SIMULTANEOUS CONVERSION OF MEASUREMENT RESULTS
FROM VOLTAGE AND FREQUENCY CHANNELS

Dariusz Świsulski

Faculty of Electrical and Control Engineering,
Gdańsk University of Technology, Poland

1. Introduction

Modern measurement systems use multi-parametric measurements, where the results are obtained from many measurement channels. If the relations between the recorded quantities are defined then during measuring of the quickly fluctuating quantities simultaneous sampling is required.

Measurement channels with conversion of the measured quantity into voltage (or current) are used most commonly. This voltage in the process of sampling and quantifying using an analogue-digital converter is converter to a digital form and then stored in the memory.

a)

b)

Fig. 1. Example of configuration of acquisition module for voltage measurement signals: A/A – signal conditioner, S&H – sample & hold, MUX – multiplexer,
A/D – analogue-digital converter

Most of the available acquisition have only one common S&H system behind the channel multiplexer (fig. 1a). This solution enables only sequential sampling in consecutive channels which causes the results to be gathered in different points of time. This makes it impossible to define relations between the signals in different channels [1].

If simultaneous sampling in different channels is required, each channel should be provided with individual S&H module, placed before the channel multiplexer (fig. 1b). The acquisition modules with simultaneous sampling are offered by various producers, but their price is higher.

Sometimes pulse frequency modulated signals are used as the intermediate signals in the measurement circuit [2, 3]. Pulse signal as an intermediate signal is used often because of a simple way of converting it to digital form and low susceptibility to disturbance e.g. when sent over long distance.

Fig. 2. Measurement system with integrated voltage and frequency channels:
x/U - measured quantity-voltage converter, x/f - measured quantity-frequency converter, A/D - analogue-digital converter, f/D - frequency-digital converter,
M - memory

Due to use of a counter as a converter of analogue quantity to digital, the resolution depends on the counter capacity and the measurement time. Selecting an appropriate gating time with the use of high capacity counter one may obtain a simple converter with resolution of 16 bit or higher, which when converting voltage may be difficult. Advantages of f/D conversion faced to A/D conversion are availability of precise standards.

Multi-parametric measurement systems often use channels with voltage and frequency data carrier (fig. 2). The author often participated in elaboration of industrial measurements systems, in which both voltage and frequency channels have been used [4]. Frequently the frequency modulated signals come from incremental encoders used in measuring rotation speed [5].

Obtaining the same sampling instants with multi-channel signal acquisition with frequency carrier is possible when a method of spectrum reconstruction with uneven sampling [6] or sampling instants conversion for digital signal. The author suggested methods making it possible to obtain measurement results with constant frequency or in the moment of signal edge in one of the channels [7].

The task gets more complicated with combination of both measurement circuit types (voltage and frequency). The information about the signal value should be obtained not only with constant and identical frequency but it is also required to gather it in the same instants. Therefore, a method for derivation of the signal values in frequency channels in the same instants as those of triggering the measurements in voltage channels has been elaborated.

2. Method assumptions

The frequency of pulse signal in the measurement channel with frequency carrier is a function of the measured quantity. The simplest method of determining the frequency of the pulse signal in any instant t_k is via measurement of the distance between two instants of this signal: preceding instant t_k and following the t_k instant (period measurement T_i).

If the signal frequency varies during measurement due to a change of the measured physical quantity and simultaneously with longer pulse signal period, the average value of the measured quantity between two pulses as a quantity obtained from measurement, may be different from the instant value during sampling time. (fig. 3) [8].

Fig. 3. Dynamic error Δ_dx in measurement of pulse signal period:
x(t_k) – measured quantity in t_k instant, - mean value
of measured quantity in T_m time

Therefore a better solution is to determine the value of frequency from two neighboring periods with the assumption of linear frequency change and that the value of frequency f_i obtained from period T_i measurement is equal to instant frequency value in the middle point of this period.

One may accept the value of frequency f_k in the t_k instant as the value obtained from two neighboring periods, assuming that the frequency changes linearly during these periods. Depending on the position of t_k instant T_i and T_i+1 (fig. 4a) or T_i+1 and T_i+2 (fig. 4b) are these periods [9].

For we calculate f_k frequency form formula (1), and for from formula (2).

a)

b)

Fig. 4. Frequency measurement from two periods:
a) for , b) for

(1)

(2)

In the t_k instant the voltages in voltage channels are sampled simultaneously with frequency measurement.

3. Method description

The presented principle of measurements requires synchronizing of the sampling of the voltage signal and connected to the sampling instants measurements of period lengths of the pulse signal. This is achieved by using of the external timing signal.

Full measurement for single channel with frequency data carrier is performed with the use of two counters operating continuously in a buffered mode. First of them counts the reference pulses along with consecutive periods of the pulse signal which are recorded in memory. The second one counts the reference signal pulses between the pulse of sampling start and the nearest pulse of the pulse signal.

In each pulse instant of the timing signal the S&H module gets the voltage value, converted then by the A/D converter into the digital form. Simultaneously a number of the last measured period is stored in the memory (the number of periods measured until the given timing pulse).

As a result for two-channel acquisition (one voltage and one frequency channel) after the measurement four mono-dimensional tables are placed in the memory:

· voltage samples converted to digital form : U₁, U₂, … , U_m,

· pulse signal periods indices for the timing instants : a₁, a₂, …, a_m,

· lengths of periods of pulse signal: T₁, T₂, … , T_n,

· distances between the sampling pulse and the nearest pulse of the pulse signal: τ₁, τ₂, … , τ_p.

