NEW INSTRUMENTS AND METHODS OF MEASUREMENT

ELECTRONIC CURRENT STABILIZERS

L. Kalinir

INTRODUCTION

The solution of many problems in experimental physics is connected with the need to maintain the current in a given electric circuit with a high degree of accuracy. Since the source voltage and the resistance of the circuit are not strictly constant, forced stabilization is used to ensure an unchanging value of the current. Devices serving this purpose are called current stabilizers.

The need for current stabilization arises in supplying the electromagnets of mass spectrometers, certain types of charged-particle accelerators, magnetron generators, various electron-optical systems, in work on the study of nuclear paramagnetic resonance, in photometric measurements of luminous fluxes of incandescent lamps, in calorimetry, and also in many other cases.

The requirements imposed on the constancy of the current are often very severe. Thus, for example, the deviation of the current from the specified value in the windings of the electromagnetic lenses of electron microscopes must not exceed thousandths of a percent. With the same, and sometimes even greater, accuracy it is necessary to maintain the current in the windings of laboratory mass spectrometers, etc.

It is usually necessary to vary the value of the stabilized current within certain limits. The limits of variation may be rather large and in particular cases may reach tens of times.

There are several varieties of current stabilizers. These include stabilizers with moving parts (mechanical automatic resistance regulators), ferroresonant stabilizers, parametric non-electronic stabilizers (barretters), stabilizers with electron tubes (electronic stabilizers), and others.

Thanks to a number of valuable advantages—low inertia, the possibility of obtaining high stabilization coefficients and wide regulation ranges, and so on—electronic stabilizers have become widely used. They are employed for stabilizing both very small currents, on the order of milliamperes and even microamperes, and large currents of units and tens of amperes.

In circuits for stabilizing currents on the order of hundreds of amperes, regulation is usually not carried out directly by electronic tubes, but is effected by varying the current in the excitation circuit of dynamo machines, or by means of magnetic amplifiers placed at the input of rectifiers, etc. Such stabilizers are not purely electronic. However, a considerable number of their elements do not differ in any way from the elements of electronic current stabilizers with a feedback amplifier, and they are briefly mentioned in § 3 of the present review.

In § 4, stabilizers of magnetic field are considered in general outline; these also have much in common with current stabilizers.

§ 1. BASIC CONCEPTS

Under normal operation of a current stabilizer, a change in the load resistance, within the limits of the specified accuracy, must not affect the magnitude of the current. Then, when the load resistance \(Z_{\text{н}}\) changes, the output voltage changes proportionally to it, and the dependence \(I=f(U_{\text{вх}}, Z_{\text{н}})\) for a current stabilizer may be written as \(I=f(U_{\text{вх}}, U_{\text{вых}})\). Considering this dependence in the stabilization region to be linear, it may be represented by the expression\(^1\)

\[ I = a + S U_{\text{вх}} - g U_{\text{вых}}. \tag{1} \]

Here \(I\) is the output current of the stabilizer (load current), \(U_{\text{вх}}\) is the input voltage of the stabilizer, and \(U_{\text{вых}}\) is the output voltage of the stabilizer (the voltage across its load).

The physical meaning of the constants in equation (1) is determined if one takes the total differential of the expression for the current:

\[ dI = \frac{\partial I}{\partial U_{\text{вх}}}\, dU_{\text{вх}} + \frac{\partial I}{\partial U_{\text{вых}}}\, dU_{\text{вых}}. \tag{2} \]

The constant \(S = \dfrac{\partial I}{\partial U_{\text{вх}}}\) characterizes the change in current as a function of the input voltage and is called the stabilization slope. The second constant \(g = -\dfrac{\partial I}{\partial U_{\text{вых}}}\) characterizes the change in current as a function of the output voltage and is called the output conductance. The minus sign indicates that an increase in \(U_{\text{вых}}\) corresponds to a decrease in the current \(I\).

Obviously, for an ideal stabilizer \(S\) and \(g\) are equal to zero. In a real stabilizer, one seeks to make them as small as possible.

Dividing both parts of (2) by the nominal value of the current \(I_0\),

\[ \frac{dI}{I_0} = \frac{\dfrac{\partial I}{\partial U_{\text{in}}}\,dU_{\text{in}}}{I_0} + \frac{\dfrac{\partial I}{\partial U_{\text{out}}}\,dU_{\text{out}}}{I_0}. \tag{3} \]

and introducing the concept of current instability \(\sigma=\dfrac{\Delta I}{I_0}\), in accordance with (3) we obtain:

\[ \sigma=\sigma_U+\sigma_R. \tag{4} \]

Here \(\sigma\) is the total current instability, \(\Delta I\) is the maximum deviation from the nominal current value \(I_0\), and \(\sigma_U\) and \(\sigma_R\) are partial instabilities, respectively reflecting the degree of influence on the constancy of the current of changes in the source voltage and the load resistance:

\[ \sigma_U=\left|\frac{\Delta I}{I_0}\right|_{R=\text{const}}, \tag{4a} \]

\[ \sigma_R=\left|\frac{\Delta I}{I_0}\right|_{U=\text{const}}. \tag{4b} \]

To characterize the operation of stabilization circuits, the concept of the stabilization factor is also used; it shows the ratio of the instability of the voltage at the stabilizer input, or the instability of the resistance value, to the instability of the current in the stabilizer load.

