BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) NAME boxdesign - enclosure design spreadsheet SYNOPSIS sc boxdesign.sc DESCRIPTION The boxdesign database for the sc spreadsheet calculator provides a simplified method of designing and simulating both sealed and vented box enclosures, given a minimal set of low frequency driver parameters (either the basic electro-mechanical or the _T_h_i_e_l_e-_S_m_a_l_l parameters). The cal- culator attempts to optimize the design of each for maxi- mally flat frequency response, and provides a comparison of frequency response, bandwidth and power handling and ulti- mate SPL between the two different enclosure types. Details of vent parameters are provided for vented-box designs. Pro- vision are incorporated for different box volumes. This particular system is based on algorithms outlined by Margolis and Small [1] for personal programmable calcula- tors, here implemented on a public domain spreadsheet calcu- lator for _U_n_i_x systems called sc, which is available from a variety of Usenet sources. It has also been implemented on a variety of other spreadsheet calculators as well [2]. If you are, in fact, using sc, it is recommended that this applica- tion be run with version 3.1 or later, as it has not been tested on any earlier versions. The database from the dis- tribution kit, _b_o_x_d_e_s_i_g_n._s_c, contains a sample driver illus- trating the basic principles. The spreadsheet is divided into 5 major sections, and each of these will be treated in turn below. In each section there may be one or more parameters that you can change, and many others that display resulting values. In most cases, data is entered and displayed in units that are convenient to the item being described, and conversion to standard units is handled within the spreadsheet database. This means that data such as diameter and excursion are entered in cen- timeters, and volume in liters, but internal calculations are based on standard MKS units. Some of the values are displayed in English units as well. Sun Release 4.1 Last change: April 19, 1987 1 BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) ELECTRO-MECHANICAL PARAMETERS In this section, you can enter the basic electro-mechanical parameters of the driver as follows: _E_f_f_e_c_t_i_v_e _c_o_n_e _d_i_a_m_e_t_e_r The effective projected diameter of the driver in cen- timeters. If not available from the manufacturer, it can be approximated by taking the diameter of the diaphragm plus two-thirds of the width of the surround. _M_a_x_i_m_u_m _e_x_c_u_r_s_i_o_n This is the maximum linear displacement of the driver to ensure less than 10% harmonic distortion, measured in centimeters. If unknown, can be set to .6 cm for high-compliance woofers. _B_l _p_r_o_d_u_c_t This is a measure of the electro-magnetic coupling in the driver, stated in either tesla-meters or (more appropriately to the problem at hand) newtons per amp. It is equal to the product length of wire in the mag- netic field (in meters) and the density of the magnetic field in the gap (in teslas). _V_o_i_c_e _c_o_i_l _d_c _r_e_s_i_s_t_a_n_c_e This is the total DC resistance, measured in ohms, that the system has to contend with. You might want to include the effective series DC resistances in the crossover, lead-in wires and so forth for maximum accu- racy. _M_e_c_h_a_n_i_c_a_l _m_a_s_s The effective mass of the driver, including air loads, in grams. This is not the same as the simple static mass of the driver (although it is related). _M_e_c_h_a_n_i_c_a_l _c_o_m_p_l_i_a_n_c_e The effective stiffness of the suspension, including the effects of the air load, in millimeters per newton. _M_e_c_h_a_n_i_c_a_l _l_o_s_s_e_s The total resistive losses in the system, in MKS mechanical ohms (kilograms per second). Many of these parameters will not be available from the manufacturer. In that case, simple move on to the next sec- tion, "Thiele-Small parameters". Sun Release 4.1 Last change: April 19, 1987 2 BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) THIELE-SMALL PARAMETERS This section displays the resulting Thiele-Small parameters derived from the electro-mechanical parameters entered above. If you have the Thiele-Small parameters already, you may enter those in the appropriate cells directly. (Note that this overwrites the equations needed to derive these parameters from the electro-mechanical parameters, so make sure you don't try to save