Transistor approximation (Ideal, Second and Higher):

An NPN transistor is shown in Fig. 10.71 (a). Voltage appearing across the emitter diode is denoted by V_BE and that appearing across the collector-emitter terminals is denoted by V_CE.

Ideal Approximation: An ideal approximation of a transis­tor is shown in Fig. 10.71 (b). Emitter diode is visualized as an ideal diode. In this case, V_BE = 0. This makes calculation of base current quick and easy. This equivalent circuit is often use­ful for troubleshooting when approximate value of I_B is needed.

The collector side of the transistor acts as a current source that pumps a collector current of β_dcI_B through the col­lector resistor. Thus collector current can be obtained simply by multiplying base current I_B by current gain.

Second Approximation: Second approximation of a tran­sistor is depicted in Fig. 10.71(c). This is more commonly used be­cause it may improve the analy­sis significantly when the base supply voltage is small. Base current is usually determined by using second approximation of the diode. Here V_BE is taken equal to 0.7 V in case of silicon tran­sistors and 0.3 V in case of germanium transistors. With the sec­ond transistor approximation, the base and collector currents will be slightly less than their ideal values.

Higher Approximations: The bulk resistance of the emitter diode becomes significant only in high power applications in which the currents are large. The effect of bulk resistance in the emitter diode is to increase V_BE to more than 0.7 V. For instance, in some high power circuits, the V_BE across the base-emitter diode may exceed 1 V.

Likewise, the bulk resistance of the collector diode may have a noticeable effect in some designs. Besides emitter and collector bulk resistances, a transistor has many other higher order effects that make hand calculations tedious and time consuming. For this reason, calculations beyond the second transistor approximation should use a computer solution.