MANUAL.HTM --- Manual for Driver Parameter Calculator --- by Claus Futtrup.
Created 10. February 1996, last revised 15. June 2004. Ported to XHTML 1.0 on 2. October 2004. Last modified 27. October 2004.

        Sections of this manual have been exported into separate
        .HTM files. README.HTM is the part you should read first.
        Then read the INSTALL.HTM for installation instructions.

        If you have been using a previous release of DPC, then read the
        HISTORY.HTM for a short description of changes/enhancements.

Table of Contents:

  1. How to use the Driver Parameter Calculator
  2. Let Driver Parameter Calculator Assist You With The Measurements
  3. Format of Database for Driver Parameter Calculator
  4. Configuration of the Driver Parameter Calculator
  5. Description of the various parameters
  6. Parameters not supported by Driver Parameter Calculator
  7. Example showing the power of Driver Parameter Calculator

How to use the Driver Parameter Calculator

Driver Parameter Calculator is a simple program to enter and calculate loudspeaker driver parameters for loudspeaker box calculation. This indirectly means that some of the parameters in Driver Parameter Calculator are related to drivers only, for which a box can be built.

The calculator is powerful because it continuously checks whether the entered data can be used to calculate further values. At Exit (and on request) the calculator will extensively check whether the entered data makes sense, which means that the calculator will only accept driver data of high quality, at least when it comes to the important ones, like the Thiele-Small parameters. Some of the data are descriptive only, and cannot be checked.

Driver Parameter Calculator is intended for Electrodynamic Transducers only, ie. no electrostatic speakers etc. Basically the transducers must be intended for box mounting (provided with Thiele-Small parameters). A basic description of this speaker concept is available in BASICS.HTM, which I hope most readers will find enlightening, educational and/or informative. To the educated reader this will be well known information, but nonetheless it can be quite giving to rethink how drivers work. Furthermore a short piece of history has been placed in INVENTOR.HTM, which is supposed to spread light on the invention of the electro-dynamic principle in 1915.

Starting Driver Parameter Calculator you will see the following menu:

        1.  Calculate from measurings
        2.  Create new data entry
        3.  Edit existing data entry
        4.  Load DriverData from disk
        5.  DPC documentation
        6.  Change setup
        7.  About DPC
        0.  Exit

Item 1 is for assistance with measuring driver T/S parameters and DPC will do the calculations for you.

Item 2 is for deleting the existing data and start with a new initialized, blank datasheet.

Item 3 is for re-entering the parameter calculator. This is convenient in case you have either loaded a .DPC datafile, or if you have previously exited the data editor to change setup and would like to study the same driver with different units.

Item 4 is for loading driver data parameters from disk into DPC. In the data editor it is possible to save the data to a diskfile, these files can be reloaded into DPC, files from other software is not supported. Loading a driver will delete whatever data is present in the data editor.

Item 5 is for loading the DPC documentation into your web browser.

Item 6 is for changing the setup regarding displayed digits, units and conversion factors (to SI-units) as well as changing some constants "on the fly." If you choose item 6 you will see the following menu:

Item 7 shows the usual Windows about box.

  1. Change custom digits: euro.dig
  2. Change custom units:
  3. Change (edit) setup files
  4. Specify air properties
  5. Change USPL voltage: 2.828 V
  6. Change gravity : 9.81 m/s2
  7. Reload dpc.ini

If you select item 4 in this menu you will be asked for new information on the following constants:

        rho : the density of air (1.29 for dry air at 0 deg. Celcius
              and normal pressure, 760 mm Hg = 0.76 m Hg).
        c   : the speed of sound (331,4 at 0 deg. Celcius etc.)

These constants depends on several factors, but for simplicity L. L. Beranek wrote in his classic book "Acoustics":

        rho = 1.29 * (273.15 / T) * (Pa / 101325)

        c = 331.4 * sqrt( T / 273.15 )

T = Temperature (in Kelvin)
P = Pressure (in Pascal)

These formulas are approximative. The nature of air also depends on its mixture of nitrogene, oxygene and argon, plus water, carbondioxide and other minor contributors (all other gases that are in the air). You can explore these relations in AIR.HTM (somewhat academic).

Driver Parameter Calculator gives you the alternative option to specify air temperature, pressure and humidity to calculate rho and c. This is beneficial when calculating sensitivity levels and driver efficiency, no, because you can read temperature, pressure and perhaps also humidity and hereby increase your precision. Surprisingly this is not important when you want to measure a driver and determine Cms. Humidity is calculated from a model of the behaviour, described in AIRMODEL.HTM, which gives you a usable temperature range in DPC from -100 degC (-148 degF) to 200 degC (392 degF). This is sufficient for car-fi people, and almost any other common situation.

