AN oscilloscope is a measurement tool for analog waveforms

Transcription

1 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 54, NO. 1, FEBRUARY Loss Waveform Interval for the Data Buffering of a Multiple-Channel Microcomputer-Based Oscilloscope System Ying-Wen Bai and Hong-Gi Wei Abstract Microcomputer-based oscilloscope instruments have been developed recently because they can easily process, store, and transmit various measured signals with the help of computers. Although this type of oscilloscope is workable and available, at the present time, we still do not know too much about the quantitative relationships with respect to the system bandwidth, the buffer size, the channel numbers, and the loss waveform interval in the data buffering mechanism of an asynchronous microcomputer-based oscilloscope. In this paper, we propose a modified queueing model for the quantitative analysis of these relationships. The primary results from this model and the measurement of the experimental system show the higher the required bandwidth, the higher the loss of the waveform interval for the measured signals. Fortunately, our oscilloscope is used to measure repetitive periodic waveforms, so the loss waveform intervals due to state transition will not cause any serious problem from a steady-state point of view. Index Terms Data buffer, loss waveform interval, microcomputer, oscilloscope, queueing model. I. INTRODUCTION AN oscilloscope is a measurement tool for analog waveforms and is used to verify the design of electronic circuits. Over the past few decades, numerous researchers have been refining different aspects of this machine in order to improve the functions of oscilloscopes. One of these proposed improvements is to digitize analog waveforms and to store the sampled signal for further processing by computers. However, due to the speed limitation of the sampling circuits, data buffers, and I/O channels of a microcomputer system, the bandwidth of a microcomputer-based oscilloscope can be very limited. Fortunately, because of the progress of VLSI technology, the sampling rate of sampling circuits can extend beyond several gigaheartz. In addition, the speed of data buffers has increased to a couple of hundred megaheartz. However, the speed of an I/O channel of a microcomputer system can still be a bottleneck from a continuous data flow point of view, although the speed of I/O channels can reach several hundred khz [1] [5]. In recent years, a couple of new technologies have been investigated: 1) high-speed A/D conversion; 2) a combination of both high-speed and a huge amount of signal data buffering; and 3) Manuscript received June 15, 2002; revised May 26, Y.-W. Bai is with the Department of Electronic Engineering, Fu-Jen Catholic University, Taipei 242, Taiwan, R.O.C. ( bai@ee.fju.edu.tw). H.-G. Wei is with the Institute for Industrial Technology Research, Hsin Chu, 310 Taiwan, R.O.C. ( Honggi@itri.org.tw). Digital Object Identifier /TIM high-speed synchronous signal data input technology. Most of these technologies have been substantially improved year by year. However, the speed of the microcomputer is slower than that of signal data buffering. Therefore, most microcomputers only attain data acquisition with the use of a synchronously controlled mechanism [6] [12]. In view of the multiple functions of microcomputers, in this paper, we have assumed that the state transition of the subsystems that occur independently of each other provides an asynchronous operation for data acquisition by the microcomputers. However, this result is not the case with regularly spaced sample acquisitions [13] [15]. From the previous observation of the speed comparison of major modules of a microcomputer-based oscilloscope, we have learned that either one must specify the lowest bandwidth of all modules as the bandwidth of the whole digital oscilloscope system, or avoid the bandwidth limitation by tolerating the existence of waveform loss mechanisms. When the speed of I/O channels is slower than that of the arriving data from a sampled signal, part of the waveform is neglected, causing waveform loss as a result of the overflow of the data buffer while the data are fed into the microcomputer. If the measured signals are periodic, then the missing part of a waveform is just an interval of the