Computer-Aided Simulation and Optimization of Multiway Loudspeaker Systems Using CALSOD 3.10
COMPUTER-AIDED LOUDSPEAKER DESIGNWhen evaluating the performance of loudspeakers, recent work presented by Toole indicates that there is a high correlation of listener preferences with high-resolution measurements of on-axis and off-axis magnitude response. Loudspeakers with a wide bandwidth, flat and smooth magnitude response, and uniformly wide dispersion, are generally rated highly by experienced listeners. In order to achieve many of these desirable design features, computer-aided design of loudspeaker systems has become an important element in the loudspeaker designer's toolbox, and is routinely used by the world's larger loudspeaker companies in an effort to control the many complex parameters that affect the performance of a complete loudspeaker system.
The last few years have seen a boom in the use of personal computers in loudspeaker design and analysis, as well as acoustic testing. This is a significant advance, because loudspeaker designers had previously always made use of expensive mainframe type computer systems. It is now economically viable for all smaller manufacturers and consultants to undertake computer-aided measurement and optimization using the powerful low-cost personal computers and acoustical measurement systems that are available today. In fact, it is viewed by many to be a necessity for keeping up in today's highly competitive audio marketplace.
Computer programs were first used in loudspeaker design to help designer's predict the performance of a given woofer in its enclosure. The important variables were the well-known Thiele-Small parameters, and by using a computer program the designer could optimize the low-frequency performance of the loudspeaker system for a given driver.
The next application of computers in loudspeaker design involved the design of crossover filters for use in multiway loudspeaker systems. Crossover design is a difficult and time consuming task, since the network must be carefully designed to integrate the behaviour of multiple loudspeaker drivers into the total system response. This task is complicated by the fact that the impedance of a driver has a significant reactive component, whereas standard filter formulae assume that the loudspeaker load is a pure resistance. The designer is also confronted with a wide variety of possible crossover network topologies, each of which presents a particular solution to the problems of off-axis radiation patterns, system magnitude and power response, and driver power handling limitations.
Computer-aided design techniques that can simulate the important characteristics of a design allow many different scenarios to be examined early in the design phase, without having to go through the expensive process of building many prototype systems. The designer can easily and quickly try different driver layouts and crossover network topologies to see their effects on the magnitude and phase response of the complete loudspeaker system. Different drivers can be inserted into the system to determine how the overall performance of system might be changed. The designer will quickly gain an appreciation of all the important variables, as well as a better understanding of the physical limitations of any particular design approach. This results in improved overall system performance.
CALSOD SPEAKER SYSTEM DESIGN SOFTWARECALSOD (Computer-Aided Loudspeaker System Optimization and Design) is a program for use in the computer-aided design and optimization of loudspeaker systems, and it makes available to all loudspeaker designers a collection of powerful analysis capabilities. CALSOD runs on PC/286/386/486 and Pentium personal computers under MS-DOS 3.0 or higher. CGA, EGA, VGA and Hercules graphics cards are supported. A maths co-processor is not required but will automatically be used if one is installed. A hard disk is recommended for efficient operation, and the amount of free RAM needed is 512 KB. If desired, CALSOD can be run from a 1.2 MB or 1.44 MB floppy disk.
CALSOD also runs in a DOS-window with Windows 95 and 98.
(Some problems have been reported with Windows NT4).
A 370-page on disk user's manual is provided (a printed manual is optional), and this gives a detailed description of all of CALSOD's features, as well as providing comprehensive tutorial examples describing the design and optimization of a two-way system. These will help the user to quickly master CALSOD and become proficient in using its full capabilities.
When using CALSOD, the designer creates a data file using a built-in text editor, and the data file is then read in and CALSOD computes all the required system response functions.
The main menu of CALSOD (see Figure 1) allows the user to set up frequency limits and various optimization parameters that are required to perform each analysis. It is easy to simulate a new loudspeaker system by simply editing models of drivers that were created previously.
