APPLICATION OF THE NIST 18 TERM ERROR MODEL TO CYLINDRICAL NEAR-FIELD ANTENNA MEASUREMENTS

Transcription

1 PPLICTION OF THE NIST 18 TERM ERROR MODEL TO CYLINDRICL NER-FIELD NTENN MESUREMENTS lle C. Newell*, David Lee** *Nearfield Systems Ic. 133 East 3 rd St., Bldg. 54 Carso, C 9745 **David Florida Laboratory, Caadia Space gecy 371 Carlig veue, Ottawa ON, Caada KH 8S bstract This paper describes error aalysis ad measuremet techiques that have bee developed specifically for cylidrical ear-field measuremets. combiatio of aalysis ad computer simulatio is used to show the compariso betwee plaar ad cylidrical probe correctio. Error estimates are derived for both the probe patter ad probe polarizatio terms. The plaar aalysis is also exteded to estimate the effect of probe positio errors. The cylidrical measuremet geometry is very useful for evaluatig the effect of room scatterig from very wide agles sice scas ca cover 36 degrees i azimuth. Usig a broad beam UT ad scaig over a large y-rage provides almost full spherical coverage. Compariso with plaar measuremets with similar accuracy is preseted. Keywords: alysis, Cylidrical ear-field, errors, measuremets. 1. Itroductio The NIST 18 term error model 1 was origially developed for plaar ear-field measuremets, ad it has bee used frequetly ad successfully to estimate the ucertaities i specific measuremets ad to evaluate plaar measuremet facilities. May of the tests ad aalyses that were developed for plaar measuremets ca be applied without chage to cylidrical measuremets. For istace, probe gai, multiple reflectios, receiver liearity, leakage ad radom errors ca be evaluated o a cylidrical rage usig the same techiques that are used for plaar measuremets. Some of the aalyses or tests do ot trasfer directly however, ad these must be modified whe applied to a cylidrical or spherical ear-field rage. This paper will report o the validatio testig of a cylidrical ear-field facility at the David Florida Laboratory ad the ew approaches that were developed for these tests. The cylidrical rage with the VST atea mouted is show i Figure 1. The VST atea is a offset reflector operatig at X-Bad. I this report special emphasis will be give to positio errors, probe correctio effects ad room scatterig tests. With the additio of aalysis ad Figure 1 Test atea ad probe o DFL Cylidrical ear-field rage. measuremets that were developed durig this program, the NIST 18 term error model ca be applied to ay cylidrical ear-field measuremet.. Probe Correctio Equatios for Plaar ad Cylidrical Near-Field Measuremets The probe correctio i the cylidrical aalysis is similar to the plaar case ad ivolves a patter correctio ad a polarizatio correctio. I the plaar case, the probe correctio equatios for a X-polarized UT reduce to, D DE D " t, ( 1a) t, ( 1 ) ' E ρ " ' s b (1) s s s E I the above, a shorthad otatio has bee used for brevity, where t t( K) = zimuth or horizotal compoet of UT plae-wave spectrum. te te( K) = Elevatio or vertical compoet of UT plae-wave

2 spectrum. s s ( K) = zimuth or horizotal compoet of X-polarized probe's plae wave spectrum. s E s E( K) = Elevatio or vertical compoet of X- Polarized probe's plae wave spectrum. D D ( K) = Fourier Trasform of data measured with X-polarized probe. D E DE ( K) = Fourier Trasform of data measured with Y-polarized probe. s ρ s ρs( K ) = Probe's polarizatio ratio = s. The oly term i Equatio (1a) ad the first term i Equatio (1b) correspod to the patter correctio ad the secod term i (1b) is the polarizatio correctio. Sice the far-field ad the plae-wave spectra are early the same for both the UT ad the probe, the effect of errors i the probe patter for plaar measuremets is straight forward. Patter errors effect both the mai ad cross compoet results i the same directio ad with the same magitude as the probe errors. The polarizatio error is derived usig