Synthesis of a Variable-Shape Pulse Generator

E. L. Sobakin

(Presented by the scientific seminar of the Department of Automation and Telemechanics)

The problem of forming a voltage of complex shape arises in many practical cases—for example, in analog computing technology when modeling various processes in time; in pulse technology when forming pulse signals of a prescribed shape; in measuring technology when calibrating electronic digital AC voltmeters, or when studying voltage stabilizers, frequency filters, etc. For these purposes special generators are used that make it possible to obtain periodic voltage oscillations of complex shape.

Various principles for constructing such generators are known; however, the most widespread is the principle in which a complex oscillation is obtained as the result of summing some number of elementary signals with variable parameters. Depending on the type of elementary signals being summed, complex-shape voltage generators can be divided into harmonic synthesizers [1], in which the elementary signals are sinusoidal oscillations of different frequency with variable phase and amplitude, and generators with summation of rectangular voltage pulses. In the latter case, a certain sequence of summed rectangular pulses is provided, in which the amplitude may vary proportionally to the ordinate of a prescribed voltage curve while the duration remains constant [2, 3], or the amplitude and duration remain constant but the sequence of their summation changes by means of adjustable delay lines.

The generators listed have various shortcomings. In particular, for harmonic synthesizers there is the difficulty of adjustment to a prescribed shape, since it is necessary simultaneously to change three parameters: the frequency of the harmonic components, their phase, and their amplitude. For the generator described in [2] there is the need for two additional generators; and for the generator [3] there is the impossibility of retuning to another frequency. The drawback of generators with summation of rectangular pulses of constant duration and amplitude and with adjustable delays consists in the impossibility of adjusting the shape of the leading and trailing edges of the output pulse independently of one another, and also in the need for an additional pulse generator.

In the present article a somewhat different method is proposed, by following which it is possible to create a generator of complex-shape voltage pulses that is to a certain extent free of the indicated shortcomings.

The method is based on representing a pulse of complex shape by means of a step curve obtained as the result of quantiza-

of the specified curve by level. By using a low-frequency filter (LF filter), the stepwise curve can be smoothed and, thereby, a continuous curve can be obtained that approximately corresponds to the specified shape of the output pulse. Naturally, the accuracy of reproducing the specified shape will be the higher, the larger the number of quantization levels selected.

Let us explain the foregoing with an example. Suppose it is required to obtain a pulse with the shape shown in Fig. 1, a (curve 1). A pulse of the specified

a)

б)

Fig. 1

shape can be approximately replaced by a pulse with the envelope given by stepwise curve 2. The degree of approximation of curve 2 to the specified curve 1 will be the higher, the more quantization levels \(X_i\) there are. It is evident from the figure that stepwise curve 2 can be obtained by summing separate rectangular pulses of equal amplitude, equal to the quantization step \(\Delta U\). The number of these pulses is determined by the number of quantization levels \(n\), and the order of their appearance and termination by the character of curve 1. For curves \(U(t)\) having one maximum, the sequence of appearance of these pulses is as follows: first the pulse corresponding to the first quantization level \(X_1\) appears, then the pulse corresponding to the second quantization level \(X_2\), and so on up to the pulse \(X_n\). The sequence of termination of these pulses is the reverse (Fig. 1, a). For pulses with an envelope \(U(t)\) having several maxima (minima), these sequences change correspondingly.

By changing the individual delays in the appearance of the quantization pulses \((\tau_0, \tau_1, \tau_2, \ldots, \tau_i, \ldots, \tau_{n-1})\), as well as the delays in the termination of these pulses \((\tau_{n+1}, \tau_{n+2}, \ldots, \tau_{n+i}, \ldots, \tau_{2n})\) independently of one another, we obtain the possibility of independently adjusting the shape of the leading and trailing edges of the output pulse. By adjusting the delay \(\tau_n\) for the termination of the \(X_n\)-th quantization pulse, one can change the duration of the top of the output pulse.

Thus, for constructing a variable-shape pulse generator, the block diagram shown in Fig. 1, b can be proposed.

In this figure, LBP is a logic switching block whose function is to generate, in a definite sequence, rectangular quantization pulses with adjustable delays at their appearance and termination. This block can operate in self-oscillating and triggered modes.

\(\Sigma\) is a summator. It sums the pulses from the LBP block and forms a stepped pulse.

LPF is a low-frequency filter with adjustable parameters; the filter smooths the stepped curve and may be implemented on integrating \(RC\) circuits. The degree of smoothing of the stepped curve can be adjusted, which provides an additional change of shape in order to select the best variant.

The final amplifier provides the required amplitude of the output pulse.

The choice of basic design solutions for the summator, filter, and amplifier does not present difficulties. Therefore, the synthesis of the generator reduces to the synthesis of the LBP block.

