THE ALIGNMENT OF A SPHERICAL NEAR-FIELD ROTATOR USING ELECTRICAL MEASUREMENTS

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1 THE ALIGNMENT OF A SPHERICAL NEAR-FIELD ROTATOR USING ELECTRICAL MEASUREMENTS ABSTRACT Th mchanical rotator mut b corrctly alignd and th prob placd in th propr location whn prforming phrical nar-fild maurmnt. Thi alignmnt i uually accomplihd uing optical intrumnt uch a thodolit and autocollimator and idally hould b don with th antnna undr tt mountd on th rotator. In om ca it may b impractical to plac th alignmnt mirror on th AUT or optical intrumnt may not b availabl. In th and othr ca, it i dirabl to chck alignmnt with lctrical maurmnt on th actual AUT and prob. Such tt hav rcntly bn dvlopd and vrifid. Appropriat comparion and analyi of two nar-fild maurmnt that hould b idntical or hav a known diffrnc yild prci maur of om rotator and prob alignmnt rror. Whil th tt ar indpndnt of th AUT pattrn, judiciou choic or placmnt of th antnna can incra th nitivity of th tt. Typical maurmnt will b prntd uing analyi rcntly includd in NSI oftwar. Kyword: Antnna Maurmnt, Nar-Fild, Maurmnt Diagnotic, Rang Calibration, Error. 1. INTRODUCTION Th phrical nar-fild thory rquir that data on th Antnna Undr Tt (AUT) b obtaind at qually pacd point in θ and ϕ on th urfac of a phr that compltly nclo th AUT. Concptually thi i accomplihd by dfining a phr that i fixd to th AUT and moving th prob ovr th urfac of thi phr. Amplitud and pha data ar thn obtaind at qually pacd point on th phr. Sinc it i difficult to contruct a mchanical dvic that will mov th prob and lav th antnna fixd, th canning i uually accomplihd by laving th prob fixd and rotating th antnna and it hypothtical phr with a two-axi rotator. If th rotator i proprly alignd, th prob will dcrib lin of contant θ or ϕ on th phr and corrct data will b obtaind. If th rotator i not corrctly alignd, th radial ditanc will chang a th AUT i Alln C. Nwll, Grg Hindman Narfild Sytm Inc E. 223 rd Strt. Bldg. 524 Caron, CA USA (310) rotatd, and th maurmnt point will not b at qually pacd intrval in θ or ϕ. Th rulting data will not produc corrct rult whn procd through th phrical program. In mot ca, th phrical rotator i alignd uing a combination of mchanical and optical dvic bfor th AUT i mountd for maurmnt. It i aumd th rotator rmain alignd whn th antnna i attachd and maurmnt ar prformd. It would b vry dirabl to hav lctrical maurmnt, i.. tho drivd from th maurd amplitud and pha data, which would vrify th alignmnt of th rotator with th actual AUT in plac. Such maurmnt could alo b ud in plac of th mchanical/optical procdur whn appropriat, and could alo b ud priodically during a maurmnt qunc to nur continud alignmnt. Thi papr dcrib uch lctrical maurmnt that hav rcntly bn dvlopd and ttd at Narfild Sytm Inc. (NSI). 2. DEFINITION OF SPHERICAL ALIGNMENT ERRORS Th variou alignmnt rror that will b conidrd ar hown in Fig 1 and 2, which ar viw in th yz and xz plan of th maurmnt phr. Th ar: 1- Non-orthogonality of th θ and ϕ ax; 2- Y-zro rror; 3- θ-zro rror; 4- X-zro rror; 5- Non intrction of th θ and ϕ ax; 6- Prob axi not paralll to th z-axi. Each of th will b dcribd along with th mthod ud to dtct mialignmnt and mak corrction. 2.1 Non-Orthogonality of θ and ϕ Ax. Th θ-axi i dfind by th axi of rotation of th lowr of two rotator, and i uually alignd to b vrtical.

