Please use this identifier to cite or link to this item: http://hdl.handle.net/11527/16191
Title: Dijital Mültimetrelerde Doğruluğu Artıran Bir Yöntem
Other Titles: A Method To Improve Accuracy In Digital Multimeters
Authors: Önal, Hasan
İkizoğlu, Serhat
14157
Elektronik Mühendisliği
Electronics Engineering
Keywords: Hata analizi
Sayısal multimetre
Error analysis
Digital multimeter
Issue Date: 1990
Publisher: Fen Bilimleri Enstitüsü
Institute of Science and Technology
Abstract: Bu tezde, dijital mültimetrelerde hatanın azaltılması için bir yöntem önerilmiştir. Burada önemli olan husus, hata azaltılırken maliyetin aşırı yükselmesine neden olmamaktır. Dijital aletlerde doğruluğa en çok etkiyen eleman A/D çeviricidir. Ve bu elemanda hız ile doğruluk ters orantılıdır. Her iki özelliğin iyileştirilmesi ise ileri teknoloji ile mümkün olabilmekte dir ki, bu da maliyetin çok artması demektir. Bu tezde uygulanan yöntemin prensibi, ölçme süresinin uzamasına göz yumarak, ölçüle cek işaretlerden alınan örnekler arasındaki süreyi açmaya dayanmaktadır. Aynı zamanda, tezde yenilik olarak sunulan düşünce doğrultusunda- işaretin frekans değişimi de takip edil mektedir. Bu nedenle tam periyodik işaret durumuna göre örnek sayısını artırmaya gerek kal mamaktadır. Böylelikle doğruluğu yüksek, fakat ucuz A/D çeviriciler kullanılarak amaca ulaşıla bilmektedir. Birinci bölümde, uygulanacak yöntemin tanıtılmasına hazırlık teşkil eden düşünceler açık lanmıştır. Buna göre, ideal halde, genlik ve frekansı hiç değişmeyen, yani tam periyottu işaret lerde ölçme süresi, ilâve bir hata söz konusu olmaksızın, istenildiği kadar uzatılabilir. İkinci bölümde konunun teorisi ele alınmıştır. Burada, işaretlerden alınan örneklerle ortala ma ve efektif değerlerin hesabı açıklanmış, ardından genlik ve frekanstaki değişimlerin ölçme sonucuna etkisi incelenmiştir. Yukarıda sözü edilen yöntem, bu tez kapsamına giren ve geri lim (U), akım (I), aktif güç (P), reaktif güç (Q), ve güç katsayısı (k) ölçen cihazın gerçeklenmesin- de, U ve I işratlerinden her periyotta 1 örnek alınarak uygulanmıştır. Bu tezde, örneklerin alına cağı anların uygun biçimde kaydırılması ile, -belli sınırlar içinde - tam periyodik işaret durumuna göre örnek sayısı artırılmadığı halde, frekans modülasyonunun doğuracağı hata miktarının, di ğer hatalar yanında ihmal edilebilecek mertebede kalacağı gösterilmiştir, işaretin biçimi değiş mediği sürece örnek sayısını belirleyici tek faktör, orijinal işaret içindeki en yüksek harmonik derecesi olarak kalacaktır. Genlik modülasyonlu halde ise, modüle eden işaretin periyodunun tesbitindeki güçlükler nedeniyle, hatanın azaltılması amacına yönelik özel bir önlem alınmamış tır. Üçüncü bölümde gerçeklenen devrenin katlan teker teker tanıtılmıştır. Dördüncü bölümde hata analizi yapılmış, toplam hatanın %0.5 ile %1 arasında kaldığı he saplanmıştır. Beşinci bölümde çeşitli fonksiyonların (U, I, P, Q, k) hesabına ilişkin yazılım ele alınmıştır. Altıncı bölümde, gerçeklenen cihaz ile doğruluğu bilinen bazı cihazların ölçü sonuçları kar şılaştırılmış, çeşitli dalga şekilleri için, cihazın, hesaplanan hata sınırları içinde doğru ölçme yaptı ğı tesbit edilmiştir. Sonuç olarak kullanılan yöntemin, dijital mültimetrelerin doğruluk ve maliyetine olumlu kat kısı olduğu, ve önemli uygulama alanları bulunduğu belirtilmiştir.
