MULTIVALUED MEASURES OF VARIABLE STRESSES

M. S. ROITMAN

A multivalued measure of variable stresses is a measuring instrument intended for obtaining a series of stress values with a specified accuracy. Multivalued measures (MM) are necessary not only for carrying out verification work. They are also highly needed for performing many scientific investigations. Their creation is a necessary prerequisite for the automation of a number of measurements and for the construction of automated control-and-measuring systems.

The requirement of universality, i.e., the possibility of using one and the same apparatus to verify voltmeters of various types and systems—rms, average, and peak—as well as to solve a wide range of problems, compels one to expand the frequency range, to provide any necessary magnitudes of the output quantity within the limits from tens of µV to hundreds of volts, and limits the permissible nonlinear distortions, above all in the odd harmonics, to 0.5% and less.

Thus, in order to create MM it is necessary to solve a number of closely interrelated problems:

1. The development of generators in which high stability of the output voltage and very small nonlinear distortions are simultaneously attainable over a wide frequency range. It should be explained that for verification purposes short-term stability is primarily important, i.e., the stability of the voltage during the time of verification. In the case of using MM to perform many scientific investigations, and especially in the automation of measurements and the construction of automated control-and-measuring systems, long-term voltage stability acquires primary importance.

2. The need to guarantee the value of the voltage with high accuracy. Both of the indicated problems, with particular urgency, put forward the requirement of creating precision broadband measuring transducers capable of operating effectively in automatic-control systems.

3. The search for ways of constructing precision broadband scale transducers (amplifiers and dividers) for obtaining the required voltage gradations from tens of µV to hundreds of volts.

The practical implementation of solutions to the above-mentioned problems inevitably leads to the need to devote very serious attention to the devel—

development of methods and means for verifying both individual units and the MM as a whole.

Regardless of the general structure of the measure, in order to ensure the required stability of the output voltage under variations of the load resistance we are forced to make the terminal self-regulation loop closed. Analysis of the relationship between the harmonic coefficients, the stabilization coefficient \((G_{\text{st}})\), and the time constants of the voltage stabilizer units with a closed chain of action shows that for systems with an rms-value converter the coefficient of the 3rd harmonic \(\kappa_{3\text{g}}\) in the low-frequency region is equal to

\[ \kappa_{3\text{g}} \approx \frac{G_{\text{st}}}{4} \sqrt{ \frac{ \prod\limits^{m_1} \left[(\omega \tau'_p)^2 + 1\right] }{ \prod\limits^{m_2} \left[(\omega \tau_p)^2 + 1\right] } }, \tag{1} \]

where \(\tau_p\) are the time constants of the IP and of the filtering units;
\(\tau'_p\) are the time constants of the correcting units of the lead type (if present). In systems with a mean-value converter

\[ \kappa_{3\text{g}} \approx \frac{G_{\text{st}}}{3} \sqrt{ \frac{ \prod\limits^{m_1} \left[(\omega \tau'_p)^2 + 1\right] }{ \prod\limits^{m_2} \left[(\omega \tau_p)^2 + 1\right] } }. \tag{2} \]

Expressions (1), (2) are valid both for stabilizers of the compensation type and for those with parametric feedback.

It follows directly from (1) and (2) that in stabilizers with a closed chain of action, for a given \(G_{\text{st}}\), the distortions depend on the values of the time constants and on the number of filtering units. The more inertial units there are, the smaller, all other things being equal, is \(\kappa_{3\text{g}}\). But if the number of units is greater than two, we immediately encounter the problem of stability. There are two ways to increase the critical stabilization coefficient: to increase the spread of the time constants of the units and to introduce additional correcting chains (as a rule, lead units)*). It is not always possible to increase the spread of \(\tau\) for various reasons (for example, when the units have already been specified). If one of the time constants is made very large, we thereby reduce the speed of response of the stabilizer. The introduction of a lead unit (or units) increases the permissible value of the loop gain, but at the same time leads to an increase in nonlinear distortions [1].

All these contradictions have to be taken into account in constructing stabilizers.

But there are several ways to weaken and even eliminate the indicated contradictions. The first way is the most obvious and consists in constructing the stabilizer in the form of a multiloop system of voltage self-regulation (see Fig. 1). The merits of such a system will be considered briefly somewhat later. The second way is connected with the use of the properties of generators with multiple spectrum conversion. Elementary analysis shows that in sources with spectrum transposition, in which 2 or more frequency mixers are used, in principle there is no contradiction between the level of nonlinear

*) In principle, a 3rd method of increasing stability is possible, consisting in the use of correcting negative reactances. But for the present we do not have acceptable technical solutions.

distortion and stability of the output voltage if the regulating action is applied before the first mixer. This is an extremely important advantage of such sources. The known drawback of generators with spectrum transposition—considerable frequency instability—can be completely eliminated when only one reference quartz generator and a frequency-conversion system are used.