CALSOD's modelling capability enables the user to accurately simulate the magnitude and phase response of the sound pressure and impedance response of an individual loudspeaker driver. Even if only magnitude response data are available, which is typical of most manufacturer's data sheets, CALSOD's curve-fitting approach produces an accurate model of the phase behaviour of the driver's sound pressure and impedance response characteristics.
Some of CALSOD's many design, analysis and optimization features include:
* simulation of sound pressure and impedance response for vented, sealed, passive-radiator, filter-assisted, compound, push-pull and bandpass low-frequency alignments
* positions of drivers on the baffle can be specified for accurate simulation of effects on summed response caused by inter-driver time delays to the observation point
* fast and robust optimization of completely general user-defined passive and active crossover networks with up to 60 components
* standard filter target functions for Linkwitz-Riley, Butterworth, Bessel, constant voltage and user-defined designs
* powerful curve-fitting optimizer for quickly creating sound pressure and impedance models of driver response
* automatic calculation of inductor dcr for air-cored coils based on user-specified wire diameter or SWG
* automatic estimation of driver Thiele-Small parameters (Qes, Qms, Qts, fs, Vas, Bl, Mms, Cms, etc) from driver impedance measurements taken under mass or compliance perturbation conditions
* driver parameter estimation and verification of enclosure tuning using a single vented-box impedance measurement
* driver impedance models use frequency dependent voice-coil inductance and resistance parameters, automatically determined by the driver parameter optimizer
* piston approximation for driver models to simulate off-axis radiation characteristics
* specify the orientation of the principal radiation axis of each individual driver used in the loudspeaker system
* provision for time delay effects on individual loudspeaker drivers
* simulation of the step in the sound pressure response caused by diffraction of sound around the baffle, including inverse response
* simulation of the effects of room gain on low-frequency response to help the tuning of low-frequency alignments
* simulation of the effects of floor reflections on the sound pressure response by setting up a system of loudspeaker sources and images
* simulation of the response of loudspeaker arrays
* importing of impedance and sound pressure measurement files from MLSSA, SYSid, System One, IMP, Audiosuite, CLIO, AMS-PC, AIRR, PC AudioLab, and LMS test systems, with support for SPL optimization using up to 5 observation points to account for off-axis radiation characteristics and direct use of measured phase response
* printer support for HP LaserJet and HP DeskJet printers, as well as popular 9-pin and 24-pin dot matrix printers from IBM, Epson, NEC and Toshiba
* screen plots can be saved as PCX files for importing into desktop publishing and word processing software
CALSOD's advanced analysis facilities allow the speaker designer to routinely inspect color graphics plots of both the magnitude and phase of all the following performance characteristics of a multiway system:
* impedance of each individual loudspeaker driver
* input impedance of the crossover network and loudspeaker combination
* voltage transfer function of each filter when it is loaded by its driver
* filtered and unfiltered sound pressure response of each loudspeaker
* desired target acoustic response function and target impedance function
* summed sound pressure response of a multiway loudspeaker system, including the simultaneous display of the response at multiple off-axis observation points
If required, plots of the magnitude and phase response can be presented using a linear frequency scale, which allows the linear-phase behaviour of the design to be easily assessed.
MODELLING LOUDSPEAKER DRIVERS WITH CALSOD
Figure 2 shows plots of the magnitude and phase of the sound pressure response of a woofer that was simulated using CALSOD.
Figure 3 shows a similar model obtained for a tweeter. The measured data points are denoted by the small dots, and there is excellent agreement between test and simulation.
A driver model is created simply by cascading a highpass filter and a lowpass filter to provide an approximation to a given driver's SPL response. The highpass filter functions use standard Thiele-Small parameters to define a closed-box, vented-box, passive-radiator or bandpass low-frequency alignment. The order of the lowpass filter can be easily adjusted to accurately fit the driver's natural high-frequency roll-off, and the user can also set the sensitivity of each driver to any required value. An effective piston diameter can also be specified for each driver to model the off-axis radiation characteristics.
