A passive radiator is a rigid membrane attached to a flexible suspension that radiates an acoustic wave when it vibrates. It is usually used to enhance the low-frequency response of small audio systems, such as compact speaker boxes, without requiring additional energy.
The following picture demonstrate how such a membrane can be integrated into an audio system.
To design an optimal speaker box incorporating a passive radiator, it is crucial to accurately model the device’s behavior. To achieve this, Seltech collaborated with the LAUM (Laboratory of Acoustics at Le Mans University) to develop a custom measurement bench, controlled by specialized software, for the automatic measurement of passive radiators.
This project was carried out by two students, Romain Degraeve and Louis DUPARC, as part of their Bachelor’s thesis in acoustics. Romain Degraeve later continued this project during an internship at Seltech. The work was conducted under the academic supervision of Dr. Manuel Melon (Research Director, LAUM) and with internal supervision by Frédéric Fallais(Acoustic Engineer, Seltech) and Arthur Di Ruzza (Acoustic technician, Seltech).
Accurately modeling the passive radiator requires determining the parameters Mm, Rm and Cm based on the lumped element modeling theory as shown in the following table and analogy shematic.
Table of fundamental parameters
Unlike loudspeakers, a simple electrical measurement is not sufficient to determine these elements. Since these parameters are related to the mechanical impedance, the measurement bench first measures the mechanical impedance and then performs a numerical fitting to obtain the corresponding parameters. To achieve this, the impedance – defined as the difference between force and velocity – is measured using a microphone to capture the force and a laser to measure the velocity. The code then calculates the force from the pressure and the velocity from the displacement, as shown in the provided equations.
This is illustrated as follows :
Once the impedance plot is calculated (orange line), the fitting process is performed (black line). This fitting is done using the circle fitting method, inspired by the work in the thesis of Dr. Herzog (Research Director).
This bench provides Seltech with a significant capability to integrate passive radiators into its customers’ loudspeakers, offering a complete solution from measurement to simulation and integration of the passive radiator into the customer’s product.
Let Seltech assist you in designing and integrating passive radiators into a speaker box, from measurement to simulation and design.
Review by:
Romain Degraeve, M1 IMDEA (International Master in Electroacoustics) Student
In collaboration with:
Louis Duparc, M1 IMDEA Student
With the support of:
Dr. Manuel Melon, Research Director, LAUM
Frédéric Fallais, Acoustic Application Engineer, Seltech
Arthur Di Ruzza, Acoustic Technician, Seltech
Sources:
[1] Daniel J. Inman. (2014). Engineering Vibration, Chapter 7: Vibration Testing and
Experimental Modal Analysis. Fourth Edition, PEARSON.
[2] D. J. Ewins. (2000). Modal Testing: Theory, Practice and Application, Chapter 1:
Overview and Chapter 2: Theoretical Basis. Second Edition, Research Studies Press LTD.
[3] Ph. Herzog, J.C. Le Roux. (1994). Modélisation basses fréquences d’un haut-parleur
électrodynamique. Journal de Physique, Volume 04, C5-225 – C5-228. https://doi.org/10.1051/jp4:1994544.