Signal flow graphs for electroacoustic transducers (or modeling made easy)

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Abstract
The simulation of an electroacoustic transducer such as a loudspeaker system requires a mathematical model that can serve as the basis for building a computer model. We have three kinds of elements in a loud speaker : electrical, mechanical, and acoustical. Understanding the model and the results of the simu lation suggests that we not follow the traditional path of converting the mechanical and acoustical eZe ments to equivalent electrical elements to form an electrical network as the model to study. Instead, we have found it easier to follow a scheme originally suggested by Larrowe1,3 and form a model based on stating all physical laws in an integral formulation. In modern notation, this is simply accomplished by drawing a signal flow graph as a mathematical model of the system. The resulting signal flow graph (if we use the "right" technique) has an optimum set of state variables in the sense that all quantities are of clear physical significance in the system. For a loudspeaker system, the state variables turn out to be voice-coiz current, voice-coil velocity, voice- coil displacement, cabinet pressure, and volume velocity at the vent. Once this signal flow graph has been drawn, an analog computer model can be formed by proper insertion of minus signs and scale factors. The state-variable differential equation read from the signal flow graph can be converted to a phasor equation and then solved by complex matrix inversion. A time-shared computer terminal or a minicomputer programmed in BASIC is a convenient way to implement a digital simulation of an electro acoustic transducer.

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