PROCEEDINGS

OF THE TOMSK ORDER OF THE RED BANNER OF LABOR POLYTECHNIC INSTITUTE named after S. M. KIROV

Volume 231
1971

REFERENCE SQUARE-WAVE VOLTAGE GENERATOR WITH ADJUSTABLE DUTY FACTOR AND FREQUENCY

M. S. ROITMAN, G. P. TROFIMOV, L. A. NAUMOV, A. V. SOKOLOV

(Presented by the scientific seminar of the Department of Radio Engineering)

In the set of problems concerned with increasing the accuracy and ensuring the uniformity of voltage measurements by voltmeters of various systems (amplitude, rms, and average-value types), an important role is played by the problem of taking into account the influence of the voltage waveform on the readings of the instrument, both during verification and in operation [1]. In this connection, an experimental approach is of primary importance, owing to the substantial mathematical difficulties encountered in an analytical solution of the problem.

For theoretical analysis it is necessary to have an accurate mathematical approximation of the dynamic characteristic of the voltmeter and then, in the general case, to solve nonlinear differential equations.

The problem of calibrating and experimentally evaluating the influence of the waveform of a voltage curve on voltmeters of various systems is, to a considerable extent, solved when a reference square-wave voltage generator with adjustable parameters is available. Here and below, by a reference generator is meant a generator whose signal parameters are known with high accuracy. A square-wave voltage generator becomes a truly universal tool if there is the possibility of accurate, mutually independent adjustment over wide ranges of the frequency, duty factor, and voltage amplitude, with negligibly small relative duration of the edges.

Two fundamentally different ways of constructing generators are possible. The first is when open-loop generation of the required functions is carried out, i.e., when the system has no feedback loops sensitive to particular signal parameters.

The second is when there are built-in units for monitoring the signal parameters (error-detection units) and for their automatic regulation (closed-loop generators). It should be noted that reference generators are subject to such high requirements for the stability of signal parameters that manual correction is practically excluded.

If, for the time being, one disregards the “cost of expenditures” and strives to obtain the best metrological characteristics, then the choice of the path is determined by the answer to the following alternative: what can be done with greater accuracy: 1) synthesizing a signal with specified parameters, or 2) estimating the deviation of the corresponding signal parameter from a specified value. In the general case, a justified answer can be obtained only after a detailed study of the issues of open-loop generation and of the potential accuracy of built-in systems for checking signal parameters.

Known methods for measuring the amplitude value of voltage do not yet make it possible to create built-in systems for active* verification of amplitude with an error of less than 0.05–0.1%. There is a real possibility of reducing the error of amplitude measurement to a value on the order of 0.01% by using the method of time-shifted comparison by substitution and an oscilloscope as a null indicator. But a system of this kind is very difficult to automate.

As regards the measurement of time intervals, satisfactory results can be obtained here by using phase methods. In this case, however, the volume and complexity of the equipment increase sharply, which is undesirable. This remark is also valid when using the method of counting the number of pulses contained in a definite interval.

Thus, preference should be given to open-loop systems. A comparative analysis of implementations of open-loop generators [2] has shown that the most rational design is based on transistor switches and flip-flops. By varying the mode of the input circuit of a transistor switch, it is comparatively easy, for a given load, to obtain a very small temperature and time drift of the collector-emitter voltage of an alloy transistor in the saturation region [3], and consequently also a high stability of the amplitude of the output signal**. Flip-flops, as well as other discrete circuits, can ensure high accuracy in setting time intervals [4].

In comparison with other discrete frequency dividers, flip-flops have a number of well-known advantages. Obviously, when static flip-flops are used, the setting of frequency and duty factor will be carried out discretely with a factor of 2. However, discrete adjustment of parameters is characteristic of standard equipment.

Let us determine the requirements for the duty factor of a rectangular voltage. To this end, consider a generator–voltmeter system with a closed input. For the time being, assume that the time constant of the input circuit of the voltmeter is infinitely large and, consequently, that droop of the top of the rectangular voltage is absent. The amplitude, rms, and mean values of a rectangular voltage depend on the duty factor, i.e., in the general case \(U_x = f(Q)\). Oscillations of the duty factor about the set value determine the instability of the corresponding voltage \(U_x\). It is convenient to find this relation in the form

\[ \frac{dU_x/U_x}{dQ/Q} = f(Q), \tag{1} \]

whence, for a given voltage error, we shall find the permissible relative deviation of the duty factor.

