Integrator-based Filters

We can convert passive RLC filters into integrator-based active filters in a systematic way using signal flow graphs.

Signal Flow Graphs

Signal flow graphs (SFGs) are topological representations of electrical circuits with two components: (1) nodes, and (2) branches. Any network that can be described by a set of linear differential equations can be represented by a SFG. In a SFG, the nodes represent the variables, e.g. voltages or currents, and the branches represent transfer functions between these node variables, specified by branch multiplication factors (BMFs). These BMFs are obtained from Kirchhoff's equations (KVL and KCL). Figs. 1-3 shows a few examples of SFG nodes and branches.

Useful SFG Properties

We can use the following properties to transform signal flow graphs into forms that can allow us to convert passive RLC filters into its active integrator-based counterparts.