repetitive parts of waveforms. Therefore, the lost waveform would not cause a serious distortion in signal amplitude. Thus, in this paper, we propose a modified queueing model, using the random signal sampling method in order to model and estimate the loss probability of the sampled data to feed into the data buffer while the microcomputer services other tasks simultaneously. In addition, by the transforming of the data loss probability into the relationship of stored and lost waveform intervals of the measured signals, we can estimate the bandwidth limitation for an individual module, which causes the length of waveform loss. Conclusively, the primary results from the queueing model reveal the relationship between the missing intervals of the measured waveforms and the bandwidth difference among the different modules of a microcomputer-based oscilloscope system [16] [18]. The rest of this paper is organized as follows. In Section II, the multiple-channel microcomputer-based oscilloscope system and its modified queueing model used to analyze the characteristics of the data buffering are described. In Section III, the estimation of the various waveform-missing intervals is discussed. In Section IV, the measurement of an experimental platform for the microcomputer-based oscilloscope system is presented. Section V draws conclusions /$ IEEE

2 46 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 54, NO. 1, FEBRUARY 2005 Fig. 1. Multiple-channel with an A/D converter sampling architecture. Fig. 3. Modified M=M=1=N queueing model for the data buffering in a microcomputer-based oscilloscope system. Fig. 2. Multiple-channel utilizing more than two A/D converter sampling architecture. II. MULTIPLE-CHANNEL MICROCOMPUTER-BASED OSCILLOSCOPE AND MODIFIED QUEUEING MODEL FOR DATA BUFFERING Generally speaking, the multiple-channel system architecture can be divided into two parts. One part contains an analog-todigital (A/D) converter and the other part contains more than two A/D converters. Fig. 1 shows a multiple-channel with an A/D converter sampling architecture. In Fig. 1, each channel inputs an analog multiplexer and outputs a selected channel, which then reaches an A/D converter to receive the sampled signal in a digital format. The data from the sampled signal are temporarily stored in a fast first-in first-out (FIFO) data buffer. This is an example of one-time sampling. For the next sampling, we can select the same channel and then sample again. We also can use a counter to select the next channel and sample the next analog channel. We can attain, scan, and sample all signals both reiteratively and alternately. If we use M channels, we only have a sample rate of CLK per channel. This architecture is similar to each channel and contains each A/D but each A/D only has a sample rate of CLK. Therefore, Fig. 2 shows a multiple-channel with the above two A/D converters architecture for a microcomputer-based oscilloscope system. In Fig. 2, the original signals, and are inputted to the wide-band amplifier and then connected with an analog to a digital conversion module to receive the sampled signal and in a digital format. The data from the sampled signal is temporarily stored in a FIFO data buffer and then alternately read into a microcomputer to be stored as a computer data file. The data can then be processed by the use of curve-fitting algorithms and displayed in its final form. As a result of the speed difference between the arrival rate and the service rate of the data buffer in Fig. 2, some arrival data may be lost if the data buffer is filled up and the service rate is not fast enough. Therefore, the data loss in the data buffer can cause the measured waveform loss. In this section, we use Fig. 4. Fig. 5. Equivalent M=M=1=N queueing model for M single data buffering. State diagram of a M=M=1=N queue. a modified queueing model for data buffering to estimate the data loss probability due to the speed difference between the data arrival rate and the data service rate of the data buffer as shown in Fig. 3, [16] [18]. For the simplicity of representation, we set, and. There are a couple of ways to analyze the modified queueing model shown in Fig. 3. A simple way, which we propose in this paper, is to separate the service rate of the server into an fraction of service rates. The