Although the model is currently running with these limits, it may not be valid this far up/down in temperature. At temperatures below freezing, H2O changes to the solid phase, and at minus 80-something degC the CO_2 will freeze too. The work will only be continued if it is asked for. Similarly unusual things may happen at high temperatures that I have not accounted for.

Also the air is in fact not linear compressible, but that is another story, and also a factor that can be neglected at normal sound pressure levels. This is treated in BOX_AIR.HTM (also somewhat academic).

Entering data

Driver Parameter Calculator does not require that all parameters are entered, but expect to find the following data (to get a description of the data - see FORMULAS.HTM):

If the above data are not entered/calculated, then Driver Parameter Calculator will not accept the entered data, ie. the data cannot be saved to a diskfile. You can choose between Quit and Continue. This is so because this information is essential for box calculations. The description is essential for your own information (and to the database which may show up in the future) - without a description the data are worthless. If a future database will include tweeters and midranges with fixed rear chamber, then the requirement for Cms may not exist in future releases.

The calculation of further values implies the following data connections. Given the other, one unknown parameter can be calculated:

This seems to be sufficient to ensure a high quality driver datasheet.

The most frequent used parameters are fres, Bxl, Re and Mms, then comes Qe, Qm, Sd, Cms and Res. The parameters Depth, Df, EBP, fLe, fmax, fpist, Gamma, KLe, Le, MagDpt, Magnet, Mcost, Pe, Pn, SPLmx, VCd, Vd, Gloss and Znom are used once (and can be recalculated by setting them to zero).

The air parameters can be changed while a driver is loaded. If you do so, and have specified parameters dependent on the air, like Sd, Vas, no or SPL etc. then you must delete your entries, or DPC will not accept to save your data entry.

Of course all these connections can create a big headacke, when trying to enter as many data as possible, because all of a sudden Driver Parameter Calculator may be capable of calculating some values, which does not match your entered data (or it can calculate the same data twice, with different results). Please let the program calculate as many data as possible. From the above list you can see, that some of the most important figures when measuring loudspeakers are:

Furthermore you must make sure that Qt can be calculated (you could enter it directly and let the program calculate Qe!). That is why it is important to either enter Qe or have it calculated by entering some other data, preferably:

If you enter Qe as suggested above you can calculate either Re or Bxl (by entering either one of them, perhaps provided by the manufacturer). This will provide you with a full set of specs, because all the important data can be calculated now.

When entering the above mentioned parameters it is important that you enter the MEASURED values first, because these are (or should be) the exact data, or at least as close as possible. Here it is important to consider how precise your measurements are - 1% to 5% is acceptable in my opinion, but do not try to enter very inaccurate data, the rest of the data will be calculated based on your entries and degrade the value of the data considerably. You must be very careful with your measuring equipment and the setup. See section "How to Measure Loudspeakers for the Driver Parameter Calculator" in MEASURE.HTM.

If you are confused as to what to enter and always gets the message saying that the Driver Parameter Calculator cannot save your data, then you can try to enter the following data only: fres, Re, Sd or Dd, Bxl or Mms, two of Qt, Qe and Qm. You will get a driver that can always be saved. Remember to check whether it represents your driver before saving it. Also remember to enter the descriptive parameters.

Please note that there is no calculation nor check on the following data entries:

These figures are provided for general information, they are descriptive parameters. These parameters are not used, when calculating boxes, but can be very helpful when determining the large signal behavior of a system (ie. they are important for the evaluation of a given design). Or they can be helpful when designing your box etc.

Specially for NomDia, two methods (rule of thumbs) are implemented, for guessing / suggesting the drivers nominal size. The simplest rule of thumb originates from J. R. Ashley. It says that the effective piston radius in centimeter equals the advertised size in inches. This converts to the equation NomDia = Dd/2 * 2.54 = Dd * 1.27. The more direct rule of thumb is that NomDia = Outer. Ashleys rule of thumb is reasonably true even for tweeters, but the alternative method is more correct for woofers and this method has higher priority of the two methods. There is no rounding of the figures. All rounding of figures is handled by the display (by changing .DIG as desired), and in this respect NomDia can be interpreted as another display of the Outer descriptive data. The full precision ensures that conversion between units works flawless and that no digits of precision is lost. Notice that no error correction is implemented on this value. The user can set the nominal size to any value, but keeping the set value at values around at least one of the two suggested methods will ensure that the NomDia spec is within normal conventions.

