EXPERIENCE OF ADVANCED METHODS BASED ON FFT TEST APPLICATION

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1 th Workshop on DC Modellg and Testg -September 9-10, ordeaux, France EXPERIENCE OF DVNCED METHODS SED ON FFT TEST PPLICTION Vladimír Haasz, Mart Pokorný Dept. of Measurement, Fac. of Electrical Eng., Czech technical university Prague Technická, CZ-1667 Prague 6, Czech Republic Phone (0 ) 5 186, Fax (0 ) , haasz@feld.cvut.cz, WWW: bstract: The methods for testg of DC dynamic quality (FFT Test, est Susoidal Curve Fit Method, Histogram Test) require a low-distortion testg signal. It brgs some problems for testg of high-resolution DCs, same as middle-resolution high-speed DCs. The paper describes an practical experience usg two alternative method - the Spectrum Correction Test and the Two-tone method. The systems for an evaluation of both tests were designed and realised. The first experience and achieved results are published this paper. The experiments have shown, that these methods are usable, but before their application for testg of high resolution DCs it is necessary to solved several practical problems. 1. INTRODUCTION Well known testg methods (FFT Test, est Susoidal Curve Fit Method, Histogram Test) standardised the IEEE Standard for Digitisg Recorders [1] use the se wave as the testg put signal. The Total Harmonic Distortion (THD) should be lower than the Signal to quantisation Noise Ratio (SNR) of the D converter under test. It can be a great problem the case of testg of high-resolution DCs. To test these DCs a wider frequency range, the advanced methods based on the FFT test can be used. It is gog on the well known Two-tone test and the Spectrum Correction Test designed and evaluated at Dept. of Measurement of CTU. The basic idea of the Spectrum Correction Test is the fact, that the FFT is a lear operation. Therefore it is possible to recognise spectral les, which belongs to the generator used and the les arisg due to non-learity of a tested DC. The spectrum measured on the DC s output is corrected for the known spectrum of the generator and the resulted spectrum corresponds to the non-learity of the tested DC. lso a computer simulation confirmed that this method can be successful applied - see []. The Two-tone method uses a modified testg signal which is mixed of two se waves stead of one hi-quality se wave. The processg part of the method is same as of the standard FFT test; that means a measured data are transformed to the frequency doma usg Discrete Fourier Transform. However, the parameters calculation (the number of effective bits and the signal to noise ratio) differs from the standard FFT test. The signal to noise ratio is usually used for the number of effective bits calculation, two-tone characterisation mode it should be better to call it Intermodulation Distortion Ratio (IMD). The IMD ratio reflects quality of the tested DC as well as the Signal to Noise Ratio - see [] and [] detail.. TWO TONE METHOD - SIMULTION The goal of this task is an evaluation of an output signal of a non-lear /D converter, whose put signal is a sum of two se waves with a defed distortion. The testg signal is expressed as fundamentals and a sum of harmonics: v N IN = 1 s( ω1t) + i s( iω1t) i= where, and N are amplitudes respectively order of harmonics. The DC s transfer characteristic is a polynomial function with a defed distortion (their order correspond to the order of harmonic caused by the non-learity; a, b, c, d, e are coefficients of the polynom): v out + = a v simplified model was used for simulation. The limited DC s transfer characteristic of the rd order was applied v N 1 s( ω t) + i s( iω t) i= + b v out = a v + c v + b v + d v + c v and two ideal se waves are considered. = sω t + s ω t vin 1 Let s apply the simplified generator output signal to the limited transfer characteristic. The sum of an offset and several harmonic functions is the result of the DC s output voltage: + + e v 5 (1) () () ()

