PREDICTION AND MEASUREMENT OF RADIATED EMISSIONS BASED ON EMPIRICAL TIME DOMAIN CONDUCTED MEASUREMENTS

Transcription

1 PREDICTION AND MEASUREMENT OF RADIATED EMISSIONS BASED ON EMPIRICAL TIME DOMAIN CONDUCTED MEASUREMENTS by LARRY FREEMAN B.S.E.C.E, The Ohio State Univerity A thei ubmitted in partial fulfillment of the requirement for the degree of Mater of Science in the School of Electrical Engineering and Computer Science in the College of Engineering and Computer Science at the Univerity of Central Florida, Orlando, Florida Summer Term 26

2 ABSTRACT Thi thei develop a novel method to predict radiated emiion meaurement. The technique ued are baed on tandard Electromagnetic Compatibility (EMC) qualification tet method. The empirical data ued to formulate the final reult wa retricted to pertinent data protocol waveform however the entire method may be applied to any waveform for which empirical radiated emiion have been meaured. The method provide a concie mean for predicting wort cae radiated emiion profile baed on empirical meaured data. ii

3 ACKNOWLEDGMENTS I would like to acknowledge Tom, Sean, Charlie, and Joe. Four wonderful upervior; I am a better engineer and peron for having known you all. Thank you for all your patience, humor, and inpiration. A pecial thank to Prof. Thoma Wu, for all hi guidance and upport in thi endeavor; he i a uperb profeional and cholar. iii

4 TABLE OF CONTENTS LIST OF FIGURES... vi 1. Introduction Premie Pat Reearch Outline Objective Waveform Meaurement Waveform Tranform Technique to Convert into Matlab Verification Matlab Tranform Verification Antenna Coupling EMC Certification Setup Coupling Model Derivation Firt Tranmiion Line Equation Second Tranmiion Line Equation Solution of Tranmiion Line Equation Meaurement Parameter Meaurement Controlled Setup Empirical Meaurement Antenna Factor Interpolation Impedance Factor iv

5 5. Radiated Emiion Profile Prediction Prediction Example Concluion Overall Technique Matlab Implementation Matrice Manipulation in Matlab Empirical Meaurement Recommendation APPENDIX A: MEASUREMENT ANTENNA FACTORS APPENDIX B: SAMPLE OF MEASURED WAVEFORMS... 4 APPENDIX C: MEASUREMENT SETUP PICTURES APPENDIX D: IMPEDANCE FACTOR PLOTS FOR TWISTED PAIR MEASUREMENTS LIST OF REFERENCES v

6 LIST OF FIGURES Figure 1-1: Conducted Emiion to Radiate Suceptibility Scenario... 2 Figure 1-2: Proce Outline... 4 Figure 2-1: Time Domain Meaurement Converion Graph... 7 Figure 2-2: Time Domain Meaurement with Ringing... 7 Figure 2-3: Sample Corrupted Meaured Waveform... 8 Figure 3-1: Power Denity of Frequency Content... 9 Figure 3-2: Matlab Program Functional Flowchart... 1 Figure 3-3: Meaured Waveform Figure 3-4: Matlab DFT Waveform Figure 4-1: Generic Radiated Emiion Tet Setup Figure 4-2: Two Wire Coupling Model Geometry Figure 4-3: Phyical Repreentation of Coupling Derivation Figure 4-4: Incremental Repreentation Figure 4-5: DM and CM Current Action Figure 4.6: Circuit Repreentation... 2 Figure 4-7: Detailed Picture of Controlled Meaurement Setup Figure 4-8: Scope Capture of Meaurement Waveform Figure 4-9: Antenna Factor Interpolation Figure 4-1: Antenna Factor Divergence Error Figure 5-1: Time Domain of TP-2T Waveform... 3 Figure 5-2: FFT of TP-2T Waveform Figure 5-3: Predicted Radiated Emiion Profile vi

