OPTIMISING THE DDD DRIVER
The DDD driver utilises a powerful ferrite magnet of our own design together with an under hung voice coil. The magnetic strength in the gap is approximately 1.2 Tesla. This gives the DDD driver a sensitivity that is on a par with that of conventional cone drivers of similar dimensions. The very high magnetic strength in the gap also provides a useful increase in efficiency in the upper two operating bands.
The linearity of the DDD driver’s magnetic circuit – a parameter that is crucial to the performance of any dynamic driver – is also extremely high and we believe it to be one of the best in the industry. This ensures that the force that the voice coil produces to drive the cone very accurately follows the input audio signal.
To limit the moving mass, the weight of the voice coil must be minimised, consequently the upper frequency limit and maximum power handling become issues. In early prototypes, the upper frequency limitations posed quite a challenge. Today we achieve a power handling capacity comparable with that of conventional woofers by using a voice coil constructed with flat wire that is wound on its edge, allowing an extremely densely packed winding and also by completely enclosing the coil within the magnetic structure, which then serves as a more efficient heat sink for the voice coil.
Controlling the Cone
In any driver of this type you want the motion of the cone to precisely follow the electrical signal that drives it. You do not want the cone to ring. This is where the cone continues to move after the impulse that excited it has finished. Essentially perfect control of the cone and an absence of ringing are easily achieved when the wavelength of the frequency propagated down the cone is greater than the length of the cone itself. It is difficult when the wavelength is shorter, since the full wave is reflected from the boundary of the cone – this is where the end of the cone opposite the voice coil is mounted to the driver chassis. The reflection will in turn produce re-reflections as the travelling wave slowly loses energy over the course of several wave cycles. Imagine small ripples in a pool and how they are reflected back from its edge in a recurring pattern. The behaviour of a rippling cone is precisely the same, as the motion tends to persist for a considerable time, which ultimately has the effect of obscuring the information being reproduced.
Our own approach to this problem is two pronged. Firstly Dicks found that bending waves disperse, i.e. the DDD driver cone exhibits an increasing velocity of propagation of waves (more correctly termed phase velocity) with increasing frequency and he was able calculate the velocity of propagation in the cone as a function of frequency and therefore determine at what frequency the velocity of a wave in the cone reached that of sound in air. This is called the Coincidence Frequency. At this frequency the waves start to detach from the cone’s surface at an angle given by the ratio of cone-speed to air-speed. A few Hertz above the Coincidence Frequency the detachment angle is close to zero, but with higher frequencies the elevation approximates to 90°. The detachment of waves from the cone describes the functional principle of the bending wave radiator. Secondly he devised an effective means of balancing damping of the cone and the characteristics of the cone termination in order to minimise the residual ringing in the cone.
The calculations required to determine this were extremely involved, which is why to the best of our knowledge, no one prior to Peter Dicks had been able to devise and solve the necessary equations. Whilst the DDD driver’s cone looks like a simple enough shape, this is deceptive because the behaviour of waves in the cone is anything but simple. Not only does the cone exhibit dispersion (different frequencies travel at different speeds), but the stiffness of the cone is not constant along its length. In fact it decreases as you move from the peak to the mouth (open end). Consequently the velocity of a wave in the cone is proportional to frequency and inversely proportional the distance from the cone’s peak.
We use both titanium and carbon fibre for the cone material. Both materials have a high velocity of propagation in their bulk form. The velocity of propagation is especially high when they are formed into a very steep, thin walled cone. As mentioned above, the velocity of propagation in a cone varies along its length, being highest at the peak and slowest at its mouth. This means that the upper part of the cone reaches the Coincidence Frequency much earlier than the lower part, and additionally, in the lower part the wave lengths are shorter and all the waves are denser and therefore more efficiently radiated into the surrounding air. This higher efficiency of radiation means that there is less energy left in the cone to be reflected at the termination (i.e. the surround) and by maximising the amount of energy being radiated a more simple form of termination for the cone may be used. This is important as the reflections would otherwise cause ringing in the cone. The theoretical way to eliminate this would be to ensure that all the remaining energy in the wave was absorbed by the termination, but this can only be done by having a termination that is the complex conjugate of the cone’s impedance and this cannot be physically realised.
Another advantage of the DDD driver is that because it produces bending waves in a wide frequency range above the bass region, movement of the cone caused by bass signals produce almost no Doppler distortion, the bane of conventional loudspeakers.
The material used for our titanium cones is 0.025 mm thick and for our carbon fibre cones it is 0.15 mm thick; very thin indeed. These materials in their sheet form are very delicate and must be handled with great care. Once formed into a cone they become more manageable. Nevertheless, assembling a DDD driver is a slow and pains taking process that can only be performed by skilled technicians. We have experimented with even thinner materials, but have found the resulting structures extremely fragile and have concluded that the present dimensions give the best compromise between efficiency and performance on the one hand and strength and maximum power handling on the other.
With its current dimensions, the DDD driver reaches the Dipole Frequency at around 6kHz for the titanium cone version and below 4kHz for the carbon fibre cone version. At this point the first standing wave starts to build up and above this frequency, the wavelengths become progressively shorter than the cone.
Once beyond the Dipole Frequency, dispersion and radiation work as damping mechanisms to control the motion of the cone, however, additional damping may be employed to smooth the pulse and frequency response even more. The precise nature of the techniques employed constitutes a trade secret. Suffice it to say that they control ringing very effectively and allow the DDD driver to operate to over 24,000Hz.