Specially for Znom, there is a calculation performed, based on Re. It is assumed that Znom is typically an even number about 1.5 times Re. For very low Re values, say 1.8 ohm, the nominal impedance level can be an odd number, in this case Znom = 3 ohm. This is only meanth as a suggestion if you specify Re and not Znom, and depending on the driver quality it may become wrong, eg. if high Rms and therefore low Qm values are present, or if a driver is not in compliance with minimum-phase. There is no error-checking on this parameter. If a false Znom value is bugging you, simply overwrite it by specifying the correct value.

Also specially for Le, KLe and fLe there is a relation between these 3 parameters:

This means that they are tied together so that if 2 are specified the 3. will be calculated, and you are not allowed to alter a calculated value. You'll have to zero one of the parameters (at least) to be able to alter another.

The sizes are defined as follows:

                                          Depth   Thick
                                        |         | |
             +  - - - - - - - - - - - - | - - - - +-+
             |                          |         | | - - +
             |         + - - - - - - - -|- - - - //      |
             |         |         +  - - ++--++ // |      |
             |         |         |      ||  ||/   |      |
             |         |         |      ||  ||____|      |
           Outer    Basket    Magnet    ||  ||____|    BoltD
             |         |         |      ||  ||    |      |
             |         |         |      ||  ||\   |      |
             |         |         +  - - ++--++|\\ |      |
             |         + - - - - - - - -|- - |+- \\      |
             |                          |    |    | | - - +
             +  - - - - - - - - - - - - | - -|- - +-+
                                        |    |

Not all console setups (keyboard and display font mappings) will show this picture properly. For example this is the case if you are using 850 Multilingual (Latin I) setup or 852 Slavic (Latin II). Try to switch to another setup like 437 English, 860 Portugal, 863 Canadian-French or 865 Nordic. On the parameter screen a square-root may also show up, but only if you use a code page which supports this character (ALT-251).

For box design you will need:

With these parameters (excluding the Basket diameter) Driver Parameter Calculator calculates the volume that the driver occupies inside a box. This volume is called Dvol (Driver volume). If all the sizes are not known, Driver Parameter Calculator will approximate Dvol in a simplified manner suggested by L. L. Beranek, which is entirely based on Outer, the outer diameter of the driver (Beranek used the nominal size of the driver).

For dome drivers, DPC supports the following definitions:

             +  - - - - - - - - - - - - - - -++
             |         + - - - - - - - - - -+||  - - +
             |         |         +  - - ++--++|      |
             |         |         |      ||  |||      |
             |         |         |      ||  |||\     |
           Outer    Basket    Magnet    ||  ||| |  BoltD
             |         |         |      ||  |||/     |
             |         |         |      ||  |||      |
             |         |         +  - - ++--++|      |
             |         + - - - - - - - -|- - ||  - - +
             +  - - - - - - - - - - - - | - -++
                                        |    |

Notice that in this case Depth should be = MagDpt - and that is all you need to do to have DPC calculate on a (tweeter/midrange) dome for you instead of the traditional cone-driver. This is not a totally true situation since you'll often find a chamber behind the magnet and a butterfly in front of the magnet. These contribute to the total depth of the driver but must be included in MagDpth to make DPC calculate the Dvol volume of the dome.

If you specify Depth larger than MagDpt, then this dome design is not assumed. If you specify Depth smaller than MagDpt you get an error-message. Any rear chamber associated with the rear of the dome is included in the Depth and MagDpt parameter. Basket diameter = hole cut diameter (excluding terminals).

When Dvol is calculated, and MagDpt and/or Depth is to be calculated (because Dvol was specified), then the cone design is assumed by DPC.

For calculation of volumes from various shapes, among these the volume of a driver with conical diaphragm, see VOLUMES.HTM distributed with Driver Parameter Calculator.

This size is included as well and it is used for calculating fpist.

Determining the large signal behavior requires a connection between no, Pe and Xmax, but this depends on the box design and must be established by the box calculation software. It will not be provided in the future for Driver Parameter Calculator. On these parameters you must rely on the entered data.

Also power compression cannot be taken into account when estimating SPLmx, since it requires knowledge of the heat dissipation of the driver. This I will let up to the box calculation software as well. See POWER.HTM for more information on this issue.

In Driver Parameter Calculator it is assumed, that the power compression is 3 dB at full power to get a more realistic value than if the power compression had been neglected entirely. This does not put any drivers in favour, though.

Driver Parameter Calculator does not generally support Dual voice coil drivers. It is possible to specify a number of coils different from 1, indicating multiple coils, but it is a descriptive parameter meaning no calculations will be performed on this information. The parameters in DPC must be given for all coils operating electrically in parallel, or alternatively you can specify Number of Coils : 2 (series) to indicate that the data is given for the coils connected in series.

When entering the decimal separator you can use either . or , because the Driver Parameter Calculator will find all commas and convert them to dots. This makes data entry easier on computers with comma at the numeric keypad.