equivalent queueing model is shown in Fig. 4 where the single data buffer is working independently. Because of the independent operations of the dual data buffer, the single queues can be analyzed separately. In order to analyze a queue in Fig. 4, we use the state diagram as shown in Fig. 5 to find out the state probability for state 0 through state. Let, denote the state probability that there are data in the data buffer. According to on the state probability model of a stationary nontime-varying system, the rateequality principle yields the set of balanced equations shown at the bottom of the next page. The argument for state 0 in the queue is that there are no data in the buffer. In other words, in state 0, the process will leave only via an arrival (which occurs at rate ) and, hence,

3 BAI AND WEI: DATA BUFFERING OF A MULTIPLE-CHANNEL MICROCOMPUTER-BASED OSCILLOSCOPE SYSTEM 47 Fig. 6. Data loss probability of the data buffer. the rate at which the process leaves state 0 is. On the other hand, the rate at which the process can enter state 0 is. Rewriting the preceding system of equations we get Fig. 7. Measured and loss waveform intervals in a dual measured signal. which when solved in terms of, yields Fig. 8. Ratio between the loss and the measured waveform intervals. By using the fact that, we obtain,. (1) Note that in this case, there is no need to impose the condition that. The queue size or the buffer size, by

4 48 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 54, NO. 1, FEBRUARY 2005 Fig. 9. Hardware block diagram of the multiple-channel microcomputer-based oscilloscope system. definition, is constant so there is no possibility of any increase [16] [18]. When the queue is in state, the arriving data will not enter the queue or the data buffer, so the sampled data of the measured data in this interval will be discarded. In particular, the probability that the queue is full is which should be the same as the probability of blocking: the probability that the signal data are turned away and not accepted by the data buffer. In other words, is the data loss probability. (2) Fig. 5 shows the characteristics of (2). If we assume the utilization, then we can obtain Fig. 6, in which the data loss probability increases with the increase in utilization. The data loss probability also increases when the size of the data buffer decreases. Therefore, to reduce the data loss probability, one can reduce the utilization, or increase the data service rate to a certain level of the data arrival rate. In order to increase the data service rate, we can reduce the I/O time delay by using faster I/O ports, assembly code and a direct memory access mechanism. Another way to reduce the data loss probability is to increase the size of the data buffer. Due to the burst characteristics of the signal data arrival corresponding to the random context switching of the microcomputer processing, we needed more buffers to store the arrival signal temporarily while the microcomputer was allowed to perform other operations. In other words, we have assumed that the state transitions occur independently of each other, which is not the case with regularly spaced sample acquisitions. III. MISSING WAVEFORM INTERVALS OF MULTIPLE MEASURED WAVEFORMS From the random sampling data point of view, the data buffer in Fig. 2 can be modeled as a queue as shown in Fig. 10. Software flowchart of the dual-channel asynchronous microcomputer-based oscilloscope system. Fig. 3. Given a data arrival rate and a data service rate, from the analysis of an equivalent queueing model in Fig. 4, we can estimate the data loss probability of the queue or the data buffer in Fig. 2. Furthermore, by transferring the data loss probability, we can also estimate the measured and loss waveform intervals in a dual measured signal as shown in Fig. 7. The data loss probability shown in (2) can be approximately equal to, where is a loss waveform

