On the Use of Standard Digital ATE for the Analysis of RF Signals

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1 On the Use o Standard Digital ATE or the Analysis o RF Signals Nicolas Pous, Florence Azaïs, Laurent Latorre, Jochen Rivoir To cite this version: Nicolas Pous, Florence Azaïs, Laurent Latorre, Jochen Rivoir. On the Use o Standard Digital ATE or the Analysis o RF Signals. ETS: European Test Symposium, May 2, Prague, Czech Republic. 5th IEEE European Test Symposium, pp.43-48, 2. <lirmm > HAL Id: lirmm Submitted on 7 Jun 2 HAL is a multi-disciplinary open access archive or the deposit and dissemination o scientiic research documents, whether they are published or not. The documents may come rom teaching and research institutions in France or abroad, or rom public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diusion de documents scientiiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche rançais ou étrangers, des laboratoires publics ou privés.

2 On the use o standard digital ATE or the analysis o RF signals N. Pous LIRMM & Verigy Montpellier, France F. Azaïs, L. Latorre LIRMM, CNRS / Uni. Montpellier Montpellier, France J. Rivoir Verigy Germany GmbH 734 Boeblingen, Germany Abstract In this paper, we investigate the use o standard digital ATE or the analysis o FM-modulated RF signals. The key idea is to use the -bit digitizer o a digital test channel in order to convert the requency inormation contained in a FM-modulated signal into a timing inormation contained in a digital bit stream; a post-processing algorithm based on the concept o zero-crossing detection is then employed to retrieve this inormation. Coherent under-sampling is exploited to extend the capabilities o test equipment with a limited sampling requency or the analysis o high-requency signals. The proposed approach is evaluated on two dierent case studies related to LTE and GSM communication standards. Both simulation and hardware experiments are presented to demonstrate the viability o the technique. Keywords: test, digital ATE, analog/rf signals, zero-crossing detection, post-processing algorithm, coherent under-sampling I. INTRODUCTION More and more, with the development o wireless and multimedia applications, analog and RF unctions become essential elements o electronic systems. In this context, it is clear that the test cost o such unctions must be kept as low as possible to be competitive in the market. However in this particular case, the test is a time-consuming procedure that requires costly and dedicated test equipment. In this work, our objective is to reduce the cost o the required test equipment. The undamental idea is to complement standard low-cost test equipment with signal processing techniques to enable the analysis o analog/rf signals. More precisely, the idea is to use the comparator o a standard digital ATE channel as a -bit digitizer that converts the requency and/or amplitude inormation contained in the analog/rf signal into a timing inormation contained in a digital signal; post-processing algorithms can then be developed to extract the analog/rf signal characteristics rom the digital bit stream. An essential motivation o this approach is that the current trend or actual circuits is to operate at lower supply voltages but with ever higher requencies. This means that modern CMOS chips undergo a degraded voltage resolution whereas they beneit rom an improved time resolution. Regarding test aspects, this trend can be translated into the act that it is more and more diicult to perorm accurate voltage measurements while it becomes easier to obtain precise timing measurements. As a consequence, our idea is to take advantage o this trend by converting the analysis o analog/rf signals rom the voltage domain to the time domain []. Moreover, another observation is that RF devices are oten tested twice, at the waer-level and again at the package-level. However implementing RF tests at waer-level is extremely costly due to probing issues and the inability to perorm multisite testing. It is thereore o great interest to develop test solutions applicable on low-cost test equipment that (i) provide waer-level test coverage and (ii) permit multi-site testing. Consequently, another important objective is the ability o perorming some levels o RF testing using standard digital ATE channels together with the possibility o perorming multi-site testing. Reerring to literature, our approach is quite innovative. Indeed, two main strategies have been investigated up-to now to diminish the test cost o analog/rf circuits. A irst strategy is to include BIST eatures in the circuit in order to reduce the