Fig. 1

frequencies. The great complexity of the frequency-conversion system greatly limits the use of such generators.

The third way consists in using in the direct-transmission path a selective amplifier \(\kappa(\omega)\). In this case the coefficient of the third harmonic is reduced by a factor of \(\dfrac{\kappa(\omega)}{\kappa(3\omega)}\). But at the same time one more time constant is introduced into the system,

\[ \tau_{\mathrm{eqv}}=\frac{2Q_{\mathrm{eqv}}}{\omega}, \]

and an additional instability factor appears,

\[ \frac{\Delta u(\omega)}{u}=2\left(\frac{\Delta\omega}{\omega}Q_{\mathrm{eqv}}\right)^2, \]

associated with possible mutual frequency detuning \(\left(\dfrac{\Delta\omega}{\omega}\right)\). It can be sharply weakened by making the selective amplifier tracking [2]. But this variant is not optimal.

Two other solutions are possible. To achieve the required selectivity and at the same time reduce \(\dfrac{\Delta u(\omega)}{u}\), the amplifier may be made band-pass (with a small steepness of the amplitude–frequency characteristic near the operating point). But as yet, for the range of low and medium frequencies, we do not have simple solutions with acceptable properties.

The influence of mutual detuning can be completely excluded if generation takes place at the frequency of quasi-resonance of the selective element \(\kappa(\omega)\) and the system contains no other frequency-dependent elements with a substantial steepness of the phase–frequency characteristic. We arrive at the generator structure shown in Fig. 2, where \(\kappa(u)\) is a nonlinear element (NE), RZ is an element with a regulated transmission coefficient, \(\kappa(\omega)\) is—

Fig. 2

selective amplifier, IP—measuring transducer, SS—comparison circuit. U—mismatch-signal amplifier.

The characteristic equation of the system, as shown in [3], when the transfer coefficient of the nonlinear element is approximated in the form

\[ \kappa \left[ u_{\mathrm{in}}(t) \right] = \kappa_0 \left[ 1-\frac{\kappa''}{\kappa_0}(U_m \sin \omega t)^2 \right] \]

is equal to

\[ \frac{G_{\mathrm{st}}}{3 \cdot 2\left(\dfrac{\kappa''}{\kappa_0} U_m^2\right)} \cdot \frac{1}{\tau_{\mathrm{eqv}}p+1} \cdot \frac{1}{p\tau_1+1} \cdot \frac{1}{p\tau_2+1} +1=0, \tag{3} \]

where

\[ \kappa''=\frac{1}{2}\frac{d^2\kappa[u]}{du^2}, \]

\(\tau_{\mathrm{eqv}}\) is the equivalent time constant of an oscillator based on a selective element,

\(\tau_1, \tau_2\) are the time constants of the measuring transducer.

Since the coefficient of the 3rd harmonic is

\[ \kappa_{3\mathrm{g}}=\frac{1}{4}\left(\frac{\kappa''}{\kappa_0}u_m^2\right), \]

it is immediately seen from (3) that, for small distortions, the system is inoperative. Therefore, to ensure stable generation at the required stabilization coefficient, one must either increase the nonlinear distortions at the output of the NE. When the characteristic of the NE is of relay type, expression (3) takes the form

\[ G_{\mathrm{st}} \frac{1}{\tau_{\mathrm{eqv}}p+1} \cdot \frac{1}{\tau_1p+1} \cdot \frac{1}{\tau_2p+1} +1=0 \tag{4} \]

and the desired stabilization coefficient can be obtained easily. But in this case the requirements imposed on the selective element become stringent.

In the case of deep two-sided voltage limiting and the need to have, at the output of the entire oscillator, \(\kappa_{3\mathrm{g}}\sim 0.01\%\), the suppression coefficient of the third harmonic by the selective element must be equal to

\[ \frac{\kappa(\omega)}{\kappa(3\omega)}=3000. \]

With such selectivity, the instability of the transfer coefficient

\[ \frac{\Delta_\Sigma \kappa(\omega)}{\kappa} \]

at the quasi-resonance frequency becomes predominant. The minimally attainable nonlinear distortions are determined by the intrinsic distortions of the selective element.