Driver Parameter Calculator is made to calculate one single driver. If you want to use multiple drivers in a project, then the properties of such drivers can be lumped into parameters for a single driver, see MULTIPLE.HTM for how to do this. It is assumed that the multiple drivers are of the same type.

Let Driver Parameter Calculator Assist You With The Measurements

If you choose to build a box for testing the driver, then Driver Parameter Calculator can assist you with the calculations and put the found values directly into the same menu as used for entering new data. With the data found during this calculation all other parameters can be calculated - except, Driver Parameter Calculator cannot quantify the electric powerhandling Pe and therefore cannot calculate SPLmx (the maximum Sound Pressure Level that the driver can provide). Pe is not a value that you normally measure yourself - for precise figures you must perform a destructive test. My advice is to enter the value given by the manufacturer. SPLmx is assuming that the radiated sound is almost linearly proportional to Pe, and that at full power the compression will be approximately 3 dB (for a wide variety of drivers it will be in the range 2--4 dB).

You do not need Pe, though. All you need to enter is a description of the driver and the data are ready to be saved. Since this method implies that you have performed some measurements yourself, I would be very happy if you would enter the Provider as well for the database - the provider is your name, or alternatively your company-name. Furthermore you can specify the date you measured and other useful stuff in the Provider field.

The way to let the Driver Parameter Calculator assist you is by choosing menu item 1 "Calculate from measurings" from the mainmenu and you will enter the following sub-menu:

        1.  Calculate Qm and Qe
        2.  Calculate Vas, Cms and Bxl (Closed Box method)
        3.  Calculate Mms (Added Weight method)
        4.  Calculate Le
        5.  Display Calculated Data
        0.  Exit

The important ones are menu item 1 and 2/3, while menu item 4 can assist you in calculating Le, using the method described in the MEASURE.HTM section.

The advantage by using the Driver Parameter Calculator for assistance is, that this software uses a more precise method than given in almost any other textbook. The closed box will have leakage losses etc. no matter how hard you try to make it perfect. The advanced method (the Carrion-Isbert method) takes losses into account. See the MEASURE.HTM section.

You should select between item 2 or 3, not both. The Added Weight method will give you an alternative way to calculate driver parameters instead of the Closed Box method. This method is also described in MEASURE.HTM. If you accidentally use both, Driver Parameter Calculator will alert you with numerous inconsistencies and you will be forced to delete either Mms or all of Vas, Cms and Bxl (if you kept Mms they will all be calculated by Driver Parameter Calculator). This inconsistency appears because, obviously, the two methods does not give you the same result.

If you want your data printed, I suggest you use PrtSc (Print Screen) on your keyboard. If you have entered the measured data into the Driver Parameter Calculator and gotten to menuitem 4. (Display Calculated Data), push PrtSc.

Using the closed box method, Driver Parameter Calculator will return Vas, Cms and Bxl. Either Cms + Bxl or Vas makes this "overdetermined." As long as you do not change the air properties, you will be fine. If you change either rho or c (or both), DPC will tell you, that there are some inconsistencies. In this case you must delete (zero) either Vas or Cms + Bxl. DPC cannot tell you which ones to delete and which to keep, it depends on what you did and want to do:

        * You measured the driver in box and was thrown into the
          parameter editor, but suddenly realize that the rho and c you
          specified for your measurements are wrong. In this case you
          delete Cms + Bxl.

        * You changed rho and c to fit your measurements, but now you
          want to change the parameters to fit a different weather
          situation (eg. the situation that is most likely to appear
          while you play music). In this case you measured Vas the
          correct way, and Cms is right---delete Vas (it will change
          when rho and c changes).

The second situation is handled automatically by DPC - since whenever you have locked Cms, Vas and Sd, but chooses to change the weather situation, then Cms and Sd is kept unchanged. Only the first situation above requires special user-attention.

If you ran into both problems above, set the constants appropriately and reenter your measurements into DPC. When finished you may want to do the latter mentioned adjustments, for Vas to fit the most likely weather situation.

Format of Database for Driver Parameter Calculator

Driver Parameter Calculator is intended to become a database, preferably accessible from the Internet. I have no idea how to do this, yet.

For now a "Save and Exit" option is available. Besides you can load the file back into DPC. Saving the data into an ASCii file will retain your data for future reference. The file format is described below. It is a compromise between readability from a users viewpoint and a computers viewpoint, and completeness.

1. The first line contains a header, which tells you "program name" and "release" version ID.

2. Then comes what air properties (c, rho and humidity values) are valid for the saved data + what USPL_Volts value is valid.

3. Then comes the descriptions (text strings).

4. The file contains the descriptive data in the actual units that were used + units information + digits information. All data are written, even if they are zero, to retain unit information for that parameter.