requirements o the external test equipment. During the past ten years, a signiicant research eort has been carried out in this direction or analog circuits [2,3] and more recently or RF circuits [4,5]. Another strategy is to reduce the test time, and a number o works have been realized to replace the classical speciication-based tests by shorter alternative tests or both analog and RF circuits [6,7]. In this work, we adopt a slightly dierent approach that consists in reducing the requirements o the external test equipment but without inserting any test eatures within the circuit itsel. In this paper, we ocus on the analysis o FM-modulated signals using the requency reconstruction technique introduced in [8]. In order to extend the application range o the method, we introduce the use o coherent under-sampling and we evaluate the perormances o the technique on two dierent case studies related to LTE and GSM communication standards. The paper is organized as ollows. Section II presents the basic principle o using standard digital ATE channels or requency estimation together with the associated postprocessing algorithm or requency demodulation. Section III introduces the use o coherent under-sampling to enable the analysis o high-speed signals using test resources with limited operating requency. Sections IV and V discuss the perormances o the technique on the two dierent case studies. Finally section VI concludes the paper //$26. 2 IEEE 43

3 II. PRINCIPLE A. Basic idea Our objective is to investigate the possibility o using digital test resources, cheaper than the RF resources, to analyze analog/rf signals. Based on the concept o level-crossing detection, the idea is to complement a standard digital test channel with a signal processing algorithm so that it can operate as an analog/rf receiver. Note that many works can be ound in the literature regarding the use o level-crossing in many dierent application domains such as image and speech processing, wireless communications However only a limited number o works deals with the use o such a technique or analog/rf test issues. Zero-crossing is used in [9] to generate a digital signature associated with Lissajou-based test. Level-crossing is used in [] to evaluate oset and amplitude o a triangular analog waveorm using digital resources. where Δ TS corresponds to the time delay between a pair o successive rising and alling transitions. Amplitude,5 -,5 - TS R,i i = 2 ΔTS ΔTS i i TS F,i Comparator Output,,2,3,4,5,6,7 TS R,i+ TS F,i+ Analog Waveorm Figure 2. Frequency determination rom zero-crossing comparator level analog/rf signal ATE Memory DUT/ATE Synchronisation ATE Clock Regular Digital Pin Electronics Signal Processing Algorithm Pass/Fail In the ideal case, level-crossings o the analog sine-wave result in unique transitions at the output o the comparator. Time Stamps can thereore be directly associated to the rising/alling transitions. However in practice, the analog signal is not a perect one but a noisy signal. The resulting digital signal at the output comparator thereore exhibits multiple transitions at the vicinity o zero-crossings, as illustrated in igure 3. An algorithm is consequently required to ilter these multiple transitions and associate a single Time Stamp to each zero-crossing. Figure. Primary idea As illustrated in igure, the comparator o the digital test channel is used as a -bit digitizer and the resulting bit stream is stored in the ATE memory. Depending on the reerence level o the comparator, the requency and/or amplitude inormation contained in the analog/rf signal is converted into a timing inormation contained in the digital bit stream. It is then the role o the post-processing algorithm to retrieve the analog/rf signal characteristics. In this paper, we ocus on requency reconstruction, so we set the reerence level o the comparator to zero. Similar solutions may be developed or amplitude reconstruction, using a comparator reerence level dierent rom zero. B. Frequency determination To illustrate the proposed approach, let us irst consider an ideal analog sine-wave: s( t) = Acos(2π t) () Assume that this sine-wave is sampled by a -bit comparator with a zero-reerence level at a sampling rate sample. The resulting signal is a digital signal that switches rom logical to. As illustrated in igure 2, a Time Stamp (TS) can be associated with each transition, which corresponds to a zero-crossing o the analog sine-wave. Then, or each pair o rising/alling transitions, the signal requency can be computed with: = 2 Δ TS (2) 44 Amplitude,5,5 -,5 - -,5 Running Avg TS R,i ΔTS i TS F,i Comparator Output,,2,3,4,5,6,7,8 Noisy Signal Figure 3. Frequency