Equatios (1a) ad (1b) givig (after some aalysis) pt p tε " " 1 + p ρ p ρ For x Polarized UT. () t s t sε ptε For y-polarized UT. (3) " " p p ρ p ρ ε t t s t s I Equatios () ad (3) p t = UT polarizatio ratio E t =. te pt ε = UT measured polarizatio ratio with error due to error i probe polarizatio deoted by ρ sε. The form of the probe correctio equatios for cylidrical ear-field measuremets is very similar to the plaar case. But sice there is a additioal calculatio after the probe correctio to calculate the far-field, the fial result of probe correctio is much differet. For example, for a X- polarized UT the probe correctio equatios reduce to I 1, ( 4 ) I I T a T + R ( 4b) 1 1 R R R I Equatio (4) T 1 T 1 ( γ ) =Horizotal compoet of UT Cylidrical wave spectrum. T T ( γ ) =Vertical compoet of UT Cylidrical wave spectrum. 1 1 R R ( γ ) = Horizotal compoet, Cylidrical wave spectrum for X-polarized probe. (4) R R ( γ ) = Vertical compoet Cylidrical wave spectrum for Y-polarized probe. I I ( γ ) = Fourier Trasform of data measured with X-polarized probe. I I ( γ ) = Fourier Trasform of data measured with Y- 1 R ( γ ) polarized probe. R R ( γ ) = = Cylidrical R ( γ ) polarizatio ratio for Y-polarized probe which measures the cross polarized data. I the cylidrical case, either the cylidrical wave spectra, 1 T, T or the Fourier trasforms, I, I are closely related to the far-field patters. The calculatio of the farfield patter requires a Fourier series calculatio i the - directio where the cotributios of the cylidrical coefficiets are combied. E r E F E i T it Eˆ e 1 ˆ (,, ) = ( ) ( ) ( γ) ( γ) = where γ = k si( E) ad i ka cos( E) e F(E)= r Combiig Equatios (4a) ad (5) for the mai compoet patter shows how the probe correctio effects the far-field. ikr (5) I ( γ ) i E (, re, ) = FE ( ) ( i) e 1 = R ( γ ) (6) Yajhia has show that the cylidrical probe correctio coefficiets, R 1 ( γ ) are equal to the probe's far-field patter. particular probe coefficiet is equal to the relative probe patter at a give azimuth ad elevatio agle where γ defies the elevatio agle, ad defies the azimuth agle. The UT far-field patter i a give directio is therefore affected by the probe patter over a rage of azimuth directios. The actual rage depeds o the measuremet geometry ad the ratio of the miimum cylider radius to the measuremet cylider radius. For the measuremets discussed here where the ratio of radii is.5, the probe patter cuts betwee ± 3 degrees i zimuth are used for the probe correctio coefficiets. We ca see the effect of the probe patter correctio by calculatig far-field cuts with ad without probe correctio ad comparig their differece with the probe patter over the same agular regio. Figure shows the pricipal plae elevatio cut for the UT measured o the DFL rage. The close compariso betwee the differece curve ad the probe patter shows that for the priciple elevatio cut the probe patter correctio is early equal to the probe patter. However for the azimuth cut show i Figure 3 the

3 mplitude (db) No Prb Corr With Corr Diff Prb Pat Elevatio (deg) Figure Far-field with ad without probe correctio ad probe patter curves, Elevatio cut. magitude of the differece curve is sigificatly less tha the probe patter curve. Three coclusios ca be made from Equatio (6) ad Figures ad 3 related to cylidrical probe patter correctio. 1- The probe correctio for ay give directio i the farfield is affected by the probe patter over a rage of azimuth values, ot a sigle directio. This is true for both elevatio ad azimuth cuts as evideced by the differeces betwee the probe patter ad differece curves i Figures ad 3. - For each elevatio agle ad for azimuth agles ear zero, the expoetial term e i, i Equatio (6) is approximately costat ad the resultig probe patter correctio is approximately the probe patter averaged over the azimuth agles. The differece curve ad the mplitude (db) No Prb Corr With Corr Diff Prb Pat zimuth (deg) Figure 3 Far-field with ad without probe correctio ad probe patter curves, zimuth cut. probe patter agree i Figure because the chage i the average at differet elevatio agles is the same as the chage i the elevatio cut. 3- For azimuth agles beyod the mai beam, the expoetial term will alterate betwee plus ad mius, real ad imagiary, ad the resultig probe patter correctio will be small. 