Looking for more information about fullrange drivers, I found the Mathcad worksheets by M.J. King and decided to try a speaker design of my own. My first try was a speaker using the Fostex FE167E, but I never made proper cabinets for them because my wife said "No way, they are too big". Searching a smaller driver the Fostex FX120, a 12 cm fullrange unit caught my eye. There is not much information available for this driver, but the feedback from people who have used was positive. On the Fostex data sheet they show a flat frequency response without great peaks and drops.

1 Section 6.0 : Design of a Front Loaded Exponential Horn For a couple of years, a front loaded horn MathCad worksheet was available for downloading from my website. The worksheet was derived to simulate the front loaded horn geometry shown in Figure 6.1. The model solved the equivalent acoustic and electrical circuits as shown in Figures 6.2 and 6.3 respectively. A unit input of 1 watt into an assumed 8 ohm voice coil resistance, was applied as a constant voltage of volts RMS. There were minor updates to this worksheet over the years to extend the scope and correct a few minor bugs. At this point, a complete analysis of the equivalent circuits could be performed and the derivations would drag on for many pages. But this type of analysis, while providing some very useful sizing and limitation relationships, would probably not provide any intuitive feel for the workings of an exponential front loaded horn speaker. So instead of a rigorous mathematical derivation, which can be found in a number of other excellent technical references, the understanding gained in the preceding sections will be used to produce a set of simulations intended to characterize how a front loaded exponential horn works and what trade-offs can be made to optimize the final system performance. In all of the following simulations, it was assumed that the cross-sectional areas are circular. Square and rectangular cross-sectional areas will have to be examined later in a separate study. Probably the most important results presented so far are the resistive nature of the acoustic impedance of the horn and the potential for a large increase in the volume velocity ratio Ε above the lower cut-off frequency f c. This means that the front of the driver is radiating into a pure acoustic resistance that is a function only of the air density, the speed of sound, and the horn throat area. ρ c Z throat = S 0 Keeping this in mind, while looking again at Figure 6.1, we are left with a driver mounted in a closed box radiating into an acoustic resistance. Once the horn speaker system is recognized as being a driver in a closed box radiating into a pure acoustic resistance, the design problem can then be split into two separate sub-systems. Sizing the driver in a closed box as one sub-system and mating it to an appropriately sized exponential horn as a second sub-system will be the approach used in the following simulations. The two sub-systems are consistent if the same tuning frequency is used. A consistent design mates a driver in a closed box with an exponential horn geometry where both have the same tuning frequencies. This last statement is an important definition that will be assumed throughout the remainder of this document. The resulting motion of the driver s cone, the driver s volume velocity, is amplified by the horn to become an even greater volume velocity at the horn s mouth. This result produces a dramatic increase in speaker efficiency compared to a closed or ported box. Looking back at Figures 5.2 through 5.5, there is no evidence of strong resonances in a correctly sized horn which would be seen as peaks in the magnitude response and rapid Page 1 of 26

Martin King Mathcad Worksheet