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TECHNICAL PAPERS

# Active Helmholtz Resonator With Positive Real Impedance

[+] Author and Article Information
Jing Yuan

Department of Mechanical Engineering,  The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kongmmjyuan@polyu.edu.hk

J. Vib. Acoust 129(1), 94-100 (Jul 31, 2006) (7 pages) doi:10.1115/1.2345678 History: Received June 27, 2005; Revised July 31, 2006

## Abstract

The impedance of a passive noise control device is strictly positive real, if the device is installed in noise fields with weak mean flows. Passive noise control devices are, therefore, more reliable than active ones. Active control may be applied to a Helmholtz resonator to introduce electronic resonance. It will affect the impedance $Zact$ of the resonator. A controller may be designed such that (a) $Zact$ is small and resistive at some tunable frequencies; and (b) $Re{Zact}⩾0$ in the entire frequency range of interest. If criterion (a) is satisfied, the active resonator can suppress duct noise at tunable frequencies. It is difficult to design a controller to satisfy criterion (b) because parameters of the controller depend on acoustic parameters of the noise field. A new method is proposed here to design an active controller to meet both criteria simultaneously. The satisfaction of criterion (b) implies a positive real $Zact$ and a robust active resonator with respect to parameter variation in the noise field. Experimental results are presented to verify the performance of the active resonator.

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## Figures

Figure 1

(a) Helmholtz resonator and an analogous spring-mass-damper system and (b) acoustic circuit of the resonator

Figure 2

(a) Active Helmholtz resonator and (b) acoustic circuit of the active resonator

Figure 3

(a) Schematic diagram of the experimental duct and the active resonator, (b) acoustic two-port circuit of a duct with an active Helmholtz resonator and (c) and (d) two equivalent acoustic circuits of (b)

Figure 4

(a) Acoustic two-port circuit of a secondary path in a duct and (b) equivalent circuit of (a)

Figure 5

Experiment results in a duct with open outlet: (i) without control (gray), (ii) with a passive resonator (dotted), and (iii) with an active resonator (solid)

Figure 6

Experiment results in a duct with closed outlet: (i) without control (gray), (ii) with a passive resonator (dotted), and (iii) with an active resonator (solid)

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