5. Finally it contains the data with interrelations. The layout is similar to item 3, but either an '*' or a '-' separates units and digits information. This tells you whether the parameter was specified by the user (*) or was calculated by Driver Parameter Calculator (-).

The lines are comma-separated, and the look is "rugged," ie. not intended for reading or printing.

When selecting "Save & Exit" you get an alternative option of creating a report. This report is suitable for reading and printing. Please see REPORT.HTM for further information.

Please remember that Driver Parameter Calculator will only expand, if sufficient feedback is given from the users.

Configuration of the Driver Parameter Calculator

You can configure Driver Parameter Calculator through DPC.INI. Here you can enter which units-file to use as well as some constants used for the calculations. DPC contains an USPL_Volts constant, which will affect how Driver Parameter Calculator calculates the voltage sensitivity USPL. The USPL_Volts constant may be changed in the DPC.INI setup file as well as in the main menu item 6, change setup. Besides the constants are 1) The air temperature 2) The air pressure 3) The humidity in the air. These values changes from day to day, but depending on your location they have a mean value and a standard deviation. If you want to improve on your loudspeaker designs you should try to find these values and include the mean value in DPC.INI. You should get different Vas and SPL figures. The last constant is the gravity, which can also be changed.

When measuring drivers you should read the temperature and air pressure, calculate the values for c and rho and enter these values into Driver Parameter Calculator before measuring. Driver Parameter Calculator supports this calculation from mainmenu item 6, Change setup and submenu Specify air properties. A submenu gives you the option to specify temperature, air pressure and humidity level directly and let Driver Parameter Calculator do the calculations for you. Specifying humidity is not extremely important, but it can add a few extra percentage of precision. See AIR.HTM for further information. Doing this before measuring will provide you with a more accurate picture of your measuring conditions. You will not per se get a more accurate measure for Cms, because the method is insensitive to changes in rho and c, simply because the physical properties regarding Vb are changed similarly.

To configure which units to use in .CU files (CU stands for Custom Units), see the section on units below. Some CU-files are distributed with Driver Parameter Calculator. The .CU files contains a long list of specifications for each parameter used in the Driver Parameter Calculator for T/S parameters and other parameters. Besides, for temperature you can specify Celcius, Fahrenheit, Rankine or Kelvin as you desire. For rho (the air density) and c (the sound speed) you can also specify alternative units.

You can also configure, for your set of units, a set of digits to use with the units for proper display of the number. The number of displayed digits are configured in .DIG files, of which some are distributed with Driver Parameter Calculator---these should fit the above mentioned .CU files.

The .CU and .DIG extensions are by convention. Driver Parameter Calculator will read files with other extensions as well. If a file is chosen, which does not conform to the information that should be found in the file(s), then Driver Parameter Calculator will stop reading the file, and halt execution. The program will abort with an error message telling you in which file and on which line an error was found.

All figures in the DPC.INI file may be changed on-the-fly from main menu item 6, Change setup, including the USPL_Volts constant, but changing it will provide you with false units for USPL because this is specified in the .CU files. The changes of the constants cannot be saved to file, for permanent changes you must edit DPC.INI directly with a text editor. Most word processors works as text editors, but do not forget to save in the MS-DOS text format (the ASCii format). For your convenience the setup menu includes a menu item 3, change (edit) setup files, which will call the editor specified in DPC.INI for quick editing. Remember than any changes made this way will take permanent effect.

Driver Parameter Calculator uses 20 uPa (micro-Pascal) as the reference pressure. Alternatives are eg. to use 1 acoustic watt as a reference, but DPC does not have this option. The 20 uPa is hard-coded into DPC.

Description of the various parameters

Over time, various books have defined loudspeaker parameters with different mnemonics, eg. the parameter Mms sometimes is called Mas, perhaps because the author wanted to include air load, and to separate the mass from the one without air load, it was called Mas instead of Mms. Most authors use the electric equivalent circuit to define the name, whether it is Xes, Xms or Xas (electrical system, mechanical system or acoustical system):

Electrical Equivalent Circuit

I will try to explain the driver-model used by the Driver Parameter Calculator.

                Bxl                    Sd
    +- Re - Le -+|+- Rms - Mms - Cms -+|+- Ra - Xa -+
    |           |||                   |||           |
   AMP          |G|                   |T|           |
    |           |||                   |||           |
    electrical     mechanical            acoustical

Re and Le are known electrical parameters.

As a connection to the mechanical part serves the coil-and-magnet, which is expressed through the force factor Bxl. When a current runs through the coil, a magnetic field is generated, but the existing field B from the magnet is disturbed and creates a movement of the coil. In mathematical terms you can convert between mechanical and electrical parameters with a socalled Gyrator, it works like a transformer, and the transformation factor (scaling factor) is Bxl squared.

