ML20116C370

Rev 1 to Test Rept for Fourier Transform

ML20116C370
Person / Time
Site:	Browns Ferry
Issue date:	06/03/1996
From:	Freeman M, Lombardo M, Metcalf M NATIONAL TECHNICAL SERVICES
To:
Shared Package
ML20116C355	List: ML20116C354 ML20116C370
References
33069-97N, 33069-97N-R01, 33069-97N-R1, NUDOCS 9607310113
Download: ML20116C370 (15)

Text

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. ATTACHMENT 2 Test Report No. 33069-97N l NTS Job No. 60789-97N Revision 1

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TEST REPORT FOR FOURIER TRANSFORM FOR TENNESSEE VALLEY AUTHORITY POST OFFICE BOX 2000 DECATUR, AL 35609 Purchase Order Number: TV-96218V The program outlined within this report (Attachment A) was conducted in accordance with the NTS/ Northeast Quality Manual, Revision 3, dated July 14; 1992. This insures that the applicable provisions of 10CFR, Part 21 and Part 50, Appendix B are fulfilled.

Reviewed and i Approved by: / At n

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Indkddent Reviewer, kuclear Services NTSLNortheast i Reviewed and j Approved by: M 3 vi > Date: 3i liY

$lality Representative, Nuclear Services NTS/ Northeast JED/6078997.RV1 9607310113 960725 PDR ADOCK 05000259 P PDR

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ATTACHMENT A

] TEST REPORT NO. 33069-97N i

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i Report No. 33069-97N l Revision 1 i i )

bY REVISION RECORD REVISION PAGE PARA APPROVED NUMBER NUMBER NUMBER CHANGES OR ADDITIONS BY 0--- -

FIRST-ISSUE---- -- ------

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Changed " Revision 0" to " Revision 1".

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Attachment 3.0 Added text.

A,4 & 5 N4p Attachment Figure 3 Replaced Figure 3.

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j Report No. 33069-97N Revision 1

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l TEST REPORT No. 33069-97N TEST REPORT FOR FOURIER TRANSFORM PREPARED FOR Tennessee Valley Authority Post Office Box 2000 Decatur, AL 35609 PREPARED BY:

NATIONAL TECHNICAL SYSTEMS / NORTHEAST 1146 Massachusetts Avenue Boxborough, MA 01719 Ths report speelnestsere and endler We bdermelsen preendwee eeritamed herein tepresort the reedte of testq erticles/peducia edentsfsed wW ecl approved by the ehent.

demonstreens eWessency, performones, rehehehty, er any other eherectorates of tte articles bems tested er esmder ereeraemere prarh er purpees.

for a petsader eartrliessen by NTS of the eeuwmers tested, ner deem it repreeww any statement sehetseewv es to as merchentebe eo e test arisese er ownder

. . Repart Number

• 33069-97N

. P.O. Number TV 96218V WO Number 60789-97N Date 21 May 1996 REVISION PAGE Rev.No. Date Pace No.

Original Para.No. Descriotion 21 May 1996 1 31 May 1996 4-5 3.0 Added Text A-3 Figure 3 Replaced Figure f

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Report Number 33069 97N

. JO Number 60789 7N Date 21 May 1996 SIGNATURES I

l Prepared bY & >>>AAs nf, Date C1//94>

Maureen E. Lombag Technical Writer I Written by -

A M# DateFJ b fc Martin J. Freepfan,'E/C Engineer Approved by Y/f-11A J 41 ._Date C-3 ^9C MartiriJ. Mgaff, EMC Ma r li

' Report Number 33069 97N P.O. Number TV 96218V IJO Number 60789-97N Date 21 May 1996 TABLE OF CONTENTS 4

l Section P_agg i

1.0 INTRODUCTION

1

2.0 REFERENCES

1 3.0 THE FOURIER SERIES / TRANSFORM 1 I.

i APPENDIXES l APPENDIX A Figures A-1 iii

Riptrt Numbir l 33069-97N P.O. Number TV 96218V I 4

UO Number 60789 97N Date 21 May 1996 j i

1.0 INTRODUCTION

To solve many engineering problems, one needs to know the response of a Linear Time. Invariant system to some input signal. If the input signal can be broken up into simple signals and one knows how the system responds to 4

these simple signals, then one can predict how the system will behave to this ,

complex input signal. Therefore anything that can break a signal down into its  !

I constituent parts would be very useful. One such toolis the Fourier Series.

2.0 REFERENCES

1 2.1 Tennessee Valley Authority Purchase Order Number TV-96218V.

I 2.2 NTS Interdivision Transfer Form and Interdivision Job Request dated 5 April 1996. -

2.3 NTS Quality Program Manual dated 17 October 1995.

1 3.0 THE FOURIER SERIES / TRANSFORM With the exception of some mathematical curiosities, any periodic signal of period T can be expanded into a trigonometric series of sine and cosine functions, as long as it obeys the following conditions:

1. f(t) has finite number of maxima and minima within T

2. f(t) has finite number of discontinuities within T, and

, 3. It is necessary that the integral from 0 to T of the function f(t)dt be less

than infinity, i.e.

