Lumped Element Modeler

ElectroacPy lumped modeler allows the simulation of loudspeaker drivers in enclosures. All velocities computed — from driver membrane to port particle velocity — can then be set as input surface-velocity in the BEM modeler. This chapter explains how to create and add drivers and enclosures to a loudspeakerSystem.

Fig. 8 Lumped-Modeler structure.

.driver[]

Loudspeaker drivers are characterized by their Thiele/Small parameters. When creating a driver, it is possible to “manually” define its lumped parameters, or to load a file containing the relevant information:

• .lem_driver(),

• .lem_driverImport().

import electroacPy as ep
import numpy as np

#%% frequency axis and system initialization
frequency = np.arange(10, 10000, 1)
system = ep.loudspeakerSystem(frequency)

#%% Woofer import
Re = 6.2        # Ohm
Le = 1.2e-3     # H
Bl = 16         # T.m
Mms = 84.9e-3   # kg
Cms = 560e-6    # m/N
Rms = 2.35      # kg/s
Sd = 508e-4     # m^2
system.lem_driver("SB34", 1, Le, Re, Cms, Mms, Rms, Bl, Sd)

#%% Midrange import
system.lem_driverImport("MR16", "../technical_data/SB MR16PNW-8.txt")

#%% Tweeter import (through T/S file)
system.lem_driverImport("TW29", "../technical_data/TW29RN-B.txt")

For now, electroacPy supports the following file format:

• .txt, (both Klippel and HornResp),

• .bastaelement (Basta),

• .wdr (WinISD),

• .sdrv (speakerSim),

• .qsp (Qspeaker).

Once parameters are loaded in a driver, it is possible to plot its electrical impedance and mechanical behavior using .plotZe() and .plotXVA(). To access these functions, the object is called from its .driver[] dictionary. Resulting plot are shown in Fig. 9 and Fig. 10.

system.driver["SB34"].plotZe()
system.driver["SB34"].plotXVA()

Fig. 9 Electrical impedance of the SB34 subwoofer in free-air.

Fig. 10 Displacement, velocity and acceleration of the SB34 subwoofer in free-air.

Before working with enclosures, two small methods are available: .sealedAlignment() and .portedAlignment(). These open a simple Tkinter window[1] with text-boxes allowing to change enclosure configuration. Useful to find “correct” acoustic alignment before adding enclosures to the system.

Fig. 11 Ported alignment tool.

.enclosure[]

The .lem_enclosure() method offers seven types of pre-defined cabinets. Each depend on the **kwargs called when creating an enclosure. When calling the acoustic volume Vb alone, the default enclosure is sealed. The following table shows how to get each pre-defined setups.

Configuration	Inputs	unit	meaning
Sealed	Vb	m\(^3\)	cabinet volume
Ported	Lp rp Sp	m m m\(^2\)	port length port radius port cross-section area
ABR (passive radiator)	Mmd Cmd Rmd Sd	kg m/N kg/s m\(^2\)	moving mass suspension compliance mechanical resistance radiating surface
Bandpass (port) - 4\(^{th}\) order	Vf Lp rp Sp	m\(^3\) m m m\(^2\)	front volume (front) port length (front) port radius (front) port cross-section area
Bandpass (passive radiator) - 4\(^{th}\) order	Vf Mmd Cmd Rmd Sd	m\(^3\) kg m/N kg/s m\(^2\)	front volume moving mass suspension compliance mechanical resistance radiating surface
Bandpass (port) - 6\(^{th}\) order	Vf Lp - Lp2 rp - rp2 Sp - Sp2	m\(^3\) m m m\(^2\)	front volume front and back port length front and back port radius front and back port cross-section area
Bandpass (ABR) - 6\(^{th}\) order	Vf Mmd - Mmd2 Cmd - Cmd2 Rmd - Rmd2 Sd - Sd2	m\(^3\) kg m/N kg/s m\(^2\)	front volume front and back moving mass front and back suspension compliance front and back mechanical resistance front and back radiating surface

In our example, we create a ported woofer and a sealed midrange. Again, .plotZe() and .plotXVA() display general characteristics of our system — see Fig. 12 and Fig. 13.

system.lem_enclosure("ported_LF", 40e-3, 
                     Lp=35e-2, Sp=78.6e-4, 
                     Qab=120, Qal=30,
                     ref2bem=[1, 2], 
                     setDriver="SB34", Nd=1,
                     wiring="parallel")

system.lem_enclosure("sealed_MF", 5.1e-3,
                     ref2bem=3, setDriver="MR16")

#%% plot data
system.enclosure["ported_LF"].plotZe()
system.enclosure["ported_LF"].plotXVA()

Fig. 12 Electrical impedance of the SB34 woofer in its ported enclosure.

Fig. 13 SB34 displacement, velocity and acceleration in its ported enclosure.

A few notes about the previous enclosure definition:

• Qab is the quality factor linked to acoustic losses inside the enclosure, generally 30<Qab<120,

• Qal is the quality factor of acoustic leakage, generally 10<Qal<30,

• ref2bem allows to link velocities to radiating surfaces in the BEM simulations. Port and passive radiator should always be defined as the last item,

• setDriver takes the corresponding driver (from .driver[]) and compute its velocity inside the enclosure,

• Nd represent the number of drivers to set in the enclosure,

• wiring is the driver configuration, it defaults to "parallel",

• the tweeter is not set in an enclosure as we assume that its acoustic load is already accounted for in its lumped parameters (which is not a generality).

Code summary

The following snippet is a summary of what has been discussed above. Four modifications are done:

• frequency is defined with 125 points (instead of \(10^4\)), to reduce computation time,

• the subwoofer is imported from a file,

• BEM reference added to the tweeter driver,

• ep.save() is used to store the current system state in numpy archives (.npz).

import electroacPy as ep
from electroacPy import gtb

#%% frequency axis and system initialization
frequency = gtb.freqop.freq_log10(1, 10e3, 125)
system = ep.loudspeakerSystem(frequency)

#%% Load drivers
system.lem_driverImport("SB34", "../technical_data/SB SB34NRXL75-8.txt")
system.lem_driverImport("MR16", "../technical_data/SB MR16PNW-8.txt")
system.lem_driverImport("TW29", "../technical_data/TW29RN-B.txt", ref2bem=4)

#%% Define ported enclosure
system.lem_enclosure("ported_LF", 40e-3, 
                     Lp=35e-2, Sp=78.6e-4, 
                     Qab=120, Qal=30,
                     ref2bem=[1, 2], 
                     setDriver="SB34", Nd=1,
                     wiring="parallel")

system.lem_enclosure("sealed_MF", 5.1e-3,
                     ref2bem=3, setDriver="MR16")

#%% save state
ep.save("03_LEM_Recap", system)

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[1]

It is important to note that Tkinter windows will block the execution of code. This is normal behavior.