determination rom running average In this objective, a simple and robust algorithm that allows the precise estimation o Time Stamps associated with level-crossings or a noisy signal has been developed. As depicted in igure 3, the algorithm relies on a running average, i.e. counting the ratio between the numbers o and on a given number o samples N avg. A Time Stamp TS R is associated to a rising transition when this ratio reaches 5% with a positive slope; similarly, a Time Stamp TS F is associated to a alling transition when the running average reaches 5% with a negative slope. C. Frequency demodulation Let us now consider the case o an FM-modulated signal expressed by: ( 2π t + βsin( π t) ) 5% SFM ( t) = Ac cos c 2 m (3)

4 where A c and c are the amplitude and the requency o the carrier signal, m is the requency o the modulating signal (urther called the message ), and β is the modulation depth given by: β = A d m (4) and d corresponds to the maximum requency deviation. In order to demodulate this signal, we can use the zerocrossing Time Stamp determination deined in the previous section. More precisely, the principle consists in estimating the deviation o the signal requency rom the carrier requency, or each period o the FM-modulated signal. From a practical point o view, the procedure is as ollows: For each TS R,i / TS F,i pair, i.e. or each period o the carrier signal, we compute the time t max,i. at which the FM-modulated signal reaches a maximum: m TSR, i + TSF, i tmax, i = (5) 2 For each pair o two consecutive maximums, we reconstruct the message with: the sampling requency is, the higher the number o captured samples per carrier period and the lower the requency estimation error. As a consequence, this may limit the range o signals that can be analyzed since the sampling requency is limited by the ATE capabilities. As an example, standard digital ATE can typically operate up to ew GHz. Targeting accuracy better than % or requency estimation, 2 samples per carrier period are required [8], and signals that can be analyzed are thereore limited to ew tens o MHz. In order to extend the application range o the method, the idea is to use a coherent under-sampling strategy. Indeed, under-sampling is a commonly-used strategy to address the capture o high-requency repetitive signals below the Nyquist rate. It basically consists in taking only ew samples within a signal period and repeating this operation several times while changing the sampling phase. The resulting multiple samples can then be reordered to obtain a satisactory sampling o the original signal. Besides, coherent sampling is a technique that guarantee that the maximum amount o inormation about a particular waveorm exists in the sample set (i.e. there are no duplicate samples). Implementing coherent sampling thereore permits to obtain a complete, periodic waveorm representation in the sample set with aster acquisition time and less computation than with non-coherent sampling. Consequently, we introduce in this section the implementation o a coherent under-sampling approach with the ATE to address the capture o high-requency analog waveorms. at A = m sˆ m ( ti ) β c m tmax, i+ tmax, i tmax, i + tmax, i+ t i = (6) 2 Note that because the reconstruction is based on the processing o the sampled comparator output, the resulting reconstructed signal is a discrete signal both in time and amplitude. The timing discretization depends on the characteristics o the signal to be analyzed, i.e. the ratio between the modulating and carrier signal requencies. The amplitude discretization not only depends on the signal characteristics but also on the sampling requency. The quantization step can be expressed by deriving equation (6): 2 A = m Q c 2 m sample From equation (7), it is clear that or a given signal, it is possible to reduce the quantization step and so to increase the number o quantization levels, by increasing the sampling requency. III. ANALYSIS OF HIGH-FREQUENCY SIGNALS The accuracy o the proposed technique obviously depends on the accuracy on the requency estimation, which is clearly related to the ATE sampling requency sample. It actually depends on the ratio between the ATE sampling requency and the requency o the analog signal to be analyzed. So the higher β (7) 45,5 -,5 -,5 -,5 - message period (Tmes),5,5 2 2,5 3 Samples reordering Number o repetition (Nrep) Time,5 Time Figure 4. Coherent under-sampling Figure 4 illustrates the principle o coherent under-sampling on a simple case o FM-modulated signal with c =khz and m =khz. To ensure coherency, the sampling requency sample, the message requency m, the number o samples N and the number o repetitions o the message signal M must ulill the ollowing relationship: N M sample m T sample samples ATE data signal message signal ATE data message = ()