7 Figure 5-4: Predicted Radiated Emiion Profile Uing Nominal Value for Impedance Factor Figure A-1: Rod Antenna Factor Figure A-2: Bi-conical Antenna Factor Figure A-3: Double Ridge Horn Antenna Factor Figure A-4: Horn Antenna Factor Figure B-1: Sample 1 Scope Capture, FFT of Scope Capture, and RE Meaurement Figure B-2: Sample 2 Scope Capture, FFT of Scope Capture, and RE Meaurement Figure C-1: 1 khz-3mhz Meaurement Setup Figure C-2: 3 MHz-2MHz Meaurement Setup Figure C-3: 2MHz-1GHz Meaurement Setup Figure C-4: Waveform Generator Figure C-5 Termination Shielding Figure C-6: Feed and Bulkhead Figure D-1: Impedance Factor for TP-1T Waveform Figure D-2: Impedance Factor for TP-2T Waveform Figure D-3: Impedance Factor for TP-3T Waveform Figure D-4: Impedance Factor for TP-4T Waveform Figure D-5: Impedance Factor for TP-5T Waveform... 5 Figure D-6: Impedance Factor for TP-6T Waveform... 5 Figure D-7: Impedance Factor for TP-7T Waveform Figure D-8: Impedance Factor for TP-8T Waveform Figure D-9: Impedance Factor for TP-9T Waveform vii

8 1. INTRODUCTION The profeion of Electromagnetic Interference (EMI) and Electromagnetic Compatibility (EMC) engineering ha long been governed by deign practice etablihed through empirical meaurement. Often detailed analyi in t an option, due to the heer complexity of the phenomena involved. The neceary parameter are either impoible to obtain or require a nearly complete deign to be of any real pertinence. The end reult i a deign driven by what ha worked in the pat. Thi often lead to more tringent deign guideline than are neceary. Many time a deign effort ha been driven by thee retrictive meaure, that often have little or no bai, other than it i what ha been done before Premie All electrical device old in the United State for commercial or military ue are required by law to undergo a battery of certification tet; to enure their proper operation will not have undeirable electrical effect on the environment of their intended ue. For example, the Federal Communication Commiion (FCC) retrict the amount of radiated emiion allowed in order that other electrical device, uch a televiion tranmitter, cell tower, etc., do not have their tranmiion inadvertently hindered. Compliance to thee requirement may have dire conequence in critical area uch a aeropace vehicle control, medical device, and communication. 1

9 Mot all of thee EMC tandard contain a uite of variou tet. The mot common are Conducted Suceptibility (CS), Conducted Emiion (CE), Radiated Emiion (RE), and Radiated Suceptibility (RS). Mot engineer over implify thee into two categorie, Stuff that get out are emiion. Stuff that get in i uceptibility. However they are much more complex. For example in Figure 1.1, within a chai or box one Printed Circuit Board (PCB) may have conducted emiion from it trace that radiate uceptibility to another PCB. From the firt card point of view thi i initially a conducted emiion problem that manifet itelf into a radiated emiion that caue a radiated uceptibility of the econd PCB card. Exiting method require the ue of invaive tool. For example, current monitor probe are frequency dependent and mut be wrapped around the conductor being teted. Thi may be impractical or even impoible. The only other alternative i to bring an Engineering Deign Unit (EDU) into the tet chamber to perform RE teting. Thi i particularly unappealing for everal reaon; uually it will affect chedule and cot. Not to mention EDU unit are never meant to be fully compliant (only functional), often they require ignificant modification to meet their functional obligation. Figure 1-1: Conducted Emiion to Radiate Suceptibility Scenario 2

10 The objective of thi thei i to invetigate an approach that eek to bridge the gap between empirical meaurement and derived analyi Pat Reearch A thorough review for imilar reearch effort wa performed. Thi literature urvey included everal text, the World Wide Web, and the IEEE EMC ociety archive dating back to 1955 [1]. Many topic covered ome apect of thi reearch effort. For example, a myriad of paper dicuing conducted emiion, radiated emiion, or the Fat Fourier Tranform were found. Even everal paper relating the two were found. Work by Profeor Clayton Paul and Donald White detail theoretical apect but do not correpond eaily to meaured parameter. Few paper ought to pecifically relate meaured data. Intead they choe to imply verify with meaured reult. The other ignificant difference were the ue of voltage meaurement veru current meaurement. Thi i attributed to the fact that 99% of thee paper concerned themelve with power line meaurement that had varying impedance. Current probe preent other iue, thee are dicued later. The other ignificant dicriminator wa the ue of pecial equipment or meaurement fixture. The ue of pecial equipment or fixture wa deemed much too retrictive to be of ue for thi effort. The reult of thi thei i to provide the detail by which an individual uing imple technique and equipment commonly found around an EMC laboratory can perform preliminary meaurement and formulate a prediction of compliance to radiated emiion. Thi i bet done uing empirical meaurement data. 3

