Operational Amplifiers and Active Filters: A Bond Graph Approach

Abstract

The most important single linear integrated circuit is the operational amplifier. Operational amplifiers (op-amp) are available as inexpensive circuit modules, and they are capable of performing a wide variety of linear and nonlinear signal processing functions (Stanley, 1994). In simple cases, where the interest is the configuration gain, the ideal op-amp in linear circuits, is used. However, the frequency response and transient response of operational amplifiers using a dynamic model can be obtained. The bond graph methodology is a way to get an op-amp model with important parameters to know the performance. A bond graph is an abstract representation of a system where a collection of components interact with each other through energy ports and are place in the system where energy is exchanged (Karnopp & Rosenberg, 1975). Bond graph modelling is largely employed nowadays, and new techniques for structural analysis, model reduction as well as a certain number of software packages using bond graph have been developed. In (Gawthrop & Lorcan, 1996) an ideal operational amplifier model using the bond graph technique has been given. This model only considers the open loop voltage gain and show an application of active bonds. In (Gawthrop & Palmer, 2003), the `virtual earth' concept has a natural bicausal bond graph interpretation, leading to simplified and intuitive models of systems containing active analogue electronic circuits. However, this approach does not take account the type of the op-amp to consider their internal parameters. In this work, a bond graph model of an op-amp to obtain the time and frequency responses is proposed. The input and output resistances, the open loop voltage gain, the slew rate and the supply voltages of the operational amplifier are the internal parameters of the proposed bond graph model. In the develop of this work, the Bond Graph model in an Integral causality assignment (BGI) to determine the properties of the state variables of a system is used (Wellstead, 1979; Sueur & Dauphin-Tanguy, 1991). Also, the symbolic determination of the steady state of the variables of a system based on the Bond Graph model in a Derivative causality assignment (BGD) is applied (Gonzalez et al., 2005). Finally, the simulations of the systems represented