### 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.

**" "**

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.

**" "**

## 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.

## Some examples of transducer diaphragm break up

**Tweeters**

**Midranges**

**Midwoofers**

- Accuton C173-6-096E
- Purifi PTT6.5X04-NFA-01
- Scanspeak 18WE8542T00
- Seas Excel W18EX001
- Seas Excel W22EX001

#### References

- Leap EnclosureShop Reference Manual p. 81-87

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