By analogy with (4a) and (4b), the notion of partial stabilization factors is introduced. The partial voltage stabilization factor \(m_U\) characterizes the reduction of current instability at the output of the stabilizer with unchanged resistance but varying input voltage; the partial load factor \(m_R\) indicates the reduction of current instability when the load changes and the input voltage is constant, as compared with the change in current that would occur if the stabilizer were absent:

\[ m_U=\left|\frac{\sigma_{U_{\text{in}}}}{\sigma_{U_{\text{out}}}}\right|_{R=\text{const}}, \tag{5a} \]

\[ m_R=\left|\frac{\sigma'_R}{\sigma_R}\right|_{U=\text{const}}, \tag{5b} \]

where

\[ \sigma_{U_{\text{in}}}=\frac{\Delta U_{\text{in}}}{U_{0\text{in}}}; \qquad \sigma_{U_{\text{out}}}=\frac{\Delta I}{I_0}; \qquad \sigma'_R=\frac{\Delta R}{R_0}. \]

The value of the required stabilization factor depends on the instabilities present and on the requirements for constancy of the load current.

Below are given formulas1 that make it possible, for known parameters of the stabilizer \(S\) and \(g\) and specified limits of variation of the voltage and load resistance, to determine the instability of the current at the output of the stabilizer and the stabilization coefficient:

\[ \Delta I = \frac{S\,\Delta E_{\text{ист}}} {g\left(Z_{\text{н}}+\dfrac{1+SZ_{\text{ист}}}{g}\right)}, \tag{6} \]

\[ \Delta I = - I_0 \Delta R_{\text{н}}\, \frac{1} {(1+SZ_{\text{н}})\dfrac{1}{g}+R_{\text{н}}+\Delta R_{\text{н}}}. \tag{7} \]

Here \(\Delta E_{\text{ист}}\) is the change in the emf of the power source as compared with the nominal value, \(Z_{\text{ист}}\) is the internal resistance of the power source, \(Z_{\text{н}}\) is the total load resistance, \(R_{\text{н}}\) is the nominal dc load resistance, and \(\Delta R_{\text{н}}\) is its change.

Formula (6) makes it possible to determine the change in current as a function of the change in voltage, and formula (7), as a function of the change in load. Both expressions indicate that the magnitude of the instability of the output current, determined by the full value of the internal resistances of the source and the load, is a function of frequency.

A change in load resistance is usually associated with the influence of temperature and occurs comparatively slowly. As for the voltage feeding the stabilizer, alongside its slow variation owing, for example, to drift of the power line, there are a number of factors causing its rapid variations. These include voltage fluctuations associated with changes in the line frequency, pulsations at the output of a rectifier or dc generator, etc. When the permissible instability is small, it is necessary to take into account not only the presence of pulsations but, in individual cases, also the influence of rather high harmonics of these pulsations23.

In the case where only slow changes of the input voltage play a role, \(Z_{\text{н}}\) is the internal dc resistance of the rectifier and is determined by the slope of its volt-ampere characteristic. If an unstabilized rectifier is used, then the internal resistance of the source \(Z_{\text{ист}}\) is determined by the resistance of the filter capacitor at the pulsation frequency.

Formula (6) indicates that, when there are high requirements on the constancy of the current, it is advisable to use preliminary stabilization of the supply voltage, which in practice is done quite often45. Preliminary voltage stabilization is advisable when stabilizing the currents of large magnets or other circuits with a large time constant also for other reasons4. In stabilization circuits employing a negative-feedback amplifier, which will be considered below, a large load time constant makes it difficult, because of the danger of self-excitation of the system,

use of an amplifier with a large gain and, consequently, impedes obtaining large stabilization coefficients. In the same case, when the line voltage is stabilized, a considerably smaller gain is required of the amplifier used in the current-stabilizer circuit.

A significant role is played by the interval of time during which it is necessary to ensure the specified constancy of the current. In prolonged continuous operation of the stabilizer, the change in the parameters (drift) of individual elements of the stabilization circuit itself (the anode current of electron tubes, the reference voltage, etc.), the influence of temperature on the load resistance, and the like, have an appreciable effect. In those cases where the load current is small, in order to reduce its dependence on temperature, a ballast resistance with a small temperature coefficient is sometimes connected in series with the load.

When it is necessary to ensure constancy of current with high accuracy over many hours of operation, use is made of a two-link stabilization circuit25,30: the first link reduces the influence of rapid disturbances on the magnitude of the current, and the second that of slow ones.

The stabilizer circuits employed may be classified according to the magnitude of the stabilized current (small currents—up to one ampere, and large currents—above one ampere), according to the accuracy with which the constancy of the current is maintained (technical accuracy—\(\delta > 0.1\%\), precision accuracy—\(\delta < 0.1\%\)), according to the time during which constancy of current is ensured (short-term-stability circuits—\(t < 1\) hour; long-term-stability circuits—\(t > 1\) hour), and according to the principle of construction (parametric-stabilization circuits and circuits employing a negative-feedback amplifier).

When working with small currents, parametric stabilizers are usually used. As for stabilizers with a feedback amplifier, they are used to stabilize both small and large currents.

The classification given is, naturally, of a conventional character.

§ 2. PARAMETRIC STABILIZERS

The circuit of a parametric current stabilizer contains one or several nonlinear resistances which, when external conditions change, alter their parameters in such a way that the current flowing through the load remains unchanged.

Parametric stabilizers are divided into simple ones and those with autoregulation. The former can provide a small accuracy of current maintenance; the latter, depending on the chosen circuit, can provide both technical and precision accuracy.

