A Modulator of Small DC Voltages Based on Silicon Triodes

M. S. Roitman, A. G. Vaisburd

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

Modulators of small DC voltages based on semiconductor triodes, despite the comparative abundance of different circuit implementations, are produced in two ways: by stabilizing the operating conditions of the transistor [1] or by carefully selecting triodes with the aim of mutual compensation of the residual parameters \(U_p\) and \(I_p\) [2, 3, etc.].

In the first case it is necessary to carry out the switching with a rectangular stabilized voltage and to rigidly stabilize the temperature of the triode [1], which is highly undesirable.

In the second case, careful rejection testing of triodes is required [2, 3], which under conditions of serial production is likewise undesirable, and often impermissible.

It is obvious that the best solution would be the construction of a modulator with small zero drift and high input resistance, capable of operating over a wide temperature range, but without requiring temperature stabilization of the triodes or their special rejection testing. Below, one of the possible variants of such a modulator design is given, in particular on the basis of the well-known circuit (Fig. 1, a) [4].

Fig. 1.

The voltage at the output of such a modulator in the absence of an input signal is equal to

\[ U_{\mathrm{out}}(t) \simeq \frac{\sqrt{2}}{\pi}\sum_{n=1}^{\infty} \frac{U_{\mathrm{r}1}-I_{\mathrm{r}2}r_i-U_{\mathrm{r}2}}{n} \left\{ \left[1-2\left(\pi\frac{\Delta T}{T}\right)^2\right]\sin n\omega t + 2\pi\frac{\Delta T}{T}\cos n\omega t \right\} + \sum_{n=1}^{\infty}\frac{2}{T} \left[ \int_{0}^{\tau_1} U_{\mathrm{b}1}(t)e^{-jn\omega t}\,dt + \int_{\frac{t}{2}+\Delta T}^{\frac{t}{2}+\Delta T+\tau_2} U_{\mathrm{b}2}(t)e^{-jn\omega t}\,dt \right]\cdot e^{jn\omega t}, \]

where \(U_{\mathrm{r}1}\) and \(U_{\mathrm{r}2}\) are the residual voltages of the first and second triodes;
\(I_{\mathrm{r}2}\) is the residual current of the second triode;
\(r_i\) is the internal resistance of the source;
\(U_{\mathrm{b}1}(t),\ U_{\mathrm{b}2}(t)\) are the spike voltages arising when the triodes are cut off;
\(\tau_1,\ \tau_2\) are the spike durations;
\(T\) is the period duration;
\(\dfrac{\Delta T}{T}\) is the relative inequality of the half-periods.

Assuming the spikes to be rectangular, \(U_{\mathrm{b}1}=U_{\mathrm{b}2}=U_b\), and \(\dfrac{\Delta T}{T}\ll 1\), we can determine the voltage of the first harmonic of the switching frequency in the absence of an input signal (this voltage is often called the “false signal”)

\[ U_{\mathrm{f.s.}} \simeq \frac{\sqrt{2}}{\pi} \left(U_{\mathrm{r}1}-I_{\mathrm{r}2}r_i-U_{\mathrm{r}2}\right) \left[1-2\left(\pi\frac{\Delta T}{T}\right)^2\right]\sin\omega t + 2\pi^2 \left[ \frac{\tau_1-\tau_2}{T}\cdot\frac{\tau_1+\tau_2}{T} - \frac{2\Delta T\,\tau_2}{T^2} \right]\cdot \sin\omega t\cdot U_b + 2\pi\frac{\tau_1-\tau_2}{T}\,U_b\cos\omega t. \]

The residual voltage \(U_{\mathrm{r}}\) is equal to [5]

\[ U_{\mathrm{r}}=\frac{kT}{q}m\ln\frac{1+\beta}{\beta}+I_b r_k, \]

where \(k\) is Boltzmann’s constant;
\(T\) is the absolute temperature;
\(q\) is the electron charge (for room temperature \(\dfrac{kT}{q}\simeq 26\) mV);
\(\beta\) is the triode current gain in the common-emitter circuit;
\(I_b\) is the base current (it is equal to the switching current);
\(r_k\) is the collector semiconductor resistance;
\(m\) is a constant determined by the density of the injected current in the base region.

