Observations of Directivity in Transducers

8/3/2019 Observations of Directivity in Transducers

1/48

1

Observations ofDirectivity in Transducers

Richard LittleDirector of Advanced Design

Tymphany HK Ltd.

13-14 November 2010Acoustic Block 2010

The Sound of Modern Design


2/48

2

Tymphany HK Ltd.

13-14 November 2010Acoustic Block 2010

The Sound of Modern Design


3/48

Abstract

The causes of transducer directivity arereviewed. The basic theoretical performance of apiston radiating from an infinite baffle is discussed,including calculations of directivity and total radiatedpower. Measurements of transducer directivity and

radiated power are reviewed for a range of transducersizes. The divergences of these measurement results,from the expectations for a piston, are examined anddiscussed.

Confidential 3


4/48

Confidential 4


5/48

Introduction to Directivity A transducers diaphragm moves back and forth during operation,

pushing and pulling on the surrounding air and creating an outgoing

pressure wave.

At low frequencies, the wavelength of the outgoing sound pressure wave

is large relative to the diaphragm, and the diaphragm operates much likea point source, radiating sound pressure waves evenly in all directions.

At higher frequencies, however, the wavelength of the pressure wave issized similarly to the diaphragm size, or even smaller. At different

observation positions, at these frequencies, there is a path lengthdifference from the observation position to different parts of thetransducers diaphragm. This means that the summed contributions tothe total pressure observed may increase or decrease, according to theeffects of the path length differences.

Typically a transducer diaphragm is symmetric around its central axis, sothe effects of the path length differences are observed to be differentaccording to the direction that the transducer is being observed, relativeto the central axis. We call this effect DIRECTIVITY.

Confidential 5


6/48

Confidential 6


7/48

Directivity of a Piston in an Infinite Baffle

In this paper, were going to limit measurements and calculationsto that of transducers and pistons operating mounted to an infinitebaffle. Were going to neglect reflections off of loudspeaker

cabinet boundaries. The figure below illustrates how the pressure at the observation

position, created by a radiating piston mounted in an infinite baffle,is calculated by integrating over the radiating surface.

Confidential 7

Infinitebaffle

piston

Observation position


8/48

Confidential 8

Infinitebaffle

piston

Observation position


9/48

Example: radiation pattern on and off axis

This example shows the radiation pattern for a transducer, on and offaxis, at different frequencies. The output of the transducer is the same

in all directions at low frequencies, but at high frequencies this is nolonger the case.

Confidential 9


10/48

Confidential 10


11/48

Calculating directivity for a infinite-baffle piston

The Directivity Index DI is a measure of the directivity of atransducer, and can be calculated from the following formulae:

Here a refers to the diameter of the diaphragms radiating area,and c is the speed of sound (345 m/s).

These formulae are approximations to more precise Besselfunction relations.

Confidential 11


12/48


13/48

Calculating directivity from measurements

The directivity factor Q is the ratio of the on axis frequencyresponse of a transducer, to the on axis frequency response for a

point source radiator producing the same amount of total radiatedpower. Q and DI are related:

Q is calculated by calculating the total radiated power, in a ratiowith the on-axis frequency response:

For a transducer which is symmetric around its central axis, thiscan be re-stated as:

Confidential 13


14/48

Q QDI

Q

Q

Confidential 14


15/48

Calculating directivity from measurements (2)

Typically, when conducting measurements, we measure off-axisin small increments of . The previous relation for Q can then be

approximated as follows:

We can then calculate DI from Q.

The results of these calculations of the DI can be comparedagainst the piston theoretical curve. Good agreement betweenthe measurement results, vs. the theoretical curve, implies thatthe transducers total radiation pattern is pistonic.

Confidential 15


16/48

(2)

0180Q

DI

DIDI

Confidential 16


17/48

Example: measured directivity vs. piston

theoretical directivity In this example, the transducers radiation pattern is pistonic, for its

radiating area, until ~ 6 kHz. Above that frequency, the driver is

effectively functioning as if its radiating area were smaller than it really is.

Confidential 17


18/48

6

Confidential 18


19/48

Break-up modes and on-axis measurements

The effect of diaphragm resonances(break-up modes) on the on-axis

frequency response can be studiedby mirroring the transducers

impedance curve onto the on-axisfrequency response curve, startingat the impedance minimum

frequency. Large deviationsbetween the impedance-projectedcurve and the on-axis responsecurve suggest mechanical

resonances have altered the

frequency response. The example to the right shows two

possible resonances: a shallowbroad resonance at 7 kHz, and asharp high-Q resonance at 19 kHz.