Simple parametric stabilizers. A simple parametric current stabilizer is a two-

a two-terminal device with a nonlinear dependence \(I=f(U)\). Among non-electronic devices, barretters, which have become widely used,^6 possess the required form of this characteristic. However, their application is limited by a number of substantial shortcomings: the possibility of stabilizing only certain fixed values of the current; thermal inertia, owing to which stabilization is absent during rapid disturbances; and the dependence of the operating current on the ambient temperature.

Electronic parametric current stabilizers do not have the indicated shortcomings, but, in comparison with barretters, are more complicated and require additional power supplies.

In circuits of simple parametric current stabilizers^6, for operation one uses the gently sloping portion of the dependence of the anode current on the anode voltage, which exists in diodes in the saturation region, and in tetrodes and pentodes at an output voltage exceeding a certain value. The value of the operating current in diodes is regulated by the filament voltage, and in tetrodes and pentodes by the voltage of the control or screen grid.

As diode stabilizers it is expedient to use tubes with a tungsten cathode, possessing a well-pronounced saturation region and permitting changes of the filament over wide limits. When tetrodes and pentodes are used, it is advantageous to increase the screen voltage, since in this case \(S\) and \(g\) of the stabilizing circuit decrease. The accuracy provided by a simple parametric current stabilizer is not high and depends on the operating conditions and on the type of tube.

Thus, for example, for a diode stabilizer using the 4Ц1М tube, with the filament voltage equal to 4 volts and with a change of the anode voltage from 100 to 250 volts, the anode current changes by an amount of 0.6 ma at an average current of about 9 ma. In this case the stabilization coefficient is \(m \simeq 12.5\). The stabilization coefficient when tetrodes and pentodes are used is of the same order.

Fig. 1.

Parametric stabilizers with self-regulation. The operation of a pentode or tetrode stabilizer can be significantly improved by introducing into the cathode circuit of the tube a resistance providing negative feedback^1, ^6, ^7, ^8, ^15. Such a circuit is shown in Fig. 1.

The correct position of the operating point on the characteristic \(I_a=f(U_g)\) is ensured by the corresponding choice of the value of the reference-

of voltage \(U_{\mathrm{op}}\), compensating the voltage drop across the resistance \(R_k\). The presence of \(U_{\mathrm{op}}\) makes it possible to use a large resistance \(R_k\) and thus to obtain a large magnitude of the signal acting on the grid of the regulating tube. The required value of the operating current is set by means of the potentiometer \(R_c\).

The stabilization transconductance and the output conductance of this circuit can be determined from the relation

\[ S = g = \frac{1}{R_i + (\mu + 1)R_k}. \tag{8} \]

In the circuit of Fig. 1 a triode may also be used, but, naturally, it gives a worse result than a tetrode or pentode, since a triode has considerably smaller \(\mu\) and \(R_i\).

A higher stabilization factor is provided by the so-called “cascade” stabilization circuit\(^8\), shown in Fig. 2. It is a further development of the circuit of Fig. 1. The lower pentode here serves as the cathode load of the first tube. When identical tubes are used, the voltage instability of this circuit is determined from equation (9), and the load instability from equation (10):

Fig. 2.

\[ (\Delta I)_{R=\mathrm{const}} = \frac{R}{R + (2+\mu)R_i + (1+\mu)^2 R_k} \cdot \frac{U_{\mathrm{in}}}{U_{\mathrm{out}}} \cdot \sigma_{U_{\mathrm{in}}}, \tag{9} \]

\[ (\Delta I)_{U_{\mathrm{in}}=\mathrm{const}} = \left( \frac{R}{R + (2+\mu)R_i + (1+\mu)^2 R_k} \right)^2 \cdot \frac{U_{\mathrm{in}}}{U_{\mathrm{out}}} \cdot \sigma'_R, \tag{10} \]

where

\[ \sigma_{U_{\mathrm{in}}} = \frac{\Delta U_{\mathrm{in}}}{U_{0\,\mathrm{in}}} \]

is the instability of the input voltage, and

\[ \sigma'_R = \frac{\Delta R}{R_0} \]

is the load instability.

In the circuits of Figs. 1 and 2, in order to increase the stabilization factor, the resistance \(R_k\) may be implemented in the form of an incandescent lamp or another nonlinear resistance, the voltage drop across which increases faster than the magnitude of the current flowing through it. However, owing to the thermal inertia of the resistance, this method has an advantage only for slow changes of voltage and load.

A common drawback of both of the circuits presented is that through the feedback resistor \(R_k\) there flows not only the anode current of the tube, but also the current of the screen grids. If it is unstable, then its variation causes a change in the voltage across the resistor \(R_k\) and, as a consequence, a change in the grid voltage of the regulating tube, i.e., ultimately, a change in the load current. It is therefore important to ensure the stability of the screen voltage and such an operating mode of the tubes in which the screen-grid current would be relatively small. The formulas given do not take into account the effect of variations in the screen current.

The capabilities of the circuits in Figs. 1 and 2 are illustrated by Table 1 for a stabilized current of \(15\) ma and a load resistance of \(3\) kohm.

Table 1

In conclusion of the consideration of parametric stabilizers, let us dwell on the \(\mu\)-circuit of current stabilization \(^{1,7,9}\). Its name is connected with the fact that it was originally developed for measuring—

of the parameters of the tubes, and only subsequently applied for stabilization purposes. The basic form of the $\mu$-circuit for stabilization is shown in Fig. 3,a. The voltage applied to the grid of the regulating tube is $\mu$ times smaller than the voltage applied to the anode

Fig. 3.

