RCL Models
Circuit models are used as low-order models of acoustically active boundaries specifying the input impedance of the external domain. For example, modeling mechanical properties of a loudspeaker cone, a microphone diaphragm, or biological tissue, as experienced by the incident wave. For such boundaries, the pressure and velocity are modulated in response to the behavior of the boundary.
An RCL model is intended to provide a simple model to represent the frequency-dependent mechanical properties of a system that typically has some loss, a mass, and a compliance. The option includes all combinations of a three-element circuit consisting of an acoustic damper (acoustic resistance, a resistor Rac), an acoustic mass (acoustic inertance, an inductor Lac) and an acoustic compliance (a capacitor Cac), which are the simplest resonating acoustic circuits. While full circuit models tend to be more sophisticated (see for example Ref. 26), one can typically identify a simple core circuit responsible for the basic response which consists of such three elements.
The acoustic impedance Zac is related to the specific impedance Zi implemented in the weak equations Equation 2-26 and Equation 2-27 by the area of the boundary A as
.
Circuit model options
A schematic illustration is provided for each circuit in the Equation Display window.
Serial Coupling of Rac,, Cac, and Lac
Parallel Coupling of Rac,, Cac, and Lac
Parallel Coupled Lac and Cac in Series with Rac
Parallel Coupled Rac and Cac in Series with Lac
Parallel Coupled Rac and Lac in Series with Cac
Serial Coupled Rac and Cac in Parallel with Lac
Serial Coupled Lac and Cac in Parallel with Rac
Serial Coupled Rac and Lac in Parallel with Cac
Limitations
A circuit model is one dimensional and considers only changes in the direction normal to the boundary; any variations across the boundary are ignored. Therefore, circuit models provide good results at low frequencies with wavelengths substantially larger than the dimensions of the boundary.
Acoustical or mechanical circuits
It is sometimes advantageous to use circuit models in mechanical units rather than acoustical units. In these cases, the overall structure of the impedance boundary condition equation does not change, but the numerical value of the parameters do. The mechanical impedance Zmech (the ratio of force F and velocity v) and the acoustic impedance Zac are related via the boundary surface area A by the expression
.