DC small signal symbolic analysis of large analog integrated circuits

This paper presents a new methodology and its implementation (AnalogSifter) for DC small signal fully symbolic analysis of large analog integrated circuits. Our new sifting approach consists of six algorithms designed to relax the circuit size limitation of previously known methods. We show fully symbolic analysis results for much larger circuits than have ever been reported. Very compact symbolic expressions for the DC small signal voltage gains of the 741 and 725 operational amplifiers were obtained in less than 40 CPU seconds on a SUN SPARCstation 2, and the simplified results were numerically within 12% of the exact values. The output is expressed in terms of products of sums which can give the user insight into the behavior of the circuit. The overall time complexity is superquadratic with respect to the number of nodes. The implementation can output simplified symbolic expressions for any desired DC small signal transfer function, including input resistances, output resistances, as well as current and voltage gains. It also provides simplified symbolic expressions for noise analysis, sensitivity analysis, and power supply rejection ratio