PRINCIPLES OF DESIGN OF HIGH-STABILITY AMPLIFIERS

M. S. ROITMAN

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

The best of the existing measuring amplifiers—the F71 amplifier—has a basic error in the frequency range 200 Hz–20 kHz of 0.05%. However, the stated accuracy can no longer be considered satisfactory. For the further improvement of reference measuring and verification apparatus, amplifiers with a long-term instability of the transfer coefficient below 0.01% are urgently needed.

An increase in amplifier stability can be achieved by the following means*):

1) stabilization of the supply voltages and, as far as possible, complete elimination of external influences;
2) stabilization of the operating conditions of the most critical elements of the circuit;
3) compensation for changes in operating conditions, as well as for external disturbances;
4) introduction of deep negative feedback (NFB);
5) automatic calibration and correction of the circuit.

Stabilization of the anode (collector) voltage is used very widely, which is justified not only by the increase in amplifier stability, but also by the reduction of background noise. However, while sufficiently fine stabilization of the anode (collector) voltage does not present substantial difficulties, stabilization of the filament is associated with the use of ferroresonant stabilizers or other still more complex solutions. Stabilization of temperature is also associated with well-known difficulties.

The second approach usually consists in stabilizing the cathode current of a tube or the collector current of a transistor. With respect to tube circuits, this direction has been considered in a number of works, the principal ones being [1, 2, 3]. At a certain value of the cathode resistance, as the supply voltages increase, the gain coefficient may even decrease. In a stage with a shielded tube, this is connected not only with a change in the cathode current, but also with a redistribution of currents between the anode and the screen grid. It should be noted that these possibilities are still little used.

The third approach consists in the fact that, under an external disturbance (for example, temperature), one of the circuit elements (a thermistor) changes its parameters in such a way that invariance of the transfer coefficient \(K\) is ensured. Unfortunately, this approach is still used insufficiently widely—

*) The division of amplifier-stabilization methods given in the present work is to a considerable extent conditional, since some of them (for example, the 2nd and 3rd) overlap, and in a number of cases coincide.

widely, although it does make it possible to obtain very effective solutions. Let us consider one such solution in more detail. Figure 1 shows the circuit of the simplest pentode amplifier stage with negative current feedback. The gain of the stage is equal to \(K=\dfrac{SR_a}{1+SR_k}\), where \(S\) is the transconductance of the tube. It is obvious that a change in the supply voltages will lead to a certain change in \(K\).

For a stage using a 6Zh1P \((R_a = 18\,\text{k},\ R_k = 100\,\Omega)\), Table 1, a gives the values of the relative instability \(\dfrac{\Delta K}{K}\) as a function of changes in the line voltage (unstabilized rectifier). If, as \(R_k\), one uses an inertial nonlinear resistance with a positive resistance coefficient, then under certain conditions it is possible to obtain not only compensation of changes in the supply voltages, but even overcompensation.

Fig. 1.

Table 1

Indeed, if \(R_k\) is a function of the cathode current, then

\[ \frac{dK}{di_k} = \left( \frac{\partial S}{\partial i_k}\cdot \frac{1}{1+SR_k} - \frac{\partial R_k}{\partial i_k}\cdot \frac{1}{1+\frac{1}{SR_k}} \right) \left( \frac{\partial i_k}{\partial E_a} + \frac{\partial i_k}{\partial U_n} \right). \tag{1} \]

and, for

\[ \frac{\partial S}{\partial i_k} < \frac{\partial R_k}{\partial i_k}\cdot SR_k \]

we have overcompensation.

The quantity \(\dfrac{\partial R_k}{\partial i_k}\) characterizes the degree of nonlinearity of the cathode resistance. The experimental data (Table 1, b) confirm the possibility of obtaining overcompensation (a small lamp with nominal voltage \(U_{\text{nom}}\approx 1.5\,\text{V}\) and \(I_{\text{nom}}\approx 20\,\text{mA}\) is connected into the cathode).