The reason for squaring Bxl is to be understood as a double-action from Bxl. When the cone is forced into motion, then F = Bxl * i, but when the cone is in motion, then the voltage -U = Bxl * v (v = cone velocity) is generated across the voice coil terminals. Both acceleration (ie. force) and velocity requires the Bxl factor.

Rms, Mms and Cms are known mechanical parameters.

Conversion of mechanical parameters to electrical parameters:

        Rms :   Res := Bxl^2/Rms
        Mms :   Ces := Mms/Bxl^2
        Cms :   Les := Cms*Bxl^2

The diaphragm serves as a connection between the mechanical and acoustical part. Mounted on top of the moving coil it transforms the mechanical movement into sound pressure. Here you can convert between mechanical and acoustical parameters with a transformer, and the transformation factor is Sd squared. For a better physical description of what happens, see BASICS.HTM.

Ra and Xa are acoustical radiation-load parameters. If the driver is mounted in a box, the radiation load changes. At low frequencies (relevant to driver data) the load is dominated by an air mass-load, which makes Xa an inductor. Ra is the acoustic radiation loss (given as a resistor), and is neglected by DPC for driver data calculations. See DATAINFO.HTM, section f4pi, or MEASURE.HTM, section mass load compensation, or section Air Load Compensation below for further details on radiation load.

When using this software to assist you in calculating Vas, changes in Xa is taken into account. After the calculation the Driver Parameter Calculator will display an electrical equivalent circuit (where all mechanical and acoustical parameters have been converted through the transformer and gyrator as described above). In the electrical equivalent circuit Xa including loss is displayed as Rl and Lb. The higher Rl value, the more loss you have in your closed box, Rl = 0 displays a perfect spring.

Please note that the Xa (which correctly is an acoustic capacitor) turns into an electrical inductor. This behavior relies on the Gyrator (and this is why it is not a normal Transformer). Similar behavior is found for the mechanical components, since a mass is a mechanical inductor, but converting it to its electrical equivalent it becomes Ces, which is a capacitor. The Gyrator is a socalled transconductance transformer.

Conversion of acoustical parameters to mechanical parameters:

        Ra :    Rma := Ra*Sd^2
        Xa :    Cma := Ca/Sd^2

You could also include:

        Xa :    Mma := Ma*Sd^2

but in the Carrion-Isbert method, influence from acoustic air-load on the driver diaphragm is neglected, or (more correctly) Mms is assumed to be constant whether the driver is in a closed box or in free air and therefore the air-load is directly included in Mms. It is not completely true that the air-load is constant, but the approximation is often used.

DPC supports air-load compensation. See section Air load compensation below for further information. When air load compensation is chosen, the Carrion-Isbert calculations are run a second time, with compensation of radiation load changes.

The electrical equivalent circuit, where all components are converted to electrical ones, and components of the same type are lumped together becomes (Carrion-Isbert, including box parameters Rl and Lb):

    + --Re--+----+----+----+
            |    |    |    Rl
           Res  Les  Ces   |
            |    |    |    Lb
    - ------+----+----+----+

Please observe that the Carrion-Isbert method is an approximation. For example Le is (as usual) entirely neglected, but mutual dependence (also related to Les and Ces) makes it wrong to calculate the parameters individually and then put them together to predict the result. Also, the model for leakage losses assumes that the contribution is not dominated by a single leak, since such a leak would be better to simulate as a bass reflex box with a lossy port. The advantage of the Carrion-Isbert method relies on, that it gives better approximation than the standard formulas, and still the data can be calculated by a straight-forward method.

A closed box for a measuring box is not a linear spring. The relations have been studied further in BOX_AIR.HTM and the conclusion is that you can completely neglect the nonlinear properties under normal circumstances. A measuring box can in real-life situations be considered a linear spring. You can see BOX_AIR.HTM for an academic in-depth discussion.

Air load compensation

Attached to the driver cone/dome there is an amount of air, which more or less sticks to the diaphragm, when in motion. This is the reactive part of the radiation load. The radiation load is dependent on the surroundings, ie. whether the driver is mounted in free air, in/on a wall, a horn, or in a type of box. In other words a closed box, eg. a measuring box, will change the mass of the moving part of the driver.

This is a problem when measuring Cms and Vas loudspeaker parameters with a closed box. Since many people have been neglecting this, and others who have used the added mass method have had other disadvantages, I really did never think that this radiation load could change things a lot - I mean, what does eg. 0.5 gram extra mass load mean for a large woofer. Apparently quite a bit, a 5% change of fcb is not unusual, with equal consequences for the other parameters (4-5% on Cms and Vas).

