Symbolic analysis traditionally suffers circuit size problems as the number of
symbolic terms generated can grow exponentially with the circuit size. This problem has
been partially mitigated by a graph-based approach, called Determinant Decision
Diagram (DDDs) [1], where the symbolic terms are implicitly represented in a graph,
which has been inspired by the success of Binary Decision Diagram (BDDs) [2] as an
enabling technology for industrial use of symbolic analysis and formal verification in
digital logic design. DDD-based symbolic analysis enables the exact symbolic analysis
of many analog circuits substantially larger than the previous methods and open new
applications for symbolic analysis. DDD-based symbolic analysis still remains the most
efficient symbolic analysis technique. This chapter will present basic concept of DDDs,
the most efficient DDD construction method based on logic operation, s-expanded
DDDs for generating s-expanded polynomials and transfer functions. We will also show
how DDDs and s-expanded DDDs can be used for constructing simplified symbolic
expressions.
Keywords: Symbolic analysis, determinant decision diagrams, analog circuits, modeling, simulation
and analysis, binary decision diagrams, compact modeling
