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February 2021, Transducer Diaphragm constant piston behavior

General
Diaphragm breakup effect
Measured SPL on-axis versus calculated SPL on-axis using TSP
Some examples of transducer diaphragm break up
References

General

Transducer cones are moving as rigid pistons in their operating frequency area. At the high frequency side,the motion of the diaphragm becomes not uniform anymore due to an effect which is called cone breakup. The SPL at high frequencies becomes difficult to predict and is not constant anymore.
In this article we like to show how the cone break up of a particular transducer can be visualized in a graph. It will become interesting to compare the cone break up effect of different transducers.

Diaphragm breakup effect

The diaphragm breakup of a transducer is a very complex behavior to understand and to describe. For some better understanding, here are some description fragments, that can be found in the Leap EnclosureShop Reference Manual.

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Diaphragm breakup is a general term used to describe the high frequency behavior of a nonrigid radiator. At these frequencies the motion of the diaphragm is not uniform and varies across the entire surface. There will be portions of the diaphragm which are vibrating out of phase with other portions. There will be many resonance modes with varying degrees of damping.
In this frequency range many design factors play a critical role such as: center drive, rim drive, cone angle, dome curvature, and phasing plugs just to name a few. Other factors such as the materials used, their shape, and even how they are glued together all combine to define and control this region of operation.
The result is an exceedingly complex mechanical system whose behavior cannot easily be predicted by any simple set of parameters. Finite element methods have been attempted for many years, but these require tremendous amounts of detailed information about the materials and construction of the device. The majority of users would not be able to obtain this kind of information. Moreover, even these techniques often fail to predict the high frequency response with the expected degree of accuracy and reliability.

There are two fundamental effects:
- Diaphragm Mass Reduction (boost)
- Lowpass Filtering (roll-off)

Diaphragm Mass Reduction

At low frequencies all portions of the diaphragm vibrate with uniform motion. Thus the mass value Mmd represents all of the diaphragm's operating area. However as frequency increases, the outer portions of the diaphragm uncouple from the voice coil former causing a decrease in the effective Mmd value.
Tests on many different transducers have shown that this decrease is roughly 50% on average of the low frequency Mmd value. This is confirmed by actual physical measurements of many diaphragm assemblies. The mass of the voice coil and former is roughly equal to that of the attached cone portion. However, the rate and frequency where this mass reduction takes place is highly variable and solely dependent on the materials and design of the diaphragm. In some cases the reduction may take place very abruptly along with a strong resonance mode. In other cases, it may occur gradually over a wide frequency range.

Diaphragm Mass Reduction example at one frequency with varying Q-factor
The straigth line in grey color is the on-axis SPL without breakup.

Lowpass Filtering

Another phenomenon which occurs at high frequencies is the diaphragm resonance and cancellation which creates additional attenuation. Since the effective size of the Sd value at these frequencies is highly variable, the corner frequency of this rolloff cannot be predicted. Furthermore, the damping may be large or small, creating highly variable peaking as the response begins to decay.

Lowpass Filtering example at one frequency with varying Q-factor
The straigth line in grey color is the on-axis SPL without breakup.

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Measured SPL on-axis versus calculated SPL on-axis using TSP

Using the Thiele Small Parameters (TSP) of a transducer, it is possible to calculate the on-axis SPL on infinite baffle.
The SPL on-axis of a transducer on infinite baffle with a constant piston behavior without breakup, and assuming at first the voice coil inductance to be zero, is a second order high pass function at frequency fs with a Q-factor Qts, and a flat SPL up to high frequencies.
As an example we take transducer Accuton C173-6-096E and calculate the on-axis SPL on infinite baffle at 1m,2.83Vrms with no voice coil inductance. For this driver fs = 47.6 Hz and Qts = 0.22.

The green curve is the calculated SPL response on-axis, the black curve is the datasheet on-axis SPL.

If we do the same SPL on-axis calculation with the voice coil inductance included, there will appear a smooth SPL roll-off at high frequencies.

The red curve is the calculated SPL response on-axis, the black curve is the datasheet on-axis SPL.

For this calculation, it is important that the measured and the calculated impedances curves have the same value for all frequencies. If not, the TSP have to be adapted to have that match. Because, for this SPL calculation using TSP, the SPL and the impedance are 1:1 related.
This calculated SPL on-axis using TSP is a very interesting curve to compare with the measured infinite baffle on-axis SPL. The frequency where the cone break up is starting and how the cone breakup is appearing can be observed.
For the Accuton C173 transducer in this example, diaphragm mass reduction starts at 800 Hz and the lowpass filter appears around 5 kHz.

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Some examples of transducer diaphragm break up

Bliesma T25B-6

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February 2021, Transducer Diaphragm constant piston behavior

General

Diaphragm breakup effect

Diaphragm Mass Reduction

Lowpass Filtering

Measured SPL on-axis versus calculated SPL on-axis using TSP

Some examples of transducer diaphragm break up

Tweeters

Midranges

Midwoofers

References