11 1.3. Outline Firt the overall proce being followed i preented; tep by tep. Then an elementary EMC certification etup i dicued; thi explain the rationale behind uch an endeavor and highlight the conception of pecific phyical modeling dicued later. Then a wire coupling model i preented along with the jutification and explanation for it expanion. The initial meaurement collection and tranformation procee are detailed. Next the entire proce i demontrated in it intended equence. Finally, a comparion i made between the predicted emiion profile and an actual empirically meaured emiion profile, along with an explanation or hypothei for any deviation. Figure 1-2: Proce Outline 4

12 1.4. Objective It i important to point out the overall objective of thi reearch. The goal of thi reearch i not to predict the precie emiion profile but rather to envelope it wort cae profile, uing relatively traightforward data meaurement. Thi will give the EMC deign engineer an early look at what i to be expected through the ue of real meaurement data. Thi will allow a deign to have a much higher certainty of compliance to meaured emiion tandard. Ideally the meaurement data gathered from conecutive meaurement will be ued to etablih a databae. Then an overall notion of accuracy can be aeed in conjunction with trong empirical data. The end reult of thi work i to formulate a proce, which can be implemented continuouly and enhanced each time it i employed. 5

13 2. WAVEFORM MEASUREMENT During an EMC certification tet, conducted emiion are mot alway directly related to radiated emiion profile. Radiated emiion from tructure or a mechanical chai are common, but radiated emiion from cabling are far more prevalent. Thi i the main reaon behind the focued crutiny on cabling of thi paper. Conductor cabling handle two ditinct ignal, digital and analog. Typical for digital line the frequency content i imply derived from tranition rate [9]. Figure 2.1 how a tandard tranform table ued to predict the potential frequency content uing known tranition rate. Analog tranmiion are defined accordingly. However neither of thee technique account for the unexpected variation that are certain to occur. For example, ringing would not be accounted for uing the tranition rate technique dicued, ee Figure 2.2. From the figure it i eay to ee how inadvertent effect uch a ringing can be overlooked by imply uing the tranition table. A better more definitive approach would be to imply meaure each tranmiion line. Thi may be accomplihed uing a current clamp or voltage probe. The current clamp i phyically large and made of ferromagnetic material, it require at leat one turn for the tranformer action to occur. Current clamp are alo frequency dependent. All of thi make current clamp extremely cumberome and intruive. For that reaon a voltage meaurement wa deemed more reaonable. Since the tranmiion line impedance i known it i a imple converion to get the current value. 6

14 Figure 2-1: Time Domain Meaurement Converion Graph A imple waveform meaurement of the conducted waveform taken in the time domain i eay to obtain uing an ocillocope. Certain ocillocope meaurement parameter uch a ample rate and time reference mut be etablihed in order to guarantee a uniformed approach; thee are dicued in a later ection. The meaured waveform can then be tranformed into the frequency domain Amplitude [V] Ti Frequency me [] [MHz] Figure 2-2: Time Domain Meaurement with Ringing 7

15 Modern ocillocope have the capability to tranform time domain meaurement into the frequency domain, however not all ocillocope ue the ame Fourier tranform technique. While mot all of the ocillocope manufacturer ue the Fat Fourier Tranform, many ue completely different weighting function and verion of the mathematical technique. For the purpoe of thi effort it wa deemed much too retrictive to rely on one particular manufacturer technique or method. Therefore each waveform meaurement wa exported into a tandard ASCI text file format, interpolated and then converted into Matlab for manipulation. Figure 2.3 how a ample of a data waveform that ha been corrupted with random noie. Figure 2-3: Sample Corrupted Meaured Waveform 8

16 3. WAVEFORM TRANSFORM The next tep i to take the meaured waveform data, hown in Figure 2.3 and interpolate it into Matlab. Figure 3.1 how how the FFT can highlight a pecific frequency of concern. The pecific DFT methodology ued i outlined in a later ection. The end reult i an accurate profile of all the frequencie that warrant conideration when deriving the emiion profile envelope. Figure 3-1: Power Denity of Frequency Content 3.1. Technique to Convert into Matlab A program, implemented in the Matlab programming language i lited in appendix A. A mentioned earlier, certain waveform parameter mut be tandardized, uch a ample rate, time reference, and duration. The Matlab program import the waveform data, tranlate from a tandard ASCI text file and perform the DFT. The program output are 9

17 the vector containing the DFT amplitude and frequency reference and plot of the variou waveform data. A imple functional diagram i hown in Figure 3.2. Figure 3-2: Matlab Program Functional Flowchart 3.2. Verification Before any further conideration a verification tep wa performed. Aide from the obviou anity check, thi tep allowed for the identification of any unintentional frequency content. For example, if an unidentified frequency component i dicovered it can be invetigated. The meaured waveform hould be taken from preliminary engineering deign, even bench top model, to allow for adequate time to correct the deign. 1