($\mu$ is the amplification factor of the tube). For this, the following relation must hold:

\[ R_{\mu}=\mu R_{k}. \tag{11} \]

In this case, the changes in anode current caused by a change in the voltage $U_{\mathrm{in}}$ will be equal in magnitude to those due to the grid voltage, but directed oppositely; i.e., the current in the load $I$ will not change. The stabilization slope of this circuit is

\[ S= \frac{ 1-(\mu+1)\dfrac{R_{k}}{R_{\mu}+R_{k}} }{ R_{i}+(\mu+1)\dfrac{R_{\mu}R_{k}}{R_{\mu}+R_{k}} }. \tag{12} \]

It is evident that, when condition (11) is satisfied, the numerator becomes zero, i.e., $S=0$ and complete compensation takes place. Since the value of $\mu$ of a tube is not strictly constant, but depends on the operating point on its characteristic, condition (12) is usually not satisfied for all values of current within the required range of its regulation and over wide limits of variation of the input voltage.

The response of the circuit to a change in load resistance is the same as that of the circuit in Fig. 1.

In Fig. 3,b a variant of the \(\mu\)-circuit is shown, implemented with a pentode, which gives a considerably better result than the triode. The ratio between \(R_\mu\) and \(R_k\), taking into account the influence of the screen grid \(^{7}\) and the resistance of gas stabilizers \(^{7}\), is determined by the formula

\[ \frac{R_\mu}{R_k} = \frac{\mu_1+\mu_2} {1+\dfrac{R_g}{R+R_g} \left[ \dfrac{\mu_1 R_2}{R_1+R_2}+\mu_2 \right]} -1, \tag{13} \]

where \(\mu_1\) is the amplification factor with respect to the control grid, \(\mu_2\) is the amplification factor with respect to the screen grid, and \(R_g\) is the dynamic resistance of the stabilovolt.

Compensation of the influence of changes in the input voltage over wider limits than can be achieved in the \(\mu\)-circuit is carried out in the circuit of a \(\mu\)-bridge with negative feedback \(^{1}\) (Fig. 4,a). Any changes in the voltage drop across the tube are rotated by the phase-inverting element through \(180^\circ\), and a definite fraction of this voltage is applied to the grid. If this fraction is equal to \(\dfrac{1}{\mu}\), then, as in the preceding case, the anode current of the tube remains unchanged. The role of the phase inverter is performed by a tube which simultaneously provides amplification of the signal (Fig. 4,b). Analysis of its operation gives the following relation for the choice of the voltage divider:

\[ \frac{R_2}{R_3} \approx \frac{\mu_1 \mu_2 R_1} {(1+\mu_1)\left[\mu_2(R_k+R_c)+R_4\right]-R_1} -1 . \tag{14} \]

A similar circuit, at a current of \(50\ \mathrm{mA}\) and a load resistance of \(3000\ \Omega\), provided complete stabilization at two points of the range and a value \(S=g\) no worse than \(0.25\cdot 10^{-6}\ \mathrm{mho}\) in the interval between these points.

Despite the fundamental possibility of obtaining ideal stabilization with respect to changes in the input voltage,

the circuits presented did not become widely used. The constancy of compensation, as already indicated, depends on the stability of the characteristics of the tubes and resistors. Their changes over time, or upon retuning within a range, lead to a disturbance of the compensation.

§ 3. STABILIZERS USING A NEGATIVE-FEEDBACK AMPLIFIER

Basic relations

The most widespread are electronic current stabilizers using a negative-feedback amplifier (with deep negative feedback) ², ³, ⁴, ⁵, ⁶, ¹⁰, ¹¹. This is explained by a number of their valuable qualities: the small dependence of the input current on changes in the parameters of the tubes used in the stabilizer circuits; the possibility of stabilizing both small and large currents over a wide range of their regulation; considerable freedom in the choice of circuit elements and, finally, the possibility of obtaining high stabilization coefficients.

Figure 5a shows the block diagram of a current stabilizer with deep negative feedback. It consists of four main elements: a regulating element, a reference (standard) resistance, a reference (standard) voltage source, and a direct-current amplifier in the negative-feedback circuit.

Fig. 5.

The output current flowing through the reference resistance produces across it a voltage drop \(IR_{\mathrm{op}}\). Connected in opposition to it is the reference voltage \(U_{\mathrm{op}}\). The change in the difference of these two voltages, arising when the current deviates from the nominal value,

is a signal fed to the input of a direct-current amplifier. After amplification this signal acts on the regulating element in such a way as to ensure constancy of the current in the load with a prescribed accuracy.

The simplest stabilizer corresponding to the block diagram of Fig. 5, a, contains two tubes: a regulating tube \((L_1)\) and a direct-current amplifier tube \((L_2)\)—Fig. 5, b. A similar two-tube circuit is used, in particular, to supply a mass spectrograph \(^{10}\).

Using the circuit of Fig. 5, b as an example, let us consider the basic relations for an electronic current stabilizer with a negative-feedback amplifier \(^{11}\). The voltage drop across the regulating tube is:

\[ U_{ak}=IR_i-\mu U_{ck}, \tag{15} \]

where \(R_i\) is the internal resistance of the regulating tube without taking account of the action of feedback, and \(\mu\) is its amplification factor. The sign before the second term takes into account the 180° phase shift between the grid and anode voltages.