5 where N and M are whole positive integer values. Moreover, N and M must be chosen as co-prime integers to guarantee that samples will dier rom one message signal period to another. Reerring to the example o igure 4, the coherency constraints can be satisied with the sampling period set to T sample =3μs and the number o repetitions set to M=3. Ater reordering, this setup permits to collect uniormly timedistributed samples on one message period, whereas the direct sampling o the signal without repetition produces only 33 samples on one message period. RF Source (Agilent N93A) MHz Synchronization V93K SoC TestHead -PS36 Digital Channel Zero-Crossing Vector { } Samples Reordering FM-modulated Signal Digital domain Running Avg. & TS Determination MATLAB Reconstructed Analog domain Signal reconstruction Instantaneous requency estimation Figure 5. FM-demodulation setup using digital ATE Transorm (DFT) algorithm on the reconstructed signal with non-uniorm samples results in a spectrum that presents both leakage and harmonics. It is thereore necessary to align data on a uniorm time scale [] or to use an Interpolated-DFT algorithm to eliminate these eects and obtain the correct spectrum o the signal. TABLE I. Final resolution ater reordering UNDER-SAMPLING PARAMETERS FOR LTE CASE STUDY Number o repetitions M ATE sampling period T sample Number o samples N ps 6 6. ns 8, ps ns 8, First experiments have been perormed in simulation. Two dierent time resolutions o ps and ps have been considered, which corresponds to about 4 and 4 samples per period carrier respectively. Taking into account that the lowest value o our ATE sampling period is 2.5ns, coherent under-sampling must be used to achieve such resolutions. The under-sampling parameters that satisy the tester constraints and the coherent requirements are given in Table I or both targeted resolutions. Also, note that a clock jitter, modeled as a Gaussian random time-shit o the sampling event with 3σ =ps, has been included in the simulation in order to consider realistic practical conditions. Figure 5 shows the proposed test setup or FMdemodulation using a digital ATE and a coherent undersampling approach. The signal to be analyzed is generated with an RF source (Agilent N93A) connected to a PS36 digital channel o the Verigy 93K ATE. In order to implement coherent sampling, synchronization is required between the signal and sample clock requencies. The MHz output o the tester is thereore used to synchronize the RF source. The postprocessing algorithm that includes samples reordering, running average computation and time stamps determination, instantaneous requency estimation, and inally signal reconstruction is implemented in MATLAB. IV. LTE-BANDWIDTH CASE STUDY To validate the proposed approach, we irst consider a case study based on the LTE standard. The purpose is not to handle the complete communication standard, but to use the requencies involved in such applications as a typical RF signal. Consequently reerring to one mode o the LTE standard, we consider a FM-modulated signal with a carrier requency o 2.5GHz, a modulation requency o 4MHz and a modulation depth β=3. Moreover to evaluate the perormances o the technique, we want to analyze the spectrum o the reconstructed message. In order to have an acceptable resolution ater the FFT, the signal to be analyzed is made o 32 message periods, which corresponds to 2 carrier periods; the message period T m considered in the experiments is thereore 8ns. Note that the reconstruction algorithm results in a discrete analog signal with non-uniorm time distribution according to equation (6). This non-uniormity should be considered or the analysis o the signal in the requency domain. Indeed, applying a classical Discrete Fourier 46,5,5 -,5 - -, a) time-domain representation b) spectral-domain representation ps resolution ps resolution,5,5 -,5 - -,5 Time(ns) Time (ns) c) time-domain representation d) spectral-domain representation ps resolution ps resolution Figure 6. Simulation results or the LTE case study Results are summarized in igure 6 that gives both the timedomain and the spectral-domain representation o the reconstructed signals or the two resolutions o ps and ps. It clearly appears that in both cases, the post-processing algorithm permits to retrieve the message. As expected, the quality o the reconstructed signal increases with time

