Proceedings
of the Tomsk Order of the Red Banner of Labor Polytechnic
Institute named after S. M. Kirov

Volume 231　　　　　　　　　　　　　　　　　　　　　　　　　1971

TEMPERATURE AND TIME STABILITY OF THE COLLECTOR–EMITTER VOLTAGE OF A SATURATED TRANSISTOR

G. P. Trofimov

(Presented by the scientific seminar of the Department of Radio Engineering)

In the design of switching devices, the problem of reducing residual parameters is often very important. In the regime of small switched currents (for example, in modulators), the inverse connection of a transistor is used exclusively. The behavior of the residual parameters of transistors in this regime has been investigated in sufficient detail [1]. The question of the method of connecting a transistor in circuits for switching currents of the milliampere range (1–20 mA), taking into account the stated requirements, remains unresolved. In a number of cases [2] it is necessary to reduce the drift of the residual parameters to a minimum. Complicating the circuits by using compensating elements is undesirable. In such a case it is necessary to try to reduce this drift by finding some optimal operating mode of the transistor.

In order to determine the possibilities of using low-power alloy transistors in sampling devices, the temperature and time drift of the collector–emitter voltage in the saturation region was investigated for normal and inverse connection circuits. The closed state of the switch is no different from the case considered in [1].

Expressions for \(U_{\mathrm{cen}}\) and \(U_{\mathrm{ecn}}\) can be obtained on the basis of considering the diffusion processes of charge carriers, taking into account the volume resistances of the collector and emitter [3]. In the indicated region of external currents, the reverse currents through the junctions may be neglected, and these expressions may be obtained in the following form:

\[ U_{\mathrm{cen}}=\varphi_T \ln \frac{B_I\left(B_N I_{b_N}-I_k\right)} {B_N\left[(1+B_I)I_{b_N}+I_k\right]} -I_k\left(r_e' + r_k'\right)-I_{b_N}r_e'; \tag{1} \]

\[ U_{\mathrm{ecn}}=\varphi_T \ln \frac{B_N\left(B_I I_{b_I}-I_e\right)} {B_I\left(B_N I_{b_I}+I_e\right)} -I_e\left(r_k' + r_e'\right)-I_{b_I}r_k'; \tag{2} \]

where \(\varphi_T\) is the diffusion (temperature) potential;

\(I_k, I_e\) are the output currents of the transistor, respectively in normal and inverse connection;

\(I_{b_N}, I_{b_I}\) are the controlling base currents in normal and inverse connection;

\(B_N, B_I\) are the amplification factors of the corresponding base currents;

\(r'_{\mathrm{e}},\ r'_{\mathrm{c}}\)—bulk resistances of the emitter and collector materials.

The values of \(B_N,\ B_I,\ r'_{\mathrm{e}},\ r'_{\mathrm{c}}\), and of the reverse currents of the collector (\(I_{\mathrm{co}}\)) and emitter (\(I_{\mathrm{eo}}\)) junctions for some of the transistors studied (50 units of each type) are given in Table 1. The reverse currents were determined at zero voltage on the corresponding junction.

Table 1

*) according to data from [3].

For a specified load and a selected transistor type, the voltage drop across the closed switch depends on the base current, i.e.,

\[ U_{\mathrm{c e}N}=f(I_{\mathrm{b}N})\big|_{I_{\mathrm{c}}=\mathrm{const}}, \tag{3} \]

\[ U_{\mathrm{e c}I}=f(I_{\mathrm{b}I})\big|_{I_{\mathrm{e}}=\mathrm{const}}. \tag{4} \]

These functions have a minimum. At small base currents the main contribution to the residual voltage is made by the diffusion component, which decreases as the base current increases. The resistive component increases as the control current increases. Figures 1 and 2 show experimental curves of the form (3) and (4). The values \(U_{\mathrm{c e}N}\) and \(U_{\mathrm{e c}I}\) calculated from expressions (1)

Fig. 1.

and (2) differ from the experimental values by no more than 20%. It follows from the data obtained that, for the same degree of saturation, the voltage drop in inverse connection is 3–4 times smaller than in normal connection. However, the required base currents \(I_{\mathrm{b}I}\) in this case are 15–25 times greater than \(I_{\mathrm{b}N}\) and may exceed the load currents. In a particular circuit, difficulties may arise in controlling the switch.

