Integrator-based Filters

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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).

Useful SFG Properties

Example: A First-Order Low-Pass Filter

Example: A Second-Order RLC Filter

Example: A 5th-Order Butterworth Low-Pass Filter

Differential Integrators

Maximizing Dynamic Range

Noise Analysis

Transmission Zeros

Example: A 5th-Order Filter with Transmission Zeros