Novel Approach to Uncertainty of Antenna Factor Measurement. Bittera Mikulas, Smiesko Viktor, Kovac Karol 1

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1 7 th Symposim IEKO TC 4, rd Symposim IEKO TC 9 and 5 th IWADC Workshop Instrmentation for the ICT Era Sept. 8-0, 00, Kosice, Slovakia Novel Approach to Uncertainty of Antenna Factor easrement Bittera iklas, Smiesko Viktor, Kovac Karol Slovak University of Technology, Dept. of easrement, Ilkovicova, 89 Bratislava, SLOVAKIA phone , fax , miklas.bittera@stba.sk Abstract-Different method to calclate ncertainty of antenna factor measrement is presented in this paper. This approach does not break the rles of standard ncertainty calclation approach, bt redces the entire ncertainty. It is obtained by performing the measrement with two reference dipole antennas and considering freqency dependent contribtions of the ncertainty as well as the possible covariance between them. I. Introdction A radiated emission measrement belongs to sch tests of the electromagnetic compatibility (EC) of electrical eqipments, which are performed in common for electrical devices. The measrement reqires a measrement of electric field strength, which is compared with a limit level []. A measring chain consists of a rf voltmeter, an antenna, which converts electric field strength to the voltage and a cabling. In EC area, the most important parameter of the antenna is so called antenna factor, via which measred otpt voltage of the antenna is converted to electric field strength. Two types of the antenna factors are known : a free space antenna factor sed at the measrement in free space, a standard method antenna factor sed at the measrement at test, i.e. space with reference grond plane. Both antenna factors are sed in EC area, in consideration of their advantages or disadvantages. Nowadays, an essential condition for accrediting a calibration laboratory is that the laboratory has inclded the relevant ncertainty components in its implementation of the measrement methods, sch as deviations from the measrement model implied by the standard. The ncertainty shall be calclated according to the international standard []. The same sitation is in EC area [, 4], even thogh decibel nits are sed (de to known properties of log-normal distribtion [5]). The standard approach leads to a relatively high vale of the ncertainty, also mtal inflence of the ncertainty contribtions covariances are neglected. In the case of antenna factor measrement, sch a parameter is freqency dependent; also the contribtions are freqency dependent. In addition, antenna factor are obtained by relatively complicated process of three measrements of attenations. The aim of this paper is to design sch a process of evalation of the standard method antenna factor measrement ncertainty, obtained from measred vales of attenations and considering all the distrbing effects, their freqency dependence and mtal inflence among the contribtions. The task is also to find sch a process which leads to decrease of the entire ncertainty vale. II. Problem description Antenna factor AF is defined as the ratio of incident electromagnetic field strength E to the voltage V on the line of the connection of an antenna: Also it can be determined as [6]: E AF V () AF 4πη Zλ ( Γ ) G () where η is impedance of free space, Z load (generally 50Ω), λ wavelength, Γ reflection coefficient of potential impedance mismatch on an antenna otpt and G is antenna gain. So, the antenna factor contains not only transmission ratio bt also losses de to impedance mismatch. According to () it is also ectly proportional to freqency of a measred signal. 64