2 antnna y-axi Thta rotator axi Sphrical y-axi Prob Axi Error, Azimuth Prob Axi Error, Elvation Prob AUT thta/phi axi nonorthogonality rror Prob y-zro rror antnna z-axi and phi axi Maurmnt phr x-zro rror z-axi Sphrical z- axi Thta zro alignmnt rror Azimuth or thta axi of rotation AUT Phi axi of rotation x-axi Figur 1 Y-Z Plan of Sphrical Coordinat Sytm. Thi alignmnt can b accomplihd vry aily by placing a prciion lvl on th rotator and placing him undr on nd to mak it lvl. Th θ rotator i thn rotatd 180 dgr and in gnral th lvl will not rmain lvld. Th upport undr th rotator ar thn adjutd to corrct half of th chang, and th him ar adjutd to corrct th rmaining chang. Thi 180 dgr rotation and adjutmnt ar rpatd for 0/180 a wll a 90/270 poition until th lvl rmain unchangd for all rotation angl. Th θ-axi i thn vrtical. A imilar tchniqu can b ud to align th ϕ-axi to b horizontal. An adjutabl mirror i tmporarily placd on th ϕ-rotator with th normal to th mirror approximatly along th ϕ- axi. Uing an optical autocollimator, and rotating th mirror with th ϕ-rotator, th mirror i adjutd until th normal to th mirror and th ϕ-axi ar coincidnt a indicatd by collimation rmaining contant with ϕ- rotation. Th upport on th towr of th ϕ-axi ar thn adjutd until th mirror axi i horizontal. If an autocollimator i not availabl, th alignmnt can b accomplihd by on of two othr mthod. On mak u of a prciion lvl and a flat prob placd tmporarily on th ϕ-rotator. Th othr u a flat mirror, low-cot lar and watr lvl. Th tchniqu will b dcribd in mor dtail lwhr. Whn th alignmnt ar compltd, th AUT i placd on th ϕ-axi rotator and lctrical tt can bgin. Currntly, th lctrical tt ar not nitiv nough to ditinguih btwn non-orthogonality and y-zro rror. It i ncary to rly on th optical or lvl alignmnt to initially t th orthogonality. Phi rotator 2.2 q-zero AND X-ZERO TESTS AND ALIGNMENT Th maurmnt to dtct th rror, and mot of th othr alignmnt rror conit of two θ-can takn at ϕ = 0 and ϕ = 180. Th 180-can i thn invrtd and compard with th 0-can by calculating th diffrnc in amplitud and pha btwn th two can a hown in Fig. 3 and 4 for a 15 db gain horn at 10.0 GHz. Th amplitud diffrnc and part of th pha diffrnc ar du to th combind x-zro and θ-zro rror. Thi i bcau th antnna i fixd to th ϕ-axi, th pattrn i rotatd about th ϕ-axi for th 180-can, and th poition of th prob rlativ to th antnna i changd. Thi i apparnt in th offt btwn th pattrn in Fig. 3 and 4. Th amplitud diffrnc i givn by, Non-Intrction of thta and phi ax Figur 2 X-Z Plan of Sphrical Coordinat Sytm. da x a = a180 a0 = θ arcin d R, (1) θ

3 5.00 Phi=0, Amp Phi=180 amp Phi =0 Pha Amp Diffrnc Phi = 180 Pha Pha Diffrnc Maurd Amplitud in db Amplitud Diffrnc in db r g D in a h P d r u a M r g D in c n r if D a h P Azimuth Angl in db Figur 3 Maurd Amplitud and Amplitud Diffrnc Showing Effct of θ-zro and X-zro Alignmnt Error. whr a i th maurd amplitud, R th radiu of th maurmnt phr, x and θ th alignmnt rror, and da dθ th lop of th amplitud curv. Th rror can b calculatd from a knowldg of th lop and th diffrnc hown in Fig. 3, howvr inc both curv ar in db, it i air to gu at th rror, mak a chang in th θ-zro tting and thn rpat th tt. It i know that a ngativ lop in th amplitud diffrnc curv impli that th θ-zro rror i alo ngativ, and th ϕ-axi mut b movd in th poitiv dirction. Th θ-zro wa changd by 0.30 dg. to mak th amplitud flat for th data hown in Fig. 3. Thi adjutmnt i gnrally mad firt inc it i th ait to mak, and it lav only th non-intrction rror to produc a diffrnc in th pha curv. 2.3 NON-INTERSECTION OF q AND j AXES Th pha curv obtaind aftr making th abov adjutmnt i hown in Fig. 5 and how that th maximum pha rror ha bn rducd to about 15 dg. a compard to 30 dg. bfor th adjutmnt wa mad. Th rmaining pha diffrnc i du to th non-intrction of th θ and ϕ ax, and th diffrnc curv i givn by, ( θ) ψ = ψ ψ = 720in L 180 0, (2) λ Azimuth Angl in Dgr -4 Figur 4 Maurd Pha and Pha Diffrnc Showing Effct of θ- Zro and X-Zro and Non-Intrction Alignmnt Error. Maurd Pha in Dgr Phi =0 Pha Phi = 180 Pha Pha Diffrnc Azimuth Angl in Dgr Figur 5 Maurd Pha and Pha Diffrnc Showing Effct of Non-Intrction Error Only. whr ψ i th pha diffrnc, L th nonintrction rror, and λ th wavlngth. For th rcivr that u th tim convntion of jω t, th pha will dcra with incraing ditanc btwn th AUT and th prob. For thi tim convntion and th pha diffrnc a dfind in Eq. (2), an offt rror in th +x dirction a hown in Fig. 2 produc a ngativ pha diffrnc lop which xplain th ngativ ign in (2) Pha Diffrnc in Dgr