The voltage on the control grid of the regulating tube (not counting the constant component, which depends on the operating mode of tube \(L_2\)) is equal to

\[ U_{ck}=-k\left(IR_{\mathrm{op}}-U_{\mathrm{op}}\right)-I\left(R+R_{\mathrm{op}}\right), \tag{16} \]

where \(k\) is the gain of the direct-current amplifier on tube \(L_2\).

The sum of the voltage drops across the regulating tube \(L_1\) and the resistances \(R\) and \(R_{\mathrm{op}}\) is equal to the input voltage

\[ U_{\mathrm{in}}=U_{ak}+I\left(R+R_{\mathrm{op}}\right). \tag{17} \]

Substituting in (17) the values of \(U_{ak}\) and \(U_{ck}\) from (15) and (16), we obtain:

\[ I=\frac{U_{\mathrm{in}}}{R_i+\mu kR_{\mathrm{op}}+\left(R+R_{\mathrm{op}}\right)(1+\mu)} + \frac{\mu kU_{\mathrm{op}}}{R_i+\mu kR_{\mathrm{op}}+\left(R+R_{\mathrm{op}}\right)(1+\mu)}. \tag{18} \]

Hence the stabilization slope is:

\[ S=\frac{\partial I}{\partial U_{\mathrm{in}}} = \frac{1}{R_i+\mu kR_{\mathrm{op}}+\left(R+R_{\mathrm{op}}\right)(1+\mu)}; \tag{19} \]

and the input conductance

\[ g_i=\frac{\partial I}{\partial R_{\mathrm{op}}} = \frac{1+\mu}{R_i+\mu kR_{\mathrm{op}}+\left(R+R_{\mathrm{op}}\right)(1+\mu)}. \tag{20} \]

Usually \(k \gg 1\). Then

\[ S \simeq \frac{1}{\mu k R_{\mathrm{op}}}, \tag{19a} \]

and

\[ g \simeq \frac{1}{k R_{\mathrm{op}}}, \tag{20a} \]

Thus, the current of the stabilizer changes approximately \(\mu k R_{\mathrm{op}}\) times less than the voltage at its input, and \(k R_{\mathrm{op}}\) times less than the change in the load.

The influence of changes in the parameters of the regulating and amplifying tubes on the operation of the stabilization circuit is small, and the larger the gain coefficient of the amplifier \(k\), the smaller it is. Similarly, the influence of changes in the parameters of the tube is the smaller, the larger their magnitude; for example:

\[ \left| \frac{\partial S}{\partial \mu} \right| = \left| \frac{k R_{\mathrm{op}}}{(\mu k R_{\mathrm{op}})^2} \right| \ll 1. \]

Unfortunately, however, this does not apply to all elements of the stabilizer circuit. For \(k \gg 1\), from (19) we obtain:

\[ I' \simeq \frac{\mu k U_{\mathrm{op}}}{1+\mu k R_{\mathrm{op}}} \simeq \frac{U_{\mathrm{op}}}{R_{\mathrm{op}}}, \tag{21} \]

therefore, changes in the reference voltage and resistance lead to a proportional change in the stabilized current. In other words, the instability of the circuit is limited by the instability of its reference elements.

The selection of the specific elements of the stabilizer circuit is carried out depending on the magnitude of the current to be stabilized, the voltage drop across the load, the permissible instability, the time during which it is required to maintain the nominal value of the current, and other considerations.

Below, the principal elements of current-stabilizer circuits are considered in more detail.

Elements of current-stabilizer circuits

Regulating element. The regulating element is usually one or several electron tubes connected in parallel (up to several tens). They are connected either in series with the current source (Fig. 6, a) or in parallel with it (Fig. 6, b). In the circuit of Fig. 6, a, when the current in the circuit decreases, the resistance of the tube also decreases, and the nominal value of the current is restored with the prescribed accuracy. When the current increases, the opposite phenomenon occurs.

In the circuit of Fig. 6, б, regulation is carried out by changing the voltage drop across the ballast resistance \(R_{\text{bal}}\). The regulating tube here plays the role not of a variable resistance, as in the preceding case, but of a variable shunt.

In practice, circuits of series regulation have found the widest use. The parallel-regulation circuit has a lower efficiency and is used more rarely. Its disadvantage is also the limited possibility of choosing the operating regime of the regulating tube. It is used in those cases when the current flowing through the load is small, and the voltage drop across it is sufficient to create the normal anode voltage of the tube. In practice it may also prove significant that the cathode of the parallel regulating tube can be connected directly to the zero-potential circuit.

Fig. 6.

In those cases when it is necessary to provide regulation of large currents (of the order of units or several tens of amperes), a series-regulation circuit is used in which not the entire current, but only a part of it, is passed through the regulating tubes. The remaining part flows through the shunt resistance \(^{41}\). Naturally, the change of current in the load is then smaller than the change of current of the regulating tubes.

It should be noted that, in designing electromagnets, whenever possible the required number of ampere-turns is sought by increasing the number of turns and decreasing the current, since the problem of stable supply with a high-resistance load (and also with a low current) is solved more simply than with a low-resistance one.

From the standpoint of increasing the efficiency of the stabilizer, the series regulating tube must pass as large a current as possible with the smallest voltage drop across it. At the same time, the power dissipated at the anode must not exceed the permissible value. As for the stabilizing action of the circuit, then in accordance with formulas (19) and (20) it will be greater the larger the amplification factor of the tube \(\mu\) and its internal resistance \(R_i\).

The requirements given are to a known extent contradictory, and the choice of tube type must be made depending on the particular circumstances. Most often, for purposes of current regulation, tubes of the types 6Н5С, 6П3С, 6П6С, 6П9, and others are used.