18 Unintentional frequency content may be a reult of the preliminary deign and not a part of the finihed product. For example, the final deign may be implemented uing DC power from a vehicle battery, thi ource i by definition not likely to caue conducted tranient. However the deign model could be powered from a DC power upply with a witching rectifier that produce frequency content into the meaured waveform. The verification tep hould conit of, a a minimum, a preliminary urvey of the intended frequency content for analog tranmiion and a comparion with Figure 2.1, for known digital tranition rate Matlab Tranform Verification In order to verify the accuracy of the Matlab program a quare wave wa meaured on the ocillocope, imported and tranformed uing the Matlab program in appendix A. Thi ame waveform wa fed directly into an Agilent pectrum analyzer and meaured directly acro frequency. Each meaurement wa then captured a an image file; both file are hown below a Figure 3.5 and 3.6. Thi trong correlation demontrate the accuracy of the Matlab implemented tranform. 11

19 Figure 3-3: Meaured Waveform Figure 3-4: Matlab DFT Waveform 12

20 4. ANTENNA COUPLING The principal ued to formulate the emiion antenna model i to determine the induced voltage due to an incident electromagnetic wave upon a wire upended overtop of a ground plane. Thi i pertinent becaue almot all EMC radiated emiion certification teting ue thi etup or one imilar to it. Thi i true for both form of radiated emiion teting, commercial and military. The mathematical derivation of thi technique wa originally documented by Edward Vance [2] and Alberta Smith [3]. The formula and derivation are delineated in the following ection with greater detail and clearer nomenclature added where deemed neceary EMC Certification Setup In the interet of uniformed crutiny almot all radiated emiion tet ue the ame etup approach, mainly with the Equipment Under Tet (EUT) and it upporting conductor being upended above a ground plane. In the interet of implicity the typical etup ued in Mil-Std-461E i ued for thi paper. Figure 4.1 below how a diagram of thi etup. Figure 4-1: Generic Radiated Emiion Tet Setup 13

21 4.2. Coupling Model Derivation Firt Tranmiion Line Equation The initial coupling model i derived from that of a two wire tranmiion line. Figure 4.2 how the geometry of the two wire coupling model. Thi ha a trong correlation to the eventual etup approach, a ingle wire above a ground plane, epecially when conidering the image plane induced by the ground plane. Thi correlation i expanded upon further in the next ection. X Z 1 Z Z 2 Z= E(x,y,z,ω) Z=l Z Y H(x,y,z,ω ) Figure 4-2: Two Wire Coupling Model Geometry Starting with Maxwell equation for the curl of the electric field over an incremental urface a hown in Figure 4.3 and 4.4, and uing Stoke theorem to integrate, the induced voltage i derived a follow: S ( E) ds = E dl = j ω B ds (1) C S Evaluating the line integral over the contour that bound the urface, uing ds = dxdz, we have b z+δz [ E ( x, z + Δz) E ( x, z) ] d x [ E ( b, z) E (, z) ] X = jω z+δz z b B Y X ( x, z) dx dz z Z Z d z (2) 14

22 Figure 4-3: Phyical Repreentation of Coupling Derivation Figure 4-4: Incremental Repreentation Dividing by the incremental tep and taking the limit a it approache zero give z b E X b ( x z) dx [ E ( b, z) E (, z) ] = j B ( x, z) d x, ω (3) Z The field term delineated are the total cattered and incident field. The voltage between the two wire i defined a Z Y 15

23 V b ( z) = E ( x, z) X d x (4) Uing thi relation the firt term of (3) may be re-written a b E X ( x z) d x = V () z z, z (5) Uing the definition for incremental voltage E Z R1 Δz = I Δz (6) 2 and ubtituting thi relation into (3), we have I 2 I1 EZ ( b, z) EZ (, z) = R1 (7) 2 where repreent the ditributed reitance in reitance per length, I and I 1 repreent R1 2 the total current within each wire. From the convention hown in Figure 4.5, the common mode (CM) and differential mode (DM) current are eparated a I 2 I1 I 2 + I1 I DM =, I CM = (8) 2 2 Since the meaured time domain data i alway differential mode; thi i becaue common mode carrie no information; it i convenient to ue (7) and the firt part of (1) to retrict the econd term of (2) to DM current with [6][8] E I ( z) I ( z) = (9) DM ( b z) E (, z) R I( z), (1) Z Z = Finally the third term of (3) can be divided into it incident and cattered component a follow b b b i ( x, z) dx = jω B ( x, z) dx jω B ( x, z)dx jω BY + Y Y (11) 16