Any peaks and dips in a driver's sound pressure response can be included by adding minimum-phase equalizers to the model, thus ensuring that the driver's phase response is correctly simulated. The frequency, amplitude and Q of each peak or dip can be easily adjusted to provide a highly accurate match with the true response. The built-in curve-fit optimizer can automatically calculate the amplitude and Q associated with any minimum-phase equalizers that the designer has used in his driver model.
The impedance model also uses Thiele-Small parameters to predict the impedance of the driver in its enclosure, and provision is made for the user to include the effects of the voice-coil inductance. If any extra peaks or dips are present in the impedance response, it is possible to introduce minimum-phase equalizers to ensure that the model matches the experimental data as accurately as possible. CALSOD can also use a frequency-dependent inductance and resistance values to model the voice-coil impedance, and the impedance curve-fit optimizer will automatically determine the required values from experimental data.
Figure 4 shows plots of the magnitude and phase of the impedance response of the woofer and tweeter. It is clear that the simulations are in excellent agreement with the measured magnitude and phase, thus ensuring that the reactive load presented by each loudspeaker driver will be correctly modelled for all subsequent crossover network calculations. Note that once these driver models have been created, they can be utilized in any subsequent designs simply by copying the required driver data modules.
Fig. 4: Magnitude and phase of impedance response models for a woofer and tweeter, together with measured data points.
SIMULATING MULTIWAY LOUDSPEAKER SYSTEMSOnce individual driver models have been created, CALSOD allows the user to specify a passive or active crossover network with up to 60 different components. The topology of the crossover network is completely arbitrary, as a general circuit solver performs the calculations. It is possible to simulate a multiway loudspeaker with up to eight drivers selected in any combination from a set of ten different driver modules. When specifying the connections of each driver in the crossover network, it is possible to adjust the polarity of any driver, so it is very easy to investigate the effects of such a change on the total sound pressure response.
Additionally, the effects of the geometric layout and relative positioning of the drivers on the baffle of the loudspeaker cabinet can be included by specifying the location of each driver's acoustic centre. CALSOD automatically takes into account the specified inter-driver time delays when computing the summed response, thus providing a means to accurately simulate loudspeaker systems that use non-coincident drivers.
CALSOD also allows the designer to specify the orientation of the principal radiation axis of each individual driver used in the loudspeaker system. This feature is particularly useful when using multiple drivers and takes full advantage of CALSOD's capability to model the off-axis response of individual drivers.
Figure 5 shows the predicted magnitude and phase response of the woofer and tweeter when driven through their respective crossover networks, together with the experimental measurements. In this particular design, the crossover filters were chosen to have a 4th-order Linkwitz-Riley acoustic response, and a few additional components were included to allow some degree of equalization of the individual driver responses. There is excellent agreement between the simulation and the experimental data in both magnitude and phase.
Fig. 5: Predicted magnitude and phase of the woofer and tweeter sound pressure responses when driven through their respective crossover networks, together with measured data points. Figure 6 shows the simulated magnitude and phase response of the two-way system, and compares it with the measured response data. Again, it is clear that the results of the simulation are in excellent agreement with the experimental data.
Fig. 6: Predicted magnitude and phase of summed response from woofer and tweeter, together with measured data points. When the models of the raw sound pressure response of the woofer and tweeter were created, no phase data were available to confirm the accuracy of the simulation at that stage of the analysis. However, from the good agreement between simulation and experiment shown in Figure 5, it can be seen that CALSOD has accurately simulated the phase response of the woofer and tweeter.
OPTIMIZING MULTIWAY LOUDSPEAKER SYSTEMS
One of CALSOD's most important features is its ability to optimize the values of the crossover network components in order obtain the best possible system response. It is possible to optimize the component values for a single driver at a time, using built-in target response functions such as Butterworth, Linkwitz-Riley, constant voltage and Bessel filters, as well as user-defined transfer functions.
We will describe the complex case that involves the interaction of a woofer and tweeter in a two-way system. Figure 7 illustrates a typical crossover network topology for a two-way system, and the table shows the values of all the components before and after the optimization.