It follows from (1) that by regulating the coefficient of nonlinearity it is possible, over a certain range of changes in the supply voltages, practically to eliminate their influence. The nonlinearity coefficient of \(R_k\) can be reduced by a parallel-series connection of certain fixed resistances. Their analytical calculation is extremely difficult, especially for multistage circuits. In practice, the problem reduces to creating a two-terminal network with an adjustable coefficient of nonlinearity and with a minimal accompanying change in its resistance. The simplest solution of this problem is the two-terminal network whose circuit is shown in Fig. 2. Its equivalent resistance is equal to:

\[ R_k = R_{\mathrm{eqv}} = \frac{2R_1RR_{\mathrm{nz}} + R_1R^2 + R^2R_{\mathrm{nz}} - \Delta R^2(R_1 + R_{\mathrm{nz}})} {(R_1 + R + \Delta R)(R_{\mathrm{nz}} + R - \Delta R)} . \]

If one assumes \(R_1 \simeq R_{\mathrm{nz}}\), then

\[ R_k = \frac{2RR_1^2 + 2R^2R_1 - 2\Delta R^2R_1} {(R_1 + R)^2 - \Delta R^2} . \]

The dependence of \(R_k\) on the value of \(\Delta R\) for the case \(R = R_1 = R_{\mathrm{nz}} \simeq 100\ \Omega\) is given in Fig. 3. Taking into account the small change in \(R_k\), the two-terminal network described above is quite suitable as an element with a coefficient of nonlinearity adjustable over wide limits. To sharply reduce the influence of the supply voltages on the transfer coefficient of a multistage

Fig. 2.

Fig. 3.

amplifier, it is sufficient to connect the nonlinear two-terminal network into the cathode of the tube and experimentally adjust its parameters. The two-terminal network must not be connected into the cathode of the output tube, since the value of the output signal will affect the transfer coefficient.

One should also keep in mind an important circumstance. Effective compensation is realizable only for slow disturbances, when the relative inertia of the compensating element is small. This assertion is not necessarily valid for all possible variants. If the external disturbance is transmitted to the circuit through an inertial link, for example, a power-supply filter, and simultaneously acts on the compensating element, then the gain coefficient, provided their transient characteristics are identical, will remain unchanged.

An effective and most widespread means of increasing the stability of the parameters of measuring amplifiers (MAs) is to enclose the amplifier in deep negative feedback (NFB). However, obtaining a large loop gain (\(k\beta > 500\)) is associated with well-known difficulties because of the need to provide a sufficient stability margin. At present, the latter, in deep NFB, is achieved by correcting the phase-frequency characteristics of the amplifier with minimum-phase circuits, i.e., in effect, by sharply narrowing the operating frequency band [4, 5]. Attempts to use negative reactances [6] to correct the phase characteristic of the amplifier, which would make it possible to ensure the necessary stability without a noticeable reduction of the bandwidth, have so far not yielded positive results.

The application of the totality of all the measures indicated above (the use of an amplifier circuit design invariant with respect to the principal destabilizing factors; the introduction of deep negative feedback; stabilization of the operating conditions of the most critical elements) still does not allow us to guarantee invariance of the amplifier transfer coefficient within \(0.002 \div 0.005\%\) over a comparatively long time. Yet these are precisely the requirements imposed on the permissible instability of standard measuring amplifiers.

The solution of this problem can be achieved by using built-in calibration systems. Correction of the transfer coefficient may be carried out manually or automatically. Measuring amplifiers with a built-in calibration circuit are already known, the circuit even performing automatic correction of the main amplifier. A detailed description of such a device is given in [7].

In these amplifiers, a divider with an attenuation equal to the nominal gain is connected at the output, and the input and output voltages are compared by a differential indicator. The advantage of such a solution is the possibility of creating measuring amplifiers capable of operating over a very wide frequency range. At present, at the Kiev Polytechnic Institute, under the direction of P. P. Ornatskii, more advanced versions of such measuring amplifiers are being developed. The metrological characteristics of such amplifiers are determined primarily by the capabilities of differential indicators (DI).