24 The reaon for thi i that the magnetic field originating from the DM current i what caue the cattered magnetic field component. The reaoning behind thi phenomenon i that DM field cancel, while CM field combine. The difference between the two differential field reult in a cattered element. Figure 4-5: DM and CM Current Action Next the inductance per unit length of tranmiion line Δz i given by Φ y L1Δ z = (12) I( z) where L 1 i the ditributed inductance per unit length and Φ y i the incremental urface cattered flux from between the conductor. By rearranging (12) to Φ y Δz = L1 I( z) (13) in term of the flux we have Φ y = B d = y z+ Δz b b Bydxdz = Δz z B ( x, z) dx y (14) 17

25 Φ Δ y b = z B ( x, z) dx (15) y Therefore, (13) and (15) give By ubtituting (16) into (11), we have b B ( x, z) dx = L I z (16) y 1 ( ) jω b B Y b i ( x z) dx jω B ( x, z) dx jωl I ( z), Y 1 = (17) Inerting (5) and (17) into (3), we get the firt tranmiion line equation with voltage ource a dv ( z) + Z1I( z) = V ( z) (18) dz where b V ( z) = jω B ( x, z) dx i y (19) and Z1 = jωl1 i erie impedance per unit length Second Tranmiion Line Equation From Maxwell equation, for the cattered field, we have H = jωεe (2) from which we obtain E x = 1 H jωε y z H y z (21) Since the current flow in z direction, we can aume / x = / y = inide the tranmiion line, we obtain E x = 1 H jωε z y (22) 18

26 Since the voltage on the tranmiion line can be expreed a V ( z) = b E ( x, z) dx = x b b i E x ( x, z) dx E ( x, z) dx x (23) inerting (22) into (23) yield V ( z) = b b i Ex ( x, z) dx + 1 d jωε dz H y ( x, z) dx (24) Since B = μ H, the integration in the econd term of (24) become b 1 b L1 I( z) H ( x, z) dx = B ( x, z) dx μ = (25) y y μ (16) i alo ued to derive (25). Inerting (25) into (24), we can obtain the econd tranmiion line equation a where di( z) + Y1V ( z) = I ( z) (26) dz jωμε Y = = (27) jω C 1 1 L1 and I ( z) = Y b i 1 E x ( x, z) dx (28) 4.3. Solution of Tranmiion Line Equation In the following, we will dicu olution procedure for tranmiion line equation (18) and (26). The circuit repreentation for thee two equation are hown in Figure

27 Figure 4.6: Circuit Repreentation We are going to dicu the olution with current ource dicu the olution with voltage ource of thee two cae. (z) V (z) I only at firt and then. And the total olution i the uperpoition When there i only current ource, we have dv ( z) + Z1I( z) = dz di( z) + Y1V ( z) = I ( z) dz (29) The olution of current in (29) can be obtained uing Green function a I z L I II () z I ( z' ) I ( z, z' ) dz' I ( z' ) I ( z, z' ) = G + z G dz' (3) where the Green function are given by I I G A = Z e Γ A + Z e 1 j k z 1 1 j k z (31) I II G A = Z 2 e j k z Γ2 A2 e Z jkl e j k ( z L) (32) 2

28 where 2 k ( z L) [ e ] j ' 1+ Γ j k z' Z e = (33) 2 1 A L ( Γ Γ e j k ) j k z' 2 z [ ] j k ' Γ1 e + 1 L ( Γ Γ e j k ) Z e = (34) 2 1 A Since we are intereted in the olution at z = L, from (3) we have I ( ) = L II L I ( z' ) I ( z, z' ) G dz' (35) Auming the tranmiion line i matched at both end, which mean Γ = Γ (35) 1 2 = Equation (34) for derived current reduce to Therefore (35) become I j k z' Ze A 2 = (36) L jk ( z' L) ( L) = I ( z' ) e dz' (37) In order to derive an empirical olution for experimental reult, we aume the tranmiion line i hort o that I ( z' ) = I ( L) i a contant, then (37) become jkl V ( L) 1+ e I( L) = = I ( L) (38) Z 2 jk Likewie, when there i only current ource, we have 21

