Metrol. Meas. Syst., Vol. XVIII (2011), No. 2, pp METROLOGY AND MEASUREMENT SYSTEMS. Index , ISSN

Transcription

1 METROLOGY AND MEASUREMENT SYSTEMS Index , ISSN DAC TESTING USING MODULATED SIGNALS Pavel Fexa, Josef Vedral, Jakub Svatoš CTU Prague, Faulty of Eletrial Engineering Department of Measurement, Tehnika 2, 16627, Prague 6, Czeh Republi ( fexap1@fel.vut.z, , vedral@fel.vut.z, , svatoja1@fel.vut.z, ) Abstrat This doument analyses qualities of methods used for testing dynamial parameters of Digital-to-Analog Converters (DAC) using a multi-frequeny signal. As the soure for these signals, Amplitude Modulated (AM) and Frequeny Modulated (FM) signals are used. These signals are often used in radio engineering. Results of the tests, like Effetive Number of Bits (ENOB), Signal-to-Noise and Distortion (SINAD), are evaluated in the frequeny domain and they are ompared with standard results of Sine Wave FFT test methods. The aim of this researh is firstly to test whether it is possible to test a DAC using modulated signals, seondly to redue testing time, while estimating band performane of DAC. Keywords: Digital-to-analog onverter, ENOB, Signal-to-noise and distortion - SINAD, FFT analysis, Crest Fator (CF) Polish Aademy of Sienes. All rights reserved 1. Introdution This work omes out from standards for Analog-to-Digital Converters (ADC) testing and uses this method for DAC testing. Almost all dynami methods an be applied to ADC as well as to DAC. In the field of dynami ADC testing there are several well-desribed methods used. Standardized methods like Sine Wave Fit Test or FFT (resp. DFT) Test are using high spetrum purity input signals. The ENOB, SINAD, Total Harmoni Distortion (THD), Signal Non-harmoni Distortion SNHR, Spurious Free Dynami Range SFDR, and Intermodulation Distortion IMD an be determined with high auray by these methods [1, 2, 3]. However, these tests are relatively time-onsuming, espeially when it is neessary to analyze the frequeny harateristi of these parameters. A possible way to shorten the test duration is to drive the input of an ADC by a multi-tone signal, or generate a multi-tone signal with a DAC. For example, the exponential signal an be onsidered as a typial example of a multifrequeny signal, and it is to be generated with a passive RC iruit driven by a retangular generator. Unfortunately, the spetrum amplitude frequeny harateristi of the exponential signal falls with a slope of -20 db per deade [4, 5, 6]. This fat auses variation of results reahed by lassi methods using a signal with onstant amplitude and the exponential signal test method. Appliations of a frequeny-swept signal suitable for eonomi tests for ADC testing are desribed in [4]. The band signal is used to save the testing time. A test using an AM signal produes the average performane of the Devies Under Test (DUT) i.e. SINAD and ENOB. It means that 3 different tones are used for testing at the same time. The time-saving benefit is ahieved using every band signal. However, AM and FM signals are frequently used in ommuniations and they an be used for DAC testing too. It is possible to use a similar approah as one used for testing of the ADCs. The DACs are widely used in signal generators, thus it is very important to test them using inartifiial signals. Still it annot be Artile history: reeived on Jan. 12, 2011; reeived in revised form on Feb. 17, 2011, aepted on Mar. 28, 2011; available online on May 20, 2011; DOI: /v