T i

k{;)l C bd 1

0 1

Rmtrt Number 33069-97N P.O. Number TV 96218V UO Number 60789 97N Date 21 May 1996 If all of these are true then the signal can be represented as:

" 00 a 2 SD .4T 2 7 n(

OwCDS.iYnt Y bh

{ (t,) s g' + nst 7 n=l and the coefficients are: .

to+T "5 T f(t) CO S 7 db to+T

= f(t) SM 7 to t,+T g,

• Any electrica! signal can be viewed from either of two different standpoints:

1. The time domain l 2. The frequency domain The domain with which we are most familiar is the time domain. This is akin to the trace on an oscilloscope, where the vertical deflection represents the i signals amplitude, and the horizontal deflection represents the time variable.

The second representation is the frequency domain. This is like the trace on a spectrum analyzer, where the horizontal deflection represents the frequency j variable and the vertical deflection represents the sign.:! amplitude at that

frequency.

1 Any give signal can be fully described in either of these two domains. We can

- go between the two domains by using a tool called the Fourier Transform.

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Report Number 33069-97N P.O. Number TV-96218V UO Number 60789-97N i

Date 21 Mey 1996 i

} Any integrable function f(t) uniquely defines its Fouriercoefficients orits Fourier j Transform. Conversely, a complete set of Fourier coefficients or a Fourier 1 Transform uniquely defines the corresponding function f(t).

i i The Fourier integral expansion describes f(t) as a " sum" of infinitesimal I

sinusoidal components with frequencies "f" or circular frequencies "W" (where

W = s(PI)f (f >0)); the functions 2(c(f)] and arg c(f) respectively define the

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amplitudes and the phase angles of the sinusoidal components. The treatment of Fourier integrals has been unified through the introduction of generalized (integrated) Fourier Transforms. These Fourier Transforms allow for the ready

calculation of the amplitudes and phase angles of the various harmonic components that make up the frequency domain representation of the time i domain signal under investigation. Many engineering and mathematics l handbooks tabulate the Fourier Transforms for various commonly encountered signal waveforms.

i 4 - In the field of EMI/EMC emissions and/or susceptibility analysis our main concern usually is not with the actual frequency domain representation of a

digital signal, _ but in the overall envelope of the frequency domain representation. Rarely does one worry about the individual sine / cosine components (harmonics) of the digital signal.

l Figure 1 in Appendix A shows a segment of a generic digital communications l j signal pulse stream in the time domain, i

i Figure 2 in Appendix A shows, qualitatively, the frequency representation of l this same digital signal pulse stream.

1 SAMPLE CALCULA TION 4

i The !EC 801-4 conducted susceptibility analysis has been selected as the vehicle for presenting a sample calculation. Since the IEC 801-4 test is performed using time domain pulses the IEC 801-4 pulse train waveform must be converted to the frequency domain so as to be directly comparable to the site survey worst case conducted emissions envelope. The vehicle '

used for this time domain to frequency domain conversion is the Fourier Transform.-

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Report Number 33069 97N P.O. Number TV 96218V UO Number 60789-97N Date 21 May 1996 The susceptibility pulse used in the conduct of a IEC 801-4 test is as shown on Figure 3 found in Appendix A.

The current 'waveform is identical in shape to the voltage waveform as it is inserted into the equipment via a 50 Ohm termination. The Fourier Transform for this pulse configuration is:

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cl +T sm nW YT Sm nM

\D gMA C n= 20 log ZA T nr 4/T oy Inserting the values for the various parameters we can calculate the amplitude of the fundamental of the sinusoidal components (158 dBuA).

The envelope of the sinusoidal components is flat up to the first breakpoint frequency given by f, = 1/(pl)d (6.3 MHz where d = 50 ns). From the first break point frequency the envelope drops off at a rate of 20 dB/ decade until the second breakpoint frequency (given by f2 = 1/(pi)t,63.3 MHz in this case where t = 5 ns), after which the envelope drops off at rate of 40 i dB/ decade. Similarly, we ca'n calculate the envelope for the pulse bursts i which has the effect of reducing the frequency of the flat portion of the spectral envelope down to a frequency of approximately 3 Hz. Figure 4 in Appendix A, shows, quantitatively, the envelope of the frequency  ;

representation of this IEC 801-4 pulse stream. The previously described analytical procedure, applicable to the IEC 801-4 pulse train conversion from the time domain to the frequency domain, is equally applicable to any and all conversions from the time domain to the frequency domain wherever tests were performed using time domain procedures.

Calculating the amplitude value of 158 dBuA is accomplished by inserting the 40 Amp amplitude value (2 KV + 50 0 = 40A) and the pulse train waveform parameters (from Figure 3) into the equation given above for Co .

Note that the terms within the absolute value bars are the form sin w/u and for small values of x the term sin x/g is equal to 1. Therefore the j equation for C, reduces to: Cn = ao I.$ [gA F + 12.0 ABuA

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, , Report Number 33069 97N P.O. Number TV-96218V UO Number 60789 97N Date 21 May 1996 Inserting the proper values into this equation (for n = 1) yields an amplitude value for the fundamental frequency component of 158 dBuA.

The formulas fori f and2 f (F, dd and Fg5 f) emperically derived and well known within the EMI/EMC community.

are Knowing the formula for both f and f 2allows one to arrive at the complete i

frequency domain representation by only calculating three items, namely, C,,

at the fundamental and frequencies f and f2.

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Report Number 33069 97N P.O. Number TV-96218V 00 Number 60789 97N I

Date 21 May 1996 i

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APPENDIX A ,

Figures  ;

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FIGURE 4: Envelope of IEC 801-4 Test Pulse Stream A-5

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