To compensate for this error 2 methods have been implemented, which can both compensate for the additional mass load by the test box. None of the methods have been tested for their validity, so it is up to the end user to try out the two methods and find out which one is believed to be the best method.

The two methods have each their advantages and disadvantages. Method 1 requires impedance data only, and is more simple to calculate (in theory). Method 2 on the other hand is a direct estimate approach which requires more calculations (by the computer), but is very simple to use.

For comparison it is possible to choose both methods, which gives the end user the advantage to compare the compensations by the two methods, and finally to have an average of the two methods calculated, which hopefully (if both methods works perfectly) will increase the accuracy of the measurements by averaging.

Sometimes it is not advisable to compensate. Most software which calculates loudspeaker cabinets does not include a method to change the mass of the driver diaphragm due to air load. If you are using such software, then my advise is to try to measure the driver parameters with extra air load in free air measurements, extra air load as if the driver had been mounted in the application box. The disadvantage is that your T/S data are tied up on the specific application.

Another (good) alternative is to compensate and save the data (for general purpose), then reload the data into DPC and alter Mms in accordance to the extra air load from the box. You'll need to have Bxl and Cms specified - and this implies that the Bxl and Cms data each are marked with an '*' asterix. This should be the case if you measured with the closed box method, but not if you measured with the added mass method - then you must let DPC calculate the Bxl and Cms values and then set the values manually to the specified value which "lock" them.

When Mms and Cms both are specified by the user, then fres must be set to 0 for DPC to calculate the new fres value. Further more you may have to set Qe = 0 and Zres = 0 if the closed box method was used because DPC over-specifies the parameter set when using this method.

What is happening is a change from locking on T/S parameters to locking on some physical driver parameters, which do not change when adding mass to the Mms.

This way all data, Bxl and Cms + Vas, gets correct and fres, Mms, Qt etc. will be correct for the given box application.

Technically speaking the following parameters are the T/S parameters:

The related mechanical/physical parameters are:

Both of the sets above are internally independent sets of parameters, but the two sets of parameters are mutually dependent.


The Driver Parameter Calculator can use any units desired by the user. Three unit files are supplied, EURO.CU, UK.CU and MKSA.CU. I suggest you copy the one you want to use to a file called DPC.CU and modify this instead of modifying the supplied files directly. You can specify in DPC.INI which unit file you want the Driver Parameter Calculator to load. The format should be "obvious" - you can edit the file with any text editor, and your result must be saved in MS-DOS text format. Ahead of an equality is the string that this software looks for (ie. never change this part) and behind it the new unit + a division factor (separated by colon).

In fact Driver Parameter Calculator in this way support any unit, if desired Driver Parameter Calculator can give you the result in average cubicinches buffaloshit per acre farmland in the US-state Rhode Island. Just do not forget to provide the conversion factor to SI-units and a short mnemonic description of your unit.

The Driver Parameter Calculator will continue to calculate everything in MKSA/SI-units, but the user will be allowed to enter the data as he/she sees fit his/her personal taste. The entered data will be divided with the factor from the datafile - and whenever the data is displayed, the factor will be multiplied again for proper display.

With this flexibility in units, it seemed necessary for the user to specify the number of digits displayed on the screen because significant digits changes when you want to display SI-units (which usually requires a lot of decimal places) compared to EURO or UK units (that are using moderate amounts of decimal places). Therefore Driver Parameter Calculator allows the user to specify a .DIG file for display of digits (each parameter is specified individually).

Driver Parameter Calculator comes with EURO.DIG, UK.DIG and MKSA.DIG that fits the above mentioned .CU files. Besides this a MAX.DIG is given, which displays maximum amount of digits---not comfortably in use nor very practical, but for demonstration purposes.

See DIGITS.HTM information on significant digits and the .DIG file format.

Some books uses two different sets of units for MKSA- and SI-units. This interpretation is naturally very personal/unnatural, and the distinction is not made in DPC. For example I have seen claims that SI-units are the absolute units, and MKSA the gravitational units, that uses Celcius degrees instead of Kelvin, centimeter instead of meter and kilogram instead of Newton. MKSA stands for meter-kilogram-second-ampere and represents the four independent units in the system of MKSA/SI-units.

I know there is a French system of units, named CGS (centimeter, gram, second) and somewhat outdated, apparently using Dyne instead of Newton. You are welcome to provide the author with additional information on this system (preferably premade .cu and .dig files), but I guess even the French people are into the MKSA/SI units.

Since I am not an experienced user of imperial UK-units or the differences to US-units, the specification in the UK.CU and UK.DIG files probably needs to be changed somewhat. When you have suggestions for changes, please contact the author.