4- For ay directio i the far-field, the chage i the UT far-field due to a error or ucertaity i the probe's patter at a sigle directio i its patter is give by, 1 I M( γ) R M( γ) im E (, re, ) = FE ( ) e 1 1 (7) R M( γ) R M( γ) where the idex M defies the specific azimuth directio of the probe error. combiatio of aalysis ad computer simulatio has show that a amplitude error i the probe patter i a sigle directio produces a approximately isotropic far-field error patter as show i Figure 4. For a amplitude error of ε db i the probe patter, the Error to Sigal level of this error patter is ERR SIG (8) ε / / * log( 1 1) GUT where G UT is the gai of the UT i db. For the simulatio i Figure 4, the probe error was 1 db ad the UT gai was 3 db. Equatio (8) predicts a error level of approximately -48 db that is cosistet with the results show i Figure 4. This error would occur i all far-field directios. By compariso, the same error i a plaar measuremet would produce a error to sigal level of -18 db at oly oe directio i the far-field. mplitude (db) No Prb Err 1 db Prb Err ERR/SIG zimuth (deg) Figure 4 Results of simulatig a error i the probe's patter for cylidrical ear-field.

4 3. Probe Polarizatio Error Estimates for Cylidrical Near-Field Measuremets The polarizatio probe correctio effect o the far-field cross compoet comes from combiig Equatios (4b) ad (5). 1 I ( γ) I ( γ) + i EE(, re, ) = FE ( ) ( i) + R () 1 γ e = R ( γ) R ( γ) (9) The polarizatio correctio is due to the secod term i (9) ad is due to the cross-polarizatio of the probe that measures the cross compoet ear-field data as represeted by the factor R ( γ ) i (9). The error is due to the ucertaity i our kowledge of the probe's polarizatio ratio, R ( γ ). For a typical probe, the secod term i (9) is small as show i Figure 5 ad ca be estimated as approximately equal to the product of the mai compoet patter of the UT times the cross compoet patter of the probe. These two patters alog with the resultig polarizatio correctio term are show i Figure 5 ad mplitude (db) Mai Cross X-Pol Corr Probe Pat zimuth (deg) Figure 5 Example of relative magitude of terms i polarizatio probe correctio for 45 degree cut. labeled respectively Mai, Probe Pat, ad X-Pol Corr. The patter cuts alog the 45 degree diagoal are used for this example sice the cross polarizatio correctio is larger i this regio. alysis ad compariso to plaar results show that Equatios () ad (3) give good estimates of the error i cylidrical measuremets with the followig modificatios. 1- The cross polarizatio of the UT at a sigle directio is affected by the probe's polarizatio ratio over a small regio of azimuth agles. For the example i Figure 5 the regio appears to be approximately 5-1 degrees. - The average error over the regio, ot the error i oe directio should be used i Equatio () or (3) to estimate the resultig far-field error. For example at + degrees i Figure 5, the polarizatio ratio of the UT is approximately +4 db ad the polarizatio ratio for the probe is approximately -7 db. From Equatio () a error of 5 db i the probe polarizatio i the regio of degrees would result i a error of oly.3 db i the UT cross compoet patter. I the sidelobe regio where the probe polarizatio is ot as good, the UT polarizatio also is worse ad for example at 3 degrees, the error due to a 5 db error i the probe is still oly. db. 4. Y-Positio Errors For Y errors, the theoretical treatmet for