4 From Fig. 5 and Eq. 2, th non-intrction rror i cm. Th ϕ-axi can b movd with a tranlation tag, or by placing him btwn th ϕ rotator and it mount. Whn thi i don th rulting amplitud and pha diffrnc curv ar hown in Fig. 6. Amplitud Diffrnc in db Amplitud Diffrnc Pha Diffrnc Pha Diffrnc in Dgr It wa notd in Sction 2.1 that th lctrical tt ar not nitiv nough to ditinguih btwn nonorthogonality rror and y-zro rror. Both rror tranlat th prob in y from th ϕ-axi. Th rult i that, in both ca, ϕ-can hown by th dahd lin in Fig. 7, ar not cntrd on th antnna z-axi. By aligning th orthogonality with th optical or mchanical procdur, only th y-zro rror rmain With Error No Error y-axi Azimuth Angl in Dgr Figur 6 Amplitud and Pha Diffrnc Aftr θ-zro and Non-Intrction Alignmnt. x-axi Additional adjutmnt could b mad to improv th alignmnt, but from Fig. 6 it i apparnt that th θ-zro rror i l than 0.04 dg. and th non-intrction i l than 0.01 cm which i adquat for thi antnna/frquncy. 2.4 ALIGNMENT OF PROBE AXIS ALONG THE Z-AXIS It can now b dtrmind if th prob i alignd with it axi coincidnt with th axi of rotation of th polarizr. Th prob i rotatd 180 dg. by th polarizr, and th alignmnt data i r-maurd. If th prob i corrctly alignd, th amplitud and pha diffrnc plot will not chang. If it i not alignd, both curv will how a chang in th lop of th diffrnc curv du to th offt of th prob in th x-dirction. Th offt can b dtrmind ithr from th curv or by moving th prob in x and rpating th maurmnt until th curv i flat again. Th prob can thn b rotatd in azimuth rlativ to th polarizr rotator until no chang i obrvd. Th corrct rotation of th prob in lvation i found with a imilar tt, xcpt that th prob and th AUT ar rotatd 90 dgr about thir ax bfor acquiring alignmnt data. Figur 7 Trac of ϕ-scan in th X-Y Plan du to Non- Orthogonality or Y-Zro Error. Thr ar lctrical tt that can dtct th y-zro alignmnt rror, but for mot antnna who nar-fild pattrn ar fairly ymmtric in th rgion clo to th z- axi, th tt will not dtct mall rror. Thi limitation can b ovrcom by ithr uing an antnna uch a a diffrnc pattrn that ha a complx fild pattrn clo to th z-axi or tmporarily mounting th antnna in an offt poition to produc a complx pattrn. Both approach hav bn trid with good ucc. Th X-band horn wa firt offt by about 2.5 inch from th ϕ-axi o that a it rotatd in ϕ, it dcribd a circl rathr than rotating about it axi. Thi ntially tranlatd th horn along th x- axi of th maurmnt phr, and th iz of th minimum phr wa thrfor incrad. Th pattrn wa thn not ymmtric about th z-axi. 2.5 Y-ZERO ERROR