6 resolution, with a signiicant reduction o the quantization in the message amplitude when improving the time resolution rom ps to ps. Hardware measurements have been perormed to urther support these results. However due to the limited capabilities o our RF source, hardware measurements are perormed with a downscaling o, with respect to simulation, i.e. the RF source is set to output an FM-modulated signal with 2.5MHz carrier requency, 4kHz modulation requency and a modulation depth o 3rad. To maintain the same number o samples as in the simulation experiments, the downscaling o, is also applied on the ATE sampling requency, which results in a time resolution o ns and ns, or 8, and 8, captured samples respectively. Note that even i the direct acquisition o the samples would be possible or the ns resolution, coherent under-sampling is implemented or both targeted resolutions. Results are summarized in igure 7. A good agreement is observed between these experimental results and simulation results.,5,5 -,5 - -,5 a) time-domain representation b) spectral-domain representation ns resolution ns resolution,5,5 -,5 - -, c) time-domain representation d) spectral-domain representation ns resolution ns resolution Figure 7. Hardware validations or the LTE case study V. GSM CASE STUDY The second case study addresses the demodulation o a FM signal with parameters close to those ound in the GSM telecommunication standard. Note that although a GMSK modulation scheme is implemented in GSM in order to control the signal spectral spreading, our study only ocuses on the determination o carried symbols based on requency demodulation. The typical GSM signal considered here is based on a sinusoidal carrier o requency c =94MHz and a requency Frequency (khz) 5 5 Frequency (khz) 47 deviation o d =±67.7kHz corresponding to and symbols. Note that this deviation is extremely small with regard to the carrier requency. In order to discriminate symbols, the precision in the measurement o the carrier instantaneous requency must thereore be higher than.5%. In other words, the targeted time resolution ater sampling and reordering should be as low as.8ps, which corresponds to about 3,5 samples collected into one single carrier period. Obviously, this is a very exigent case and it is interesting to evaluate the perormance o the proposed technique under such demanding conditions. Additionally it is worth noting that the symbol rate in GSM is about 27kHz; each symbol is thereore emitted during 3.7μs, which corresponds to 3,385 carrier periods. Considering a time resolution o.8ps, the amount o data to collect within one single symbol then reaches 46Mbits, which is way beyond ATE capabilities. In this study, irst attempts to demodulate a GSM signal is addressed by setting the total amount o captured data to 6Mbits, which corresponds to our ATE memory capability. As a result, the capture window is lower than the duration o one symbol, and it is assumed that there is no change in the carrier requency during the capture process. Dierent time resolutions are investigated, i.e..ps,.5ps and.ps, which corresponds to,, 2, and, samples per carrier period respectively. Obviously, coherent under-sampling is implemented to achieve such resolutions. The ATE sampling period and the number o repetitions are adjusted according to the targeted time resolution (ATE sampling requency is adjusted around its minimum value o 2.5ns). Table II summarizes the under-sampling parameters used both in simulation and or experimental validation. TABLE II. Final resolution ater reordering UNDER-SAMPLING PARAMETERS FOR GSM CASE STUDY Number o repetitions ATE sampling period Number o samples / carrier period Number o carrier periods. ps ~ 22,8 ~ 2.5 ns,,6.5 ps ~ 45,7 ~ 2.5 ns 2, 8. ps ~ 228,5 ~ 2.5 ns, 6 Simulations have been carried out using two signal requencies o c = MHz and c =94.677MHz corresponding to and symbols respectively. Again, a Gaussian jitter with 3σ=ps is considered or the sampling clock. The post-processing algorithm is applied on the captured samples to estimate, or each carrier period, the instantaneous requency. Results are summarized in igure 8, which gives the distribution o the instantaneous requency calculated or each carrier period, or the three dierent time resolutions. It can be observed that the instantaneous requency exhibits a Gaussian distribution well-centered on the expected requencies or and symbols, or the three dierent cases. On the other hand, the standard deviation strongly depends on the time resolution: the iner the time resolution, the lower the standard deviation. In particular, the standard deviation reduces down to about 3kHz when using a.ps resolution, which permits to discriminate symbols based on a single period measurement.

