Reprinted from ELECTRONICS - January, 1954

By L. J. GIAGOLETTO - Radio Corporation of America
RCA Laboratories Division - Princeton, New Jersey

The liquid-filled enclosure, shown in detail in Fig. 1A, is a reasonably simple and effective method of construction. The transistor is fabricated by standard techniques and then encased in a liquid-filled metal shell. Heat generated by the transistor is transferred to the metal shell by the liquid coolant. Benzene, toluene, and xylene are suitable liquids. Toulene has proved the most successful due to its low viscosity and relatively high boiling point. In addition to the simple method of construction, the liquid-enclosed power transistors have been particularly attractive because the germanium junctions suffer very little deterioration.

The use of a liquid, particularly an inflammable liquid, is not a very satisfactory solution for most applications. Consequently, the method of construction shown in Fig. 1B was developed. Here, a large metal surface is soldered directly to the germanium assembly. Heat is transferred to the large metal surface by metallic conduction with very little drop in temperature. The metal surface may be soldered to any of the three transistor elements and then encased in plastic for mechanical and environmental protection. The sketch shows a metal cup soldered to the collector.

The operation of a junction transistor has been analyzed *3). Careful measurements of small-signal junction transistors indicated that Shockley's analysis may be used for quantitative results if it is applied to an ideal intrinsic transistor. The actual transistor has certain extrinsic elements which must be added to the intrinsic transistor. A very important extrinsic element is a base-lead resistance, shown diagramatically in Fig. 2.

One of the basic assumptions of Shockley's analysis is that the minority carrier density is much smaller than the majority carrier density throughout the base region. This assumption is hardly satisfied by power transistors where the minority carrier density is generally many times the majority carrier density.

Nevertheless, as will be seen, many of the gross aspects of power-transistor characteristics are given by the Shockley analysis. In those cases where there is a considerable difference, use can be made of modified analyses *4) to determine the appropriate results.

According to Shockley's analysis, the d-c characteristics of a junction transistor are given by equations.

In these equations Ie and Ic are the emitter and collector d-c currents respectively and V eb and Vcb are the emitter-to-internal-base and collector-to-internal-base d-c voltages respectively. The four g's are d-c conductance coefficients which can be considered similar to the perveance coefficient employed in electron tube studies.

The Greek letter A is used in place of e/kT where e is the charge of an electron in coulombs, k is Boltzmann's constant in joules per degree K, and T is the operating temperature in degrees Kelvin (At room temperature, 27 C (300 K), A = -38.6 volts hoch -1 for electrons and +38.6 volts hoch -1 for holes.). *6)

Currents Ice and Ics are the emitter and collector saturation currents, respectively, and represent currents due to thermally-generated carriers in the base that flow to the emitter and collector when both are biased more than a few tenths of a volt in the reverse direction.

If the d-c conductance coefficients are known, the intrinsic-transistor characteristics can be readily,computed by means of formulars 5, 6 and 7 (formulars not shown here). This has been done for the collector current for a typical power transistor, and the results are shown by the dotted curve in Fig. 3.

The measured d-c conductance coefficients used in these calculations together with the corresponding d-c current coefficients and saturation currents are tabulated in Table I under the appropriate temperature heading of 40 C.

The dotted curve of Fig. 3 can be considered to be the intrinsic transfer characteristic of the transistor; that is, the transfer characteristic that would be obtainable if Rbb were zero.

The graphical relationship between the intrinsic and actual base characteristic is shown in Fig. 4A. The actual base-to-emitter voltage is obtained by adding to the intrinsic voltage Vb'e the voltage drop Vbb' across the base-lead resistance. The latter voltage will generally be several times larger than the former, particularly at larger currents, so that the base characteristics will be essentially linear. That is the base current will be approximately linearily related to the base-to-emitter voltage.

Actual transfer characteristics can be obtained by a similar graphical construction with the use of the base characteristics. An alternate method of calculation is to use the relationship between collector current and the base current. This relationship can be expressed in terms of a d-c current-amplification factor "alpha" cb.

Figure 4B shows how the d-c and a-c collector-to-base current-amplification factors are related to the currents. As shown in Fig. 5, the d-c current-amplification factor decreases approximately hyperbolically at larger collector currents. This drop-off is an important aspect of power-transistor operation and can be explained by modified analyses. *4)

With the aid of Fig. 5 the actual transfer characteristics can be determined.

For small-signal operation the input equivalent circuit has the form shown in Fig. 7. The resistor marked rb'e represents the flow of carriers to the base and is reciprocally proportional to base current. For a power transistor operating at a collector current of 100mA, rb'c would be of the order of 10ohms.

Capacitor Cb'e represents the storage of charge carriers in the base region. Its value is directly proportional to the square of the base thickness and to emitter current. Accordingly the actual value of Cb'c will depend greatly upon the base thickness.

As an example, for a base thickness of 0.002 in. Cb'e would be of the order of 0.5 uf at a collector current of 100mA. On a small-signal basis, Cb'e will have a pronounced frequency effect.

For large-signal operation, rb'e and Cb'e will vary with the applied signal. It is this variation together with similar variations in other reactive elements that complicate even an approximate study of large-signal frequency characteristics.

For convenience, this temperature correction factor which is approximately the same for both n and p germanium normalized to room temperature of 25 C is given in Fig. 8. It is apparent from the values of the temperature correction factor that the saturation currents and current coefficients will change rapidly with temperature. The data in Table I exhibit this very rapid variation with temperature.

The manner in which the calculated transfer characteristics change with temperature is shown in Fig. 9. For these calculations, it was assumed that the transistor was made of 4 ohm-cm n-type germanium. Maximum resistivity of this material occurs at approximately 50 C, and the resistivities at 25 C and 75 C are about equal.

The circuit operation when RG > 0 can be determined by Thevenin's theorem, considering the source as a voltage generator VG in series with RG. In the transistor circuit Ra is in series with rbb and the two can be lumped together and considered part of the transistor. The result is a transistor with a larger effective rbb' being driven from a generator of zero internal resistance.

The transfer characteristics for the new transistor can be constructed in the same manner as already described. Figure 3 shows two transfer characteristics determined in this manner when RG = 50 and 100 ohms. The base-to-emitter voltage includes the voltage drop across RG and is therefore the generator voltage. The corresponding measured transfer characteristics are also shown.
To get satisfactory operation over a range of temperatures, the biasing of the output stage must be given careful attention.

Figure 10 indicates the change in the operating point with changes in temperature. For stability, constant-current bias has the most advantages even though it is more difficult and expensive to achieve. An absolute constant-current bias is not feasible; an intermediate bias condition is generally used.

Two methods of obtaining intermediate bias for class-A operation are shown in Fig. 11A and 11B. The biasing of a push-pull class-B stage is somewhat less complicated. A typical arrangement is shown in Fig. 11C. Since the base current will generally decrease as the temperature is increased (Fig. 9), the base bias with the circuit of Fig. 11C will tend to increase as the temperature is increased.

The net result of these two effects will be to cause the quiescent collector current to increase. This factor must be taken into account in designing the class-B stage to insure that operation remains within the maximum limitations of the transistor. One method of achieving stability is to use a temperature-sensitive resistor for R, or Rs.

Complementary symmetry circuits *9 and *10) provide numerous additional circuit possibilities for audio output stages using power transistors. For example, the relatively simple biasing requirements of the push-pull amplifier can be taken advantage of without addition of bulk and weight in the form of transformers.
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