Representing the transistor by an equivalent resistor

During the analysis of circuits containing multi transistors, the researcher is faced with a tremendous problem. This is due to the fact the MOS/BJT transistor is a four/three-terminal device with a large number of specifying parameters. In order to simplify the analysis, the four/three-terminal complicated MOS/BJT transistor can be replaced by a two-terminal fictitious resistor with a proper resistance. In this paper, a procedure is described to find a formula for the equivalent resistance of the MOS or the BJT transistor, and thus simplifying the analysis of such circuits considerably. Also, the procedure is applied to circuits containing a single transistor and to circuits containing series and parallel connections of transistors in order to estimate the propagation delays. The derived formulas are verified by comparison with the simulation results adopting the 65 nm CMOS technology with a power-supply voltage of 1 V.