LOW-FREQUENCY LOGARITHMIC AMPLIFIER

Yu. M. ACHKASOV, S. A. ZHURIKOV, V. E. STENNIKOV

(Presented by the Scientific-Technical Seminar of the Research Institute of Nuclear Electronics)

At present, the following methods exist for constructing a logarithmic amplifier (LA):

inclusion of logarithmic elements in the load circuit of the amplifier [1–3];

inclusion of logarithmic elements in the feedback circuit (usually negative) [1, 4];

the method of successive addition of logarithmic effects [5–7];

use of linear elements to create a nonlinear logarithmic characteristic [8].

The amplifier analyzed below operates on the principle of including logarithmic elements in the circuit of overall negative feedback. In its circuit implementation it is close to the amplifier described in [4], and differs from it by the use of diodes instead of a voltage regulator tube as the logarithmic elements and by the method of connecting the feedback circuit. The feedback encompasses both the input (coupling) and output (coupling) capacitors. Owing to this, the capacitances of the coupling capacitors can be chosen to be substantially smaller than in the case of constructing an LA according to [4].

Figure 1 shows the schematic diagram of a low-frequency LA intended for operation in laboratory seismic equipment.

Fig. 1 (T1–T4—2T312 V; D1–D3—D223)
C2 = 0.22

The amplifier consists of three amplifying stages \((T_1, T_2, T_3)\), connected in a common-emitter circuit, and a follower \((T_4)\), encompassed by common negative feedback, which consists of two back-to-back parallel-connected diodes and a resistor \(R_c'\). The resistor \(R_r\), connected at the input, is fundamentally necessary for operation of the logarithmic amplifier. The resistor \(R_c'\) is included for a preliminary reduction in the values of the coupling capacitors \(C_1\) and \(C_3\). Diode \(D_1\) is intended for thermal compensation of the amplifier’s dc operating point. Adjustment of the gain of the LA occurs through variation of the dynamic resistance of diodes \(D_2, D_3\) as the amplitude of the input signal changes. The gain can be determined from the formula

\[ K_c \approx -\frac{R_c}{R_r}, \tag{1} \]

where \(R_c\) is the dynamic resistance of the feedback circuit \((D_2, D_3, R_c')\).

As the amplitude of the input signal increases, the amplifier bandwidth increases.

The stability condition of the LA in the low-frequency region is described by the formula

\[ x_1 > \frac{x}{1+\dfrac{R_2}{R_3}+\dfrac{R_c}{R_3}} - 1, \tag{2} \]

where

\[ x=\frac{\tau_2}{\tau_1};\quad x_1=\frac{\tau_3}{\tau_1};\quad \tau_1=R_r C_1;\quad \tau_2=R_2 C_2; \]

\[ \tau_3=(R_n+R_{\text{out}})C_3, \]

where \(R_{\text{out}}\) is the dynamic output resistance of the LA without taking capacitor \(C_3\) into account.

In practice, amplifier stability can be ensured both by an appropriate selection of the capacitances of capacitors \(C_2\) and \(C_3\), and by changing the resistances \(R_2, R_3, R_r, R_{\text{out}}\).

Figures 2 and 3 show, respectively, the amplitude and frequency characteristics measured from an experimental model of the logarithmic amplifier. It follows from both characteristics that the amplitude of the output signal depends on the ambient temperature and changes

Fig. 2

at a rate of 5.9 mV/°C. Logarithmic conversion with an accuracy of approximately 10% is achieved over the input-signal amplitude range of 5–1000 mV, as is seen from Fig. 2, in which the dashed line corresponds to ideal logarithmic conversion.

The phase characteristic of the logarithmic amplifier (Fig. 4) was measured for the case in which the phase shifts of the output signal are largest, i.e., with the minimum input signal and for the low-frequency branch of the frequency characteristic.

As a result of tests of the experimental prototype of the LA, the following characteristics were determined:

the amplifier dynamic range with respect to the input signal — 46 dB.

the dynamic range with respect to the output signal within the regulation limits — 8 dB;

Fig. 3. — $t=+22^\circ\mathrm{C}$; ------ $t=+50^\circ\mathrm{C}$

Fig. 4

passband — 4–300 Hz;

initial logarithmic-conversion threshold with respect to the input signal — 5 mV peak;

the amplitude of the output signal corresponding to the start of the logarithmic-conversion threshold at $t=20^\circ\mathrm{C}$ — 0.26 V peak;

temperature coefficient of the output voltage — 5.9 mV/°C;

maximum phase shift within the regulation range at a frequency of 20 Hz — not more than 5°;

power consumed from the supply source — not more than 1.5 mW.

Conclusions

1. The described low-frequency LA, unlike known ones, has smaller ratings of the low-frequency capacitors, owing to the fact that the negative-feedback circuit encompasses the input and output capacitors.

2. The dynamic range of the LA with respect to the input signal can be increased to 60 dB if resistor $R_c^1$ is excluded from the circuit; however, in that case, for the same passband, the capacitances of capacitors $C_1$–$C_3$ must be increased by a factor of 5–10.

References

1. V. M. Volkov. Logarithmic Amplifiers Using Transistors. Kiev, “Tekhnika,” 1965.

1. G. M. Krylov, A. S. Kakunin, V. I. Panov. Calculation of logarithmic amplifiers with nonlinear elements in the load circuits. “Energiya,” 1969.

2. P. P. Yushkov. An amplifier with a logarithmic amplitude characteristic. “Pribory i tekhnika eksperimenta,” 1969, No. 6.

3. E. G. Trendell. Wide-range logarithmic amplifier, “Electronic Engineering,” 1968, vol. 40, No. 485, p. 404.

4. R. S. Hughes. New log amp cascades to desired range, “Electronic Design,” 1969, vol. 17, X, No. 22.

5. M. J. Morris. Application of saturating operational amplifiers in an alternating-current amplifier with a logarithmic characteristic. “Electronics” (USA), 1970, vol. 43, No. 19.

6. B. J. Karakatsanis, Ant. Spetsakis, A. logarithmic amplifier, “Electronic Engineering,” 1969, vol. 41, No. 498, pp. 46–48.

7. L. R. Simmering, T. A. Sildaj. Precision logarithmic amplifier. Express Information “Control and Measuring Technology,” 1969, issue 46, ref. 339.