##### 6.6 THE SATURATION PARAMETERS OF A TRANSISTOR AND THEIR VARIATION WITH TEMPERATURE

The output characteristics of *n–p–n* transistor having *P _{T}* = 250 mW at room temperature in the CE configuration are given in Fig. 6.36. The dc load line for

*R*= 400 Ω is superimposed on the characteristics. However, from the characteristics in Fig. 6.36 the saturation voltage

_{L}*V*

_{CE(sat)}can not be found as its value is typically a fraction of a volt (0.1 V for Ge and 0.2 V for Si). A transistor is said to be in saturation when the emitter and collector diodes are forward-biased.

*R _{L}* = 400 Ω,

*V*= 10 V

_{CC}To draw the dc load line:

*V*_{CE(cut-off)} = *V _{CC}* = 10 V

To be able to read *V*_{CE(sat)}, the characteristics in the voltage range 0 to 0.5 V are expanded and the dc load line for *R _{L}* = 400 Ω is again superimposed, as shown in Fig. 6.37(a). The region [see Fig. 6.37(b)] around

*I*= 0.175 mA is expanded to see the variation in

_{B}*I*for larger values of

_{C}*I*as shown as the dotted region in Fig. 6.37(a). It is seen for

_{B}*I*0.175 mA, that there is no appreciable change in the collector current for a change in the base current as shown in Fig. 6.37(b), which indicates that the transistor is driven into saturation. Again from these characteristics we see that for

_{B}>*I*= 0.175 mA,

_{B}*V*

_{CE(sat)}= 250 mV and for

*I*= 0.35 mA,

_{B}*V*

_{CE(sat)}= 125 mV. This variation explains that, the larger is the value of

*I*, the smaller is the value of

_{B}*V*

_{CE(sat)}. At a given operating point, the ratio of

*V*

_{CE(sat)}

*/I*is called the saturation resistance

_{C}*R*at the point

_{CS}. R_{CS}*Q*is

**FIGURE 6.36** Typical output characteristics of an *n*−*p*−*n* transistor in the CE mode

From the plots shown in Fig. 6.37(a) and (b) we infer that *I _{C}* varies by larger amounts for smaller values of

*I*and by smaller amounts for larger values of

_{B}*I*, indicating that saturation has been reached and there will be no further increase in the collector current when the base current is increased. Also, we see that for smaller values of

_{B}*I*

_{B}, V_{CE(sat)}is larger and is smaller for larger values of

*I*.

_{B}The above discussion essentially focuses on the dependence of *V*_{CE(sat)} and *I _{C}* on

*I*. We conclude from the above discussion that variation in

_{B}*V*

_{CE(sat)}is dependent on

*I*. If

_{B}*I*is large,

_{B}*V*

_{CE(sat)}is small and vice-versa. Similarly, as

*I*tends to become larger the variation in

_{B}*I*becomes smaller. For smaller values of

_{C}*I*, the variation in

_{B}*I*is relatively large.

_{C}Figure 6.38, gives the variation of *V*_{BE(sat)} as a function of *I _{C}/I_{B}*, keeping

*I*constant and varying

_{C}*I*. These plots, which are normally given in the data sheets, tell us that

_{B}*V*

_{BE(sat)}is larger for smaller

*I*ratio, for a given

_{C}/I_{B}*I*and decreases with increasing ratio of

_{C}*I*.

_{C}/I_{B}**FIGURE 6.37(a)** Expanded characteristics from 0 to 0.5 V

**FIGURE 6.37(b)** Expanded characteristic in the dotted region in Fig. 6.37(a)

**FIGURE 6.38** The variation of *V*_{BE(sat)} as a function of *I _{C}/I_{B}* with

*I*as a parameter

_{C}Some data sheets specify *R _{CS}* for a few values of

*I*. Sometimes data sheets specify the value of

_{B}*R*by the plot that gives the variation of

_{CS}*V*

_{CE(sat)}as a function of

*I*for various values of

_{C}/I_{B}*I*. A typical plot is shown in Fig. 6.39.

_{C}*V*_{BE(sat)} varies with temperature and has a typical temperature sensitivity in the range of −1.5 to −200 *mV/*°C. Variation of *V*_{BE(sat)} with temperature is presented in Fig. 6.40. The variation of *V*_{CE(sat)} as a function of temperature with *I _{B}* and

*I*as parameters is shown in Fig. 6.41.

_{C}**FIGURE 6.39** The variation of *V*_{CE(sat)} with of *I _{C}/I_{B}* for

*I*as a parameter

_{C}**FIGURE 6.40** The variation of *V*_{BE(sat)} as a function of temperature with *I _{B}* and

*I*as parameters

_{C}**FIGURE 6.41** The variation of *V*_{CE(sat)} as a function of temperature with *I _{B}* and

*I*as parameters

_{C}**FIGURE 6.42** Variation of normalized *h _{FE}* as a function of temperature with

*I*as parameter

_{C}Variation of normalized *h _{FE}* (

*h*at a given temperature divided by

_{FE}*h*at 25°C) as a function of temperature with

_{FE}*I*as a parameter is shown in Fig. 6.42. This indicates that

_{C}*h*varies by larger amounts with temperature at smaller values of

_{FE}*I*. For larger values of

_{C}*I*is insensitive to temperature variations.

_{C}, h_{FE}