Thus, for a rational solution of the problem it is desirable to have

\[ \frac{\kappa(\omega)}{\kappa(3\omega)}>1000 \]

at minimum values of the relative instability

\[ \frac{\Delta_\Sigma \kappa}{\kappa} \]

and of the introduced nonlinear distortions \(\kappa_{fb}\).

Known selective RC amplifiers with feedback do not satisfy the indicated requirements. First, even the very realization of an equivalent quality factor \(Q_{\mathrm{eqv}}>375\) (which corresponds to the value

\[ \frac{\kappa(\omega)}{\kappa(3\omega)}>1000 \]

) is substantially hampered because of possible instability. Second, increasing \(Q_{\mathrm{eqv}}\) inevitably leads to an increase in the instability of the transfer coefficient at the quasi-resonance frequency. Third, special measures have to be taken to reduce \(\kappa_{fb}\). All these difficulties are overcome in constructing selec-

tive amplifier based on a harmonic-compensation link [4]. In such amplifiers, attainable values are \(\frac{\kappa(\omega)}{\kappa(3\omega)} = 3000\), and the nonlinear distortions introduced are negligibly small. When distributed RC networks made of manganin microwire are used as zero circuits, and \(Q_{\mathrm{eq}} = 1000\), \(\frac{\Delta_{\mathrm{e}}\kappa}{\kappa} \ll (\pm 0.05)\). The proposed selective amplifiers greatly simplify the construction of a simple generator with small nonlinear distortions and high stability of \(U_{\mathrm{out}}\), and make it possible to implement precision sources according to the structural scheme shown in Fig. 2, both by the action of the converter on the link and by the adjustable transmission coefficient (RZ) [5], and by the action of the converter on the limiter \(\kappa(u)\) itself (the RZ link becomes unnecessary). Amplitude-stable generators with highly selective amplifiers possess the following fundamentally important advantages:

1. Owing to the increase in the admissible cutoff angle, the value of the attenuation coefficient for the influence of instability of the self-oscillator links, at which the system is still stable (see expression (3)), sharply increases; i.e., the possibility of stabilizing \(U_{\mathrm{out}}\) at a given level of nonlinear distortions is facilitated.

2. The influence of the finite value of the converter inertia on nonlinear distortions in the low-frequency region is almost completely eliminated (see (1)).

3. The requirement on the linearity of the adjustable link is greatly weakened, which leads to a simplification of the generator circuit and to the possibility of using inertia-free controlled elements. A consequence of this is a reduction in the order of the self-regulation system and an increase in its stability.

4. Fluctuation phenomena are substantially reduced.

All that has been said above gives grounds to assert that this direction in the construction of amplitude-stable generators with a low level of nonlinear distortion is very promising.

Unfortunately, the generators considered operate only at fixed frequencies. Good results are attainable in generators with a low-pass filter*), in which the latter simultaneously serves to obtain the phase-balance condition. A version of the generator with a low-pass filter has a definite advantage in the sense that all the links of the self-oscillator itself can be made comparatively easily stable and, most importantly, because, owing to the low sensitivity of the transmission coefficient to variations in the filter elements, the generator can be made range-tunable [6]. The prospects of this direction will depend on the extent to which a rational solution of the LPF is found that satisfies the requirements:
a) suppression of the 3rd harmonic by more than 1000; b) the adjustable elements are of the same type and their number does not exceed 3; c) small instability of the transmission coefficient; d) nonlinear distortions introduced below 0.01%; e) the phase- and amplitude-balance conditions throughout the entire system are fulfilled only at one frequency. At present we do not have such LPFs. Therefore, when smooth frequency adjustment is needed, preference has to be given to generators with several self-regulation loops.

The overall stabilization coefficient is equal to the product of the stabilization coefficients of each loop (stage), while the nonlinear distor-

*) These also include generators based on integrators.

...distortions—the root-mean-square sum of distortions in all loops (in the worst case, the arithmetic sum). In multiloop systems whose final loop is closed, the merits of a stabilizing stage with an open action circuit are fully realized (in it there is no contradiction between the stabilization coefficient and nonlinear distortions, nor is there any danger of instability), and especially of a stage with combined action. For reasons considered below, when it is necessary to ensure high long-term stability of \(U_{\mathrm{out}}\) over a wide frequency range, in most cases we are forced to use multiloop automatic-control systems. The attainable stability and accuracy of the value of \(U_{\mathrm{out}}\) are then determined primarily by the characteristics of the measuring transducer (MT). When choosing the type of MT, it should be remembered that in precision sources, along with ensuring small nonlinear distortions, two other basic problems have to be solved:

1. To stabilize \(U_{\mathrm{out}}\). For this, the time stability of the MT is of primary importance.

2. To guarantee the value of \(U_{\mathrm{out}}\), i.e., to have a small conversion error. It is very good when both functions can be combined. But hybrid implementations are also possible if the effect achieved justifies the complication of the source.