Let us consider the dependence of the residual voltages on temperature. In the general case, expressions (1) and (2) may be represented as certain functional dependences of the form

\[ y=f(x_i),\quad i=1,2,\ldots,n, \tag{5} \]

where the arguments \(x_i\) reflect the physical parameters and external currents of the transistor. The latter can be stabilized, and their temperature dependence can be neglected. The remaining \(m\) parameters (excluding \(\varphi_T\)) are determined by the physical characteristics of the materials \(z_j\)*, which are subject to the influence of temperature, i.e.,

\[ x_i=\varphi_i[z_j(T)]; \quad j=1,2,\ldots,l. \tag{6} \]

Fig. 2.

Taking the latter expression into account, the total differential of the function will have the form:

\[ dy=\sum_{i=1}^{m}\sum_{j=1}^{l} \frac{\partial f}{\partial x_i}\, \frac{\partial \varphi_i}{\partial z_j}\, \frac{\partial z_j}{\partial T}\,dT, \tag{7} \]

where \(\dfrac{\partial f}{\partial x_i}\), \(\dfrac{\partial \varphi_i}{\partial z_j}\) are deterministic functions;

\[ \frac{\partial z_j}{\partial T} \]

is the temperature coefficient of the parameter;

\(dT\) is the temperature increment.

The quantity \(dy\) determines the total absolute deviation of the function under study from some initial value when the temperature changes by \(dT\) degrees. The difficulties of analytically calculating \(dy\) lie in the fact that the parameters \(z_j\) depend on temperature implicitly, are connected with the characteristics of the material by nonlinear empirical dependences unknown to the equipment designer, and are subject to the influence of many random factors of a technological and production nature, etc. Therefore the calculation of \(dy\) proves cumbersome and has a considerable error.

For a qualitative estimate it is necessary to know the nature of the temperature dependences of the parameters entering into expressions (1) and (2). With an unchanged load and stable sources, the output currents \(I_k\) and \(I\) may be considered constant. When controlling the transistor from a generator—

* Geometric dimensions, the method of manufacturing the transistor, and other similar factors are not taken into account here.

the current gain values \(I_{\delta N}\) and \(I_{\delta I}\) also do not depend on temperature. Since the remaining parameters of expressions (1) and (2) increase with temperature, the temperature coefficient of the voltages (TCV) \(U_{\mathrm{CE\,sat}}\) and \(U_{\mathrm{EC\,sat}}\) proves to be positive.

When driven from a voltage source and for small values of the equivalent-generator resistance \(R_{\delta}\) (hundreds of ohms to a few kilohms), the base currents increase with temperature, while the coefficients \(B_N\) and \(B_I\) decrease. The character of the expressions \(U_{\mathrm{CE\,sat}} = f(T)\) and \(U_{\mathrm{EC\,sat}} = f(T)\) proves to be more complicated, and the sign of the TCV depends on the operating mode and on temperature.

In Fig. 3 experimental characteristics are given for one of the MP116B transistors at various \(R_{\delta}\). Similar dependences were obtained for all the other transistors studied, in normal and inverse connection. From the data obtained it follows that, in the case of small values of \(R_{\delta}\), at a certain control current (denote it by \(I_{\delta T}\)) the sign of the TCV changes. This circumstance makes it possible to create high-quality thermally stable circuits with a TCV of less than \(10\ \mu\mathrm{V}/\mathrm{deg}\) (in the narrow temperature range \(20 \div 40^\circ\mathrm{C}\)).

Fig. 3. Experimental characteristics for transistor MP116B: \(U_{\mathrm{CE\,sat}}\), mV, versus \(T\), \(^\circ\mathrm{C}\). Curves are shown for \(R_{\delta}=0.51\ \mathrm{k}\Omega\), \(R_{\delta}=1.4\ \mathrm{k}\Omega\), and \(R_{\delta}=3.0\ \mathrm{k}\Omega\), at \(I_{\delta}=0.3\ \mathrm{mA}\), \(0.4\ \mathrm{mA}\), \(0.5\ \mathrm{mA}\), \(0.75\ \mathrm{mA}\), and \(1.0\ \mathrm{mA}\).