Parameters not supported by Driver Parameter Calculator

There may of course be many parameters, which are not supported by the Driver Parameter Calculator. You have the option to write me a letter (email) and describe the parameter to me. Then I may write it into the source code and let future releases of DPC support the calculation.

There are some parameter, which I so far have chosen not to support with Driver Parameter Calculator:

Xmag : The driver excursion where the magnetic force from a given
       current is reduced to 71% of the value at rest. This parameter is
       given by the DUMAX measurement system, but I do not know of any
       software that utilizes this information, and I do not know of any
       other measuring equipment that supports measurement of this
       parameter. Therefore I tend to believe it is not widely accepted.
       I personally find it to be much more trust-worthy than then usual
       Xmax value, and information regarding the non-linearity of the
       motor system in one form or another could be very informative.

Xsus : The driver excursion where the suspension compliance has become 4
       times stiffer, ie. Cms is only 25% of its value at rest. This
       parameter is given by the DUMAX measurement system, but I do not
       know of any software that utilizes this information, and I do not
       know of any other measuring equipment that supports measurement
       of this parameter. Therefore I tend to believe it is not widely
       accepted. I personally find it to be much more trust-worthy than
       the usual Xlim value, and information regarding the non-linearity
       of the suspension in one form or another could be very

As far as I know the DUMAX measuring system picks either Xmag or Xsus (which ever is the smallest value) to be the specified Xmax value. This is not in compliance with the Xmax specifications for DPC or given by other providers of data (eg. loudspeaker manufacturers) as far as I know of. I would expect Xmag to be smaller than Xsus in all situations, perhaps I am wrong in special situations that I do not know of, eg. how about compression drivers.

Data from the DUMAX measuring system is not widely supported. I know of only one software package, which uses these data for calculation of distortion when simulating loudspeaker cabinets. The software is named Speak_32, by Geddes.

Finally, it is very easy to invent new parameters, but DPC does not support them at first. If you have a wish for support regarding a specific new parameter, then please inform me. Usually these parameters are new ways of looking at the same information, or simple figures of merit for the performance of a driver from a specific viewpoint. Such examples, which are not supported by the Driver Parameter Calculator, could be:

Gamma * Sd      = a figure of merit for the amount of air that is
                accelerated per ampere.

Mpow / Mms      = a figure of merit which could be named the power-
                acceleration factor (as opposed to Gamma, which is the
                current-acceleration factor) and is therefore
                independent of the nominal impedance level.

Driver Parameter Calculator supports some of these figure-of-merit values, eg. Mpow is such a parameter.

I can only recommend the DIY speaker builder to try to invent as many figure-of-merits as possible. They can help you to select the best possible driver for a specific application (only taking the driver parameters into account). If you find a very intelligent one (one that you find use for all the time), then please let the speaker building community hear about it.

Example showing the power of Driver Parameter Calculator

I hope that this example will illustrate the true power of DPC. I will use an old datasheet for Dynaudio 24W100 as an example. It comes with the following specs (2. February 1986):

Cms = 0.93 mm /N
Vas = 62 liter
Sd = 220 cm2

Here something goes "wrong" because this cannot be true with standard air properties. I can assume Cms = 0.918 = 0.92 mm/N and Vas = 63 liter. It becomes worse if you measure the cone, it is probably around 173 mm in diameter, so Sd = 235 is a better figure. Then if Cms = 0.93 you get Vas = 73 liter.

Mms = 30 g
fres = 32 Hz

Adding the Mms parameter gives you fres = 30 Hz, but if you follow the specified fres you get Mms = 26.6 g. Assuming fres = 31 Hz and Mms = 28.3 g is a compromize.

Bxl = 6.26 Tm
Re = 5.2 ohm
Qms = 1.6

When entering these I get Qe = 0.73 and Qt = 0.50. This is far from what the specs said:

Qes = 0.45
Qts = 0.35
Rms = 3.5 kg/s

I have Rms = 3.45, so that is reasonable. I tend not to believe the specifications from the old datasheet, DPC is much closer to a realistic value of Qe and Qt. By the way, the specs said that the sensitivity is 90 dB/W/m but DPC gets 87 dB/W/m. Mind you, the datasheet says that the Thiele/Small parameters are measured dynamically and not statically. I do not know what this implies, but it does not follow our Thiele/Small model and so it cannot be interpreted in a normal way.

I think this is a good illustration of how powerful DPC is. You enter some known parameters and DPC gives you the other parameters, based on the Thiele/Small model. It will locate any errors or possible misconceptions present in your datasheets. When you work with the Driver Parameter Calculator you can be 100% sure that the driver data is in compliance with the traditional Thiele/Small model.