5 BAI AND WEI: DATA BUFFERING OF A MULTIPLE-CHANNEL MICROCOMPUTER-BASED OSCILLOSCOPE SYSTEM 49 Fig. 12. Program segment for the signal data fed into a microcomputer. TABLE I ASSEMBLY CODE FOR INPUT DATA INTO A MICROCOMPUTER Fig. 11. system. The modules of the dual-channel microcomputer-based oscilloscope interval and is the measured waveform interval in Fig. 7 and. As a result, we can obtain (3). Fig. 8 shows the characteristic curves for (3). With the data buffer size bytes, the utilization varies from 0 to 5 and the channel number increases from 1 to 6. The three-dimensional curves show the smaller the utilization, the smaller the loss waveform interval in the measured waveform interval, or similarly the smaller the number of the channel, the smaller the distortion. In addition, the larger the buffer size for the data buffer in Fig. 2, the smaller the loss of the waveform interval is. Although there exists a missing waveform interval of the measured waveform, the microcomputer-based oscilloscope can still show part of the repetitive periodic waveforms. If the missing interval of the measured waveform belongs to part of the repetitive waveform, then a missing mechanism will not cause a serious distortion in comparison with the functions of a traditional analog oscilloscope. IV. IMPLEMENTATION AND MEASUREMENTS OF THE EXPERIMENTAL SYSTEM In order to fulfill the multiple-channel microcomputer-based oscilloscope system shown in Fig. 2, we set the number of channel at two. And we have designed and implemented a dual input channel experimental system using the hardware (3) Fig. 13. Measured waveform without a missing waveform interval as shown in the experimental system. block diagram and software flowchart as shown in Figs. 9 and 10, respectively. Fig. 11 shows the physical implementation of a dual-channel microcomputer-based oscilloscope system circuit board. Fig. 12 is the program segment translated into an assembly code, which is shown in Table I. Since, in this system the quartz crystal frequency of the 8051 is 12 MHz with a total range variation of 200 ppm, the clock cycle period is 1/12 s and has limited clock jitter. Each machine cycle period is 12 times the clock cycle period in an 8051 and a machine cycle period is 1 s. The 28 machine cycles in Table I require 28 s to read a byte, or a sampled point of the measured waveform. A 28- s data input period is equivalent to a 36-kHz bandwidth for the sampled point of the measured waveform. If we need ten sampled points for each period, we may only be able to have a 3.6 khz bandwidth for the measured waveform without missing a waveform interval as shown in Fig. 13. If we can tolerate the missing waveform interval for the measurement of the periodic waveforms, then we can obtain a scalable bandwidth of the measured signals. From the scalable relationship shown in (3), we learn that if the equivalent service rate is 2 = 18 kb/s, and the arrival rate is from 1 kb/s to 20 MB/s, we can then obtain the ratio between the loss waveform

6 50 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 54, NO. 1, FEBRUARY 2005 Fig. 14. Relationship between the sampled data rate and the loss waveform interval. Fig. 15. Sampled signal shown in the dual-channel microcomputer-based oscilloscope system. Fig. 17. Dual signal after the curve-fitting program. has been proposed. In this model, the random arrival process and the departure process can represent the sampled signal input and data output process of a data buffer, respectively. The microcomputer can work with the data buffer in an asynchronous operational manner. From a steady-state behavior analysis, we can obtain the approximate results for the data loss probability and the loss waveform intervals. This probability is dependent on the average data arrival rate and the average data service rate of the data buffer and the number of channels of this system. The higher the bandwidth of the measured signals required, the higher the data arrival rate and the data loss probability will be. At the same time, the more channels of the measured signals needed, the higher the loss waveform interval ratio will be. Fortunately, the oscilloscope is used to measure repetitive periodic waveforms, so the loss waveform intervals may not cause any serious problem from a steady-state point of view. We have also designed and implemented an experimental microcomputer-based oscilloscope. The measured data are in very good agreement with the result of the theoretical analysis. Overall, the primary results from this model and the measurement of our experimental system agree with each other. Fig. 16. Curve-fitting program for dual sampled signals. interval and the measured waveform. As seen in Fig. 14, if