GOLDMUND - Swiss Made High-End Audio Equipment

With the aim of ensuring the perfect functioning of our loudspeaker systems, we have implemented a modelling procedure enabling any component, as well as the whole systems themselves, to be under control.

This procedure allows us to be very efficient in case of driver and filter modification or replacement. On top of that, it allows any possible problems encounter by our dealers to be analysed with the aim of correcting them. Finally, it will constitute a sound theoretical basis for any of our future loudspeaker system development.

The procedure comprises 5 steps, which are explained below with examples:

1. Thiele and Small parameter measurements (added-mass method)
2. Preliminary calculations:
   • Electrical, mechanical and acoustical lumped-constant parameters
   • Input impedance, volume velocity and membrane displacement (infinite baffle, closed-box, vented-box,…)
   • First estimation of drivers and port radiating sound pressure
3. Crossover modelling and transfer function calculation
4. Modelling comprising crossover, driver and enclosure lumped-constant parameters:
   • Input impedance with and without cross-over
   • Volume velocities with and without cross-over
5. Final loudspeaker system calculations:
   • Introduction of the modelled filtered volume velocities into calculation code
   • Calculation of the loudspeaker system sound pressure in amplitude and phase, taking into account driver finite radiating surface and diffraction at the enclosure edges

To sum up, this procedure offers various possible loudspeaker response calculations, allowing our systems to be studied and analysed in different ways depending upon the application under consideration:

• Loudspeaker system input impedance (amplitude and phase)
• Electrical impedance at any location, like for example at the driver terminals
• Volume velocities in amplitude and phase (active and passive drivers, port,...)
• X-over transfer functions
• Sound pressure level valid in the near field as well as in the far field, and taking into account the diffraction at the enclosure edges (GTD and UTD methods)
• Sound pressure phase and group delay (active and passive drivers, port, loudspeaker system)

This well-known method enables the TS parameters to be measured without test enclosure. The measurement is carried out manually and/or automatically to ensure a high level of accuracy. The figure below shows an example of automatic measurement (Logos Sub active driver).

Coming from the average of several driver measurements, the TS parameters (R_e, L_e, f_s, Q_ms, Q_es, Q_ts, V_as) are finally compared with the constructor ones before being introduced in calculation code.

Firstly we need to determine:

• The force factor Bl
• The mechanical parameters linked to the mobile system: mass m_s, resistance R_ms and compliance C_ms
• The acoustic equivalent parameters of enclosure, port and losses due to leakage: C_ab, m_ap, R_leak
• The acoustical radiation impedance m_ar and R_ar

These lumped-constant parameters enable input impedance, membrane displacement, as well as drivers and port volume velocities to be calculated. According to the hypotheses of membrane coincidence and monopole radiation, they lead to a first estimation of drivers and port radiating sound pressure.

The figure below shows the example of the Minilogos calculation results:

• Drivers input impedances
• Drivers membrane displacements
• Port and drivers volume velocities
• Port and drivers radiating sound pressure estimated at 1W/1m

The above calculation of port and drivers sound pressure radiated at 1W/1m, enable the crossover cut-off frequencies and slopes to be estimated.

The figures below show the example of the MiniLogos crossover modelling and transfer function calculation.

The points 2 and 3 lead to the final system modelling. The latter enable the filtered input impedance and volume velocities to be calculated.

The figures below show the MiniLogos final modelling and the resulting calculated filtered input impedance and volume velocities:

The modelled volume velocities of drivers and port are introduced in calculation with the aim of calculating the sound pressure radiated by the loudspeaker system.

The sound pressure is then calculated in amplitude and phase taking into account the driver finite radiating surface, the drivers and port locations in the enclosure and the diffraction at the enclosure edges (GTD / UTD methods). The figure below shows the MiniLogos sound pressure level at 1W/1m with and without box edges diffraction calculation:

The irregularities are calculated in order to compensate those of the driver ones. Thus, in case of a new loudspeaker system development, it is necessary to measure the driver frequency responses (baffle assembly). It is also necessary of course to measure the final product in an anechoic chamber in order to validate the calculation procedure.

Finally, it should be noted that the sound pressure phase derivative enables the group delay to be calculated with a great accuracy. This last loudspeaker response is very important for the development of in-phase drivers and analysis of fast response systems.