5 For any non-ymmtric antnna pattrn, thr ar thr diffrnt tt that can b ud to dtct y-zro alignmnt rror. Th firt mak u of th am tt dcribd abov whr θ-can ar takn for ϕ = 0 and 180 dg. Th y-zro rror i indicatd by th fact that th amplitud diffrnc curv do not pa through zro at θ = 0 a hown in Fig. 8 for th offt horn. Th y-zro rror wa in for thi data, and th y-alignmnt wa unchangd from Fig. 3 and 6. Th offt poition of th horn mad th data mor nitiv to thi rror. Amplitud in db 0-20 Phi Scan Polarization Scan 5.00 Phi=0, Amp Phi=180 amp Amp Diffrnc 0.50 Maurd Amplitud in db Azimuth Angl in db Figur 8 Maurd Amplitud and Amplitud Diffrnc Showing Effct of Y-Zro Error. A cond maurmnt alo how th ffct of thi rror. Thi maurmnt compar a ϕ-can takn at θ = 0 whr th antnna i rotatd about th ϕ-axi with a polarization can whr th prob i rotatd about it axi. If thr i no y-zro rror, th two hould produc idntical data. If thr i a y-zro rror, th polarization can will b takn at a point on th maurmnt phr, whil th ϕ-can will dcrib on of th dahd circl hown in Fig. 7. A ampl of thi maurmnt i hown in Fig. 9 for a diffrnc pattrn antnna with a y-zro rror of 0.35 in. Both Fig. 8 and 9 clarly indicat an alignmnt rror, but it i difficult to quantify th rror from th maurd data. Th corrct tting for th y-poition of th prob i found by taking a ri of maurmnt for diffrnt y- poition and noting th convrgnc of th curv toward zro croing in Fig. 8 and idntical curv in Fig. 9. Sinc th can can b takn and plot producd in jut a fw minut, thi proc can b don fairly quickly. Th proc can b pdd up with th third typ of maurmnt, if th prob i mountd on a planar cannr. Two mini-planar-can can b takn ovr a fw inch around th z-axi for ϕ = 0 and ϕ = 180 dg. and contour Amplitud Diffrnc in db Phi or Polarization Angl in Dgr Figur 9 Maurd Amplitud on a Diffrnc Pattrn Antnna for ϕ-scan and Polarization Scan Showing Effct of Y-Zro Alignmnt Error. plot of ithr th amplitud or pha producd. Comparion of th two contour plot will quickly quantify th y-zro rror a wll a any ridual x-zro rror. Two ampl contour plot ar hown in Fig. 10 and 11. Th y-zro offt i found by rotating Fig dgr about th origin and tranlating it in x and y until th contour in Fig. 10 and 11 match. In thi ca Fig. 11 wa tranlatd 0.7 inch in th y-dirction which i twic th y-zro offt. Aftr th prob wa rt, th tt hown in Fig wr rpatd to vrify corrct alignmnt. 3. VERIFYING THE ALIGNMENT TECHNIQUES W hav ud two approach to vrify th alignmnt tchniqu. Th firt wa a comparion of th rult of complt phrical maurmnt on th X-Band Horn in both th on-axi poition and offt by 2.5 inch. Th phrical rult in th offt poition ar vry nitiv to all th alignmnt paramtr. Th good comparion dmontratd that th alignmnt wa indd corrct. A mor rigorou tt of th alignmnt procdur involvd chcking th alignmnt with an optical autocollimator and prciion lvl. Th rult of th comparion will b prntd in th talk. 4. Concluion A ri of lctrical tt hav bn dvlopd that can b ud to align and chck th alignmnt of a phrical

6 nar-fild rotator. Thy ar fat and accurat and built into th NSI Sphrical oftwar. Th θ-zro and nonintrction rror wr ud uccfully in th fild for fin alignmnt of th NSI ytm intalld in China. Thi ytm i th ubjct of a companion papr bing prntd in th potr ion. Som of th NSI phrical ytm ar dignd to b portabl, and th ability to rapidly t up th cannr and prform lctrical tt for th alignmnt nhanc th uability and accuracy of th ytm. Th author ar planning additional tt and rfinmnt to th tchniqu dcribd in thi papr Th nitivity of th tt may b a good indication of how critical an alignmnt paramtr i. For intanc, if th antnna pattrn i fairly ymmtric about th z-axi, th tt i quit innitiv to y-zro alignmnt rror. Thi may indicat that thi rror i rlativly unimportant for uch antnna, but thi nd to b vrifid. Th tt hav om limitation. W cannot ditinguih btwn θ-zro and x-zro rror, nor can w ditinguih btwn orthogonality and y-zro rror. Bcau of thi, om additional alignmnt procdur mut b ud that t on of ach pair of th paramtr. REFERENCES 1.0 Hann, J. E., Editor (1988) Sphrical Nar-Fild Antnna Maurmnt, Sction 5.3.3, London: Prgrin Wittmann, R. C., Stubnrauch, C. F., (1990) Sphrical Nar-Fild Scanning: Exprimntal and Thortical Studi, National Intitut of Standard and Tchnology (US) NISTIR 3955 Y-Poition in Inch X-Poition in Inch Figur 11 Planar "Mini-Scan for ϕ = 180 on Diffrnc Pattrn Antnna with.35 inch Y-Zro Error.

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8 Y-Poition in Inch X-Poition in Inch Figur 10-Planar "Mini-Scan" for ϕ = 0 on Diffrnc Pattrn Antnna with 0.35 inch Y-Zro Error. 8

[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then

[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then SYSTEM PERFORMANCE Lctur 0: Stady-tat Error Stady-tat Error Lctur 0: Stady-tat Error Dr.alyana Vluvolu Stady-tat rror can b found by applying th final valu thorm and i givn by lim ( t) lim E ( ) t 0 providd