The functional and schematic diagrams of the LBP block can be found by logical methods of synthesis using results from the theory of relay devices and finite automata.

Let us consider an example of synthesizing an LBP block for a generator of voltage pulses with an envelope having one maximum. For simplicity, let us take the number of pulse quantization levels to be four, and then generalize the synthesis results to a larger number of levels. In this case the LBP will have one input and four outputs. We shall carry out the synthesis of the indicated block under the following conditions:

1. It is required to synthesize a device having one input \(a\) and four outputs \(X_1, X_2, X_3, X_4\). The device must operate cyclically (self-oscillating mode) when a potential signal is applied to its input, and must execute one switching cycle if a pulse signal is applied to the input (triggered mode).

2. The output signals must appear upon application of the input action in the following sequence: after the time interval \(\tau_0\) following the moment of application of the input signal, the output signal \(X_1\) must assume the unit value; after the interval \(\tau_1\) following the moment at which signal \(X_1\) appears, the output signal \(X_2\) assumes the unit value; after the time interval \(\tau_2\) following the appearance of signal \(X_2\), output signal \(X_3\) assumes the value 1; and after the interval \(\tau_3\) following the moment at which signal \(X_3\) appears, signal \(X_4\) assumes the unit value.

Table 1

1. The zero values of the output signals must be assumed in the reverse sequence with delays respectively equal to: \(\tau_4\) after the moment at which signal \(X_4\) is switched on, \(\tau_5\) after signal \(X_4\) is switched off, \(\tau_6\) after signal \(X_3\) is switched off, \(\tau_7\) after signal \(X_2\) is switched off, and the device must return to its initial state after the time interval \(\tau_8\) following the switching off of signal \(X_1\).

Fig. 2.

1. The device must pass into the stable initial state, in which all output signals have zero values, only when the switching cycle has ended and the input signal has a zero value.

Using the mathematical apparatus proposed in [4] and the synthesis method of D. A. Huffman, we design the LBP block in the following order.

1). According to the specified conditions, we compile the primary state table (Table 1). This table is compiled by conditionally distinguishing the internal states of the device being synthesized, numbering them, recording the values of the output signals in these states, and recording the transitions of the device from one state to subsequent ones for the corresponding values of the input signal. The difference between this table and those known from [5, 6] consists in the additional accounting for the durations of the internal states and in recording the corresponding durations in a separate column.

2). Simplifying the structure of the device being synthesized, we choose the output elements \(X_1, X_2, X_3, X_4\) as intermediate elements. In this case, to implement the sequence of changes of the output signals specified by Table 1, an additional intermediate element \(U\) is needed, which would be switched on when the input signal is applied, would provide a delay \(\tau_0\) when the output element \(X_1\) is switched on, and would be switched off when the output element \(X_4\) is switched on, providing a delay for its switching off. Taking this additional element into account, we construct a secondary state table (Table 2), in which, while preserving the specified sequence of output signals, we encode the internal states of the device by the values of static and pulse variables [4]. We specify the duration of the states by delays in the transitions from one internal state to another.

3). Using Table 2 and matrices for potential-pulse functions [4], we construct the transition matrix of the device in Fig. 2.

4). Replacing the numbers of the subsequent states in the transition matrix by the corresponding values of the static variables taken from Table 2, one can construct matrices for the output functions \(X_1, X_2, X_3, X_4\) and for the intermediate function \(U\). Because of the limited length of the article, the corresponding matrices are not presented.

5). From the function matrices, according to the rules given in [4], we find their algebraic expressions:

\[ Y = a\bar{x}_4 \bar{x}_{18}^{\,\prime} + y\bar{x}_4, \]

\[ X_1 = y^{\bar{0}} + x_2^{\bar{7}^{\,\prime}}, \]

\[ X_2 = y\bar{x}_1 + x_3^{\bar{6}^{\,\prime}}, \tag{1} \]

\[ X_3 = yx_2 + x_4^{\bar{5}^{\,\prime}}, \]

\[ X_4 = y_4^{\prime}x_3. \]

The expressions obtained specify the functional circuit of the LBP block. In order to implement expressions (1) on contactless devices (transistors), we transform them somewhat; then they take the following form:

\[ Y = \overline{a\bar{x}_{18}^{\,\prime} + y + x_4}, \tag{2} \]

\[ X_1 = \overline{\bar{y} + (\bar{y})_{\bar{0}}^{\prime} + x_2^{\bar{7}^{\,\prime}}}, \tag{3} \]

Table 2

\[ X_2=\overline{\bar y+(x_1)^{\tau'_1}+x_3^{\tau'_6}}, \tag{4} \]

\[ X_3=\overline{\bar y+(\bar x_2)^{\tau'_2}+x_4^{\tau'_5}}, \tag{5} \]

\[ X_4=\overline{\bar y^{\,\prime}+(\bar x_3)^{\tau'_3}}. \tag{6} \]

When these expressions are implemented using transistors of the \(p\)—\(n\)—\(p\) type, a negative potential is taken as the unit signal. In this case, constructing a coincidence circuit for two negative signals requires two transistors. In order to reduce the number of transistors in the device being designed, in expression (2) we take as the unit value of the variables \(a\) and \(x_1^{\tau'_8}\) a positive (zero) potential; then the coincidence circuit can be made with resistors and diodes. In this case the triggering of the static trigger described by expression (2) will be effected by positive signals.