Confidential 19


20/48

7KHzQ19KHzQ

Confidential 20


21/48

On and off axis measurements

A transducers radiation pattern will become directional at frequenciesabove ka=1 (from our previous equation). The graph below highlightsthis point in the frequency response (the radiation dispersion frequency).

Confidential 21


22/48

(ka=1)()

Confidential 22


23/48

Break-up modes and directivity

A case study Were going to compare the radiation patterns of two drivers, with

essentially the same diaphragm, but two different voice coil diameters(one smaller, one bigger).

A sketch of the diaphragm and voice coil are shown below. Because ofthe difference in coil sizes, the break-up frequency of the diaphragmshould be different in the two cases.

Confidential 23

voice coil

diaphragm

surround

voice coil

diaphragm

surround

Small coil Large coil


24/48

Confidential 24

voice coil

diaphragm

surround

voice coil

diaphragm

surround



25/48

Case study comparison of on-axis response

and break-up mode behaviorSmall coilBreak-up modes small until 19 kHz

Large coilBreak-up modes affect response above 4 kHz

Confidential 25


26/48

-

19KHz 4KHz

Confidential 26


27/48

Case study: comparison of off-axis frequency

responseSmall coilResponse off-axis remains roughly pistonic untilthe effects of the resonance at 19 kHz enhance

the off-axis response

Large coilOff-axis performance kept close to on-axisperformance due to effects of ~12 kHzresonance

Confidential 27


28/48

-

19KHz 12KHz

Confidential 28


29/48

Case study: Directivity index comparison

Small coilDriver performs roughly like a piston until above10 kHz

Large coilDriver shows large diversions from pistonicbehavior above 10 kHz, effectively losingradiating area due to mechanical resonances.

Confidential 29


30/48

-

10KHz 10KHz

Confidential 30


31/48

Case study: radiation pattern comparison


Confidential 31


32/48

-

Confidential 32


33/48

Notes from the case study

Small coil

Smaller coil = cheaper motor

Lower coil inductance

Higher on-axis frequencyresponse bandwidth

Low resonance design more repeatable response inproduction

Higher directivity at higherfrequencies

Large coil

Large coil = expensive motor

Higher coil inductance

Lower on-axis frequencyresponse bandwidth

Design depends uponresonances

Lower directivity at higherfrequencies

Confidential 33


34/48

=

=

Confidential 34


35/48

Typical radiation pattern 25 mm Vifa NE silk

dome tweeter NE25VTS-04

Confidential 35

25 Vif NE


36/48

25 mm Vifa NE

NE25VTS-04

Confidential 36


37/48

Typical radiation pattern 25 mm ring

radiator tweeter XT25SC90-04

Confidential 37

25


38/48

25 mm

XT25SC90-04

Confidential 38

T i l di ti tt NXT BMR46 f ll


39/48

Typical radiation pattern NXT BMR46 full-

range driver

Confidential 39


40/48

NXT BMR46

Confidential 40

T i l di ti tt 180 Vif NE


41/48

Typical radiation pattern 180 mm Vifa NE

woofer NE180W-04

Confidential 41

180 Vif NE


42/48

180 mm Vifa NE

NE180W-04

Confidential 42



43/48


woofer NE315W-04

Confidential 43

315 mm Vifa NE


44/48

315 mm Vifa NE

NE315W-04

Confidential 44


45/48

Conclusions The method of calculating the directivity index and radiated power was

reviewed.

The effects of resonances (break-up modes etc.) in the frequencyresponse of a transducer can be identified by comparing the on-axis

response curve to the predicted fall-off curve, due to the increase inimpedance with frequency.

The directivity index function for a piston of a particular size can beused as an approximate directivity index function for a transducer of

same-sized diaphragm, up to the point where the diaphragm goes intobreak-up and the effective radiating area of the transducer decreases.

Transducer off-axis frequency response and directivity can beimproved through mechanical resonances in the diaphragm, but thereare trade-offs:

It is difficult to have a well-behaved polar radiation pattern.

Mechanical resonances in the diaphragm can also produce undesiredlarge peaks in the on-axis frequency response.

Mechanical resonances are often poorly dampedhard to control.

Confidential 45


46/48

Confidential 46


47/48


48/48

Acoustics, Leo Beranek, 1993 edition.

Confidential 48

Documents

Observations of Directivity in Transducers