# 6.6 The Saturation Parameters of a Transistor and their Variation with Temperature – Pulse and Digital Circuits

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

The output characteristics of n–p–n transistor having PT = 250 mW at room temperature in the CE configuration are given in Fig. 6.36. The dc load line for RL = 400 Ω is superimposed on the characteristics. However, from the characteristics in Fig. 6.36 the saturation voltage VCE(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.

RL = 400 Ω, VCC = 10 V

To draw the dc load line:

VCE(cut-off) = VCC = 10 V

To be able to read VCE(sat), the characteristics in the voltage range 0 to 0.5 V are expanded and the dc load line for RL = 400 Ω is again superimposed, as shown in Fig. 6.37(a). The region [see Fig. 6.37(b)] around IB = 0.175 mA is expanded to see the variation in IC for larger values of IB as shown as the dotted region in Fig. 6.37(a). It is seen for IB > 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 IB = 0.175 mA, VCE(sat) = 250 mV and for IB = 0.35 mA, VCE(sat) = 125 mV. This variation explains that, the larger is the value of IB, the smaller is the value of VCE(sat). At a given operating point, the ratio of VCE(sat)/IC is called the saturation resistance RCS. RCS at the point Q is

FIGURE 6.36 Typical output characteristics of an npn transistor in the CE mode

From the plots shown in Fig. 6.37(a) and (b) we infer that IC varies by larger amounts for smaller values of IB and by smaller amounts for larger values of IB, 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 IB, VCE(sat) is larger and is smaller for larger values of IB.

The above discussion essentially focuses on the dependence of VCE(sat) and IC on IB. We conclude from the above discussion that variation in VCE(sat) is dependent on IB. If IB is large, VCE(sat) is small and vice-versa. Similarly, as IB tends to become larger the variation in IC becomes smaller. For smaller values of IB, the variation in IC is relatively large.

Figure 6.38, gives the variation of VBE(sat) as a function of IC/IB, keeping IC constant and varying IB. These plots, which are normally given in the data sheets, tell us that VBE(sat) is larger for smaller IC/IB ratio, for a given IC and decreases with increasing ratio of IC/IB.

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 VBE(sat) as a function of IC/IB with IC as a parameter

Some data sheets specify RCS for a few values of IB. Sometimes data sheets specify the value of RCS by the plot that gives the variation of VCE(sat) as a function of IC/IB for various values of IC. A typical plot is shown in Fig. 6.39.

VBE(sat) varies with temperature and has a typical temperature sensitivity in the range of −1.5 to −200 mV/°C. Variation of VBE(sat) with temperature is presented in Fig. 6.40. The variation of VCE(sat) as a function of temperature with IB and IC as parameters is shown in Fig. 6.41.

FIGURE 6.39 The variation of VCE(sat) with of IC/IB for IC as a parameter

FIGURE 6.40 The variation of VBE(sat) as a function of temperature with IB and IC as parameters

FIGURE 6.41 The variation of VCE(sat) as a function of temperature with IB and IC as parameters

FIGURE 6.42 Variation of normalized hFE as a function of temperature with IC as parameter

Variation of normalized hFE (hFE at a given temperature divided by hFE at 25°C) as a function of temperature with IC as a parameter is shown in Fig. 6.42. This indicates that hFE varies by larger amounts with temperature at smaller values of IC. For larger values of IC, hFE is insensitive to temperature variations.