29 = + = + ) ( ) ( ) ( ) ( ) ( 1 1 z Y V dz z di z V z I Z dz z dv (39) The olution for of thi cae hould be dual to olution for of (29). Therefore, we have (L) V ) I(L jk e L V L V jkl 2 1 ) ( ) ( + = (4) Then, the olution of = + = + ) ( ) ( ) ( ) ( ) ( ) ( 1 1 z I z Y V dz z di z V z I Z dz z dv (41) i uperpoition of (38) and (4), which reult in jk e Z L V L I Z L V jkl 2 1 ] ) ( ) ( [ ) ( + + = (42) From (19) and (28), we know that and both come from the incident field. Thi mean that they are correlated. We can generally aume V I (43) i y i x H Z E = α(ω) For uniform plane wave normal incidence 1 ) ( = ω α, otherwie, it jut a general contant. From (19) and (28), we have ) ( Z V I ω α = (44) which mean (42) can be expreed in a format a = + + = b i x jkl dx L x E Y L I jk e Z L V ), ( ) ( ) ( ) ( 2 1 ) ( 1 ) ( ω ω α ω α (45) 22

30 where 1 + e Y ( ω) = jk jkl α( ω) + 1 2α ( ω) jωc e = Z jkl α( ω) + 1 2α ( ω) (46) 4.4. Meaurement Parameter By the reciprocal property of antenna the incident electric field may be interpolated to a ditance of one meter; the tandardized meaurement ditance. The driving current ource i the meaured ocillocope waveform, initially interpolated into the frequency domain, uing the technique outlined. From (45), becaue we are intereted in E-field radiation, we begin by taking the abolute value of each component. ( L) b V i Z( ω ) = E x ( x, z)dx Z (47) Note that (47) ha only a vertical component of the E-field. Thi i conitent with the meaurement etup and the definition for the E-field component. By definition the meaured radiated emiion i a meaurement of the E-field component, it ha no phae component and correlate to the abolute value of the E-field component. However, the time domain meaurement i a voltage meaurement. Thi wa deemed the mot unobtruive ince it i relatively imple and require no correction other than to divide by the characteritic impedance of the tranmiion line. Equation (47) divide the current ource by the characteritic impedance and olve for the impedance factor in term of the time domain voltage waveform. 23

31 b i ( ) E x x, z dx Z( ω ) = (48) V ( L) Z However, the E-field component in (47) doe not directly correlate to the radiated meaurement. Thi i becaue the radiated emiion meaurement ue antenna factor that account for the antenna lo. Thee factor are imply programmed into the receiver ytem and added to the detected E-field ignal. Thee factor and their impact on the meaurement data are dicued in more detail in a following ection. The final tep i to etablih a meaurable ample tet etup. The challenge i to aure direct correlation between the meaurable controlled etup and that of the tandard EMC qualification etup. For the purpoe of thi work, the Mil-Std-461 military tet etup i ued. However the controlled etup i jut a applicable to virtually any tandard radiated emiion qualification tet etup, commercial or military Meaurement Controlled Setup Thi etup i a imple repreentation of a tandard Electromagnetic Compatibility qualification tet. It main function i to provide an empirically meaurable cable antenna, o that the radiated emiion profile may be meaured and then directly correlated in term of the parameter outlined above. Thi meaurement data can then be interpolated in term of the derived mathematical form. Finally, reultant profile baed in term of the initial waveform capture, in the time domain, can be ued to furnih a ueful prediction of the radiated emiion profile, baed mainly on meaured waveform eaily captured in the time domain. 24

32 Signal Generator Penetration Plate Ground Plane Load Termination 5 cm Standoff 2 m Meaurement Antenna Figure 4-7: Detailed Picture of Controlled Meaurement Setup Meaurement acro the frequency range were made uing the Figure 4-7 etup. The cabling timulu ued for thi evaluation i a tandard quare wave pule with the characteritic hown in Figure

33 Figure 4-8: Scope Capture of Meaurement Waveform 4.6. Empirical Meaurement Laboratory meaurement alway have an unavoidable degree of uncertainty. The typical radiated emiion equation i hown in (49) below. Note (49) ha unit in decibel. E = E + AF Lo (49) Meaured Antenna + The two field component are divided into the meaured electric field and the incident electric field on the meaurement antenna. The additional term i the pre-calibrated antenna factor of the meaurement antenna; thee are given in appendix B. The final lo term i due to variou meaurement attenuation, i.e. Component Inertion Lo, Cable lo, etc. 26

34 Antenna Factor Interpolation The meaurement antenna factor require linear interpolation between any two meaurement point. For example, the antenna factor meaurement file may not have the exact number of meaurement point that the time domain waveform will. Nor are the file likely to have the required correponding frequency point. Therefore a program that firt determine the cloet meaurement point and then linear interpolate between them, in order to calculate a correponding frequency component. Thi interpolation technique ha been implemented uing a Matlab program, given in appendix C. Thi technique inherently introduce a margin of error, but thi margin i low, approximately.1%. Once the antenna factor ha been determined, it can be ubtracted from the meaured field along with the lo and then the meaured electric field can be interpolated to the electric field incident on the cabling. Figure 4-9: Antenna Factor Interpolation 27