Taking into account the remarks made, from formulas (2)–(6) a functional diagram of the LBP block has been constructed, shown in Fig. 3. The transformations of the original structural formulas of device (1) and the conventional designations of the logic elements in Fig. 3 have been made in accordance with the rules and designations adopted in [4].

Fig. 3.

Considering formulas (2)–(6), it is not difficult to generalize them to the case in which, in quantizing the pulse, \(n\) levels are adopted. In this case the potential-pulse logical functions describing the operation of a similar LBP block will have the following form:

\[ Y=\overline{a\cdot \bar{x}_1^{\tau'_n}+y+x_n}, \]

\[ X_1=\overline{\bar y+(\bar y)_{x_0}^{\prime}+x_2^{\prime\,2n-1}}, \]

\[ X_2=\overline{\bar y+(x_1)^{\prime\,1}+x_3^{\prime\,2n-2}}, \]

\[ \ldots \]

\[ X_i=\overline{\bar y+(\bar x_{i-1})^{\prime\,i-1}+x_{i+1}^{\prime\,2n-i}}, \]

\[ \ldots \]

\[ X_{n-1}=\overline{\bar y+(\bar x_{n-2})^{\prime\,n-2}+x_n^{\prime\,n+1}}, \]

\[ X_n=\overline{(\bar x_{n-1})^{\prime\,n-1}+\bar y^{\prime\,n}}. \]

By selecting particular variants for realizing the indicated expressions on transistors, a basic circuit of the generator was obtained, shown in Fig. 4, taking into account eight quantization levels.

In the triggered mode, the generator provides voltage pulses with linearly rising leading edges, rectangular pulses of various durations, pulses of the most varied stepped shape, and pulses with convex-concave edges. The generator can be triggered from any standard generator by positive pulses with an amplitude of not less than \((7 \div 8)\) volts and a duration of not less than four microseconds.

In the self-oscillating mode, the generator reproduces periodic oscillations of various forms: sinusoidal, triangular, trapezoidal, sawtooth, rectangular, stepped oscillations of various variants, and other oscillations of irregular shape. The duration of the output pulses in the triggered mode and the frequency of oscillations in the self-oscillating mode can be varied by changing the total value of the delays and depend on the choice of the parameters of the delay circuits. For the manufactured prototype, the frequency of periodic oscillations, without changing their shape, was regulated within approximately \((50 \div 250)\) Hz. Generation of sinusoidal oscillations is possible from 50 to approximately 400 Hz, and of rectangular oscillations—from 200 Hz to 25 kHz.

Figure 5 shows some oscillograms of the output voltage of the generator operating in the self-oscillating mode. Adjustment of the generator to a specified form of the output-voltage curve was carried out visually using an oscilloscope, but it can be performed using scales on variable resistors that regulate the individual delays. For this purpose it is necessary to compile tables indicating the position numbers of the sliders of the adjustable resistors for each curve shape, and to set these sliders to the corresponding positions. To change the oscillation frequency for a given shape, all delays must be changed proportionally in one direction or the other.

The designed generator has, in comparison with known ones, a number of advantages:

Figure 4.

1) does not require additional generators,
2) is easy to tune to the selected oscillation waveform.

Fig. 5.

3) permits the possibility of changing the oscillation waveform on any segment of the curve independently of other adjustments,
4) makes it possible to change the oscillation frequency without changing its waveform.

LITERATURE

1. A. D. Band. A new harmonic synthesizer based on multivibrators with emitter coupling. Express information, “Instruments and Elements of Automation,” issue 23, ref. 127, 1965.

2. F. Yu. Oldernser, V. P. Berezhnoy, V. A. Shuvaev. Generator of video pulses of arbitrary shape. Izv. vuzov, “Radio Engineering,” vol. 8, No. 3, 1965.

3. Ward John Joseph. Electric impedance waveforming generator, U.S. Patent, class 328—186, No. 3249879.

4. E. L. Sobakin. On the use of logical methods for the synthesis and analysis of potential-pulse relay devices. Dissertation for the degree of Candidate of Technical Sciences, Tomsk, TPI, 1967.

5. N. P. Vasil’eva, I. Gashkovets. Logical elements in industrial automation. Library on Automation, issue 68, GEI, 1962.

6. S. Koldunov. Logical synthesis of relay devices. IL Publishing House, 1962.