For alloy germanium transistors (P13–P16), \(m\simeq 1\), \(r_k<0.2\ \Omega\), and \(U_{\mathrm{r}}\) for high-quality triodes lies within \(0.3\div 0.6\) mV. For silicon triodes, \(m\simeq 1.5\div 2\), \(r_k<1.2\ \Omega\), and \(U_{\mathrm{r}}=0.6\div 3\) mV.

Obviously, from the point of view of the magnitude of \(U_{\mathrm{r}}\), preference should be given to germanium triodes. However, for germanium triodes \(I_{\mathrm{r}}\geq 2\cdot 10^{-8}\) A (at \(20^\circ\)C), and the zero drift, with a source resistance greater than several tens of ohms, depends very substantially on the instability of \(I_{\mathrm{r}}\) (\(I_{\mathrm{r}}\) changes by \(7\div 8\%\) per \(1^\circ\)C).

The influence of \(I_p\) can be eliminated by switching with a unipolar voltage. But in this case the input resistance drops sharply, and a modulator based on germanium triodes becomes unsuitable for operation at elevated temperatures. Therefore, when it is necessary to operate over a wide temperature range and with an internal source resistance greater than 50 ohms, preference should be given to silicon triodes or to more complex modulator circuits [3].

The investigations we carried out showed that, among domestic silicon triodes, the MP103A have the best characteristics. Table 1 gives data for the quantities \(\alpha\), \(U_p\), and \(I_p\) for six MP103A units.

Table 1

The dependences of \(U_p\) and \(I_p\) on the switching current \((I_b)\) and voltage \((U_b)\) are given in Fig. 2, a, b.

Fig. 2.

Since for \(t = 60^\circ\mathrm{C}\), \(I_p \ll 5 \cdot 10^{-9}\ \mathrm{A}\), then for \(r_i \le 5\ \mathrm{k\Omega}\) at low frequencies
\(U_{\text{l.s.}} \approx (U_{p1} - U_{p2})\dfrac{\sqrt{2}}{\pi}\). If resistors are connected in series with the collectors (Fig. 1, b), then

\[ U_{\text{l.s.}} \approx (U_{p1} + I_k r_1 - U_{p2} - I_k r_2). \]

It is obvious that if \(|U_{p_1}-U_{p_2}|<I_k(r_1+r_2)\), then, by changing the ratio between \(r_1\) and \(r_2\), i.e., by adjusting potentiometer \(R\), \(U_{\mathrm{d.c.}}\) can be reduced to a very small value.

However, \(I_k\) is a function of the switching voltage \(U_k\), and \(U_p=f(U_k,T)\).

To estimate the actual magnitude of the zero drift \(U_d\), i.e., the change in \(U_{\mathrm{d.c.}}\), it is necessary to determine the influence of various factors, above all changes in temperature and in the switching voltage. The dependences \(U_{\mathrm{d.c.}}=f(t^\circ\mathrm{C})\) for various triodes used in the practical modulator circuit (Fig. 3) are given in Table 2.

Table 2

\[ U_d^{\mathrm{equiv}}=f(t^\circ\mathrm{C}) \]

The experimental data confirm the obvious assumption that the greatest drift is exhibited by pairs of triodes with the greatest difference in residual voltages \(U_p\) (Table 1). In triodes 1 and 2 there is a very substantial difference in the current gain coefficients. The ratio

\[ \frac{\beta_2}{\beta_1}>3.7 \]

greatly exceeds the value permitted by GOST for triodes of one group. Experimental testing showed that, if MP103A triodes with \(\beta_{\min}\ge 40\) and a ratio

\[ \frac{\beta_{\max}}{\beta_{\min}}\le 2 \]

are used, then for any combinations of triodes and under switching conditions with nominal current the zero drift upon heating to \(60^\circ\mathrm{C}\) is less than 30 µV (in practice it lies within \(\pm 20\) µV).

Fig. 3.

As the nominal value of the switching current \(I_b\) we adopted 0.5 mA.