2 7 th Symposim IEKO TC 4, rd Symposim IEKO TC 9 and 5 th IWADC Workshop Instrmentation for the ICT Era Sept. 8-0, 00, Kosice, Slovakia measring distance HF generator receiving antenna height - 4 m amplifier transmitting antenna measring receiver Figre. Standard measrement antenna factor measrement system The antenna factors vales shold be obtained by three-antenna methods [7]. Its principle is based on performance of three measrements of the attenation, given by the difference between a voltage on transmitting antenna inpt and a received voltage on measring antenna otpt, for different pairs of antennas. These measrements can be exected in free space or at standard test s with a reference grond plane. If antenna factor is measred at the test given parameter is called as standard measrement antenna factor. Sch an antenna factor is different from free-space antenna factor (p to db) [8] and may be obtained by three measrement of attenation SA [6]: SA 48.9 AF SA 48.9 AF SA 48.9 AF AF 0log f E AF 0log f E AF 0log f E where f is freqency and E Dmax is theoretically obtained vale of electromagnetic field strength at given freqency, measring distance and polarisation of an antenna. Parameter E Dmax in () is assmed in ncertainty calclation as a constant. Site attenation vales SA may be simply obtained as: () SA V V (4) where V is a measred voltage when a signal generator is ectly connected with the rf voltmeter. V is measred voltage when antennas, by which the attenation is measred, are added in measring chain. From () we can determine reqired vales of antenna factors AF: AF AF AF ( SA SA SA ) ( SA SA SA ) log f E log f E ( SA SA SA ) log f ED max The ncertainty of sch a antenna factor measrement may be calclated by standard approach according to the ISO docment []. The entire ncertainty is given by integration of type A evalation and type B evalation. Since vales of antenna factor (as well as other parameters) are in decibels, sing theory of log-normal distribtion [5] it is possible to se approach of [] in this case. III. Soltion The vales of ncertainties of rf voltage measrement (V) and attenation measrements (SA) shold be known at first to get the ncertainty of standard method antenna factor measrement. The process of the ncertainty (V) calclation is known [9], while the ncertainty (SA) shold be determined. The following model of measrement of attenation SA may be bilt p (according (4)): ( V δ PSV ) ( V δpsv δd δh δpc δz δf ) SA (6) This model is extended with parameters which has zero vale bt affects the ncertainty of the measrement: δpsv is correction of impedance mismatch of given measring chains, δd correction of measring distance, δh correction of height of transmitting antenna, δpc correction of phase centre location, δz h correction of antenna s inpt impedance height variation and δf is correction of antenna s ectivity. Corrections δpc, δz h and δf are sms of contribtions of both (transmitting and receiving) antennas. Then we can determine the ncertainty of attenation measrement as: h (5) 65

3 7 th Symposim IEKO TC 4, rd Symposim IEKO TC 9 and 5 th IWADC Workshop Instrmentation for the ICT Era Sept. 8-0, 00, Kosice, Slovakia (7) D h PC Zh F ( SA) ( V ) ( V ). ( V, V ) where D, h, PC, Zh and F are maximal variations cased by given effects with rectanglar probability distribtion and and are maximal errors cased by impedance mismatching according [0]: ( Γ ) 0 log ± Γ (8) Γ a and Γ r are reflection coefficient of antenna and receiver, respectively. U-shaped probability distribtion [0] is assmed in case of. It is evident from (7) that all the sensitive coefficients are assmed to be one. De to weak interdependence (close to zero), the parameters of (7) may be considered as independent. It is advisable to se dipole antennas, which has zero vales of PC and F, to obtain low vales of ncertainties (SA). Also Zh can be considered as zero, if height of transmitting antenna over grond plane is kept constant. So final ncertainty of attenation measrement is given: ( SA) ( V ) ( V ) a D h (9) If antenna factor AF is measred by three antenna method (5) the ncertainty of sch a measrement may be calclated as: ( SA ) ( SA ) ( SA ), ( AF ) ( SA, SA ) ( SA, SA ) ( SA SA ) (0) where the covariance are determined: rij ( SA, SA ) ± ( SA ) ( SA ) i j r i j () 4 The sign in eqation () is changing with regard to choice of antenna factor AF in (5). If sbstitting (6) into (5), the antenna factor measrement ncertainty changes: ( AF ) ( V ) ( V ) PC PC PC Zh Zh Zh F F d F h C * where ij is maximal error cased by the impedance mismatch if i-th and j-th antenna is inclded into measring chain at the attenation measrement, PCi, Zhi and Fi are contribtions of phase centre variation, inpt impedance height variation and ectivity of i-th antenna. Parameter C* represents all possible covariances (between the same vales in (), e.g. the voltage measred with the same rf voltmeter, etc), which are expected in contrast to other works of ncertainties in EC area. In sch case we considered strong dependence between the parameters (r ), otherwise we considered no dependence (r 0). It is appropriate sing a pair of dipole antennas combined with measred antenna to minimize the ncertainty of antenna factor measrement. The eqation () is changing for measred antenna : Zh 4F D h () ( AF ) 4( V ) In eqation () we do not consider neither with vale of PC, which is possible to redce if other two antennas are dipoles antennas [8]. The vale of ncertainty of antenna factor measrement may be calclated generally, for the entire freqency range considering maximal contribtions, errors, in (), or individally for discrete freqencies. In the second approach we can redce the inflence of some contribtions, which effects may be evident at varios freqencies. IV. Reslts The advantages of sch an approach were examined in case of Bilog antenna. Tested Bilog antenna sed in this () 66