2 P. Fexa, J. Vedral, J. Svatoš: DAC testing using modulated signals lear why just modulated signals are used, a similar spetrum has generally a multi-tone signal, whih is omposed of sum of hosen sine-waves. In this ase the answer is very simple: only 4 are needed to desribe the modulated signal (amplitude, arrier frequeny, modulation frequeny, modulation index). It is signifiant when the number of tones is inreasing. A FM signal whih is omposed of 33 spetral omponents is still defined by 4 parameters; a general multi-tone signal is defined by 33 amplitudes, 33 frequenies and optionally 33 phase shifts. This paper shows only AM and FM signals for ADC or DAC testing, however the original idea is to test a general DUT by the signal whih results from natural appliation of eah DUT or it is similar to appliation. In radio engineering a DUT is for example a generator with hosen modulation and a reeiver. The result from this test is the Bit Error Rate Ratio BERR, in this ase it is a mixed signal test. The testing signal in this ase is the hosen modulated signal. In this paper the DUT is not a transmitter, a hannel with noise and a reeiver, but the DAC and its performane is measured using SINAD and ENOB. Not every type of signal is suitable for DAC testing. It has to impeah limitation of DACs like bandwidth or slew rate et. (digital modulation like QAM represents this type, whih is not suitable for DAC testing) 2. FFT tests The performane of the DUT is evaluated in the frequeny domain in a FFT test. The data u 0, u 1... u M 1 are sent to the input of the DAC, generated, measured by an ADC and transformed by the DFT (FFT) algorithm. In ase of oherent sampling the following ondition is valid: K f SIGNAL = m f SAMPLING, where K and m are integers. If this ondition annot be satisfied it is neessary to apply a window. 2.1 Standard sine wave FFT test of AD onverters Signal Noise and Distortion SINAD is the ratio of the RMS value of the arrier frequeny to the mean value of the root-sum-square of all other spetral omponents, inluding harmonis, but exluding the DC omponent [1, 2,3]. SINAD Signal NAD RMS = 20 log, (1) where n is the number of nominal bits of the onverter under test. For a single-tone signal, SINAD and ENOB are given by the following equation [7], RMS SINAD = 6.02ENOB (db). (2) When the oherent sampling ondition is not satisfied, it is neessary to apply the proedure of input signal windowing. Every operation, inluding windowing, whih hanges the shape of the signal, hanges also the CF. Then another formula for an ENOB omputation has to be applied (6). This phenomenon is stated in [8], its priniple will be briefly shown. For estimating ENOB, it is neessary to ompensate the CF influene. There is the known formula for SNR: σ 12σ SNR = 10 log = 10 log (db); (3) σ 2 2 x x n 2 n X PP X SNR n CF σ PP = log = log (db), (4) n

3 where σ n is standard deviation of noise, σ x is standard deviation of the input signal, X pp is the peak-to-peak value of the input signal, n is the nominal number of bits and CF = X pp / (2σ x ). For a sine wave signal or FM signal, the amplitude X m = X pp /2 = FS/2, theσ x = X PP / 2 / 2, then n is given by the next equation [8], SNR 1.76 n = (bit). (5) 6.02 It is possible to express the general formula for ENOB using the CF orretion [9]: ENOB or SINAD log CF = (bit). (6) 6.02 For the SINAD orretion the formula (2) is used, only ENOB is replaed by ENOB or. This approah is equivalent to the orretion of window influene [10]. 2.2 Amplitude modulation FFT test The amplitude modulated signal is defined by formula [11] ( osω ) u = U + U t sinω t = AM m m U m = U sinωt + sin ( ω ωm ) t + sin ( ω + ωm ) t. 2 The modulation depth m AM = U m /U affets the harater of the frequeny spetrum of the signal. We onsider Dual Side Band amplitude modulation with m AM 1. Its spetrum ontains a arrier with frequeny ω, amplitude U and two sideband omponents with frequenies ω ± ω m and amplitude U m /2. In the speial ase when U = 0, the arrier frequeny is eliminated, but the sidebands remain. That is double-sideband suppressed-arrier transmission. In fat, we an use it as Dual Tone Test with symmetrially distributed spetral omponents and signal proessing is the same as in the lassi Dual Tone methods. It is possible to fit the AM signal by the Multi-tone Fit Test (least square fit method), whih optimizes 3 amplitudes, 3 frequenies, 3 phase shifts and 1 offset. The easier way to obtain results is to apply spetral analysis of an AM signal. We an define SINAD AM similarly as in a lassi FFT test without CF orretion [9]: SINAD = 2 2 U U m + 2 4, U U U AM f m f 0, f, fm where U a U m are amplitudes of the arrier and the modulation, U f represents amplitudes of other spetral omponents. Input voltage in the time domain should be equal to full-sale of the ADC, i.e. it is neessary to satisfy the following ondition: (7) (8) U = U + U. (9) FS m The CF of an AM signal an be expressed by:

4 P. Fexa, J. Vedral, J. Svatoš: DAC testing using modulated signals CF AM = 2(1 + mam ) mam The ENOB is omputed from SINAD (6); the orreted SINAD has to be again reomputed by formula (2). Another approah is to ompute SINAD and ENOB using standard formulas and then apply a orretion SINAD (11) and ENOB (12): AM ( CFAM ) (10) SINAD = 20log / 2 (db); (11) SINADAM ENOBAM =. (12) 6.02 Table 1. SINAD and CF redution in ase of using an AM signal m AM CF SINAD (db) ENOB (bits) Frequeny modulation FFT test The FM modulated testing signal is defined as u = U sin[ ω ( t) t], modulation frequeny ω ( t) = ω 0 + ω os( ω t), where ω is the frequeny deviation of the modulated m signal, m FM = ω/ω m is the modulation index. The waveform of the frequeny modulated signal is [12] : ω ufm U sin = ωt + osω mt. (13) ωm Spetrum of the FM onsists of a arrier with frequeny ω and symmetrially displaed spetral omponents around the arrier ω with multiples of frequeny ω m. Amplitudes of spetral omponents are given by first order Bessel funtions with argument ω/ω m. In Tab. 2, the amplitudes of spetrum of the frequeny modulated signal are shown for a modulation index m FM = ω/ω m in the range from 0 to 2. Table 2. FM signal amplitudes of the spetral omponent m FM ω ω ± ω m ω ± 2ω m ω ± 3ω m Fitting this signal is similar to the previous ase, it is possible to use the Least Square method (Multi Tone Fit Test), but it is very difiult to optimize too many parameters. It is onvenient to evaluate a signal in the spetral domain and determine the Signal Noise and Distortion SINAD FM, [9] FM

5 SINAD U km k = 1,2,.. FM = U f 0, f, k fm f U U km k= 1,2,.. U, (14) where U is the RMS value of the arrier omponent,u km orresponds to the RMS value of signal omponents around the arrier frequeny, U f are RMS values of other spetral omponents. The peak-to-peak value of an input voltage in the time domain has to over the full sale of the ADC (U FS = U ), see (13). The FM signal has the same CF as a sine wave signal, therefore equation (2) an be used for ENOB alulation. 3. Test setup and results An appliation of modulated signals for DAC has to satisfy the following riteria: The DAC should be tested near its full sale range. The amplitude of the signal should respet this fat. The modulation index of the AM signal affets the amplitude of side-band spetral omponents. In this work the modulation index is hosen as A lower modulation index auses that the averaged ENOB is reassembling to the single tone test. The FM modulation index is essential for DAC testing, beause it affets the signal bandwidth. The arrier frequeny sets the entral frequeny of the signal in the spetral domain and the modulation frequeny sets the spaing between spetral omponents. For pratial verifiation of the AM and FM methods, a PXI system was used. The first output hannel of the DAQ NI PXI 6251 (2 analog outputs: 16-bit, 1.25 MSa/s or 1 analog output: 16-bit 1.8MSa/s, 16 analog inputs: 16-bit ADC, 1.25 MSa/s) was tested. The Digitizer (NI PXI bit, 500 ksa/s, or 16 bits, 15 MSa/s) was hosen as a referene devie. The modulation method was ompared with a sine wave DFT test. For all measurements the Hanning window was used. 1 MSa were aquired during measurement. Fig. 1 Three arrangements of the testing system