Specifying the magnitude of the voltage step \(2U\) (Fig. 1) and taking into account the equality of the areas of the positive and negative half-waves, we find the amplitude of the rectangular voltage after the coupling capacitor:

\[ U_m = \frac{2(Q-1)}{Q} U . \tag{2} \]

Equating the sum of the indicated areas to a certain mean-rectified*** voltage acting during the period, i.e., to the quantity

* Active verification is understood as verification whose results are used to eliminate deviations of the signal parameters from the norm.

** In what follows it is assumed that the instability of the parameters of the closed transistor does not affect the characteristics of the output signal.

*** In what follows we shall use the term “mean voltage.”

$U_0T$, we obtain

\[ U_0=\frac{4(Q-1)}{Q^2}\,U. \tag{3} \]

Similarly, for the rms value of the voltage,

\[ U_m^{\prime 2}T_{\mathrm{i}}+(U_m')^2(T-T_{\mathrm{i}})=U_d; \]

whence

\[ U_d=\frac{2\sqrt{Q-1}}{Q}\,U. \tag{4} \]

Fig. 1.

The obtained relations make it possible to find the crest factor

\[ K_p=\frac{U_m}{U_d}=\sqrt{Q-1} \tag{5} \]

and the voltage form factor

\[ K_F=\frac{U_d}{U_0}=\frac{Q}{2\sqrt{Q-1}}, \tag{6} \]

which is convenient for comparing calibration results with sinusoidal and rectangular voltages.

The values of $U_0$, $U_d$, $K_p$, and $K_F$, calculated for several duty-factor values, with $U=10$ V, are given in Table 1. For existing voltmeters, the crest factor of the calibration voltage does not exceed 4. From the data presented it is evident that this value of $K_F$ is reached at $Q=16$. Consequently, the indicated series of duty-factor values may be considered sufficient.

Table 1

Differentiating expressions (2), (3), and (4) with respect to duty factor and taking into account the relations obtained for \(\dot U_m\), \(U_0\), and \(U_d\), we find dependences of the form (1). These dependences and their numerical values for several duty-factor values are given in Table 2.

Table 2

Permissible deviations of the duty factor of a rectangular voltage
for a voltage error of \(3 \cdot 10^{-4}\)

The best domestic voltmeters for amplitude, rms, and average voltage values have an accuracy class of 0.2–0.3. For their calibration and verification it is sufficient to have a voltage error

\[ dU_m/U_m = dU_0/U_0 = dU_d/U_d = 3 \cdot 10^{-3}. \]

The permissible values of \(dQ/Q\), calculated from the dependences in Table 2, are given in Table 3.

Ultimately, the required instability of the duty factor determines the maximum frequency of the generated voltage. According to our estimate, for transistor circuits in ordinary implementation this frequency is limited to \(10\ \text{kHz}\).

Fig. 2.

The upper frequency of the generated voltage is also limited by the permissible losses of signal energy due to the finite switching time of transistor keys. For alloy-junction transistors this time lies within \(100\ \text{ns}\), which does not allow the generation frequency to be increased above \(10\ \text{kHz}\) (without deterioration of the characteristics of the output voltage).

Let us now consider the case when the time constant of the input circuit of the voltmeter is finite. The exponential decay of the top of the rectangular pulse leads to additional errors in the amplitude, rms, and average voltage values.

The voltage amplitude in the presence of a coupling capacitance (Fig. 2) is found from the obvious relation

\[ \left(U_{mc} e^{-\frac{t}{\tau}} - 2U\right)e^{-\frac{t-T_{\text{и}}}{\tau}} + 2U = U_{mc}, \]

whence

\[ U_{mc}=\frac{1-e^{-\frac{T-T_i}{\tau}}}{1-e^{-\frac{T}{\tau}}}\,2U . \tag{7} \]

Expanding the exponential terms in a series and retaining only two terms of the expansion, we obtain

\[ U_{mc}=\left(1+\frac{1}{Q}\cdot\frac{1}{2\tau f-1}\right)U_m, \tag{8} \]

where, in the final expression, the period has been replaced by the frequency. The additional relative change of \(U_{mc}\) in comparison with \(U_m\) will be

\[ \delta U_{mc}=\frac{1}{Q(2\tau f-1)} . \tag{9} \]

Taking into account the equality of the areas of the positive and negative half-waves, for the voltage averaged over a period we have

\[ U_{oc}=2\int_{0}^{T_i} U_{mc}\cdot e^{-\frac{t}{\tau}}\cdot dt . \]