X-Y errors i plaar measuremets ca be used. For the case where the mai beam is approximately ormal to the Y-axis, the errors i gai ad sidelobe are, ( RMS ) 87. y GdB ( E, ) g E, Mai Beam ηl y ( E ) ( ) [ ] 43. y, PdB ( E, ) g E, Sidelobes L ( ) [ ] (1) where G is the atea gai, P the relative patter L the atea major dimesio, η the aperture efficiecy, ad y the y positio error. g(e,) is the reciprocal of the sidelobe level i voltage ot db, for istace, for a 4 db sidelobe, g(e,) is Probe radius ad azimuth positio errors The effect of errors i the radius is similar to the z- positio errors i plaar measuremets sice it maily produces a phase error as a fuctio of y ad azimuth. For a fa beam UT where the ear-field phase is essetially costat o a cylider, the equatio for radius errors is idetical to the z-error equatio for plaar. But for a pecil beam atea, the amout of phase chage for a give radius error varies with azimuth agle. s a result we will use the plaar equatios for the case of a beam steered to 45 degrees from the z-axis which will approximate the average phase error i the cylidrical case. The two equatios for the mai beam ad sidelobe regio are, δ r ( rms) GdB ( E, ) g ( E, )[ Mai Beam] (11) η λ 1 δ( θφ, ) P (, ) r db E g ( E, )[ Sidelobes] (1) λ

5 The effect of azimuth positio errors ca also be determied by usig a modified versio of the z-error equatios. The modificatio uses the z-positio error iduced by a azimuth positio error. The z-positio of the probe as it moves o the measuremet cylider ad the z- error that results are respectively, z = r(cos( ) 1), δ ( Z ) = r si( ) δ (13) z The z-positio errors that produce the major effect are those that occur withi the collimated regio of the ear-field which is essetially withi the aperture regio of the UT. For a atea with a aperture width of L x i the x- directio, the collimated regio o the measuremet cylider is bouded approximately by the azimuth agles, Lx c = ± arcsi( ) (14) r The z-error will therefore vary betwee zero whe = ad a maximum of π Lx δ δz( ) = for δ i degrees (15) 36 The average z-error equal to oe half of Equatio (15) is used i Equatios 11 ad 1 with δ r = δ z to determie the effect of azimuth positio errors. I additio to the estimates usig the plaar aalysis, measuremet tests were also performed where a specific positio error was iduced by mis-aligig the azimuth rotator. The base of the tower was tilted to iduce a kow agular tilt betwee the y-axis ad the azimuth axis of rotatio. This is a typical type of positio error that might be ecoutered i cylidrical measuremets. The tower was rotated about its x-axis by.1 degrees ad a measuremet was performed. Compariso of the far-field patters with ad without the aligmet error gives a direct measure of the effect of this specific kid of error. The rotatio of the tower produces a maximum radius error of.44 iches ad a RMS error of.3 iches. Equatio (11) predicts a gai error of.5 db ad the observed gai chage was.5 db. 6. Room Scatterig Measuremets Room scatterig errors are the combied multipath scatterig effects of everythig i the ear-field rage other tha the probe. This icludes the scaer, floor, ceilig ad other fixed objects i the room. This quatity is usually idetified by chagig the UT Z positio while keepig the probe-to-ut separatio distace costat. Measuremets are made at each Z-positio, the far-fields are calculated, ad the patters are subtracted. If the aligmet is ot chaged, ad all other errors should remai costat, ay chage should be due to chages i the room scatterig. I the measuremets take i the the DFL earfield rage, room scatterig measuremets were performed usig the VST atea show i Figure 1 ad also usig a stadard gai hor. I both cases, measuremets were performed with the probe ad UT at, 4 ad 9 iches. The hor gave more complete evaluatio of the scatterig sice its broad patter illumiated more of the