| Engine manufacturers have taken an interest in making mufflers into active filters that can attenuate the fundamental frequency emitted by their engines. One way of constructing an active filter is to design a tracking side-branch resonator, a notch filter that can moved, that is keyed to the revolutions per minute of the engine, thus the fundamental frequency of the exhaust. Typically, a cavity will only resonate at one specific frequency, but by terminating it with a composite piezoelectric transducer that is loaded with a variable impedance, this frequency can be altered. In this dissertation an active filter is discussed using an exponential horn as a cavity and a composite piezoelectric transducer as the termination. The use of the exponential horn is to relocate a stationary notch outside the desired bandwidth. A mathematical model is developed for the electroacoustic system using acoustical-to-mechanical, mechanical-to-electrical, and analog-to-digital transformations using two-port analysis. The implementation of the loading on the composite piezoelectric transducer is with a processor having a digital filter and necessary conversion circuits. In the design of the digital filter. this research shows how a backward Euler transform compares to a bilinear transform. For the use of impedance generation, the bilinear digital filter is more suited. This research also shows the difficulty in producing impedance over a bandwidth with a processor. The difficulty is the phase delay through the analog-to-digital-to-analog circuitry. This phase shift through the circuit is accounted for in two novel ways, (1) a procedure to minimize the time for calculation of the filter, and (2) a compensation filter to remove the remaining phase shift through the circuitry. Results for design and testing of the circuitry are presented. For the electroacoustic model with the designed/tested electrical load, the active filter predicts a notch that is 5-10 dB deep between 200 Hzand 420 Hz and 15-20 dB deep between 420 Hz and 769 Hz. A digital circuit is a viable way of loading the piezoelectric transducer to shift the natural frequency. |