At operating currents on the order of tens and hundreds of amperes, it is necessary to abandon the use of electronic tubes as the direct regulating element. If the supply is from a rectifier, then regulation is usually resorted to not in the direct-current circuit, but in the alternating-current circuit, by acting on the output voltage of the rectifier by means of a magnetic amplifier ^{12, 35}, or by using a controlled rectifier on thyratrons ^{30, 31}.

Preference should be given to the first method, since it provides high stabilization efficiency. In addition, controlled rectifiers have the disadvantage that they create fluctuations caused by the operation of the thyratrons ^{32}. The use of \(LC\)-filters for smoothing them at high currents is associated with considerable practical difficulties; moreover, such filters greatly increase the time constant of the rectifier.

At high currents, motor-generator sets are often used for supply instead of rectifiers. In this case regulation is usually performed by acting on the excitation circuit of the generator ^{4, 34, 40}. However, this method does not make it possible to combat current fluctuations caused by rapid disturbances: harmonics of the fundamental rotational frequency of the generator, the effect on its operation of changes in the frequency of the supply network, etc. To eliminate such effects, an electronic system was developed ^{2, 32} which, at a magnet current of 160 amperes, made it possible to obtain a stability on the order of \(10^{-4}\%\) over one minute of operation.

Reference elements

It was indicated above that the instability of the reference elements—resistance and voltage—is not compensated by negative feedback and is transferred to the output of the stabilizer. Thus, it is precisely these elements that ultimately determine the maximum attainable current stability. Naturally, great attention is paid to their selection and operating conditions.

The requirements for constancy of resistance in current stabilizers are higher than in voltage stabilizers, since in the latter the ratio of the divider resistances is important, whereas in a current stabilizer it is the absolute value of the resistance.

Usually reference resistors are made of wire with a low temperature coefficient, most often of manganin. In precision circuits, alloys are used whose temperature coefficient is equal to zero to the seventh decimal place ^{13}. The instability of specially hardened and annealed reference resistors does not

exceeds \(10^{-3}\%\) per year. Sealing them reduces the instability by roughly another order of magnitude \(^{11}\).

If it is not necessary to ensure stability over a long period of time and the current is small, non-wire resistors are sometimes used, with a large reserve of the power dissipated in them being provided. With a stabilized current of tens of amperes and more, the problem of making a stable resistor becomes much more complicated, since considerable power is dissipated in it. In many cases the resistor is placed in an oil bath and the oil temperature is maintained with an accuracy of fractions of a degree \(^{26}\).

To reduce the power dissipated by the reference resistor, it is sometimes necessary to decrease its value appreciably, which leads to weakening of the signal and, as a consequence, may cause difficulties in constructing a direct-current amplifier. These difficulties can be eliminated if the signal is applied to the amplifier input not directly from the resistor, but by means of a highly sensitive differential transducer consisting of a mirror galvanometer and photocells. The voltage at the output of the photocells depends on the position of the spot from the mirror of the galvanometer, which is connected into the circuit of the reference resistor \(^{34}\). The voltage taken from the resistor in this circuit is only 200 millivolts.

The source of the reference voltage may be gas-discharge tubes or chemical current sources (dry cells or Weston cells).

Gas-discharge tubes (voltage regulators), from the operational point of view, are the most convenient sources of reference voltage. This explains their wide use in current stabilizers \(^{3,10,14}\). With their help one can obtain a current instability of less than \(5 \cdot 10^{-3}\%\) over the course of one hour \(^{14}\) and reduce this value still further for shorter time intervals \(^{3}\). However, when it is necessary to obtain a high constancy of current over a prolonged time, voltage regulators cannot compete with chemical sources of reference voltage. Benson \(^{16}\) gives a value for the instability of gas-discharge tubes of the order of \(0.4\%\) per 1000 hours of operation. The drift of domestic voltage regulators amounts to \(0.1 \div 0.2\%\) of their nominal voltage \(^{17}\).

The voltage of a voltage regulator depends on a number of circumstances: the magnitude of the current flowing through it, the temperature of the bulb, service life, the time of operation after switching on, etc. \(^{16,17,18}\). Usually an individual selection of voltage regulators is made, since they are characterized by a considerable spread of parameters among different specimens of tubes of the same series. It is also desirable that the current flowing through the voltage regulator vary within the smallest possible limits.

Dry cells can provide a high constancy of the reference voltage for a long time. Their instability is thereby

...the smaller the discharge current of the battery. With small leakage currents (less than 1 microampere) and within small ranges of temperature variation, the instability of dry batteries may be less than 0.05% over a number of months ^19. In those cases where it is necessary to ensure high current stability, the battery is placed in a thermostat. In this case it is undesirable to use temperatures above 50° C, since such a temperature substantially reduces the service life of the battery. The auxiliary current stabilizer described in ^19 and operating with a 90 V reference battery had an instability, over many hours, of less than 0.02%, and over several hours—less than 0.01%.

To vary the value of the reference voltage, the battery is sometimes connected to a potentiometer, which increases the current consumption. In such cases the battery is first “formed,” i.e., before operation it is discharged with the rated current for a definite interval of time. By way of example, we note that with continuous discharge at a current of 1 mA of a BAS-G-80 battery, a comparatively flat portion of the voltage-versus-time dependence begins on the 12th day. Then, over a day, the voltage decreases by an amount of about 0.25% of the initial discharge voltage. This change is not smooth. In individual time intervals, a certain increase in voltage is observed ^20. The discharge current of the reference battery must be minimal, and it is desirable not to vary it. In cases where the stabilizing circuit must ensure especially high constancy of current over a long time, a Weston standard cell of the 2nd or 3rd class is used.

