Topological Approach to Automatic Symbolic Macromodel Generation for Analog Integrated Circuits

In the field of analog integrated circuit (IC) design, small-signal macromodels play indispensable roles for developing design insight and sizing reference. However, the subject of automatically generating symbolic low-order macromodels in human readable circuit form has not been well studied. Traditionally, work has been published on reducing full-scale symbolic transfer functions to simpler forms but without the guarantee of interpretability. On the other hand, methodologies developed for interconnect circuits (mainly resistorcapacitor-inductor (RCL) networks) are not suitable for analog ICs. In this work, a topological reduction method is introduced that is able to automatically generate interpretable macromodel circuits in symbolic form; that is, the circuit elements in the compact model maintain analytical relations of the parameters of the original full circuit. This type of symbolic macromodel has several benefits that other traditional modeling methods do not offer: First, reusability, namely that designer need not repeatedly generate macromodels for the same circuit even it is re-sized or re-biased; second, interpretability, namely a designer may directly identify circuit parameters (in the original circuit) that are closely related to the dominant frequency characteristics, such as dc gain, gain/phase margins, and dominant poles/zeros. The effectiveness and computational efficiency of the proposed method have been validated by several operational amplifier (opamp) circuit examples.