Fig. 7: Typical crossover network topology for two-way system, and component values before and after optimization. Figure 8 shows the summed sound pressure response of the woofer and tweeter, together with their individual filtered responses, prior to optimization.
Fig. 8: Summed sound pressure response of two-way system before optimization of crossover network components. Figure 9 shows the results after optimization, and it is seen that a much improved result has been obtained. For this design the entire optimization process took about 10 iterations, and the elapsed time was only a few seconds on a 25 MHz 80386 computer fitted with an 80387 maths coprocessor.
Fig. 9: Summed sound pressure response of two-way system after optimization of crossover network components. In the above example the acoustic centre of the woofer was about 25 mm behind that of the tweeter, simulating the actual conditions if the woofer and tweeter were mounted on a flat baffle. CALSOD allows the locations of the drivers and the observation point to be specified arbitrarily using an XYZ coordinate system. CALSOD also calculates the input impedance of the complete two-way system, which is shown in Figure 10.
Fig. 10: Input impedance of the two-way system consisting of the woofer and tweeter and their crossover network. CALSOD can compute the summed response of a multiway system at up to five different user-defined observation points, the positions of which can be conveniently specified using a spherical coordinate system. This makes it easy to evaluate the off-axis performance of any multiway system. If the designer wishes, CALSOD's optimizer will also take into account a weighted combination of the responses at these off-axis positions when optimizing the component values in the crossover network. This helps to ensure that the sound pressure response of the complete system will vary smoothly from the on-axis design case to the off-axis locations.
Figure 11 shows the response of the two-way system calculated on-axis as well as for two off-axis positions. The dashed and dotted curves correspond to ±15° above and below the principal radiation axis, respectively. Such simulations provide very important performance checks of the loudspeaker's off-axis radiation characteristics.
Fig. 11: Response of two-way system calculated on-axis, as well as ±15° above and below the principal listening axis.
IMPORTING MEASUREMENT FILES
CALSOD imports data files from test systems such as DRA Laboratories' MLSSA, Ariel's SYSid, Audio Precision's System One, Liberty Instruments' IMP and Audiosuite, Kemsonic's AMS-PC, Bunn's AIRR, Microacoustics' PC Audiolab, Audiomatica's CLIO, and LinearX's LMS. Both SPL and impedance measurements are supported, and the crossover optimizer can take into account the measured response at up to five different observation points. A special CALSOD file format is also available to enable you to create CALSOD-compatible files if your equipment is not supported directly. Imported files save the designer time that would normally be spent in setting up curve-fit models of a driver's sound pressure and impedance responses, as well as ensuring that the most accurate data are used in the design process. Imported impedance data files are used directly by the driver parameter optimizer.
OPTIMIZING CONJUGATE IMPEDANCE NETWORKS
CALSOD can also optimize the values of crossover networks to achieve a user-defined target impedance response, which is usually a pure resistance. The impedance optimizer is very useful in quickly determining the component values of Zobel networks, as used to equalize the high frequency impedance rise of individual drivers. It is also possible to optimize conjugate load matching networks that are applied to equalize the total system input impedance, therefore ensuring that the power amplifier sees a load that closely approximates a pure resistance.
DESIGNING LOW-FREQUENCY ALIGNMENTS
As part of its overall analysis capabilities, CALSOD also allows the designer to compare a number of low-frequency alignments in order to make a choice as to which is the most suitable for a given driver. For example, Figure 12 shows four vented-box systems with different vent tuning frequencies being compared to one another.
Fig. 12: Comparison of four vented-box systems with different vent tuning frequencies.
Fig. 13: Experimental data points and fitted impedance response functions obtained when determining driver Thiele-Small parameters under mass perturbation conditions.
THIELE-SMALL PARAMETER ESTIMATION
A built-in driver parameter optimizer uses two impedance response measurements taken under added-mass or enclosure volume-change conditions to automatically determine least squares estimates of Qes, Qms, Qts, Vas, fs, Bl and other parameters for the particular driver. Table 1 shows the results of Thiele-Small parameter estimation using two impedance measurements taken under mass perturbation conditions.