Variations of the emf of a Weston cell of the 2nd class with small temperature fluctuations amount to about \(4 \cdot 10^{-3}\%\) per 1° C, and of a Weston cell of the 3rd class—about \(10^{-3}\%\) per 1° C. Usually Weston cells are thermostated. If several series-connected cells are used, then, in order to reduce leakage, they are immersed in oil.

The disadvantages of standard cells are their small emf and low discharge current, which must not exceed 100 microamperes. The smaller it is, the higher the stability of the voltage of the standard cell. Measures are usually taken to reduce all possible leakages, to limit the grid current of the tube of the first amplification stage, and to protect the reference cell against accidental increases in current consumption ^5.

Direct-Current Amplifiers

To amplify an error signal proportional to the deviation of the current from its nominal value, amplifiers capable of amplifying slowly varying voltages are used. Such amplifiers are usually called direct-current amplifiers. The parameters

the direct-current amplifier (gain factor, passband width, etc.) to a considerable degree determine the parameters of the stabilization circuit: the stabilization coefficient, its speed of response, the magnitude of the current instability over a specified time interval, and so on.

Direct-current amplifiers possess a number of characteristic features. According to the principle of their construction they may be divided into two classes: amplifiers with amplification directly in direct current (galvanic coupling between stages) and amplifiers with conversion of direct current into alternating current. A large number of works are devoted to direct-current amplifiers. In the list of cited literature only the most interesting among them, known to the author, are given \(^{2,21,22,23,25,36}\).

If the stabilizer must ensure operation over short time intervals, the manufacture of a direct-current amplifier does not present serious difficulties. It is constructed according to a circuit of direct amplification of direct current and consists, depending on the required gain, of one or two or three stages. To increase stability with respect to changes in the input voltage, a voltage from a resistive divider connected to the stabilizer input is sometimes applied to the screen grid of the tube of the amplifying stage \(^{33}\).

In addition to the high sensitivity of direct-current amplifiers to fluctuations of the supply voltages, the principal drawback limiting their use is the influence on their operation of cathode drift. The latter is caused by processes taking place in the cathode and consists in a slow change in the tube characteristics, occurring even when the supply voltages are kept strictly constant. The influence of drift is strongest in the tubes of the first stages, where the signal level is small. Changes in the amplifier output voltage caused by drift cannot be distinguished from changes caused by the signal. Therefore drift leads to a change in the stabilized current. There are a number of methods for reducing the influence of drift on the operation of an amplifier \(^{6,21}\). In a stabilizer circuit the effect of drift is the smaller, the larger the value of the reference voltage.

Since drift occurs most intensively during the first hours of tube operation, before installing a tube in the circuit it must be aged in the nominal regime for not less than 50–60 hours \(^{36}\). However, even after careful selection of tubes of one series and their aging, after the use of special circuits for reducing drift and operating regimes with reduced electrode potential of the tubes, it is difficult to obtain a drift of less than several millivolts per hour. Usually the drift is 10 or more millivolts per hour.

In view of the fact that a change in the operating regime of the tube is also equivalent to the appearance of a spurious signal on the grid, the anode and screen circuits

DC amplifiers are usually powered from stabilized power supplies. In a number of cases the power supplies for filament circuits are stabilized, in particular the filaments of the first stages of the amplifier. Sometimes they are connected through dropping resistors to a source of stable anode voltage.

In the absence of filament-voltage stabilization, one must take into account that a change of it by \(\pm 10\%\) is equivalent to a spurious signal of the order of \(0.05\)–\(0.3\) V (depending on the circuit). The use of self-stabilizing circuits reduces the spurious signal severalfold[^36].

To increase the stability of operation of DC amplifiers and to reduce the influence in them of variations in the supply voltages, negative feedback is widely used.

To illustrate what has been said, we note that in the current stabilizer of a mass spectrometer[^14], containing a three-stage amplifier with direct DC amplification and negative feedback, a current instability of less than \(5 \cdot 10^{-3}\%\) was obtained for an operating time of up to one hour. The amplifier is powered from a stabilized rectifier, to the output of which the filament circuits of several tubes are also connected. A change in the line voltage by \(\pm 10\%\) changes the current in the load by less than \(1 \cdot 10^{-3}\%\).

In those cases where it is necessary to ensure prolonged operation of the stabilizer with small output instability, amplifiers with conversion of direct current into alternating current are used[^21],[^23]. These amplifiers are free from the main shortcomings of direct-amplification circuits, but are distinguished by greater complexity. Their sensitivity can be brought to fractions of a microvolt. It is determined mainly by the principle of operation and the structural design of the conversion element.

The use of amplifiers with conversion of direct current into alternating current in combination with a thermostatted Weston cell as a reference-voltage source makes it possible to obtain an instability of less than hundredths and thousandths of a percent over many hours of operation2,[^26],[^37],[^38], and of ten-thousandths over short time intervals2.

§ 4. STABILIZATION OF THE MAGNETIC FIELD

It was indicated above that current stabilizers are often used to ensure constancy of the field of electromagnets. However, even with ideal stabilization of the current in the magnet winding, the magnetic field in its gap may change owing to changes in the geometrical dimensions of the gap, the influence of external fields, etc. When the magnet is retuned, because of hysteresis, several different values of the magnetic field may correspond to one and the same nominal current. Thus, in a number of cases current stabilization cannot provide the required high accuracy in maintaining the magnitude of the magnetic field.

