B.9. Signal or Incremental Common-Emitter Current Gain

Since β_DC/I_B is a variable function of I_C, the incremental β_ac is, in general, different from the dc β_DC. (The incremental β_ac is often referred to as β_o, but β_ac is consistent with SPICE.) To get an approximate value, we could calculate β_ac from

Equation B.42

with I_C1 = I_C2 and where (B.39) is used to obtain β_DC at the two currents. The definition of β_ac is from the limiting case of I_C2 → I_C1, that is,

Equation B.43

Performing this operation with the use of (B.39) leads to

Equation B.44

The result indicates that β_ac > β_DC (n_E > 1) and that the two converge in the limit for high I_C. This is the expression used in SPICE for the incremental β_ac, and it is used by SPICE when NE and ISE are included in the model. Otherwise, SPICE uses β_ac = β_DC = β_F. (If IS and BF are not specified in the model, SPICE will use default values, typically, BF = 100 and IS = 10^–16 A. For the project transistors, IS is about 10^–13 A.)