2 + = b + a s ω1t + a s ω t vout cos ω 1t b cos ω t c b 1 c s ω t + b cos( ω1t ω t) s ω t b cos( ω1t + ω t) + c s(ω t ω1t) + + c s(ω 1t ω t) c s(ω t + ω1t) c s(ω 1t + ω t) (5) s mentioned above, the amplitude spectrum of the v out contas an offset, fundamentals, harmonics of the first frequency X(iω 1 ), harmonics of the second frequency X(iω ), and termodulation les X(jω 1 ± kω ). Let s defe the symbol IM(jω 1 ± kω ) as a termodulation le and H(iω) as a harmonic le. The formula (5) shows the fact that the termodulation ratio IMD reflects the quality of the tested DC by the same way as the SNR does. The coefficients of the non-lear DC s transfer characteristic conta both IM and H terms of v out. The simulated spectrum shows important les presented the v out (Fig. 1.). The les caused by the harmonic distortion of the generator are deep under the noise floor (quantisation noise of the 16bit DC), its amplitude level is a multiplicand of the amplitude of the distortion le and the correspondg coefficient of the DC s characteristic b or c. C C C C C C where the numerator of the fraction is an RMS value of the two ideal se waves with amplitude equal to the quarter of the DC s full scale. The denomator is an RMS value of the quantisaton noise of an ideal DC. Simplification of the formula leads to: SNR DT = 6.0n 1.5 (7) where n is the number of bits of the DC. The formula for the ENO is defed by a substitution of ENO to n and SNR to SIND. Signal to noise and distortion ratio can be calculated usg SIND X ( ω1) + X ( ω ) 10log M / X ( i) DT = i kω1, kω where k is a positive teger begng two (to remove harmonic distortion).. MESUREMENT RELISTION ND PROLEMS CONNECTED WITH IT The measurg systems for testg of D board dynamical parameters which apply the both methods mentioned above were design and realised to verify the theoretical consideration and the computer simulations. The 16-bits plug- D board T-I-16XE-10 was used for this purpose. However, the practical realisation brgs several problems, which is necesssary to solve..1. Spectrum Correction Test The 1-bits D board T-MIO-16-E and the low-cost generator HP 10 with warranted THD < -68 d was applied for the first experiment. Their THD is too high for a direct testg of a 1-bits board and therefore it is suitable for verification of the designed method. The low-distortion generator SRS-DS 60 with warranted THD < -100 d was used to compare the results of the direct FFT method and of the Spectrum Correction Test. The spectrum of the low-cost generator was measured directly this case (without a Notch filter) usg the 16-bits D board T-I-16E-10. The connection of the system used for this test is shown the Fig.. (8) Fig. 1. Simulated spectrum Two-tone Method. DC s characteristic is non-lear ( - first frequency, - second frequency, C - termodulation). The Effective Number of its (ENO) is calculated from the dual-tone Signal to Noise plus Distortion ratio (SIND). Let s defe Signal to Noise Ratio (SNR), similarly to the sgle tone: LOW-COST GENERTOR OF TESTING SIGNL (HP 10) LOW-DISTORTION GENERTOR OF TESTING SIGNL (SRS-DS 60) T-I-16XE-10 T-MIO-16E- Fig.. The system for the first experiments usg Spectrum correction test. PC RMS SNR DT = 10log RMS s qi (6) The achieved results are shown Table 1. The results confirm, that the designed method is applicable practice.

3 TLE 1. THE COMPRISON OF RESULTS OF THE SPECTRUM CORRECTION TEST USING LOW-COST GENERTOR, ND DIRECT FFT TEST USING LOW-DISTORTION GENERTOR. Spectrum correction test Direct FFT test Without correction fter correction Low-distortion generator SIND Number of eff. bits However, two additional problems have to be solved to apply this test method for testg of high resolution boards - the accurate spectrum measurement of the testg signal, and the implementation of a suitable correction algorithm. spectrum of the low-distortion sewave generators is usually measured usg a notch filter for suppression of the fundamental. The measured spectrum must be corrected for the characteristic of the notch filter used this case. dditionally, the samplg of the DC and the FFT analyser has to be synchronised to ensure exactly the same conditions for the test of DC and for the generator s spectrum measurement. Notch filter characteristics are measured by a standard method usg a circuit analyser. The algorithm which is applied for the correction of the transfer function uses the measured frequency characteristic (both the amplitude F(f i ) and the phase PF(f i )) the form of a data table. The whole characteristic is reconstructed from a table values for each frequency b usg a lear terpolation: F(f i ), PF(f i ) F(f m ), PF(f m ). Then the amplitude and phase characteristics of the notch filter are transformed to the complex plane - to the -phase and the quadrature part: F(f m ), PF(f m ) Re F(f m ), Im F(f m ). The correction of the measured spectrum is then very easy - it is a subtraction of competent components of the measured spectrum of the testg signal TS M (f) and of the filter characteristic F(f): Re TS COR (f m ) = Re TS M (f m ) - Re F(f m ); Im TS COR (f m ) = Im TS M (f m ) - Im F(f m ). critical part of the notch characteristics is around the notch frequency, where the amplitude is changg rapidly and the phase turns from -π to +π. Fortunately this narrow frequency region is not necessary to correct. The correction algorithm is also described by the flowchart the Fig.. The system for an evaluation of the samplg synchronisation was also realised. The high resolution high frequency digitizer HP E10 was used for measurement of the spectrum of the testg signal, because a commercial stand alone FFT spectrum analyser are not able to measure the complex spectrum (both -phase and quadrature components) and make not possible to synchronise samplg rate. The hardware synchronisation of the generated signal and the samplg rate of both a plug- board and the VXI module were applied to use the FFT without a wdow function. The correction should be easier and more precise this case, because no wdow function have to be used. The most simple solution usg an external clock generator was realised for the first experiments - see Fig.. However, the achieved results have shown the followg problem - when an external clock (5 MHz) is used for synchronisation of a tested D board, a significant additionally ternal disturbance arises. It is good perceptible from a grow of spurious the output spectrum of the tested D board usg an external clock. Therefore the more complicated solution have to be used. Read data from table F(f i ) F(f m ), PF(f i ) PF(f m ) F(f m ), PF(f m ) Re F(f m ), Im F(f m ). Re TS COR (f m ) = Re TS M (f m ) - Re F(f m ) Im TS COR (f m ) = Im TS M (f m ) - Im F(f m ) m = 1,...,m MX GENERTOR OF TESTING SIGNL (HP 10) SYNCHRONISTION GENERTOR OF SYNCHRONISTION SIGNL Corrected spectrum of testg signal Fig.. The flowchart of correction algorithm NOTCH FILTER TESTING SIGNL T-I-16XE-10 HP E10 PC VXI MIN- FRME LN Fig.. The system for evaluation of the samplg synchronisation One possible solution is e.g. to use an ternal clock of the tested board for the synchronisation of other struments. However, this signal must be leaded to an output connector of the tested D board, and the used low-distortion generator has to enable synchronise with an external clock signal. The second solution makes it possible to use any low distortion generator without a clock put. Two additionally frequency multipliers are used here - see Fig. 5. The first is used for a generation of a samplg frequency of the tested board. Its multiply coefficient m 1 determed the number of samples per period. The second generates the clock frequency for the VXI digitiser used - its multiply coefficient m should be equal to the used decimation coefficient of digitiser. The external samplg signal should not theoretically cause the additional ternal disturbance. The