A current stabilizer with a negative-feedback amplifier can be converted into a magnetic-field stabilizer if, as the sensor, one uses not a reference resistance in the current circuit, but some element directly coupled with the magnetic field. Such an element may be a magnetron[^27], a sensor based on the phenomenon of nuclear paramagnetic resonance[^28],[^39], a rotating coil[^29], etc. The other elements of the field stabilizer may remain without any fundamental changes as compared with the current stabilizer. Field adjustment is, as a rule, carried out by varying the magnetizing current.

Magnetic-field stabilization using nuclear paramagnetic resonance ensures an extremely high stability of the field, making it possible to maintain the field in the gap with an accuracy of hundredths of a gauss[^28].

In some circuits the reference voltage is obtained with the aid of a standard magnet. Thus, for example, in work[^29] a stabilizer is described in which a synchronous motor rotates two coils: one in the stabilized field of an electromagnet, the other in the field of a standard permanent magnet. The emf of both coils is rectified by contact converters, compared with each other, and their difference, representing the signal, is fed to the input of the dc amplifier.

A detailed consideration of magnetic-field stabilizers is beyond the scope of the present survey. The purpose of the exposition has been to point out certain limitations in the application of current stabilizers for producing constant magnetic fields and, at the same time, to emphasize the commonality of a number of elements of a current stabilizer and magnetic-field stabilizers.

REFERENCES

1. W. R. Hill, Proc. Inst. Rad. Engrs. 33, 765 (1945).
2. H. S. Sommers, P. R. Weiss and W. Halpert, Rev. Scient. Instr. 22, 612 (1951).
3. V. V. Polivanov, Stabilization of the electric supply of an electron microscope, 1953 (Candidate dissertation).
4. D. Cero, Y. Parry, J. Scient. Instr. 26, 374 (1949).
5. S. Giordano, G. K. Green and E. I. Rogers, Rev. Scient. Instr. 24, 848 (1953).
6. A. M. Bonch-Bruevich, Application of electron tubes in experimental physics. State Publishing House of Technical-Theoretical Literature, Moscow, 1954.
7. K. B. Mazel, Radiotekhnika 9, No. 5, 36 (1954).
8. I. N. Van Scayoc, E. H. Schulz, Proc. IRE 32, 415 (1944).
9. I. G. Goldreer, Voltage Stabilizers, Gosenergoizdat, 1952.
10. H. E. Duckworth, Rev. Scient. Instr. 21, 54 (1950).
11. M. W. Jervis, Electronic Engineering 25, 429 (1954).
12. M. S. Wills, Electronic Engineering 25, 250 (1953).

1. A. S. Zaimovskii and V. V. Usov, Metals and Alloys in Electrical Engineering, Gosenergoizdat, 1949.
2. R. L. Graham, A. L. Harness and H. G. Thode, J. Scient. Instr. 24, 5, 119 (1947).
3. J. H. Guire, Electronic Engineering 27, 529 (1955).
4. F. A. Benson, Electronic Engineering 24, 456 (1952).
5. Yu. D. Rogozin, Proceedings of the Moscow Power Engineering Institute named after V. M. Molotov, Applied Electronics, issue 4, 1949.
6. B. Schumann, Frequenz, 5, 5 (1951).
7. Parts and Components of Radar Stations, part II, Sovetskoe radio, 1952.
8. G. G. Morozov, Fundamental and Operational Features of Galvanic Anode Batteries, Moscow, 1948.
9. L. I. Naida and A. A. Semenkovich, DC Electronic Amplifiers, Gosenergoizdat, 1953.
10. M. Artzt, Electronics 8, 112 (1945).
11. G. Kebler, Archiv für Technisches Messen 1, 204, 19 (1953).
12. G. N. Patchett, Electronic Engineering 22, 424 (1950).
13. K. Kandian, D. E. Brown, Proc. Inst. Electr. Engin. 99, 2, 314 (1952).
14. I. G. Gottingham, W. H. Moore, E. I. Rogers, G. M. Turner, Rev. Scient. Instr. 24, 816 (1953).
15. Nier, Rev. Scient. Instr. 6, 254 (1935).
16. M. E. Packard, Rev. Scient. Instr. 19, 435 (1948).
17. W. T. Van der Walt, Rev. Scient. Instr. 24, 413 (1953).
18. M. M. Novakovic, Bull. Instr. Nucl. Scien. 8, 61 (1953).
19. M. Henderson, M. White, Rev. Scient. Instr. 9, 19 (1938).
20. H. S. Sommers, P. R. Weiss and W. Holpern, Rev. Scient. Instr. 20, 244 (1948).
21. M. E. Haine, J. Inst. Electr. Eng. 94, 1, 447 (1947).
22. W. Y. Chang, Phys. Rev. 69, 60 (1946).
23. M. A. Rozenblat, Radiotekhnika 8, No. 2, 51 (1953).
24. Tube Amplifiers, vol. II, Sovetskoe radio, 1951.
25. E. I. Rogers and G. M. Turner, Rev. Scient. Instr. 24, 805 (1953).
26. E. I. Rogers, Electronics 10, 151 (1955).
27. V. I. Mikhailov and V. M. Morozov, ZhTF 25, 9, 1649 (1955).
28. S. Rubin, D. C. Sachs, Rev. Scient. Instr. 26, 1029 (1955).
29. R. W. Deichert, Electronics 8, 170 (1955).