Nonlinear synthesis and design can be informally defined as a constructive procedure to interconnect components from a catalog of available primitives, and to assign values to their constitutive parameters to meet a specific nonlinear relationship among electrical variables. This relationship is represented as an implicit integro-differential operator, although we primarily focus on the synthesis of explicit algebraic functions,

(2.1)

where y is a voltage or current, f (·) is a nonlinear real-valued function, and x is a vector with components that include voltages and currents. This synthesis problem is found in two different circuit-related areas: device modeling [8, 76] and analog computation [26]. The former uses ideal circuit elements as primitives to build computer models of real circuits and devices (see Chapter 1). The latter uses real circuit components, available either off the shelf or integrable in a given fabrication technology, to realize hardware for nonlinear signal processing tasks. We focus on this second area, and intend to outline

y f= ( )x

systematic approaches to devise electronic function generators. Synthesis relies upon hierarchical decomposition, conceptually shown in Figure 2.1, which encompasses several subproblems listed from top to bottom:

• Realization of nonlinear operators (multiplication, division, squaring, square rooting, logarithms, exponentials, sign, absolute value, etc.) through the interconnection of primitive components (transistors, diodes, operational amplifiers, etc.).