At present the most accurate method for measuring an alternating voltage is the method of comparing it, by effective value, with a known constant voltage. For comparing voltages over a wide frequency range, from units of hertz to hundreds of MHz, electrothermal MTs are used [7]. The studies carried out by us [8, 9, 10, 11, 12] showed that, among the class of electrothermal MTs, photoelectric transducers (PTs) are very promising, above all because of the possibility of obtaining high sensitivity and small asymmetry error. These advantages of PTs, as well as a number of others, make it possible to sharply simplify the apparatus. When choosing the type of incandescent lamps (L) for PTs, it is necessary to proceed from the permissible error in the low-frequency region, which is equal to

\[ \delta_{f\mathrm{n}} \approx -\frac{1}{16\left[1+(2\omega\tau_{\mathrm{l}})^2\right]} \left[ K_{\mathrm{PT}}-K_{\mathrm{l}}\alpha_R \frac{R_{\mathrm{l}}-R}{R_{\mathrm{l}}+R} \right], \tag{5} \]

where \(\tau_{\mathrm{l}}\) is the time constant of the incandescent body of L,

\[ K_{\mathrm{PT}}=5\div 10,\qquad K_{\mathrm{l}}= \frac{2}{4+\alpha_R\left(\dfrac{R_{\mathrm{l}}-R}{R_{\mathrm{l}}+R}\right)} \]

are the transfer coefficients of the PT and L, respectively;

\[ \alpha_R \approx 1.2 \]

is the coefficient of nonlinearity of the change in resistance of the incandescent body \(R_{\mathrm{l}}\) with variation of the temperature of the incandescent body;

\(R\) is the resistance connected in series with L in order to extend the voltage-comparison limits.

The normalized characteristics for \(\tau_{\mathrm{l}}\) can be written in the form [13]

\[ \frac{\tau_{\mathrm{l}}}{\tau_{\mathrm{l}3}} \approx \left(\frac{T}{T_3}\right)^{-3} \approx \left(\frac{I}{I_3}\right)^{-2.15} \approx \left(\frac{U}{U_3}\right)^{ -\dfrac{6}{4+\alpha_R\dfrac{R_{\mathrm{l}}-R}{R_{\mathrm{l}}+R}} }, \tag{6} \]

where \(\tau_{\mathrm{l}3}\), \(T_3\), \(I_3\) are the parameters of the incandescent body at the “ignition” temperature \((T_3 \approx 940^\circ\mathrm{K})\).

Increasing the time constant \(\tau_{\mathrm{l}}\) by reducing the current \(I\) at the operating point is, in principle, permissible only down to the value \(I=0.2\,I_{\mathrm{nom}}\), since

As \(I\) is further reduced, \(\tau_{\ell}\) begins to decrease [13]. Therefore, if it is necessary to increase \(\tau_{\ell}\), one has to use lamps with a larger specific mass of the filament, i.e., lamps with a larger rated current. For example, for lamps of type NSM \(6 \times 150\), in the operating mode \(I_{\ell}=32 \div 38\) mA, the frequency error at 20 Hz is below 0.02%. In the frequency range from 100 Hz to 20 kHz, the compensation error can comparatively easily be reduced to 0.002% [11, 12]. Unfortunately, this figure cannot yet be practically realized in multivalued measures of variable voltages intended for broad use, because of the absence of corresponding measures of constant voltage (the error on direct current is, in the best case, within the limits \(0.001\% \div 0.002\%\)).

Comparators based on the FP are well matched with voltage self-regulation systems, performing both stabilization of the output voltage and guaranteeing its value [14]. This makes it possible, on the basis of the FP, to create simple, high-quality wide-range measures of variable voltages [15, 16, 17]. But the FP, like all measuring transducers of the effective value suitable for comparison and for use in self-regulation systems, have comparatively low time stability*). Therefore, if long-term constancy of the output voltage is desired, the system must be hybrid, or else in the terminal loop it is necessary to use the principle of automatic substitution. The latter is effective only in multiloop systems, since periodic conversion makes it possible to sharply attenuate only slow time variations of the voltage. Consequently, the first loops (or the first loop) must ensure small short-term instabilities of \(U_{\text{out}}\), which is practically feasible, while the terminal stage must eliminate slow time variations of \(U_{\text{out}}\) and guarantee the value itself of \(U_{\text{out}}\).