35 Figure 4-1: Antenna Factor Divergence Error 4.7. Impedance Factor From equation 37 the impedance factor ha been empirically meaured for a ditinct etup cenario, a twited pair wire over a ground plane. Both conductor are 22 AWG; thi i the mot commonly ued conductor ize for known protocol uch a Mil-Std- 1553, RS-422, RS-485, and Low Voltage Differential Signal (LVDS) ignal interface. Ditinct waveform meaurement with varying rie time, fall time, and pule width were meaured for both etup. Thee are lited below. 28

36 Setup Rie/Fall Time Pule Width Deignator Ambient NA NA AMB Twited Pair 1n 4n TP-1 Twited Pair 1n 1u TP-2 Twited Pair 1n 1u TP-3 Twited Pair 1n 1u TP-4 Twited Pair 1n 1u TP-5 Twited Pair 1n 1u TP-6 Twited Pair 1n 1u TP-7 Twited Pair 1u 1u TP-8 Twited Pair 1u 1u TP-9 The impedance factor for each meaurement i hown in appendix D. 29

37 5. RADIATED EMISSIONS PROFILE PREDICTION Once the incident electric field ha been meaured and the attenuation lo factor have been accounted for, the radiated emiion profile can be predicted. The emiion profile prediction ue equation (48) and (49), defined in term of the meaurement parameter [5] [6]. The final equation i hown a equation (5) below V Z + AF = Z interpolated E Radiated Emiion (5) 5.1. Prediction Example For implicity we will ue dicrete meaurement etup waveform TP-2T. Beginning with a cope meaurement hown in Figure 5.1 for waveform TP-2T the FFT wa taken. Figure 5-1: Time Domain of TP-2T Waveform 3

38 Figure 5-2: FFT of TP-2T Waveform Next the amplitude in voltage wa divided by 5 ohm to get the current value; thi wa the ize of the termination impedance ued. The impedance factor wa calculated already, thi i diplayed in Figure D-2. From thi figure the impedance factor from low to high frequency range in amplitude from to 1 2. However thi impedance factor cannot be aumed, ince the objective i to predict the radiated emiion profile. Therefore a jutifiable alternative would be to ue the next highet impedance factor; thi i the TP-1T impedance factor waveform. Therefore uing the TP-1T impedance factor waveform and the calculated FFT from the TP-2T time bae meaurement we are able to predict the emiion profile. Figure 5-3 how the predicted veru meaured radiated emiion profile. 31

39 Figure 5-3: Predicted Radiated Emiion Profile Notice the predicted emiion envelope differ from the meaured profile by 2dB. Thi emiion profile tell the cognizant deign engineer preciely how much hield attenuation thi cable will require, relative to the pecification limit. Another alternative would be to imply chooe a threhold impedance factor value. Figure 5-4 how a predicted emiion profile baed on a nominal impedance factor value of 1. Notice the peak emiion i till well within the expectable margin. 32

40 Figure 5-4: Predicted Radiated Emiion Profile Uing Nominal Value for Impedance Factor 33

41 6. CONCLUSIONS 6.1. Overall Technique The overall technique i ound and intuitive. However the actual implementation wa fraught with logitic type iue. Empirical data meaurement were required and thi correpond directly to budgetary contraint on man hour, equipment time, and lab ue. Thi thei i the non-recurring engineering portion of the proce. From here on data will be taken in conjunction with routine teting effort; however thi effort laid the ground work Matlab Implementation Matlab cannot upport data manipulation of matrice larger than Thi i a fundamental deign concept and cannot be overcome. The FFT require more data ample for better accuracy o thi wa a natural inhibitor. However 2 2 wa deemed ufficient, any more would have diminihing return Matrice Manipulation in Matlab Matrice require ditinct mathematical technique. For example, indexe mut correpond. Thi i impoible with empirical data. Receiver and Ocillocope have predefined interval meaurement baed on environment, pan, etc. Therefore interpolation wa required for all of the empirical data; thi wa unforeeen and led to a lengthy delay. 34