7 '' '' T res =.ps 93,6 93,7 93,8 93, , 94,2 94,3 94,4 94,5 Figure 8. Simulation results or the GSM case study More generally, these results demonstrate the potentialities o the proposed approach to handle GSM-type signals. However it should be highlighted that the use o a very ine time resolution may not be the more eicient option in terms o acquisition time and subsequent post-processing. An interesting alternative may be to use a degraded time resolution together with an averaging approach. For instance with a.ps resolution, it is possible to achieve a standard deviation comparable to the one obtained with.ps resolution by averaging the estimated requency over 4 carrier periods only '' '' T res =.ps 93,6 93,7 93,8 93, , 94,2 94,3 94,4 94, ,25 999,5 999,75,25,5,75,25 T res =.ps T res =.ps ,25 999,5 999,75,25,5,75,25 Figure 9. Hardware validations or the GSM case study Finally, hardware measurements have been perormed to urther validate these results. A simple GHz signal send to two distinct tester channels on the same PS36 board and the post-processing algorithm has been applied to estimate the requency at each signal period. Results are summarized in igure 9. Frequency distribution is again very well-centered on T res '' '' T res =.5ps 93,6 93,7 93,8 93, , 94,2 94,3 94,4 94,5 Avg (MHz) σ Avg (MHz).ps 93,9323,8 94,6763,23.5ps 93,9322,83 94,6779,83.ps 93,9326,36 94,678, T res Results summary ,25 999,5 999,75,25,5,75,25 Avg (MHz) GHz σ T res =.5ps σ σ 2.ps,3, ps , ps ,36.96 Results summary the expected GHz requency and the standard deviation reduces when the time resolution improves. However compared to simulation results, the standard deviation is about three times higher on channel and more than 5 times higher on channel 2. This dierence may come rom the jitter on the capture event that can have slightly dierent values rom one channel to another. VI. CONCLUSION In this paper, we have validated a technique that permits to reconstruct the message contained in a FM-modulated signal using standard digital ATE channels, converting the analog/rf signal into a bit stream whose transition time inormation represents the analog/rf signal characteristics. We have also established that coherent under-sampling can eiciently complement the technique to process signals at requencies much higher than the ATE acquisition rate. Validations have been perormed through simulations and experimental measurements, and the viability o the technique has been illustrated on two case studies with very dierent characteristics. ACKNOWLEDGMENTS The authors would like to acknowledge B. Pradarelli, R. Lorival, P. Coscat and L. Ollivier or technical support during hardware validation. Hardware experiments have been perormed using the equipment o the CNFM Test Resource Center in Montpellier sponsored by Verigy and Region Languedoc-Roussillon. REFERENCES [] Rivoir, J; (Agilent Tech.), Analog to digital signal conversion method and apparatus, Patent No. US 6,462,693 B, Oct. 22 [2] Khaled, S.; Kaminska, B.; Courtois, B.; Lubaszewski, M.;, Frequencybased BIST or analog circuit testing, Proc. IEEE VLSI Test Symp., pp , 995. [3] Hao-Chiao Hong; Jiun-Lang Huang; Kwang-Ting Cheng; Cheng-Wen Wu;, On-chip analog response extraction with -bit - modulators, Proc. IEEE Asian Test Symp., pp , 22. [4] Negreiros, M.; Carro, L.; Susin, A.A., Low cost analogue testing o RF signal paths, Proc. Design, Automation and Test in Europe Conerence and Exhibition, pp , 24. [5] Staszewski, R.B.; Bashir, I.; Eliezer, O.;, RF Built-in Sel Test o a Wireless Transmitter, IEEE Transactions on Circuits and Systems II: Express Bries, Volume 54, Issue 2, pp. 86-9, Feb. 27. [6] Variyam, P.N.; Chatterjee, A.;, Enhancing test eectiveness or analog circuits using synthesized measurements, Proc. IEEE VLSI Test Symp., pp , 998. [7] Haider, A.; Chatterjee, A.;, Low-cost alternate EVM test or wireless receiver systems, Proc. IEEE VLSI Test Symp., pp , 25. [8] Pous, N.; Azaïs, F.; Latorre, L.; Nouet, P.; Rivoir, J., Exploiting zerocrossing or the analysis o FM modulated analog/rf signals using digital ATE, Proc. IEEE Asian Test Symp., pp , 29. [9] Brosa, A.M.; Figueras, J.;, Digital signature proposal or mixed-signal circuits, Proc. IEEE Int l Test Con., pp. 4-5, 2. [] Su, C.C.; Chang, C.S.; Huang, H.W.; Tu, D.S.; Lee, C.L.; Lin, J.C.H.;, Dynamic analog testing via ATE digital test channels, Proc. IEEE Asian Test Symp., pp , 24. [] Rivoir, J.; (Verigy), Converting non-equidistant signals into equidistant signals, Patent Application No. WO 28/22653 A, Feb. 28, 28 48