After substituting into this equality the value of \(U_{mc}\) from expression (8) and carrying out the transformations, one can obtain

\[ U_{oc}=\frac{2\tau f}{2\tau f-1}\,U_0 \tag{10} \]

\[ \delta U_{oc}=\frac{U_{oc}-U_0}{U_0}=\frac{1}{2\tau f-1}. \tag{11} \]

Similarly, for the rms value of the voltage one can also find

\[ U_{dc}=U_d\sqrt{\frac{Q+1}{Q}\cdot\frac{2\tau f}{2\tau f-1}}, \tag{12} \]

\[ \delta U_{dc}=\sqrt{\frac{Q+1}{Q}\cdot\frac{2\tau f}{2\tau f-1}}-1 . \tag{13} \]

The time constant of the divider circuit of voltmeters of various systems ranges from \(0.01\div0.5\) sec, and the additional error over all voltage values at low frequencies will be considerable. To take the correction into account, it is necessary to know the true value of \(\tau\).

The generator is implemented according to the functional diagram shown in Fig. 3.

The shaper (F) converts the sinusoidal oscillations of the reference LC generator (ZG) into sharp-ended pulses for triggering the flip-flop circuits. The scaling circuit on flip-flops Tg1—Tg10 determines the frequency of the output rectangular voltage in accordance with the required overlap factor of the frequency range \((2^{10})\).

Flip-flops Tg11—Tg20 and gate V form the duty-factor shaping circuit. The operation of the circuit is explained by the timing diagrams shown in Fig. 4. The gate is a transistor series coincidence circuit for negative signals and has two inputs: a level input from flip-flop Tg19 and a pulse input from one of the flip-flops

Tr11–Tr13 depending on the required duty factor (positions of switch B2-1).

The pulses are formed by differentiating the voltage steps from triggers Tr11–Tr13 and are fed continuously to gate B.

Fig. 3

Signals from the left output of trigger Tr10, through the recalculating circuit on triggers Tr14–Tr18, switch Tr19 into a state in which a high negative potential is established at its left output. Gate B is prepared for operation. After half a period of operation of Tr10, the next pulse from one of the triggers Tr11–Tr13 causes gate B to operate; its output signal switches trigger Tr20 and, through switch B2-2, trigger Tr21. The second output pulse of gate B, arising—depending on the position of switch B2-1—on the second pulse of one of the triggers Tr11–Tr13, switches triggers Tr20 and Tr21 back to their initial position.

Fig. 4.

The signal from Tr20 returns Tr19 to the state in which a zero potential is established at its left output. In this case the gate does not respond to the third pulse. The next two pulses are issued by the coincidence circuit after the next operation of Tr19 at the left input. Thus, during the time interval between these two pulses, trigger Tr21 is in one state, and during the remaining part of the period determined by trigger Tr19 it is in the other. Signals from trigger Tr11 form a duty factor of 16, from Tr12—8, and from Tr13—4. A duty factor of 2 is formed by ordinary division, by trigger Tr21, of the frequency of the signals from the left output of Tr17 (in Fig. 4 only the signals from the right output of Tr17 are shown; the actual signals are shifted by half a period of operation of Tr17).

To obtain a small error in duty factor, the generator circuit uses high-frequency triggers with built-in emitter followers, whose main transistors operate in the nonsaturated mode. The duration of the voltage steps of the trigger, with a magnitude of 9.5 V, is 40 nsec.

Identical bipolar voltage is obtained by means of a transfer transistor switch K (Fig. 3 and Fig. 5).

When a high negative level arrives from trigger Tr21, transistor PP1 is open and the voltage across the load is \(+U\); at the zero level of the trigger signal the voltage across the load is negative \((-U)\).

To obtain an identical bipolar voltage across the load (the voltage drops across saturated transistors, the internal resistances of sources \(E_{01}\), \(E_{02}\), and the wires are different), the dc sources are regulated.

The static operating mode of the generator with a specified polarity of the output voltage is ensured by applying a positive voltage to the corresponding base of trigger Tr21 through contacts 2 and 3 of switch VZ-2 (in the general circuit of the generator this switch is not shown). In the first and fourth positions of switch VZ the dynamic mode of the generator is provided. When transistors PP1 and PP2 are switched, a bipolar square-wave voltage is obtained across the load.

Fig. 5.

Fig. 6.

The latter remains equal to a constant value only if the voltage drops across the transistor switches and the internal resistance of sources \(E_{01}\) and \(E_{02}\) do not change dynamically, and the capacitances of these sources with respect to “ground” are negligibly small (otherwise the durations of the transitions increase and the rms value of the square-wave voltage decreases).