we can tolerate the loss waveform at 99% of the measured waveform, then we can have 350 khz of the measured bandwidth shown as point A for the experimental system. Fig. 15 shows a sampled signal in the dual-channel microcomputer-based oscilloscope system. This sampled signal is processed by the curve-fitting program as shown in Fig. 16 with which we can obtain a reconstructed signal that is shown in the display of our computer in Fig. 17. V. CONCLUSION In this paper, a modified queueing model for the data buffering of a mutually independent operation of a multiple-channel microcomputer-based oscilloscope system REFERENCES [1] M. J. Riezenman, Test and measurement, IEEE Spectr., vol. 32, pp , Jan [2] S. A. Chickamenahalli and A. Hall, Interfacing a digital oscilloscope to a personal computer using GPIB, in Proc. Frontiers Education Conf., 27th Annu. Conf., Teaching, Learning Era Change, vol. 2, 1997, p [3] S. Matsukura, T. Asaka, Y. Sugihara, and N. Tonosaka, Fast up-date techniques for digital oscilloscope, in Proc. 8th IEEE Instrumentation MeasurementTechnology. Conf., 1991, pp [4] H. B. Crawley, R. Mckay, W. T. Meeyer, E. I. Rosenbergg, and W. D. Thomas, Using IEEE standard 1057 for testing analog-to-digital converters, in Proc. Nuclear Science Symp. Medical Imaging Conf., vol. 1, 1995, pp [5] A. Luh, Instrumentation integrated system, in Proc. WESCON, Idea/Microelectronics Conf., 1994, pp [6] J. Kelly, K. Roberts, and B. Yamrone, LeCory MQT-charge to time conversion, in Proc. IEEE Nuclear Science Symp., vol. 1, 1996, pp [7] S. Ems and S. Naboicheck, 5 GHz sampling oscilloscope front-end based on heterojunction bipolar transistors (HBT), in Proc. Technical Gallium Arsenide Integrated Circuit Symp., Oct. 1993, pp [8] W. A. Earle and V. G. Zavarzin, A 500 k event/sec 12-bit ADC system with high-speed buffered PCI interface, in Proc. IEEE Nuclear Science Symp., vol. 1.1, 1998, pp

7 BAI AND WEI: DATA BUFFERING OF A MULTIPLE-CHANNEL MICROCOMPUTER-BASED OSCILLOSCOPE SYSTEM 51 [9] S. Y. Chuang and T. L. Sculley, A digitally self-calibrating 14-bit 10-MHz CMOS pipelined A/D converter, IEEE J. Solid-State Circuits, vol. 37, pp , June [10] G. Borrianoff, I. Kourbanis, S. Peggs, T. Satogata, and G. Tsironis, Unix data acquisition system, in Proc. IEEE Accelerator Science. Technology: Particle Accelerator Conf., vol. 1, 1991, pp [11] M. J. Lauterbach, New scope tools boost circuit design, IEEE Circuits Devices Mag., vol. 12, pp , Mar [12] F. Cruger, J. Regazzi, and B. Zarlingo, Combining the information and measurement worlds to improve system performance and operational readiness, in Proc. IEEE AUTOTESTCON, 2002, pp [13] Y. Lembeye, J. P. Keradec, and G. Cauffet, Improvement in the linearity of fast digital oscilloscopes used in averaging mode, IEEE Trans. Instrum. Meas., vol. 43, pp , Dec [14] E. R. Pratico and M. A. Eltzmann, A microcomputer-based data acquisition system for transient network analyzer operation, IEEE Trans. Power Syst., vol. 9, pp , May [15] J. Q. Zhang, Z. Xinmin, H. Xiao, and S. Jinwei, Sinewave Fit Algorithm Based on Total Least-Squares Method with Application to ADC Effective Bits Measurement, IEEE Trans. Instrum. Meas., vol. 46, pp , Aug [16] S. M. Ross, Introduction to Probability Models, 6th ed. New York: Academic, [17] G. Bolch, S. Grener, H. DeMeer, and K. S. Trivedi, Queueing Networks and Markov Chains. New York: Wiley, [18] R. Nelson, Probability, Stochastic Processes, and Queueing Theory. New York: Springer-Verlag, Ying-Wen Bai received the M.S. and Ph.D. degrees in electrical engineering from Columbia University, New York, in 1991 and 1993, respectively. He is an Associate Professor in the Department of Electronic Engineering at Fu-Jen Catholic University, Taipei, Taiwan, R.O.C. His research focuses on mobile computing and microcomputer system design. Between , he was with the Institute for Information Industry, Taiwan. Hong-Gi Wei received the M.S. and B.S. degrees in electronic engineering from Fu-Jen Catholic University, Taipei, Taiwan, R.O.C., in 1996 and 2002, respectively. He is currently with the Institute for Industrial Technology Research, Hsin Chu, Taiwan, R.O.C. His main research interest is hardware architecture design and system integration of the remote Windows-based measurement system, including oscilloscope and signal generator.