Fist two tables have equal number of m elements. The fourth table in case the longest pulse signal period is smaller or equal to the sampling period (max T_i ≤  T_s), has the same number of elements as the two first tables (p = m) (fig. 5).

Fig. 5. Sampling for max T_i ≤ T_s

If however the longest period of the pulse signal is greater than the sampling period (max T_i > T_s), the fourth table may have less elements than the first two tables (p ≤  m). This is due to operation of counters in the mode of measuring the distance between the pulses of different signals. After the pulse starting the measurement it is terminated with the first pulse of the second signal, no matter if next pulses will appear in the first signal (fig. 6).

Fig. 6. Sampling for max T_i > T_s

In order to consider the “left over” distances τ_j between pulses of two signals in the fourth table, it is necessary to insert instead of a single element τ_j for τ_j > T_s a w number of elements τ’₁, τ’₂, …, τ’_w (fig. 7), where:

, ,

(3)

(4)

and trunc[x] means the integer part of the number x.

Fig. 7. τ_p table conversion

In this manner we obtain the table τ₁, τ₂, … , τ_m with m elements, where the consecutive value correspond to distances between each sampling pulse and nearest pulse of the pulse signal.

The values of the frequency f_k of the pulse signal for the instant of k pulse of the timing signal is determined on the basis of formulae (1, 2) from two periods ( and or and ) and distance , where a_k is the index of the preceding period of the timing pulse.

For frequency f_k is calculated from:

(5)

But for the frequency f_k is calculated from the formula:

(6)

After this operation of measurement in two channels (one voltage and one frequency) we obtain two mono-dimensional tables:

· voltage values: U₁, U₂, … , U_m,

· frequency values obtained for the same sampling instants: f₁, f₂, …, f_m.

Obviously the number of channels in which the measurement is performed can be larger. For voltage channels its limit is set by the amount of S&H modules, for frequency channels by the amount of counters (two counters per one channel

4. Summary

The article presents a method that allows integration of measuring channels with voltage and frequency data carrier in one acquisition system. It makes it possible to obtain information about the signal values in the same time instants. The described method can find its application when the results of multi-channel recording are used to find relations between particular quantities, fluctuating with great dynamics.

The presented method can be used as well in a microprocessor autonomy device as in virtual instrument [10]. In order to get it working as a virtual instrument it is necessary to use voltage signal acquisition module, counter systems module and additional generator operating as a timing source, determining sample instants.

The presented method is applicable for off-line analysis, when data processing is made after the measurement. For on-line analysis the method must be modifies in such a way that the value of the frequency in the sample instant is extrapolated on the basis of the length of two preceding periods prior to sampling instant [11].

5. Reference

  [1] Świsulski D.: Systemy pomiarowe. Laboratorium. Wydawnictwo Politechniki Gdańskiej, Gdańsk 2001.

  [2] Kirianaki N. V., Yurish S. Y., Shpak N. O., Denega V. P.: Data acquisition and signal processing for smart sensors. John Wiley & Sons, Ltd, Baffins Lane 2002.

  [3] Świsulski D.: Cyfrowa rejestracja sygnałów impulsowych z częstotliwościowym nośnikiem informacji. Wydawnictwo Politechniki Gdańskiej, Gdańsk 2006.

  [4] Galewski M., Wołoszyk M., Świsulski D., Porzeziński M.: Revitalization of building machines for road engineering applications. Proceedings of International Conference on Clean, Efficient & Safe Urban Transport CESURA’03, Gdańsk/Jurata, June 4-6, 2003, p. 1‑10.

  [5] Świsulski D.: Effect of the incremental encoder's errors while measuring the angular velocity. Proceedings XIV IMEKO World Congress "New measurements - challenges and visions", 1-6 June 1997, Tampere, Finland, vol. 8, Topic 14, p. 222‑227.

  [6] Jenq Y. C.: Perfect reconstruction of digital spectrum from nonuniformly sampled signals. IEEE Transactions on Instrumentation and Measurement, vol. 46, No 3, June 1997, p. 649‑652.

  [7] Świsulski D.: Elimination of errors due to measurement-time variation in continuous measurements of time-encoded signals. Proceedings of 9th International Fair and Congress for Sensors, Transducers & Systems SENSOR’99, vol. 2, Nürnberg, May 18-20, 1999, p. 463‑468.

  [8] Świsulski D.: Selection of PFM signal period for T/D conversion. Proceedings XVI IMEKO World Congress IMEKO 2000. Sept. 25-28, 2000 Vienna, Austria, vol. 4 Topic 4-Measurement of electrical quantities, p. 293-298.

  [9] Świsulski D.: Wielokanałowa akwizycja z torami pomiarowymi z napięciowym i częstotliwościowym nośnikiem informacji. Pomiary Automatyka Kontrola, nr 6/2006, p. 27-29.

[10] Lesiak P., Świsulski D.: Komputerowa technika pomiarowa w przykładach. Agenda Wydawnicza PAK, Warszawa 2002.

[11] Referowski L., Świsulski D.: Digital measurement of frequency with linear interpolation in dynamic states. Elektronika ir elektrotechnika, nr 4(76)/2007, p. 47-50.