UDC 681.1

OSCILLOGRAPHIC APPROXIMATOR

V. N. Bereza, V. F. Dyadik

(Presented by the scientific seminar of the Faculty of Physics and Technology)

At the present time, for purposes of automatic monitoring and control of continuous nonstationary processes and spatial physical fields, discrete methods are finding wide application. Their principal advantages are speed, accuracy, and ease of implementation on electronic apparatus and on control computers. In discrete operational monitoring, the representation of numerical results, curves of parameter distribution, and functional dependences is conveniently carried out on cathode-ray tubes (CRTs) [1].

One of the discrete methods is the method of continuous-sequential readout, in which discrete data on a continuous quantity, in the form of a sequence of continuously following rectangular pulses of corresponding amplitude, are fed to the input of a low-pass filter (LPF), and the signal at the output of the LPF, after its correction, approximates the original quantity analogously to the Kotelnikov series.

In the present work, an instrument implementation is considered for an algorithm for reconstructing continuous distributions by the method of continuous-sequential readout according to series (1). In choosing the algorithm, the criteria adopted for its optimality were: reconstruction accuracy for a fixed number of discrete samples, and rationality of technical implementation.

\[ \begin{aligned} Q(t)={}&\sum_{\kappa=-1}^{\kappa=6} y_\kappa \{0.0125 e^{t-2.5\kappa} + e^{0.5(t-2.5\kappa)}[0.098\sin 0.866(t-2.5\kappa) \\ &\qquad -0.11\cos 0.866(t-2.5\kappa)]\}\cdot 1(-t+2.5\kappa+0.9) + \\ &+ y_\kappa \{11.18 e^{-(t-2.5\kappa)} + e^{-0.5(t-2.5\kappa)}[-3.38\sin 0.866(t-2.5\kappa) \\ &\qquad -3.298\cos 0.866(t-2.5\kappa)]\}\cdot 1(t-2.5\kappa-0.9). \end{aligned} \tag{1} \]

Figure 1 shows a block diagram of the device implementing series (1). The device is intended to operate both with low-level signals (on the order of \(0 \div 10\) mV) and with high-level signals (up to 10 V).

Signals from the sensors \(d_1 \div d_5\) are fed to the inputs of the switching unit—BK, whose key elements are integrated interrupters IP-1. Control of the operation of the switching unit is performed by the control unit—BU on semiconductor ele-

elements, the CU consists of a clock-pulse generator, a binary counter, and a matrix decoder. The signal at the output of the BC is a sequence of rectangular pulses with a duty factor equal to 1 and with amplitude corresponding to the readings of the sensors \(d_1 \div d_5\), \(-d_1\) and \(-d_5\) (Fig. 2, upper oscillogram). After passing through the amplifier—DCA (for input signals of \(0\text{–}10\) mV), the low-pass filter—LPF, and the corrector—C—the signal is fed to the screen of the indicator—I. The positive part of this signal corresponds, with some error, to the original distribution curve (Fig. 2, lower oscillogram).

Fig. 1. Block diagram of the indication device

As the amplifier, an a.c. transistor amplifier with galvanic coupling, overall negative feedback, and a voltage gain of 1000 is used [2].

The LPF is an active transistor Butterworth \(RC\) filter of the 3rd order with frequency-dependent positive feedback; Darlington circuits are used as decoupling elements [3]. The cutoff frequency of the LPF corresponding to series (1) is calculated by the formula

\[ f_{\mathrm{c}} \,(\mathrm{Hz})=\frac{\pi}{2\delta_{\mathrm{n}}\cdot t_{\mathrm{i}}\,(\mathrm{s})}, \tag{2} \]

where \(\delta_{\mathrm{n}}\) is the normalized duration of the input pulses. For the selected algorithm \(\delta_{\mathrm{n}}=2.5\), and for an input-pulse duration \(t_{\mathrm{i}}=100\,\mu\mathrm{s}\), the cutoff frequency \(f_{\mathrm{c}}\) is \(6.28\) kHz.

The corrector is built using transistor differential amplifiers and two inductive delay lines that correct the pre-action oscillations in the pulse response arriving from the output of the LPF [4].

Fig. 2. Photo-oscillograms of reconstruction of a continuous curve from five discrete samples

Fig. 3. Photo-oscillograms of pulse characteristics at the output of the LPF (bottom) and at the output of the corrector (top)

The time for forming the distribution curve is \(900\,\mu\mathrm{s}\). A further increase in the operating speed of the device can be achieved—

by reducing the duration of the pulses \(t_i\). This device can be used for simultaneous and selective indication of distributions over several channels when supplemented with a channel switch.

In the department laboratory, a working model of an eight-channel device for reconstruction and indication of continuous distributions from five discrete samples was built, and laboratory studies of it were carried out. Figure 2 shows photo-oscillograms of the reconstruction of a continuous curve from five discrete samples; Fig. 3 shows the pulse characteristic of the LFF (below) and of the filter-corrector path (above).

Conclusions

1. A device has been developed that implements an algorithm for reconstructing a continuous function by the method of continuous-sequential reading.

2. As a result of investigation of the device model, its principal technical characteristics were determined:

— input-signal range — \(0.5 \div 10\ \text{mV}\)
\(\phantom{— input-signal range —}\) — \(0.1 \div 10\ \text{V}\);

— time for forming and indicating the distribution curve — \(900\ \mu\text{s}\);

— basic instrumental error — \(3\%\).

References

1. Radioelectronic Equipment 1970 (Review). “Elektronika,” 1970, vol. 43, no. 1, pp. 3–38.

2. Yu. I. Konev et al. Transistor Circuits of Automatic Control. Design and Calculation. Moscow, “Sovetskoe radio,” 1967.

3. G. N. Stavskii. Active \(RC\) Filters and Selective Amplifiers. Moscow, “Svyaz,” 1966.

4. V. I. Kulya. Orthogonal Filters. Kiev, “Tekhnika,” 1967.