A smaller value of \(I_b\), as follows from the dependence \(U_p=f(I_b)\) (Fig. 2a), is undesirable. Increasing \(I_b\) does not lead to a significant decrease in \(U_p\), but at the same time causes an increase in the duration and amplitude of transients when the triodes leave saturation¹.

Changes in the switching voltage \(U_k\) by \(\pm 5\%\) lead to a zero drift of no more than \(\pm 15\ \mu\mathrm{V}\).

D220 diodes are used to reduce the effect of changes in \(U_k\), and also to improve the shape of the voltage curve when transformer distortions are present.

Preference was given to D220 diodes because they have low dynamic and considerable static resistance (at a current of \(2 \div 5\ \mathrm{mA}\), \(r_d \approx 10\ \Omega\), \(r_{\mathrm{st}} \approx 150\ \Omega\)) and a forward voltage close to the optimum value \((U_{\mathrm{fr}} = 0.7 \div 0.8\ \mathrm{V})\).

The instability of the input-voltage conversion coefficient is practically determined only by the instability of the duty factor of the switching voltage.

If an amplifier with a small phase shift in the frequency band is connected to the modulator output and the amplified voltage is rectified by a synchronous detector to which the switching voltage is applied from the same source as to the modulator, then deviation of the duty factor does not change the input-signal conversion coefficient.

The input resistance of the modulator is \(R_{\mathrm{in}} \geq 5\ \mathrm{M}\Omega\) and depends both on the operating mode of the triodes and on the ambient temperature. The averaged dependence \(R_{\mathrm{in}} = f(t^\circ\mathrm{C})\) is given in Fig. 4.

As the frequency increases, the input resistance decreases (Fig. 5). This is due to the fact that with steep edges of the switching voltage \((t_{\phi+} < t_n\) and \(t_{\phi-} < t_r + t_c)\) there is substantial through-conductance of the modulator during a time interval \(\tau\), approximately equal to

\[ t_r + t_c - t_n . \]

Fig. 4.

Fig. 5.

where \(t_n\) is the rise time of the collector current;
\(t_r, t_c\) are, respectively, the minority-carrier storage time in the base and the fall time.

Obviously, as the frequency increases the ratio \(\frac{\tau}{T}\) increases, where \(T\) is the period duration.

When the triodes are switched by a sinusoidal voltage, the input resistance at frequencies \(f > 400\ \mathrm{Hz}\) is higher; however, the zero drift \((\pm 50 \div 60\ \mu\mathrm{V})\) and the harmonic content at the modulator output increase substantially, owing to the possible nonidentity of the triodes.

We did not carry out a detailed investigation of \(U_r(t^\circ\mathrm{C})\) as a function of \(I_b\) for MP103A triodes, although such work would be highly desirable.

References

1. I. C. Hutcheon, D. Hemmers. A low-drift transistor chopper-type D.C. amplifier with high gain and large dynamic range. IEE.

2. N. S. Nikolaenko, V. P. Fedotov. Design of converters for small DC signals using semiconductor triodes. Izvestiya VUZov. Priborostroenie, No. 2, 1962.

3. M. S. Roitman, A. N. Karmadonov, Yu. S. Ryabinkin, S. A. Gofman. Converters of small DC EMFs using semiconductor devices. Proceedings of the Second Conference on Automatic Control and Electrometry, Publishing House of the Siberian Branch of the USSR Academy of Sciences, Novosibirsk, 1962.

4. R. L. Bright, A. P. Kruper. Electronics, 28, No. 4, pp. 135–137, 1955.

5. J. Carroll. Electronic Circuits Using Semiconductor Triodes, pp. 71–79, Foreign Literature Publishing House, 1959.

1. The optimum value of \(I_b\) is determined not only by the indicated factors, but also by the temperature dependences \(U_p=f(t^\circ\mathrm{C})\) for the given current \(I_b\). At small switching currents the temperature coefficient of \(U_p\) is negative; at large currents (\(I_b>2\)) it is positive and, evidently, in some interval of \(I_b\) values it is minimal. ↩