4 7 th Symposim IEKO TC 4, rd Symposim IEKO TC 9 and 5 th IWADC Workshop Instrmentation for the ICT Era Sept. 8-0, 00, Kosice, Slovakia paper is 785 mm long and 660 mm wide, with 5 pairs of dipole elements and a bow-tie part. All the measrements, mentioned above, were exected in semi-anechoic chamber of EC Laboratory of Slovak University of Technology. All the ncertainty contribtions were obtained in or previos work [] (all these contribtions are freqency dependent). (AF) (db) standard approach withot covariances with covariances f (Hz) a) b) Figre. Antenna factor measrement ncertainties of varios calclation for horizontal a) and vertical b) polarizations of antenna (AF) (db) standard approach withot covariances with covariances f (Hz) 000 The comparison of calclated ncertainties is shown in Fig.. Standard approach according [] cont with maximal vales of ncertainty contribtions in the entire freqency range and therefore we get only one vale of both sign ±.4 db (pink line). Sch ncertainty is mch higher than vales of the freqency dependant ncertainties. Assming process of calclating ncertainties in discrete freqencies (black line), the entire ncertainty can be decreased de to restriction of two most evident ncertainty sorces the ectivity of Bilog antenna [], which cases errors mainly at higher freqencies, and the impedance mismatch of Bilog antenna, which increases the ncertainty at lower vales of freqency. In sch case the final ncertainty is not single valed nor it is symmetrical (eqal for both signs). aximal positive vale of ncertainty is.55 db and negative one 0.94 db for both polarisations. The main difference between the polarizations is at higher freqencies de to antenna ectivity. Considering also correlations between ncertainty contribtions, other redction of the ncertainty may be achieved (ble line). aximal ncertainties are a bit smaller. db or 0.9 db. V. Conclsions Different view to the calclation of the antenna factor measrement ncertainty is described in this paper. Althogh the calclation is based on standard process of ncertainty calclation, some improvements were applied, which redce the entire ncertainty. It was achieved by sing of pair of the dipole antennas in combination with the measred antenna, assming of freqency dependence of ncertainty contribtions and assming of covariances. The entire ncertainty was redced from.4db to max..db. However, sch a redction is on the expense of time of ncertainty calclation. Acknowledgment This research was financially spported by the project VEGA VG /055/09 and by the inistry of Edcation of the Slovak Repblic nder grant 00SP References [] CISPR 6--4: Specification for radio distrbance and immnity measring apparats and methods Part -4: Radio distrbance and immnity measring apparats Ancillary eqipment Radiated distrbances, 005. [] ISO/IEC Gide 98: Gide to the expression of ncertainty in measrement, 995. [] CISPR 6-4-: Specification for radio distrbance and immnity measring apparats and methods Part 4-: Uncertainties, statistics and limit modelling Uncertainty in EC measrements, 00. [4] NIS 8: The treatment of ncertainty in EC measrements,

5 7 th Symposim IEKO TC 4, rd Symposim IEKO TC 9 and 5 th IWADC Workshop Instrmentation for the ICT Era Sept. 8-0, 00, Kosice, Slovakia [5] Kyatt, C.E., Corrections to Appendix IV of NIS 8, ANSI C6 Uncertainty Workshop, Chicago, pp. 7-8, 996. [6] Kodali, V.P., Engineering electromagnetic compatibility Principles, measrements and technologies, Piscataway, New York, 996. [7] ANSI C6.5: Electromagnetic compatibility radiated emission measrement in electromagnetic interference control - calibration of antennas [8] Garn, H., et al, Primary standards for antenna factor calibration in the freqency range of (0 to 000)Hz, IEEE Trans. on Instrmentation and easrement, Vol.46, No., pp , 997. [9] Stecher,., A detailed analysis of EI test receiver measrement ncertainty, IEEE EC Int. Symposim, ontreal, pp , 00. [0] Bronagh, E.L., Heirman, D.N., Estimating measrement ncertainty. A brief introdction to the sbject, IEEE EC Society Newsletter, pp. -4, 004. [] Bittera,., Some aspects of radiated emission measrement. Dissertation Thesis, Bratislava, 007. [] Bittera,. et al: Interference between grond plane and Bilog antenna and its effect on EI measrement ncertainty. Asia Pacific icrowave Conference, Hong Kong,