42 6.3. Empirical Meaurement Empirical meaurement by definition have many inherent apect that are otherwie over looked or jut undertood. However every apect mut be accounted for in a theoretical derivation. For example, antenna correction factor are meaured quantitie. Antenna are required to undergo a routine annual calibration. However the calibration i not recorded a continuou, intead it i made at dicrete point along the frequency pectrum. Another, everely limiting factor wa the inability to view real-time data collection of the ocillocope meaurement. Becaue the cope waveform were o tightly ampled; imple program uch a Microoft Excel were unable to view them. Microoft Excel i limited to 65,536 value. Thi wa a real problem later becaue ome data had become corrupted or wa not recorded correctly and needed to rerecord. However the opportunity to ue laboratory time and equipment had paed Recommendation The author goal wa to etablih a proce, the non-recurring portion at leat, o that progreively more and more recorded meaurement could be ued in conjunction with thee technique to further bolter the accuracy of thi approach. The only recommendation for improvement would be delineate according to rie time and pule width a much a poible. Thi would allow more direct comparion, even though a thi paper demontrated it i not neceary. Alo, the author would like to ee the overall technique re-programmed into an alternate program language and made into an executable file for ditribution. A it tand now each program component i not well 35

43 mehed with it predeceor. However, much more fluent programming i well beyond the cope of thi effort and the author kill. 36

44 APPENDIX A: MEASUREMENT ANTENNA FACTORS 37

45 1. Correction Factor In db Frequency In MHz Figure A-1: Rod Antenna Factor 3. Correction Factor In db Frequency In MHz Figure A-2: Bi-conical Antenna Factor 38

46 Correction Factor In db Frequency In MHz Figure A-3: Double Ridge Horn Antenna Factor 5. Correction Factor In db Frequency In GHz Figure A-4: Horn Antenna Factor 39

47 APPENDIX B: SAMPLE OF MEASURED WAVEFORMS 4

48 Figure B-1: Sample 1 Scope Capture, FFT of Scope Capture, and RE Meaurement 41

49 Figure B-2: Sample 2 Scope Capture, FFT of Scope Capture, and RE Meaurement 42

50 APPENDIX C: MEASUREMENT SETUP PICTURES 43

51 Figure C-1: 1 khz-3mhz Meaurement Setup Figure C-2: 3 MHz-2MHz Meaurement Setup 44

52 Figure C-3: 2MHz-1GHz Meaurement Setup Figure C-4: Waveform Generator 45

53 Figure C-5 Termination Shielding Figure C-6: Feed and Bulkhead 46

54 APPENDIX D: IMPEDANCE FACTOR PLOTS FOR TWISTED PAIR MEASUREMENTS 47

55 Figure D-1: Impedance Factor for TP-1T Waveform Figure D-2: Impedance Factor for TP-2T Waveform 48

56 Figure D-3: Impedance Factor for TP-3T Waveform Figure D-4: Impedance Factor for TP-4T Waveform 49

57 Figure D-5: Impedance Factor for TP-5T Waveform Figure D-6: Impedance Factor for TP-6T Waveform 5

58 Figure D-7: Impedance Factor for TP-7T Waveform Figure D-8: Impedance Factor for TP-8T Waveform 51

59 Figure D-9: Impedance Factor for TP-9T Waveform 52

60 LIST OF REFERENCES 1. IEEE EMC Society Sympoia Record 1955 to 1995, Volume IEEE1 through IEEE4, (IEEE Publihing, New Jerey, 1995) 2. Military Handbook-241B, Deign Guide for Electromagnetic Interference (EMI) Reduction in Power Supplie, (3 September 1983) 3. E. Oran Brigham, The Fat Fourier Tranform, (Prentice Hall Inc., 1974) 4. Robert A. White, Spectrum & Network Meaurement, (Noble Publihing Inc., 1993) 5. Mathwork Technical Note 172, Uing FFT to Obtain Simple Spectral Analyi Plot, (The Mathwork Inc., 1994) 6. Albert A. Smith, Jr., Coupling of Electromagnetic Field to Tranmiion Line, 2nd Edition (Interference Control Technologie Inc., New York, 1989) 7. Edward Vance, Coupling to Shielded Cable, (John Wiley & Son Inc., 1978) 8. Clayton R. Paul, Introduction to Electromagnetic Compatibility, (John Wiley & Son Inc., 1992) 9. William E. Boyce and Richard C. DiPrima, Elementary Differential Equation and Boundary Value Problem, (John Wiley & Son Inc., 1992) 1. Joeph J. Carr, Practical Radio Frequency Tet & Meaurement: A Technician Handbook, (Newne, 1999) 11. David Pozar, Microwave Engineering, (John Wiley & Son Inc., 1998) 53