The most critical device of a digital multimeter, effecting the accuracy, is the Analog / Digital Converter (ADC). By this element, the speed is inversely proportional to the accu racy, unless an advanced technology is used. In this thesis, a new method is proposed to reduce error in digital multimeters, without causing the cost to increase extremely. The principal of this method is based upon the fact, that the time interval between the samples taken from the measured signal, will be widened, hereby accepting the measur ing period also to enlarge. Besides that, -according to the method developed in this work- the frequency change of the signal will be followed, which has the advantage, that the number of the samples is not needed to be increased compared with the case of fully periodic waveform. Thus, it will be possible to use cheap, but high accurate ADC to achieve our aim. Any periodic function with the amplitude X, can be defined as x(t) = X. P(cot), where P (cot) is a periodic function with its peak values +1 and -1. If the amplitudes of the har monics higher than the n-th order are small enough to be ignored, then we have to take 2n samples per period for real time processing. This means a sampling period of n I con. But if we are sure of the amplitude remaining unchanged, in other words, if the signal is fully periodic, so, after taking one sample, we can wait m periods to pass before taking the next sample; and in the m-th period, the sample will be taken after an advance of n I con. Thus, the measuring period will be lenghtened to 2- (2nm + 1). re / co instead of 2- n / co. In practice, we generally want to measure either RMS values of signals, or power, which is the average value of the multiplication of two similar signals. For all these meas urements, it is very convenient to use a microprocessor to process the samples. As it is also explained in the second part of this thesis, for periodic signals, the follow ing items can be shown easily: 1) The average value of the 2n samples / period is equal to the mean value of the sig nal. 2) The square root of the average value of the 2n samples / period is equal to the RMS value of the signal. 3) The average value of the multiplication of 2n samples / period each from two signals is equal to the mean power, considering the one signal to be the current, and the other the voltage. But here, one point is important to draw attention to: Although according to Nyquist criterium, the number of the samples / period (N) may be chosen N > 2n, in practice, one should choose N > 2n, to avoid the possibility, that all samples coincide with zero- cross ing points of the n-th order harmonic. In this thesis, the proposed method is used by selecting m = 1. Accordingly the sam pling points are shown in Fig. 1. 1st zero crossing 2nd z. c. (i+1)stz.c. Figure 1 - Sampling points for m = 1 Using this method, an instrument has been developed to measure RMS- values of volt- age and current, mean power, reactive power (according to the formula: Q = V U2. I2 - P2 ), and power factor k= P / Ul. In part 2, it has further been analyzed, at which rate the frequency (FM) / amplitude (AM) modulation effects the total error. In the case of FM, actually there is no concern about additional error, if one can follow the frequency change, and accordingly shift samples to appropriate points. This is be cause, the amplitude remaining unchanged means the RMS-value being the same as in the case of fully periodic waveform (no modulation). But the impossibility of the prediction of the duration of the current period (T) led us here to determine the sampling points as i-l t"i= £Tk + TM.(G-l)/N) k=l i£2 and the first sampling point (i = 1) is the first zero crossing point of the signal 1st zero crossing 2nd z. c. Ti/32 32nd z. c. * t * t 31T31/32 Figure 2 - Sampling points in the case of FM (for m = 1) The instrument developed here, is designed to measure signals with nmax = 15. Thus N is chosen to be N = 32 (Fig.2). Calculations show, that by using the method developed in this work and explained VIII -* Load Figure 3 - Block schematic of the circuit above, FM will not have considerable effect upon total error, as far as the signals in prac tice are concerned. According to this method, the 'Pulse Timing Circuit' (Fig. 3) will be synchronized with each voltage zero-crossing (positive to negative), which is assumed to be the beginning of the new period. Thus the frequency change will be followed and the effect of FM upon total error will be minimized. But in the case of AM, the RMS-value is not directly proportional to the amplitude of the signal. This means one has to determine the period of the modulated signal in order to define the right positions for samples; or the measuring period should be taken large enough to keep additional error within negligible limits. Because of the inconvenience of either of these two alternatives, with our instrument we did not try to measure signals with minimum error, which are effected by AM. In part 3, the block diagram (Fig. 3) of the realized circuit is given first, and then various parts are explained in detail. On Fig. 3, the functioning of the system can be explained briefly as follows: A certain ratio of the voltage on the network is applied to the zero-crossing detector (ZCD). This stage is followed by a pulse timing circuit (PTC), which performs the task, to produce pulses at appropriate moments. These pulses are used to trigger two sample- hold circuits (SHC), one for current, the other for voltage. The samples taken will be transferred to the microprocessor (u.P) across an analog-to-digital converter (ADC). After completion of taking 32 samples each from voltage and current, the u.P performs calcula tions according to the selected function and the result will be displayed. The fourth part handles the error analysis. Studying each stage seperately shows, that the most critical stage is the PTC. By this stage the most effective property on the error is the frequency of the crystal, being used to clock the CMOS-ICs. Thus to reduce the er ror, the frequency is to be increased. For our application, the frequency is chosen 1 MHz., causing an approximate error of 0.2 % for this stage. The ADC has a 12-bit resolution, with an absolute error of 1.22 mV (Reference volt age: 5 V). IX C Start J Display <- 00 Wait for interrupt Load u and i samples Determine selected function Perform according subroutine Display Figure 4 - Flow chart of the program Programming the u.P is explained in Part 5. The flow chart of the program is given in Fig. 4. In the sixth part, results of some measurements are given to prove the quality of the realized instrument. The results are compared with those of instruments, of which the ac curacy is known. Thus, it is shown, that the proposed method is a cheap solution to re duce error in digital multimeters. Finally, in the concluding part, some important properties of the study are reviewed, and some further considerations are explained, such as to make use of the instrument to build up an accurate digital Watt-hour meter (Wh-meter).
Description: Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1990
Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1990
URI: http://hdl.handle.net/11527/16191
Appears in Collections:Elektronik Mühendisliği Lisansüstü Programı - Doktora

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