the new template in place of the old one). To enter the Thiele-Small parameters directly, you must sup- ply the following: _E_f_f_e_c_t_i_v_e _c_o_n_e _d_i_a_m_e_t_e_r _a_n_d _M_a_x_i_m_u_m _l_i_n_e_a_r _e_x_c_u_r_s_i_o_n Both of these parameters are the same as those in the previous section, and can be entered in either section. _R_e_s_o_n_a_n_t _F_r_e_q_u_e_n_c_y This is the fundamental free-air resonance of the driver, measured in hertz. _E_q_u_i_v_a_l_e_n_t _v_o_l_u_m_e This is a volume of air(in liters) whose compliance is equal to that of the driver. If this parameter is stated in cubic feet, multiply by 28.3 to get liters. _M_e_c_h_a_n_i_c_a_l _Q This is the Q of the driver due to purely mechanical losses. _E_l_e_c_t_r_i_c_a_l _Q This is the Q of the driver due to purely electrical losses. All of the rest of the Thiele-Small parameters can be derived directly from these few, and there is no need to enter any more data in this section. Several other values are displayed here: _T_o_t_a_l _Q The Q of the driver due to all losses (mechanical and electrical). _R_e_f_e_r_e_n_c_e _e_f_f_i_c_i_e_n_c_y This is the total conversion efficiency of the driver, a measure of the how much of the electrical input power is converted to acoustical output. It refers, essen- tially, to the mid-band efficiency, which would be relatively unaffected by the low-frequency enclosure effects. This is the maximum available efficiency of the driver. Sun Release 4.1 Last change: April 19, 1987 3 BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) _O_u_t_p_u_t _l_e_v_e_l This is the expected output level of the driver into a hemispherical load, measured 1 meter from the driver, when driven by 1 watt of electrical input power. _E_f_f_e_c_t_i_v_e _a_r_e_a This is the effective projected area of the driver, measured in square centimeters. _M_a_x_i_m_u_m _d_i_s_p_l_a_c_e_m_e_n_t This is the maximum volume of air the driver is capable of moving. It is a function of the drivers effective area and its maximum linear excursion. Sun Release 4.1 Last change: April 19, 1987 4 BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) PERFORMANCE COMPARISONS This section provides a side-by-side comparison of the response characteristics of the closed box and vented box system designs. It compares certain performance parameters for the two systems: _E_n_c_l_o_s_u_r_e _v_o_l_u_m_e The net volume of the enclosure that was either calcu- lated by the spreadsheet, or that you supplied. -_3_d_B _f_r_e_q_u_e_n_c_y The frequency where the output of the driver is 3 dB below that of the midrange response of the driver. The speaker rolls of below this point. _P_e_a_k _r_e_s_p_o_n_s_e _r_i_p_p_l_e The amount of frequency response deviation from flat due to misalignment (intentional or otherwise). In a closed box system, it indicates the height of the "bump" in the response when the Q is too high. _M_a_x_i_m_u_m _a_c_o_u_s_t_i_c _o_u_t_p_u_t The maximum attainable output of the system (in acous- tic watts) at the point where the excursion of the cone is the greatest, measured at 1 meter from the driver. _M_a_x_i_m_u_m _S_P_L The same measurement as above, stated in sound pressure level, when the system is working into a hemispherical load. _M_a_x_i_m_u_m _e_l_e_c_t_r_i_c_a_l _i_n_p_u_t The amount of input power needed to attain the above acoustical maximums. When reviewing the power figures, it is important to realize what they mean. There are two driver parameters which limit the ultimate power output and handling capabilities of a loudspeaker system. First, there is excursion limiting. The woofer, because of limits in its suspension or motor system, cannot move enough air linearly to produce the needed acous- tic power. Secondly, there is thermal limiting. Most of the electrical power you put into a loudspeaker is dissipated as heat in the voice coil and if the voice coil is unable to rid itself of this waste heat faste enough, it may fail catastrophically. The figures quoted here are for excursion limitations only. They are determined by the worst case excursion found within the passband of the system. These values do not account in any way for thermal limitations and for excursion limits caused by signals below the cutoff frequency of the system. Sun Release 4.1 Last change: April 19, 1987 5 BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) In the case of closed box systems, the worst case excursion usually