frequency divider usg the dividg coefficient d = m 1-1 (samplg d period, one sample each period) have to be connected to the output of the first multiplier to apply a stroboscopic samplg,. TLE.

4 frequency divider usg the dividg coefficient d = m 1-1 (samplg d period, one sample each period) have to be connected to the output of the first multiplier to apply a stroboscopic samplg,. TLE. THE NUMER OF EFFECTIVE ITS EVLUTED Y THE DUL TONE METHOD ND THE STNDRD FFT METHOD f (khz) ENO-DT(-) ENO-ST(-) LOW-DISTORTION GENERTOR TESTING SIGNL T-I-16XE-10 PC LN f Sa = m 1.f SIG f Sa = (m 1-1). f Sa EXT.SMPLING NOTCH FILTER HP E10 VXI MIN- FRME C C f Cl = m.f Sa (f Cl = m.f Sa) EXT. CLOCK Fig. 5. The system usg two additionally frequency multiplier for synchronisation a) f 1 = 108 Hz, f = 1187 Hz, f s = 98 khz, M = 768,.. Two tone method Prciple of the system used is illustrated by the block diagram Fig. 6. The 16-bits /D board T-I-16XE-10 produced by the National Instruments has been tested usg the method. Two rüel&kjaer K1051 generators and a passive resistors circuit for a signal summation have been used. C C C C C C Generator 1 Generator SUM tested DC FFT Spectrum Fig. 6. lock diagram of two-tone method dependence of ENO on the put signal frequency has been measured. Table shows a results evaluated by the Two-tone method and by the standard FFT Test. The difference between results is probably caused by the low spectral purity or the higher noise floor of the second generator and consequently by the crease of the whole noise and above all the termodulation les IM(ω 1 +ω ) and IM(ω -ω 1 ). This fact is shown Fig. 7. (The second harmonic of the Generator is 5d higher then of the first one.). CONCLUSION The methods for testg of /D converters described above - the two-tone method and the Spectrum Correction Test - makes it theoretically possible to test middle resolution converters by harmonic generators, which quality would not be sufficient for a direct testg usg the FFT Test or the est Susoidal Curve Fit Test. However, the results of the first experiments showed, that there are some problem by practical realisation. These problems and their solution will be described full paper. b) f 1 = 56.6 Hz, f = Hz, f s = Hz, M = 768, Fig. 7. Real measured spectrum - plug- board T-I-16XE-10, Dual-Tone Method: lackmann-harris wdow ( - first frequency, - second frequency, C - termodulation) 5. CKNOWLEDGEMENT The results of the project No. 101/98/1508 New methods for testg of systems for dynamic measurement which is supported by the Grant gency of the Czech Republic were used this paper REFERENCES [1] IEEE Std IEEE standard for digitisg waveform recorders The Institute of Electrical and Electronics Engeers, Inc., New York, 199. [] Pokorný, M., Roztoèil, J., Haasz, V.: Suppression of Test Signal Distortion by D-modules Dynamic Testg. Symposium IMEKO TC-, Naples 1998, pp [] enkais, M., Le Masson, S., Marchegay, P.: /D Converters Characterization by Spectral nalysis Dual-Tone Mode. IEEE Transactions on Instrumentation and Measurement, vol. no. 5, October [] Dallet, D., enkais, M., Le Masson, S., Marchegay, P.: n Overview of the different methodologies for the spectral nalysis the Dynamic Characterisation of /D Converters. International Workshop on DC Modellg, Smolenice 1996, pp

Measurement of RMS values of non-coherently sampled signals. Martin Novotny 1, Milos Sedlacek 2

Measurement of RMS values of non-coherently sampled signals. Martin Novotny 1, Milos Sedlacek 2 Measurement of values of non-coherently sampled signals Martin ovotny, Milos Sedlacek, Czech Technical University in Prague, Faculty of Electrical Engineering, Dept. of Measurement Technicka, CZ-667 Prague,