6 P. Fexa, J. Vedral, J. Svatoš: DAC testing using modulated signals The whole PXI testing system was programmed in LabView. For purpose of testing, 3 modifiations of virtual instrument were developed, as shown in Fig. 1 The first two virtual instruments use one PC to ontrol generating data and data aquisition. The generating part runs in one ore of the proessor and data aquisition runs in the seond ore. The third arrangement is suitable for those ases where the performane of the PC is not suffiient. A distributed measuring system was developed. The generating part runs in a PC and ontrol soundard. The data aquisition part runs in a PXI with ontroller. Synhronization is made via the TCP protool. 3.1 Results of DAC testing using a sine wave DFT test Firstly the DUT was tested by a single tone test. It was tested using four different frequenies ( Hz, Hz, Hz and Hz), see Fig. 2 and Fig. 3. Fig. 2 Spetrum of sine wave signal f 1 = khz (left) f 2 = khz (right) Fig. 3 Spetrum of sine wave signal f 3 = khz (left) f 4 = khz (right) f (Hz) CF Table 3. Sine wave DFT test results CF w SINAD (db) ENOB (bits) SINAD or (db) ENOB or (bits)

7 Results are shown in Tab. 3. For inoherent sampling the Hanning window was applied. It is neessary to orret the influene of the Hanning window. The original sine wave has CF = 2. CF w respeting the fat that the window hanges the shape of the signal. 3.2 Results of DAC testing using an AM DFT test Seondly the DUT was tested by an AM DFT test. Two different arrier frequenies f (7.785 khz and khz) were used for testing, while the modulation frequeny f m is still the same (3.36 khz). The modulation index was hosen as 0.25, 0.5 and 1, see Fig Fig. 4 Spetrum of AM signal f =7.785 khz, f m =3.36 khz, m AM =0.25 (left), m AM =0.5 (right) Fig. 5 Spetrum of AM signal f =7.785 khz, f m =3.36kHz, m AM =1 (left), f = khz, f m =3.36 khz, m AM =0.25 (right) Fig. 6 Spetrum of AM signal f = khz, f m =3.36 khz, m AM =0.5 (left), m AM =1 (right)

8 P. Fexa, J. Vedral, J. Svatoš: DAC testing using modulated signals Results are shown in Tab. 4. In this ase not only the window but also the modulation index affets the CF. Table 4. AM DFT test results f m =3.36 khz m AM f n CF CF w SINAD ENOB SINAD or ENOB or (khz) (db) (bits) (db) (bits) Results of DAC testing using a FM DFT test Thirdly the DUT was tested by a FM signal. Parameters of the signal were the following: arrier frequeny f = 9785 Hz, modulation frequeny f m = Hz. The modulation index was hosen as 0.25, 0.5, 1, 2, 4 and 8, see Fig Fig. 7 Spetrum of FM signal f =9.785 khz, f m = Hz, m FM =0.25 (left), m FM =0.5 (right) Fig. 8 Spetrum of FM signal f = khz, f m = Hz, m FM = 1 (left), m FM = 2 (right)

9 Fig. 9 Spetrum of FM signal f =9.785 khz, f m = Hz, m FM =4 (left), m FM =8 (right) Results from the FM FFT Test are shown in Tab. 5. It is interesting that m FM hanges do not affet the CF. Table 5. FM DFT test results 4. Summary m FM CF f n =9785 Hz, f m = Hz SINAD ENOB (db) (bits) CF w SINAD or (db) ENOB or (bits) In Tab. 6. AM, FM methods with sine wave FFT test are ompared. The omparison is made in suh a way that the results from the test using a modulated signal with ertain arrier frequeny are ompared with sine wave FFT test results using a similar signal frequeny. For example a FM FFT test with 9.8 khz arrier frequeny is ompared with a 9.8 khz sine wave FFT test. The biggest value of the differene between the referene method and nontraditional method is equal to 0.3 bits. The reason why AM and FM methods show better results than a single-tone method, is that more signal spetral omponents over a broader frequeny band and potentially an mask distortion. f (khz) Table 6. Results of omparison between AM, FM methods and sine wave method Sine wave AM FM, f n = 9785 Hz ENOB m FM ENOB or ENOB or m AM f n ENOBor (bits) (bits) (bits) (khz) (bits) ENOB or (bits)