occurs at the system resonance, and improves above that point with the square of the frequency. This means that above a certain point, the power output is determined by thermal limits, and the below that, they are determined by excursion limits. Where that crossover point occurs is very driver and system dependent. In vented box systems, the worst case excursion occurs at the driver-enclosure resonance point, and drops dramatically as you approach the enclosure-port resonance frequency (where the excursion of the driver is at a minimum. Below that point, the driver excursion increases rapidly again. Here we run into the perennial vented box problem of little cabinet loading below the system cutoff. This implies that the excursion-limited power capabilities of a vented box system can be severely reduced when there is a large amount of sub-sonic noise present, causing large, nonproductive excursions. Limiting the bandwidth of the system with low frequency high-pass filters will substantially reduce these problems. In any case, it is important to remember that, within the passband of the system, these excursion limits are the worst case figures. The loudspeaker systems based on these designs are safe with amplifiers of considerably greater output capabilities than these figures might indicate. FREQUENCY RESPONSE In addition to these performance figures, the spreadsheet provides a point-by-point comparison of the frequency response of each configuration at a variety of frequencies. You can select the following measurement parameters: _I_n_t_e_r_v_a_l_s _p_e_r _o_c_t_a_v_e Determines the frequency resolution of the measure- ments. The most useful parameter here is 3, giving 1/3 octave response. _S_t_a_r_t_i_n_g _f_r_e_q_u_e_n_c_y Determines the lowest frequency that will be displayed. By setting these two parameters accordingly, you can display either gross response characteristics, or center around a specific frequency for detailed measurements. Sun Release 4.1 Last change: April 19, 1987 6 BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) CLOSED BOX DESIGN This section allows you to design a closed box system based for the driver parameters you have entered. You can design the system given one of two targets, either a specified sys- tem Q (and, therefore, a particular response characteris- tic), or a given size enclosure. There are three parameters you can set and change in this section: _D_e_s_i_r_e_d _s_y_s_t_e_m _Q This is the Q factor for the resultant system. If this value is non-zero and the desired box volume parameter is 0, then the spreadsheet will attempt to derive a design to meet this system Q. For maximally flat (Butterworth) response, a Q of .707 is appropriate. For critically-damped response, a Q of .5 is needed. This should never be set to less than the driver's total Q (shown in the Thiele-Small parameter section), other- wise impossible volumes might result. _D_e_s_i_r_e_d _b_o_x _v_o_l_u_m_e Set this parameter to non-zero if you want to see the effect of a driver in a given volume. Setting this value causes the desired system Q parameter and ***> the recommended volume to be ignored. _E_n_c_l_o_s_u_r_e _d_a_m_p_i_n_g This is a measure of the effect of stuffing the cabinet with differing amounts of acoustical damping. A value of 0 indicates no internal damping, while a value of 5 (the maximum) indicates a cabinet fully stuffed with 100% effective damping. Trying to damp the enclosure any further than this will result in loss of effective volume and no increase in damping. For typical selaed box cabinets with a loose filling of fiberglass, a value of 3 is reasonable. Once the appropriate parameters are entered, as described above, the spreadshee ***>t derives the rest of the system parameters: _R_e_c_o_m_m_e_n_d_e_d _b_o_x _v_o_l_u_m_e This is the volume needed, given the driver charac- teristics and enclosure damping, to achieve the desired system Q, if possible. If this value seems unimaginably large for your driver (say, 500 liters for a 6 inch woofer), it is probably because the desired system Q is lower than the driver's total Q. Short of reverting to techniques such as resistive loading or driving the system with a negative-impedance amplifier, there is little to be done to get a reasonable design, given the driver and the target response. This value is used in further calculations only if the desired box volume Sun Release 4.1 Last change: April 19, 1987 7 BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) parameter is 0. _T_u_n_i_n_g _r_a_t_i_o This is the ration between the driver compliance and the box compliance. _S_y_s_t_e_m _r_e_s_o_n_a_n_c_e This is the resonant frequency of the total system. _A_c_t_u_a_l _s_y_s_t_e_m _Q This is the resultant Q of the system, regardless whether the system was derived from the desired Q or the desired volume. -_3_d_B _f_r_e_q_u_e_n_c_y The frequency at which the response of the systemhas dropped to half of its mid-band level. _P_e_a_k _r_e_s_p_o_n_s_e _r_i_p_p_l_e The height of the peak above the mid-band response tdue to system having Q's greater than .707. The maximum output figure are discussed above. Sun Release 4.1 Last change: April 19, 1987 8 BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) VENTED BOX DESIGN This section designs vented box enclosures, given the characteristics of the driver. The spreadsheet will, by default, attempt to design an enclosure whose response approaches the flattest possible. The follwing parameters are displayed: _R_e_c_o_m_m_e_n_d_e_d _b_o_x _v_o_l_u_m_e This is the volume calculated by the spreadsheet to achieve the flattest possible response, given the characteristics of the driver. It will be used for sub- sequent design and pereformance calculations if the desired box volume is 0. _D_e_s_i_r_e_d _b_o_x _v_o_l_u_m_e You can set this parameter to some non-zero value to override the recommended volume in susbsequent calcula- tions. _T_u_n_i_n_g _r_a_t_i_o This is the ration of the driver's compliance to the box's compliance. _E_n_c_l_o_s_u_r_e _r_e_s_o_n_a_n_c_e This is the frequency the enclosure is tuned to to achieve the desired response. _R_e_c_o_m_m_e_n_d_e_d _v_e_n_t _d_i_a_m_e_t_e_r This is the diameter of a circular vent need to ensure that, given the maximum displacement volume of the driver, no non-linearities will occur in the air moving through the vent. This figure is extremely conserva- tive, and somewhat smaller vent diameters can usually be used successfully. _D_e_s_i_r_e_d _v_e_n_t _d_i_a_m_e_t_e_r You can enter a different figure for the vent diameter here. There are several reasons for doing this. First, you may not be able to obtain a tube of the recommended diameter (tubing is usually available in only 1/4 or 1/2 inch increments). Secondly, the recommended diame- ter may result in a vent length that to far to long to be practical, so reducing the diameter may result in a vent that can fit in the cabinet. In any case, be sure to add the volume taken up by the vent to the net volume when building your enclosure. _V_e_n_t _l_e_n_g_t_h This is the length of the vent, presuming that it is mounted flush with a cabinet boundary. It is a good idea when building the cabinet, to make the vent a bit longer than recommended, then trim the vent to length, Sun Release 4.1 Last change: April 19, 1987 9 BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) measuring the performance of the system. This will account for slight deviations in driver parameters, box losses, and so forth. The rest of the measurement parameters are analogous to those in the closed box section. Sun Release 4.1 Last change: April 19, 1987 10 BOXDESIGN(1) USER COMMANDS BOXDESIGN(1) BUGS Many of the bugs are sc bugs. For example, when loading the database, many log math error messages are generated. This is because of the simple-minded re-calculation order built into sc. This in no way compromises the accuracy and the efficacy of the model, it is only a cosmetic nuisance. The algorithm for determining the vented box parameters is somewhat simple minded in that its only goal is to search for a maximally flat alignment. This may be desirable in most cases, but precludes designs optimized for maximum power handling/bandwidth products, or minimal excursion con- figurations, and so forth. Including these capabilities has the potential for severely complicating the model, destroy- ing the elegance of its simplicity. AUTHOR Dick Pierce 17 Sartelle Street Pepperell, Ma. 01463 REFERENCES [1] Margolis, G. and Small, R. H., "Personal Calculator Programs for Approximate Vented-Box and Closed-Box Loudspeaker Design," _J. _A_u_d_i_o _E_n_g. _S_o_c., vol. 29, no. 6, pp. 421-440, 1981 June. [2] Pierce, R., "A Novel Approach to Rapid Loudspeaker Design and Prototyping," (_u_n_p_u_b_l_i_s_h_e_d), 1987 March. Sun Release 4.1 Last change: April 19, 1987 11