Early Effect - Small-signal Model

Small-signal Model

The Early effect can be accounted for in small-signal circuit models (such as the hybrid-pi model) as a resistor defined as

in parallel with the collector–emitter junction of the transistor. This resistor can thus account for the finite output resistance of a simple current mirror or an actively loaded common-emitter amplifier.

In keeping with the model used in SPICE and as discussed above using the resistance becomes:

,

which almost agrees with the textbook result. In either formulation, varies with DC reverse bias, as is observed in practice.

In the MOSFET the output resistance is given in Shichman–Hodges model (accurate for very old technology) as:

,

where = drain-to-source voltage, = drain current and = channel-length modulation parameter, usually taken as inversely proportional to channel length L. Because of the resemblance to the bipolar result, the terminology "Early effect" often is applied to the MOSFET as well.