room. The azimuth spa was over 36 degrees for the room scatterig tests ad the y-spa was also icreased to icrease the elevatio coverage. mplitude (db) Z= Z=4 i. ERR/SIG zimuth (deg) Figure 6 Results of room scatterig showig peaks ear boresight due to aligmet chages. The patter subtractio is very sesitive to small chages i the magitude ad positio of the beam peak. Sice we are tryig to measure scatterig levels of -4 to -6 db below the peak amplitude, differeces i peak amplitude of oly a few hudredths of a db ad beam aligmet chages of hudredths of a degree effect the results sigificatly. This is illustrated i Figure 6 which shows the results of a scatterig test o the Vast atea. The curve idetified as ERR/SIG is derived from the differece i the far-field patters measured at the two Z-distaces. It is a measure of the room scatterig relative to the atea mai beam sigal. The two peaks ear boresight are ot actually due to room scatterig but are due to small chages i the atea agular aligmet whe it is moved i Z. If the patter take at 4 iches is shifted i azimuth by.3 degrees ad i elevatio by.1 degrees the peaks disappear ad the full curve is below -6 db. It is importat to look closely at the beam peaks ad to adjust for small aligmet chages before calculatig the room scatterig so that such effects are ot misiterpreted as room scatterig.

6 Elevatio i Degrees I additio to sigle cuts similar to Figure 6, cotour ad surface plots that covered the full measuremet sphere were also geerated from the stadard gai hor data. These give a much more complete evaluatio of the room scatterig from the complete rage. Oe result is show i Figure7 as a cotour plot. The darkest cotours ear -9 degrees i elevatio ad ear degrees i azimuth are at - 45 db. The adjacet medium dark cotours are at -5 db, mplitude (db) zimuth i Degrees Figure 7 Cotour plot of room scatterig results o the DFL cylidrical rage from stadard gai hor measuremets Cyl Meas Plaar Meas Elevatio (deg) Figure 8 Compariso of mai compoet far-field patter results from plaar ad cylidrical earfield measuremets. ad the gray cotours are at -55 db. The majority of the cotours i the regios above -3 degrees i elevatio ad beyod the elevatio ceterlie are at -6 db. The mai features that represet actual room scatterig are those betwee -6 ad -9 degrees i elevatio. These features were i all of the results from the hor measuremets ad are probably due to lights ad other scatterig objects that were i the ceilig above the measuremet rage. These tests cofirm that there are o scatterig objects other tha the ceilig withi the measuremet facility that adversely effect the patters above the -55 db level. 7. Compariso With Plaar Results The VST atea was used previously for measuremets at a NSI plaar ear-field facility ad the data from those measuremets was available for compariso. Figures 8 ad 9 show the compariso of mai ad cross compoet patters obtaied o the cylidrical ad plaar rages. The agreemet betwee the measuremets was cosistet with the estimates of ucertaity for the two rages. mplitude (db) Cyl Meas zimuth (deg) 8. Coclusios Plaar Meas Figure 9 Compariso of cross compoet far-field patter results from plaar ad cylidrical earfield measuremets. Mathematical aalysis ad measuremet techiques have bee developed that exted the NIST 18 term error aalysis to cylidrical measuremets. These ew developmets were for probe patter ad polarizatio errors ad cylidrical positio errors. I additio results of room scatterig tests have demostrated the uique ability of the cylidrical measuremets to evaluate all of the measuremet facility. 1 Newell,. C., "Error aalysis techiques for plaar ear-field measuremets," IEEE Trasactios o teas ad Propagatio, Vol. P-36, pp , Jue Yaghjia,.D., "tea Measuremets o a CylidricalSurface: Source Scatterig-Matrix pproach", Natioal Bureau of Stadards Techical Note 696, 1977, 34 p., Boulder, CO.