10 P. Fexa, J. Vedral, J. Svatoš: DAC testing using modulated signals The aim of this artile is to verify possibilities of DAC testing using multi-harmoni signals suh as AM and FM signals. Signal proessing of these signals in the time domain using fitting methods is quite ompliated. An advantage of those methods is asertaining DAC parameters in a wider frequeny range without the need of measuring their frequeny harateristi. Therefore it an be expeted that the desribed methods will find appliation in industry for less-demanding and eonomial tests. Another goal of this paper is to find a suitable testing signal whih overs an evenly hosen bandwidth of the DUT and this signal is not ompletely artifiial. This method is suitable for testing arbitrary generators (Agilent 33120A an generate an FM signal with f from 10 mhz to 10 khz and deviation from 15 mhz to 15 MHz). However this paper does not show results suitable for i.e. audio appliations (the arrier frequeny of the signal is muh higher than the band of the modulated signal). For example, if one yle of data olletion takes 2 seonds and 20 yles are neessary for an averaged FFT, then measurement at 1 frequeny lasts 40 seonds. If we want to test arefully the performane of the DAC in a range of 20 khz in 33 steps, the test will take 1320 seonds. If we use an FM signal with m = 8, the duration of the test will be only 40 seonds. However the ENOB measured using an FM signal, represents the average performane of the tested DAC. It is possible to shorten the test duration by reduing the number of samples. Tab. 7 shows how the number of samples affets the results of the test; a single tone test and a test using a FM signal with m = 1 was arranged for omparison. The single-tone FFT method is robust and works fine even if the number of samples is very limited (RMS of the signal and noise does not hange signifiantly). A FM test for hosen parameters works properly, if up to 250 ksamples are aquired, otherwise the spetral lines are too lose. This paper does not show results suitable for i.e. audio appliation (the arrier frequeny of the signal is muh higher than the band of the modulated signal), whih needs speial sampling methods. 5. Aknowledgment Table 7. Results of omparison between AM, FM methods and the sine wave method Single-Tone FM signal Samples (MSa) ENOB or (bit) ENOB or (bit) This projet is supported by the researh program No. MSM "Researh of Methods and Systems for Measurement of Physial Quantities and Measured Data Proessing" of the CTU in Prague sponsored by the Ministry of Eduation, Youth and Sports of the Czeh Republi and the grant SGS10/207/OHK3/2T/13 Digitization, synhronization and signal proessing in sensors and sensor networks.

11 6. Referenes [1] DYNAD (2000). Methods and draft standards for the Dynami haraterization and Testing of Analogue to Digital Converters. [2] IEEE Standard (2000). IEEE Standard and Terminology and Test Methods for Analog-to- Digital Converters. New York. [3] IEEE P1658 TM/D03.6. (1988). Draft Standard for Terminology and Test Methods for Digital-to-Analog Converters. New York. [4] Vedral, J., Fexa, P., Svatoš, J. (2009). Methods for eonomial test of dynami parameters ADCs. Metrology and Measurement Systems, 15(1), [5] Vedral, J. (2008). Exponential Fit Test - Theoretial Analysis and Pratially Implementation 13th Workshop on ADC Modelling and Testing [CD-ROM]. University of Florene Florene, [6] Holer, R., Mihaeli, L. (2003). DNL ADC Testing by the exponential shaped voltage. IEEE Transation on Instrumentation and Measurement, 52 (3), [7] App. Note 641. (2002). ADC and DAC Glossary. Sunnyvale: Maxim Integrated Produts, 22. [8] Oppenheim, A., Shafer, R. (1989). Disrete-Time Signal Proessing. Prentie-Hall. [9] Vedral, J. (2010). ADC testing with poly-harmoni signals. Mixed-Signals, Sensors and Systems Test Workshop (IMS3TW). IEEE 16th International. IEEE, 1-4. [10] Dallet, D., Silva, J. (2005). Dynami haraterisation of analogue-to-digital onverters. Springer Verlag. [11] Newkirk, D, Karlquist, R. (2004). Mixers, modulators and demodulators. The ARRL Handbook for Radio Communiations (81st ed.). Newington: ARRL, [12] Boashash, B. (2003). Time-Frequeny Signal Analysis and Proessing A Comprehensive Referene. Elsevier Siene. Oxford.