To estimate the difference between the collector-emitter voltage of a saturated switch, \(U_{\text{ken}}\), in the static and dynamic modes, two transistors of the same type (MP16B or MP38A) were connected according to the circuit shown in Fig. 6. The control voltage is applied from opposite arms of a high-frequency trigger. The trigger was stopped alternately in one state and then in the other, and, using a low-ohmic potentiometer \(r_{\text{p}}\), equality of the voltages at the transistor collectors was achieved in the static mode. Then the trigger was started, and the change in \(U_{\text{ken}}\) was monitored with an R309 potentiometer. In the dynamic mode, at an output current of \(10\ \text{mA}\), the voltage \(U_{\text{ken}}\) decreased by \(5 \div 10\ \mu\text{V}\) for MP38A transistors, and increased by \(10 \div 20\ \mu\text{V}\) for MP16B transistors. To determine the causes of the change in \(U_{\text{ken}}\), the switching frequency of the trigger \((5\ \text{Hz} \div 50\ \text{Hz})\) and the degree of saturation were varied, and the transient processes were also monitored. The investigations showed that the principal influencing factor is a decrease in tempera-

in the transistor, on alternating current, owing to the reduction of the power dissipated in it (almost by a factor of two). As the output current of the switch increases, this error increases. Therefore the generator output current was chosen equal to 10 mA. Data on the temperature and time stability of \(U_{\text{k-e}}\) are given in [2, 3].

Let us estimate the effect of the internal resistance of sources \(E_{01}\) and \(E_{02}\). The consumption of the source on direct current is twice as high as on alternating current. This leads to a change in the square-wave voltage, in comparison with the direct-current value, by

\[ \Delta U_{ri}=\frac{r_{i1}+r_{i2}}{2} I_{\text{n}} . \]

The internal resistances of the implemented sources are \(r_{i1}=-0.007\ \Omega\), \(r_{i2}=+0.003\ \Omega\), and the square-wave voltage increases by \(+20\ \mu\text{V}\) (\(I=10\ \text{mA}\)). In the same way, one can determine the change in amplitude for any value of the duty factor. The instability of the voltages \(E_{01}\) and \(E_{02}\) does not exceed \(10^{-6}\) in 10 minutes.

To change the parasitic capacitance of sources \(E_{01}\) and \(E_{02}\), they are supplied through an additional transformer Tr2 (Fig. 7). The parasitic capacitance of the secondary winding of Tr2 relative to “ground” in this case is determined by the series-connected interwinding capacitances of transformers Tr1 and Tr2 and, according to measurements, is 80 pF.

Fig. 7.

Calibration of the generator on direct current was carried out with an R309 potentiometer. On alternating current, in order to evaluate the metrological characteristics of the output rectangular voltage, specially selected measuring converters were used: a multi-element thermoelectric converter (TEM), a vacuum noncontact converter (TVB), and a photoelectric integrating-type converter developed at the department. Frequency instability was determined with a Ch3-12 frequency meter, and the front duration with an S1-11 oscilloscope (marker value 10 ns).

The calibration gave the following results.

1. Instability of the rms voltage value: \(\pm 5 \times 10^{-5}\%\) per hour.
2. Frequency instability: \(\pm 2 \times 10^{-\, [[unclear: exponent]]}\%\) over 5 hours.
3. Duty-factor instability: \(+10^{-\, [[unclear: exponent]]}\%\) per hour.
4. Front duration: 50 ns.

The detailed procedure and calibration data are given in [2].

The main characteristics of the generator (see Fig. 8) are: output-voltage amplitude \(\pm 10\ \text{V}\), output current 10 mA, duty factor \(2^m\) (\(m=1, 2, 3, 4\)), frequency \(10\cdot 2^n\ \text{Hz}\) (\(n=1, 2,\ldots,10\)).

REFERENCES

1. B. E. Rabinovich, A. M. Fedorov. Present state of the technique of graduation and calibration of electronic voltmeters. Izmeritel’naya tekhnika, No. 10, 1966.
2. M. S. Roitman, G. P. Trofimov, L. A. Naumov, A. V. Sokolov. Research report, Reference generator of rectangular voltage with adjustable parameters, No. 68371510, VNIITI, 1970.
3. G. P. Trofimov. Temperature and time stability of the collector-emitter voltage of a saturated transistor (in the present volume).
4. E. I. Dolbak. Study of highly stable transistor circuits and their application in chronometry. Dissertation, Novosibirsk, NETI, 1965.