The most accurate differential indicators of effective voltage values make it possible to register with confidence deviations of the order of \(0.005 \div 0.01\%\) [8, 9]. However, precision DIs are rather complex devices, and for reliable registration of deviations of the order of \(0.005\%\) a whole series of calibration operations is required.

More simply and effectively, in low-frequency measuring amplifiers, calibration of the transfer coefficient can be carried out by the unbalanced compensation method [9].

In [10] a standard measuring amplifier with a built-in calibration circuit is described in comparatively great detail. Its functional diagram is shown in Fig. 4.

Fig. 4.

At the output of measuring amplifier (MA) 1 there is connected a precision frequency-independent voltage divider 2 with an attenuation coefficient equal to the transfer coefficient of the MA.

The input of amplifier 1 and the output of divider 2 are connected to the input of an additional amplifier 3, while the outputs of amplifier 1 and of additional amplifier 3 are connected to the inputs of phase-sensitive detector 4, the signal from which is fed to electrical measuring instrument 5. The indication of instrument 5 makes it possible to judge the magnitude and sign of the deviation of the gain coefficient from the nominal value. The analysis carried out in [10] makes it possible to assert the possibility of monitoring, by the indicated method, a gain instability of the order of \(0.001 \div 0.002\%\).

The presence of a built-in system for continuous calibration of the amplifier makes it possible easily to correct the amplifier; moreover, if desired, this correction may be performed automatically. Amplifiers of this kind—

...can be constructed according to the functional diagram shown in Fig. 5. A precision divider 2 is connected to the output of the main amplifier 1. The unbalance voltage between points \(a c\) is amplified by the auxiliary measuring amplifier 3 and rectified by the phase-sensitive detector 4. The rectified signal is fed to the gain-instability indicator 5 and to the low-frequency filter 6; the voltage from the filter output is modulated by modulator 7, amplified by the ac amplifier 8, and, together with the reference voltage from the auxiliary generator 9, is applied to the adjustable divider 10, thereby providing automatic stabilization of the transfer coefficient of the main amplifier 1.

Fig. 5.

As the controlled element that does not introduce noticeable distortion into the amplifier, a photoelectric transducer may be used [11]. It is obvious that built-in checking systems may also be intended for periodic checking. In this case it is advisable to connect the divider not at the output but at the input of the measuring amplifier, and to connect the auxiliary amplifier between the input of the divider and the output of the main measuring amplifier.

It should be noted that the described implementation variants of the unbalanced compensation method of checking an amplifier are applicable only to aperiodic measuring amplifiers with series voltage negative feedback, i.e., to measuring amplifiers whose phase shift is \(\varphi_y \approx 2 n \pi\). In the case of parallel voltage negative feedback or series current negative feedback \([\varphi \approx (2n-1)\pi]\), the checking circuit should be modified*) (Fig. 6).

Fig. 6.

The voltage from the output of generator \(\Gamma\) is applied through divider \(D\) to the amplifier. Between the divider input (point \(a\)) and the amplifier output (point \(v\)) two approximately identical resistances \(Z_{ac}\) and \(Z_{vc}\) are connected. Between point \(C\) and “ground” a highly sensitive phase-sensitive indicator PSI is connected. For a certain ratio of the circuit resistances and the voltage transfer coefficient, \(U_{co}=0\) [12]. Instability of the measuring amplifier leads to unbalance of the circuit and is registered by the indicator. Rational use, within certain limits, of a combination of the first four ways (i.e., without substantially complicating the amplifier and the power supplies) makes it possible to achieve gain-coefficient instability within 0.001% over 10 min.

*) In a continuous checking system the divider is placed at the output of the measuring amplifier, and the resistances \(Z_{ac}\) and \(Z_{vc}\) are connected between the amplifier input and the divider output.

With such small instabilities, the use of automatic calibration and correction in low-frequency measuring amplifiers is hardly justified at present. In critical cases of metrological practice, it appears possible to confine oneself to introducing built-in verification circuits into the measuring amplifier and to manual gain correction.

The use of automatic gain correction should be considered justified in selective and broadband measuring amplifiers.

REFERENCES

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