ADDED-MASS METHOD OF PARAMETER ESTIMATION FOR A WOOFER ESTIMATED LOUDSPEAKER DRIVER PARAMETERS Fs = 40.0074 Hz Rg = 0.0010 ohms Qms = 3.0007 Re = 6.0000 ohms Qes = 0.3499 Le = 0.8783 mH Qts = 0.3134 Le Kmp = 16.0392 mohms Vas = 45.0259 litres Le Xmp = 0.6698 Sd = 0.0230 m^2 Le Kr = 7.9511 mohms Mms = 26.4029 grams Le Xr = 0.6698 Cms = 0.5994 mm/N Le Ki = 13.9297 mohms Bl = 10.6682 T.m Le Xi = 0.6698 No = 0.7991 % SPLref = 91.0444 dB RMSerr1 = 0.0317 ohms Sens = 92.2938 dB RMSerr2 = 0.0472 ohms The SEN, SOF, and IMP submodules for this driver are: DRIVER T-S MODEL SOUND PRESSURE SEN 92.29 DB SOF 40.01 0.313 HIGHPASS IMPEDANCE IMP 40.01 6.00 57.46 1.604E-02 0.6698 0.313Table 1: Results of Thiele-Small parameter estimation using two impedance measurements taken under mass perturbation conditions.
A single impedance measurement of a driver mounted in a vented-box enclosure can also be used to determine the driver and enclosure tuning parameters, allowing an indirect means of measuring the low-frequency sound pressure response without the use of an anechoic chamber.
When performing the vented-box impedance fits, CALSOD automatically creates a model of the sound pressure response of the driver in its vented-box enclosure. You can then plot out the response when the estimation has been completed.
EXAMPLE CALSOD DATA FILE
The CALSOD program requires the user to prepare a data file with the integrated text editor. This approach allows the designer the maximum amount of flexibility, and is similar in philosophy to circuit analysis programs such as SPICE. The data file used to analyze the two-way system discussed earlier is shown in Table 2.
CIRCUIT IND 0.43E-3 1 2 0.0 VARIABLE ! Filter network for the woofer RES 8.40 2 3 VARIABLE ! Inductor and Zobel network CAP 31.97E-6 0 3 VARIABLE CAP 6.19E-6 1 4 VARIABLE ! Filter network for the tweeter IND 0.29E-3 0 4 0.0 VARIABLE ! 2nd-order filter + resistor RES 0.34 4 5 VARIABLE SPK 1 0 2 0.0 -0.10 -0.030 POSITIVE ! Drivers connected to crossover SPK 2 0 5 0.0 0.10 0.000 POSITIVE ! network and baffle positions ! TARGET SPL ! Target sound pressure function for optimizer. XYZ 0.0 0.0 0.0 ! Flat response here, but can be Butterworth, SEN 92.0 DB ! Linkwitz-Riley, etc. ! DRIVER 1 ! This driver referred to by SPK 1 in CIRCUIT module Woofer SOUND PRESSURE SEN 92.0 DB SVB 33.8 0.261 4.0 1.5 7.0 ! Vented-box for sound pressure MPE 580.0 3.993 -1.145 DB ! Minimum-Phase Equalizers for MPE 2000.0 1.910 2.625 DB ! modelling peaks and dips BUT 4350.0 4 LOWPASS ! Lowpass filter for HF response IMPEDANCE IVB 33.8 6.10 0.00722 0.701 0.01317 0.690 6.127 0.273 4.0 1.5 7.0 MPE 420.0 4.23 1.203 LINEAR ! DRIVER 2 ! This driver referred to by SPK 2 in CIRCUIT module Tweeter SOUND PRESSURE SEN 90.0 DB HLR 532.5 0.0 3.14 0.43 0.0 MPE 1200.0 2.219 1.013 DB ! Minimum-Phase Equalizers MPE 3500.0 6.336 2.149 DB ! MPE 6000.0 2.131 -2.160 DB ! The required parameters are MPE 9000.0 4.774 1.834 DB ! obtained automatically by MPE 12000.0 0.548 0.879 DB ! the curve-fit optimizer. MPE 16000.0 4.666 4.304 DB ! BUT 19000.0 4 LOWPASS IMPEDANCE IMP 532.5 6.10 34.80 3.147E-3 0.5749 8.898E-4 0.7063 0.537 MPE 2000.0 4.6782 1.2545 LINEAR MPE 4000.0 1.6142 1.0788 LINEAR MPE 16000.0 9.2615 1.1476 LINEAR
Table 2: CALSOD data file for modelling a two-way loudspeaker system and its crossover network.
