Efficient Approximation of Symbolic Expressions for Analog Behavioral Modeling and Analysis

Abstract

Abstract-Efficient algorithms are presented to generate approximate expressions for transfer functions and characteristics of large linear analog circuits. The algorithms are based on a compact determinant decision diagram (DDD) representation of exact transfer functions and characteristics. Several theoretical properties of DDDs are characterized, and three algorithms, namely, based on dynamic programming, based on consecutive k-shortest path based, and based on incremental k-shortest path, are presented in this paper. We show theoretically that all three algorithms have time complexity linearly proportional to |DDD|, the number of vertices of a DDD, and that the incremental kshortest path based algorithm is fastest and the most flexible one. Experimental results confirm that the proposed algorithms are the most efficient ones reported so far, and are capable of generating thousands of dominant terms for typical analog blocks in CPU seconds on a modern computer workstation.

Behavioral Modeling of Mixed-Mode Integrated Circuits

“…The solution of the NA formulation can be obtained by applying determinant decision diagrams (DDD) (Fakhfakh et al, 2010;Tan & Shi, 2004). Now we are able to generate the symbolic behavioral model of low-voltage amplifiers.…”

“…Additionally, transistors and parasitic elements can be modeled into hardware description languages (Alvarado et al, 2010), so that the development time of integrated circuits may be shrinked and the models can be tested before they are included into commercial simulators, namely SPICE and ELDO. An important issue is the application of symbolic analysis to generate analytical expressions to describe the behavior of devices and circuits (Beelen et al, 2010;Tan & Shi, 2004). More recently, McConaghy & Gielen (2009) introduced a template-free symbolic performance modeling of analog circuits, mainly focused on operational transconductance amplifier (OTA) based circuits.…”

“…Some recent research has been oriented to apply model order reduction (MOR) techniques (Qin et al, 2005;Shi et al, 2006;Sommer et al, 2008;Tan & He, 2007), to capture the dominant behavior, but as already mentioned in (Shi et al, 2006), a reduced symbolic expression is very difficult to generate with MOR techniques. In this manner, this book chapter highlights some recent developments in applying symbolic analysis to generate behavioral models of mixed-mode integrated circuits (Bhadri et al, 2005;Krishna et al, 2007;McConaghy & Gielen, 2009;Sánchez-López, Fernández & Tlelo-Cuautle, 2010;Tan & Shi, 2004;Tlelo-Cuautle et al, 2009;Tlelo-Cuautle, Sánchez-López & Moro-Frias, 2010). In the following sections, we show the generation of behavioral models of mixed-mode devices and circuits.…”

Approximation Techniques in Symbolic Circuit Analysis

“…In order to generate only the dominant terms by using DDDs, several algorithms based on dynamic programming (DP) have been proposed [37]- [39]. The main idea is to compute partial dominant terms for each DDD vertex pointing to a 1-edge.…”

“…However, the method described above is not applicable to s-expanded DDDs, because there are vertices with incoming 1-edges and 0-edges. It is worth mentioning that it is necessary to duplicate some vertices in order to apply the method described above, as has been described in [37]- [39]. To solve this drawback, another DP-based algorithm has also been proposed in [39].…”