Table 2 gives experimentally obtained TCV values at currents \(I_{\delta T}\). When the base current is reduced in comparison with \(I_{\delta T}\), the TCV increases sharply (up to hundreds of \(\mu\mathrm{V}/\mathrm{deg}\)), and the sign becomes negative. For \(I_{\delta} > I_{\delta T}\) the sign of the TCV is positive. The table gives TCV values at the current \(I_{\delta U}\), which determines the minimum values of the voltages \(U_{\mathrm{CE\,sat}}\) and \(U_{\mathrm{EC\,sat}}\) on the volt-ampere characteristics (3) and (4). The maximum TCV value at deep saturations does not exceed the values at \(I_{\delta U}\). The currents \(I_{\delta T}\), for given \(I_C\) or \(I_E\), differ substantially for different transistor samples even from the same batch (for example, at \(I_C = I_E = 10\ \mathrm{mA}\) for MP116B transistors in normal connection \(I_{\delta T} \div (0.7 \div 2)\ \mathrm{mA}\), and in inverse connection \(I_T = (4 \div 13)\ \mathrm{mA}\)). However, in any case, as the output current increases, the value of \(I_{\delta T}\) decreases. It has also been established experimentally that p-n-p transistors are more critical with respect to the stability of \(I_T\).

Table 2

The curves presented in Fig. 4 show that, if necessary, by changing the base current it is easy to select a pair of unlike transistors with equal TCVs, whose signs are the same or opposite.

In order to obtain empirical dependences $U_{\mathrm{ke}} = f(T)$ and $U_{\mathrm{ek}} = f(T)$ with allowance for the operating mode, the experimental data were processed on an M-20 computer. Two external currents and the temperature in degrees Celsius were chosen as the independent parameters. The desired dependences were sought in the form

\[ U_{\mathrm{ke}} = f(I_{\mathrm{k}}, I_{\mathrm{bN}}, T); \tag{8} \]

\[ U_{\mathrm{ek}} = f(I_{\mathrm{e}}, I_{\mathrm{bI}}, T). \tag{9} \]

The results obtained show that the best agreement with the experimental data (within 10%) is obtained when the dependences (8) and (9) are approximated by a complete polynomial of the second degree. The polynomial coefficients vary from specimen to specimen. For this reason, it is not meaningful to present the desired particular result.

The time drift of the output voltage of a saturated switch was investigated. In an analytical approach here it is necessary to take into account the difficulties mentioned earlier. The aging of components is influenced by an even larger number of factors and in a more random manner. The search for general regularities requires the processing of a large amount of data—

... over a long period of time. It was found experimentally that in all cases, when testing a transistor that had not previously been used, the time drift in the initial time interval is rather large and amounts to 1–2 mV per hour. After two hours of “burn-in” it decreases to 10–20 microvolts/hour. It has been observed that, at base currents near the values of \(I_{\delta T}\), the time drift is minimal. However, in any operating mode, the voltage on the saturated transistor decreases with time.

Fig. 4.

Fig. 5.

Studies of the collector-emitter voltages were carried out using the circuit shown in Fig. 5. The external currents were set by P33 resistance boxes from the stabilized source U1199. The magnitude of the base current was monitored with an M1109 milliammeter of class 0.2; the output-current values were set, from the voltage drop across a standard resistor, by a P307 DC potentiometer of class 0.015. When determining the temperature dependence of \(U_{CE\,sat}\) (or \(U_{EC\,sat}\)), the transistor under investigation was placed in a thermostat. The volt-ampere characteristics and time drift were determined under room conditions.

The data obtained make it possible to assert that, for a certain ratio of the control and output currents, the collector-emitter voltage of a saturated alloy transistor turns out to depend only weakly on temperature and time, which makes it possible to use such transistors for constructing highly stable devices. From the standpoint of the magnitudes of the temperature and time drift of the collector-emitter voltage, the normal and inverse switch circuits are equivalent. A somewhat smaller value of \(U_{EC\,sat}\), compared with \(U_{CE\,sat}\), is achieved at significantly higher base currents. Since the current of the control circuit is limited, preference should be given to the normal connection of the transistor.

The author expresses sincere gratitude to V. I. Denisov, a staff member of the Novosibirsk Electrotechnical Institute, for his extensive work in processing the experimental data on a computer. The author is grateful to Associate Professor, Candidate of Technical Sciences M. S. Roitman for reviewing the manuscript and for his comments.

References

1. V. N. Anisimov, A. P. Golubev. Transistor Modulators. “Energiya,” Moscow–Leningrad, 1964.

2. M. S. Roitman, L. A. Naumov, A. V. Sokolov, G. P. Trofimov. A reference rectangular-voltage generator with adjustable frequency and duty cycle. In the present collection.

3. T. M. Agakhanian. Electronic Switches and Nonlinear Pulse Amplifiers. “Sovetskoe Radio,” Moscow, 1966.