Figure 1 shows the structure of a system with independent terminal regulation loops, and Fig. 3 a structure with coupled loops, where SG is the setting generator, MA the matching amplifier, PA the power amplifier, S the automatic switch which, together with measuring transducer \(\text{MT}_2\), comparison circuit \(\text{CC}_2\), and the amplifier-converter unit, forms a comparator of the effective value of voltage with periodic conversion.

Fig. 3

It should be especially noted that the practical implementation of such a comparator with an error of the order of 0.01% is associated with the need to overcome many technical difficulties [19].

The second system may be simpler than the first, but it has substantially greater limitations with respect to the attainable stabilization factor and stability.

*) It is possible that semiconductor anisotropic elements [18] constitute a pleasant exception.

For voltage stabilization in “continuous regulation” systems, any “inertia-free” and inertial nonlinear elements may be used, as well as various voltage converters possessing high long-term stability and the required frequency properties. But when using one or another type of nonlinear element or converter, the need naturally arises to take its specific features into account. For example, amplitude stabilization is identical to stabilization of the effective voltage value (or the mean value) only when nonlinear distortions are negligibly small or when the shape of the curve is unchanged. Stabilization of oscillations by “inertia-free” nonlinear elements, however, when it is desirable to have a low NI level, inevitably leads to the need to use frequency-dependent links in the system.

From the standpoint of maximum time stability, at present the most suitable are temperature-compensated stabilitrons, synchronous detectors, and converters based on operational amplifiers with rectifiers in the feedback circuit. The frequency range of amplitude-stable generators with stabilitrons is limited from above by the considerable capacitance of the latter (it is equal to \(\sim 500\ \mathrm{pF}\)) and by transient processes in \(p\)-\(n\) junctions [20]. Very high time stability in the frequency region up to 10 kHz is possessed by two-half-period synchronous detectors on germanium transistors in inverse connection (see Fig. 4). The preference for germanium transistors over silicon ones is due to the fact that the resistance of the former in saturation mode is 3–5 times less than the resistance of the latter. The value of the residual current in cutoff mode in two half-periods of the SD does not play an essential role [21].

Fig. 4

The instability of the conversion coefficient of the SD at \(U_{\text{out}} = 10\ \mathrm{V}\) and the optimal commutation current (with the aim of sharply weakening the influence of ambient temperature) does not exceed \(0.005\%\) over several months and \(0.001 \div 0.002\%\) over 10 minutes. Because of transient processes in the transistors, the conversion error increases substantially with increasing frequency. In converters based on SDs it is possible to eliminate the influence of any odd harmonic (the even harmonics have only a slight effect anyway) by appropriate adjustment of the cutoff angles [21], or by using two or more SDs and summing their output signals [22]. But this approach leads to unnecessarily complex solutions. As applied to voltage stabilizers, results no worse can be obtained by combining SDs with stabilitrons (see Fig. 5).

Converters based on operational amplifiers with rectifiers in the feedback circuit can operate over a significantly wider frequency range [23, 24, 25, etc.]. The comparatively small frequency error and the high long-term stability of these converters make it possible to use them as measuring converters that carry out both stabilization of the output quantity and control of its magnitude [26]. In the measuring converters under consideration, the influence of the instability and nonlinearity of the diodes is reduced by as many times as the feedback factor \((F_{\mathrm{oc}})\). But with an increase in the depth of feedback, the frequency band in which the required value of \(F_{\mathrm{oc}}\) is maintained decreases. This circumstance and transi-

processes in diodes have a decisive influence on the upper limiting frequency of the voltage converter. Even in the best converters the error from \(0.01\%\)* at \(1\ \text{kHz}\) increases to \(0.05\%\) at \(20\ \text{kHz}\). Therefore the conclusion suggests itself that it is advisable to reduce somewhat the depth of feedback and to attain the desired quality of the voltage converter by other methods (for example, structural ones). This approach is already being used in practice [25] and appears to be very promising.