PARTIAL LIST OF INTERNATIONAL CALSOD USERS
Barlow Associates Australia
Elecoustics Australia NOVA Sound Australia M.P. & C. P.V.B.A. Belgium A.E.D. P.V.B.A. Belgium Bell Northern Research Canada Novatel Communications Canada Electrolab Denmark Veng Audio Denmark B & W Loudspeakers England Canon Loudspeakers England Carlsbro Electronics England Martin Audio England NAD Electronics England Cator Finland Gradiente Finland Cabasse Electroacoustics France Gaertner Consulting France Grundig Germany Hi-Tech GmbH Germany Nokia Graetz Germany Proraum Germany Solton Music Germany Teufel Germany Willi Studer Germany Elina S.A. Greece Soza Manufactures Greece R & S Electronics India Chario Loudspeakers Italy Oyster s.a.s. Italy Acoustic Control Mexico A.J. van den Hul Netherlands Duran Audio Netherlands Omnitronics Netherlands G & L Norway Volvo Sweden Volken Engineering Switzerland Magnepan USA Marantz USA Snell Acoustics USA Sterling Sound USAQUOTES FROM CALSOD REVIEWS
From Elektor Electronics, 1 Harlequin Avenue, Brentford TW8 9EW, England. (c) Copyright 1989. All rights reserved.
"The redesign feature of the program was tested on existing loudspeaker systems. Remarkably, CALSOD's computed response was found to correspond exactly with the measured response."
"CALSOD is capable of optimizing the complete system, working effectively towards the realization of the target response."
"CALSOD is a well-designed and remarkably practical program that will prove invaluable to the designer ..."
"... this tool greatly simplifies formerly often tedious and time-consuming work."
"The optimizing procedure can provide really good results, and the options for analysing a complete system are unique."
"... the program performs a lot of slick tricks. One of the more spectacular of these is allowing the designer to specify the location of driver acoustic centers using an XYZ coordinate system."
"The User Manual is well written and adequately describes the various program functions and contains an excellent tutorial example, which demonstrates the use of the program."
From Vance Dickason, Voice Coil, PO Box 176, Peterborough, NH 03458, USA. (c) Copyright 1988. All rights reserved.
"Obviously, CALSOD is an extremely flexible tool that will allow you to move into many uncharted areas, and perform the kind of system modelling which has never before been possible on a desktop computer."
From Dick Olsher, Stereophile, 208 Delgado, Santa Fe, NM 87501, U.S.A. (c) Copyright 1990. All rights reserved.
"I cannot imagine tackling another speaker project without such a computer-aided design tool as CALSOD."
"CALSOD includes an outstanding user's manual. It is extensive and worth its weight in gold. There are plenty of design examples, proceeding from the simple toward the complex. Installation, the structure of the program, the input file format, and all of the input modules are very well explained."
"CALSOD enabled me to narrow down the field from a bewildering array of crossover possibilities without having to spend time and money chasing down dead ends. It is a fantastic design tool that affords the speaker builder flexibility and design sophistication previously available only to industry giants."
"Listening tests and measurements with the Neutrik system confirmed that CALSOD's predictions were quite close to the mark."
"This is a mature and polished program, a product typical of what one would expect from a large software-development house."
"The real potency of CALSOD lies in its ability to optimize the summed acoustic response of the entire driver array."
More information:New features in 3.10 compared to 3.00.
New features in 1.40 compared to 1.30.
CALSOD 3.10 compared to 1.40.
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