By David Johns Ken Martin
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Extra resources for Analog Integrated Circuit Design
A distributed RC model for a transistor in the active and the channel-to-substrate capacitance are modelled as distributed elements. However, the I-V relationships of the distributed RC elements are highly nonlinear because the junction capacitances of the source and drain are nonlinear depletion capacitances, as is the channel-to-substrate capacitance. Also, if Vos is not small, then the channel resistance per unit length should increase as one moves closer to the drain. This model is much too complicated for use in hand analysis.
157) The small-signal resistance, '0' models the dependence of the collector current on the collector-emitter voltage. 160) which is inversely proportional to the collector current. As an aside, note that 9m'0 = VA/VT is a constant value independent of the transistor operating point. This constant is usually between 2,000 and 8,000 for an npn BIT and is an upper limit on the attainable voltage gain for a single-transistor amplifier. The resistor rb models the resistance of the semiconductor material between the base contact and the effective base region due to the moderately lightly doped base p material (see Fig.
8 -~ m- lnng transist or ), Thi s eq uiva lent series so urce resistan ce is typicall y larger than the physi ca l so urce resistance. Thi s sat ura tio n cau ses the sq uarelaw characteristic of the current-vo ltage relation ship 10 be inaccurate. and the lrue relationship will be so mewhe re bel ween linear and sq uare. In many vo ltage-to-current conv ersion ci rcuits that rely on the square-law characteristic. this inaccuracy can be a maj or source o f error. Taking channel len gth s larger than the minimum allo wed help s to minimi ze this degradation.