It should be noted that fairly good time stability of conversion is attainable in the simplest two-half-period diode rectifier with thermal compensation by an auxiliary diode \(D_3\)** (see Fig. 6). Since the diode temperature coefficient of voltage depends substantially on the current [27], thermal compensation is carried out by adjusting \(R^*\). In a source developed by us for VNIIM [28], with a converter analogous to that shown in Fig. 6, the instability over one hour did not exceed \(0.001\%\). The widest-band voltage converters, capable of operating up to the microwave range, apart from a number of thermoelectric ones, are of the amplitude-compensation type [29]. At \(U_{\text{out}}>5\ \text{V}\) and a low noise level, they have long-term time instability of no more than \(\pm 0.1\%\). If operation over a wide range (up to hundreds of kHz) is required, then in order to obtain minimum error and time instability it is necessary to use two voltage converters: one for stabilizing \(U_{\text{out}}\), and the second for periodic correction of the system.

Fig. 5

Fig. 6

As indicated earlier, scaling devices must provide voltage levels from tens of microvolts to hundreds of volts. To obtain levels below a certain value, dividers are used. Dividers with close inductive coupling (ID) have the highest accuracy in a comparatively narrow frequency range. The exceptionally acute need for accurate wide-band dividers has made it necessary to consider possibilities for the maximum widening of the operating frequency band of ID with minimum loss of accuracy, as well as combined solutions that realize the merits of ID.

It seems possible to solve the indicated problem in four ways. The first, but not the most effective, way consists in equal—

* Advertising data.
** Throughout, a fixed value of the level of the stabilized voltage is meant.

...of the values of equivalent capacitances shunting the individual windings by means of auxiliary correcting capacitances [30 et al.]. The second path is associated with new types of winding and design solutions [31, 32, 33]. The third path consists in using a system of two dividers—an inductive divider (ID) and a frequency-independent resistive one. Such a solution is used in Hewlett–Packard 745A calibrators [1] (frequency range 10 Hz–100 kHz) and in the GK-6 (frequency range 5 Hz–30 MHz) [16]. If necessary, the two dividers can be coupled by an automatic-control system [34 et al.]. The fourth path makes it possible to avoid many difficulties and consists in using two or more simultaneously switched IDs, each of which operates only in its own frequency range. Switching the IDs as a function of the frequency range is easily carried out automatically. This effective path was used by us in developing the multivalued measure GK-12 [35].

To solve the problem of obtaining the required voltage levels of several hundred volts, two approaches are possible. The first is to seek possibilities for creating a precision wideband high-voltage divider and to connect it to the output of a powerful high-voltage source. The second is to seek possibilities for creating a high-voltage reference amplifier and to use it together with a low-voltage wide-range divider. For very many reasons we consider the second approach preferable*).

The presence of a high-voltage reference amplifier makes it possible to dispense with a low-voltage wideband ID, which serves to obtain levels below a certain value; in the final analysis this makes it possible to create both more accurate and simpler measures of variable voltages. A very important circumstance is also that the reference measuring amplifier can be widely used as an independent instrument as well (in the first variant this is excluded), expanding the capabilities of measuring technology.

The creation of high-voltage reference amplifiers without resorting to methods of extracting the “error” and using it for automatic action on the amplifier is impossible. Therefore special attention must be paid to built-in systems for extracting the “error” and to the search for rational implementations of automatic-control systems [36, 37, 38]. The latter is to a considerable extent restrained by the absence of a sufficiently complete comparative analysis of the various variants of automatic correction of the instantaneous value of the amplifier transmission coefficient, taking into account the need to ensure the required bandwidth and stability. Many difficulties in the practical implementation of reference high-voltage amplifiers are due to the absence of the necessary component base—wideband precision dividers, power transistors with an operating voltage on the order of 1 kV and a limiting frequency \(f_{\alpha} > 5\) MHz, integrated differential amplifiers with high input resistance and common-mode rejection of more than \(10^5\), and a number of others. This forces one to look for roundabout paths and leads to a substantial complication of the amplifiers.

Within the scope of the present article, a fuller and more comprehensive consideration of the problem of constructing high-voltage reference amplifiers does not seem possible.

*) It is impossible to use an inductive divider (ID) at the 300 V level (and still more so at 1000 V) over a wide frequency range. Therefore one has to use either two dividers (an ID at a fixed frequency and a wideband resistive one) and a “transfer” method, or a precision resistive divider with a corresponding low-noise output preamplifier of the measuring converter and to enclose the entire system in feedback.

Among the priority tasks in the field of multivalued measures of variable voltages, along with improving their metrological properties, are the tasks of creating fully automated installations capable of operating according to a program, and multivalued measures with a regulated voltage-curve shape.

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