B.7. Collector-Emitter Voltage and Collector Current in the Saturation Region

An equation for V_CEsat (V_CE in the saturation region) can be obtained using the equations for I_B, (B.27) (with leakage components neglected), and I_C, (B.23), to eliminate V_BE. The approximate equation for I_B is again

The equation for I_C, (B.23), which neglects the V_AF term (well justified at low voltage of the saturation region), and the –1 is

Equation B.33

Eliminating V_BE between the approximate form of (B.27) and (B.33) gives

Equation B.34

where

Equation B.35

The subscript comes from “beta forced,” the conventional way to define I_C/I_B in the saturation region. Note that by definition, β_forced < β_F, as I_C < I_Cact defines the saturation region.

For example, we compute V_CEsat at I_Csat = I_C/2. Assume that β_F = 100 and β_R = 1 such that β_forced = β_F/2 = 50. For this case, V_CEsat = 120 mV. Note that this is the midrange for the validity of (B.30).

It should be noted that V_CEsat is not defined for β_forced → β_F. This is because of the neglect of the –1 from the equations. Technically, the maximum V_CEsat is V_CEsat ≈ V_BE, as this is the maximum V_CE at which the base – collector junction is forward biased, the condition for the onset of the saturation region. At V_CE values very near V_BE, the –1 terms in the current equations are not mathematically negligible. On practical grounds, though, (B.34) is valid for when the output characteristic is clearly in the saturation region.

A value for β_R can be obtained, using (B.34), from one set of data points, I_Csat and V_CEsat from a measurement, with β_F known. If this proved to vary with the I_Csat chosen for the calculation, it would suggest that the discussion at the end of Unit B.5 applies. That is, the leakage current is not negligible and the effective β_R, β_Rleak, is a variable throughout the saturation region.