism (of AUT and pobe towe) and the eos in the eo position of the aimuthal diection with espect to the AUT can be measued by optical pocedues (lase tacke ). The adiation pattens can be coected once these deteministic eos ae evaluated.
The positioning eos in x and y diection can be vey impotant because of the windy outdoo conditions. Theefoe, an analog sevo have been designed to educe these eos. A lase impinges on a quadant detecto and two signals (one fo each diection) ae obtained. These two signals excite both PLC that contol the x and y positions of the pobe (installed ove a xy double slide). The esidual eos in these diections ae estimated in ± mm. The effect of these eos ae evaluated though simulations. The positioning eos in diection ae due to themal expansions and positioning eos (encode, PLC ). These eos ae estimated in ± 0.5 mm. 6. ERROR SIMULATOR The simulation pocess pefomed can be epesented in the following diagam (Fig.9): IDEAL Acquisition CNIFT (Nea-To-Fa Field Tansfomation) Fa field Radiation Patten COMPARISON Acquisition with ERRORS CNIFT (Nea-To-Fa Field Tansfomation) Fa field Radiation Patten Vaiation in the Z pobe axis Vaiation in the X pobe axis Pobe y Figue 9. Diagam of the simulation pocess Fom all the scenaios studied we epesent the most elevant ones. Fist, Fig. 0 and Fig. shows the effect of a vaiation in x position of the pobe in vetical and hoiontal planes. Then, Fig. epesents the eo in y position in the vetical plane and finally, Fig. 3 and Fig. 4 illustate the eo in amplitude and phase in the hoiontal and vetical plane. Vaiation in the Y pobe axis x. Case : Random Eo in Xpobe (3 iteations, σ=±mm). Figue 8. Positioning eos studied The tempeatue vaiations duing a measuement (aound 90 minutes) can be estimated in 0ºC. This shift can poduce up to 8 degees in the vaiation of the phase. The system cannot suppot this high deviation, so it must be ectified. The coection pocedue consists in measuing seveal times the same position (cental position) duing the acquisition, obtain the vaiation (a complex facto) due to tempeatue changes in the 5 times, and intepolate this coection facto fo all the times. Each acquied value is coected with this tem. With this coection the eo is estimated in ± deg. Figue 0. Random eo in Xpobe, Hoiontal plane. The S/N in the eceive is evaluated fo the effect on the lobe Side levels. The effect is accomplished adding a andom noise to each value of the acquied field. Fo the estimations, a dynamic ange in the imum equal to 75 db (theoetical value) is consideed. This eo cannot be coected. Othe possible eos consist in including a andom amplitude and phase in each point. A andom value equal to ± 0. db in amplitude and ± 3 degees in phase is consideed in the eo calculations. Figue. Random eo in Xpobe, Vetical plane.
. Case : Random Eo in Ypobe (3 iteations, σ=±mm). Figue. Random eo in Ypobe, Vetical plane. 3. Case 3: Random Eo in Amplitude and Phase (3 iteations, σ=±0.db and σ=±3º). Futhemoe, a detailed analysis of the main souce of eos in this outdoo ange has been pefomed, and some eos have been coected using some algoithms o optical systems (based on a lase, a quadant detecto and an analogue sevo). Fo othe souces of eos a Montecalo simulato is pepaed, and the fist simulations ae caied out. The pimay analysis of the esults show that the main souces of eos ae due to x vaiation in the position of the pobe (bigge effect than y o vaiation) and the eos in amplitude and phase (andom noise added to the signal). This study is going to be completed with a lage numbe of simulations, including the diffeent eos, and the esults will be pesented in the symposium. These esults will show a quantified eo on diffeent paametes: beamwidth, SLL, diectivity and pointing diection. ACKNOWLEDGEMENT The authos want to acknowledge the suppot fom INDRA Sistemas fo the development of this wok. REFERENCES Figue 3. Random eo in Amplitude and Phase, Hoiontal plane. Figue 4 Random eo in Amplitude and Phase, Vetical plane.. 7. CONCLUSION A cylindical nea to fa field tansfomation softwae fo a L-band RADAR antenna measuement system has been implemented and evaluated though simulations. [] Jøgen Appel Hansen, On Cylindical Nea-Field Scanning Techniques, IEEE Tansactions on Antennas and Popagation, Vol. AP-8, No., pp. 3-34, Mach 980. [] W. Mashall Leach, J. and Demetius T. Pais, Pobe Compensated Nea Field Measuements on a Cylinde, IEEE Tansactions on Antennas and Popagation, Vol. AP-, No. 4, pp. 435-445, July 973. [3] Athu D. Yaghjian, An Oveview of Nea-Field Antenna Measuements, IEEE Tansactions on Antennas and Popagation, Vol. AP-34, No., pp. 30-45, Januay 986. [4] J. J. Seano Bemejo, Softwae paa la convesion de campo póximo cilíndico a campo lejano incluyendo coección de sonda. Maste Thesis. Septembe 003. [5] W. Rudge, K. Milne, A.D. Olve and P. Knight, The Handbook of Antenna Design, Vol, 98, pp. 609-64. [6] Alan V. Oppenheim, Alan S. Willsky with Ian T. Young, Signals and Systems, Ed. Pentice-Hall Intenational Editions. [7] O. M. Bucci, Use of Sampling Expansions in Nea-Field-Fa- Field Tansfomations: The Cylindical Case, IEEE Tansactions on Antennas and Popagation, Vol. 36, No. 6, pp. 830-835, June 988. [8] Z. A. Hussein, Y. Rahmat-Samii, Pobe Compensation Chaacteiation in Cylindical Nea-Field Scanning, IEEE, pp. 808-8, 993. [9] Robet S. Elliot, Antenna Theoy and Design, Ed. Pentice- Hall, Inc., Englewood Cliffs, New Jesey. [0] Jøgen Appel Hansen, Spheical Nea-Field Antenna Measuements, Edited by J. E. Hansen and published by Pete Peeginus Ltd., on behalf of IEE, London, United Kingdom, 988. [] Edwad B. Joy, Nea-Field Rang Qualification Methodology, IEEE Tansactions on Antennas and Popagation, Vol. 36, No. 6, pp. 836-844, June 988. [] A.C. Newell, Eo Analysis Techniques fo Plana Nea Field Measuements, IEEE Tansactions on Antennas and Popagation, Vol. 36, No. 6, pp. 754-768, June 988.