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1 @ Copyright 2016 VCLLabs

Speaker Design using IEC baffle measurements and Leap simulations

Date: 26th of June 2016

Author: Paul Vancluysen

Version: final

Contents

1 Introduction ..................................................................................................................................... 2

2 Design steps ..................................................................................................................................... 3

2.1 IEC baffle measurement .......................................................................................................... 3

2.1.1 SPL on IEC baffle .............................................................................................................. 3

2.1.2 Impedance on IEC baffle .................................................................................................. 4

2.2 Creation of the transducer model in Leap .............................................................................. 5

2.2.1 The TSP transducer model ............................................................................................... 5

2.2.2 The final Leap infinite baffle transducer model .............................................................. 8

2.2.3 Frequency response correction on the Leap transducer model ..................................... 9

2.3 “Transducer in enclosure” response ..................................................................................... 10

2.3.1 “Transducer in enclosure” simulation ........................................................................... 10

2.3.2 Frequency response correction on the “transducer in enclosure response” ............... 11

2.4 Design of the speaker system crossover filter in Leap CrossoverShop ................................. 12

2.4.1 Import the transducer in enclosure responses ............................................................. 12

2.4.2 Creating targets for the individual transducers responses in enclosure ....................... 13

2.4.3 Crossover filter design ................................................................................................... 14

Abbreviations

SPL Sound Pressure Level

TSP Thiele Small Parameters

FR Frequency Response

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1 Introduction The always recurring problem with the design of speakers is to perform reliable measurements of the

speaker responses, especially at lower frequencies. To make a speaker with a very flat SPL, a correct

sound pressure level and impedance response of each transducer in the enclosure as a function of

frequency is necessary. It is not that easy to find a good place to measure these responses. Good

anechoic rooms are not available for many people. Outdoor measurements are difficult to do,

because the speaker has to be placed high above the ground, which is not that easy especially for

heavy enclosures. Therefore, another way to create the transducer responses in the enclosure is

presented. At first a model for all the transducers with a correct infinite baffle sound pressure level

and impedance response is created. The model parameters are derived out of an IEC baffle

measurement or, in the case the transducers are not available yet, out of the supplier transducere

specification. After that, the responses in the enclosure are simulated by a good software package.

Leap is one of the tools which is very powerful to perform these simulation tasks. Doing it in a correct

way Leap delivers responses even better at very low frequencies than in an anechoic room. Such

rooms have also their low frequency accuracy limits.

This article describes the approach to do a complete speaker design using an IEC baffle measurement

in a reverberant room and Leap as the simulation for the responses. Following this design path

results in an accurate speaker design without the real need of an anechoic room or outdoor

measurements. A very good match between simulation and measurements is realized. Several cross

checks of this design methodology has been done comparing simulations with anechoic room

measurements. The four design steps are:

1. Measurement of SPL and impedance of all transducers on an IEC baffle

2. Creating the transducer models in Leap EnclosureShop

3. Simulation of the “transducer in enclosure” responses in Leap EnclosureShop

4. Design of the speaker system crossover filter in Leap CrossoverShop

Step 2 is described in most detail as it contains the chosen approach as a part of this speaker design

method. The other design steps are added to present a complete speaker design in this document.

Summarized, an IEC baffle measurement of all transducers together with the effective use of Leap

delivers the enclosure response curves for a very accurate design of a top speaker. This design

method is very useful also for concept studies of new speaker systems based on the supplier

transducer specification, without the real need of any immediate invest in speaker units and

enclosure.

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2 Design steps

2.1 IEC baffle measurement Each transducer is measured on a IEC baffle using a mls measurement. For our designs we have a

standard IEC225Hz baffle installed on our attic, see Figure 1. The sound pressure level is measured at

1m distance on axis for 2.83Vrms. The impedance is measured at 2.83Vrms.

Figure 1

2.1.1 SPL on IEC baffle

As an example the IEC baffle measurement of the Accuton C90 6-724 (will be used in a future design)

is shown in Figure 3. The measured SPL on our attic can be considered as the SPL on an IEC baffle in a

reverberant environment. The impulse response arrives 3ms after the start of the measurement and

the first reflections after 8.5ms. So we have a reflection free impulse response of 5.5ms long

available for the FFT. Out of this frequency response, together with the measured impedance, a

transducer model will be created in Leap. This transducer model will be used in later “transducer in

enclosure” response simulations.

Figure 2

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Comparing the IEC baffle measurement with the transducer infinite baffle response, created later on

in Leap, shows some differences, see Figure 3. The infinite baffle response is the red curve, the IEC

baffle measurement is the green curve. For low frequencies there are measurement deviations due

to the IEC baffle diffractions and also due to the finite duration of the measured impulse response

(frequencies lower than 200Hz). For higher frequencies the infinite baffle response is measured in a

correct way on the IEC baffle. In the next chapters there will be explained how corrections are made

to the IEC baffle measurement to create a transducer model with a correct infinite baffle response in

Leap.

Figure 3

2.1.2 Impedance on IEC baffle

The impedance is measured on the IEC baffle at 2.83Vrms. Out of this measurement the Thiele Small

Parameters (TSP) are calculated. The values of Qms, Qes and fs are directly calculated out of the

impedance measurement. Re is measured with an accurate DC multimeter. For Sd the supplier

specification value is used. The values of BL and Mms are derived using the absolute SPL value at 1m

distance at 2.83Vrms. Good calibrated equipment is needed to measure the absolute SPL level. All

the above parameters are used in Leap to create the transducer model.

Figure 4

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2.2 Creation of the transducer model in Leap

2.2.1 The TSP transducer model

Out of the loudspeaker theory we know that the Thiele Small parameters can be used to calculate

the low frequency SPL and impedance response of a transducer on infinite baffle. Also in Leap these

TSP parameters are used to create the TSP transducer model for low frequencies on infinite baffle.

For the given driver unit Accuton C90 6-724 the transducer parameters are shown in Figure 5 . The

parameters will be slightly adapted for the best mapping of the SPL and the impedance of the

transducer model on the SPL and the impedance of the IEC baffle measurements.

Figure 5

2.2.1.1 Impedance mapping of the TSP model on the IEC baffle measurement

In Figure 6 the measured impedance in green color and the impedance of the transducer model in

brown color are shown. The TSP parameters are adapted for the best mapping of the model

impedance curve on the measured IEC baffle impedance.

Figure 6

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2.2.1.2 SPL mapping of the Leap TSP model on the IEC baffle measurement

First the TSP transducer model on infinite baffle is simulated. It is the red curve in Figure 7. It is

difficult to interpret if this red curve has the correct mapping on the measured SPL green curve,

because the measurement is disturbed by baffle diffractions and MLS measurement constraints. For

higher frequencies there is the non piston behavior of the transducer, which is not included yet in the

TSP transducer model. Therefore we will compare the IEC baffle measurement with also a IEC baffle

simulation.

Figure 7

Comparing in Figure 8 the TSP transducer model simulation on IEC baffle (blue curve) with the IEC

baffle SPL measurement (green curve) shows much better mapping. The TSP parameters of the TSP

model are slightly adapted to realize the best mapping.

Two important conclusions can be made:

1. Comparing the IEC baffle (blue curve) and the infinite baffle simulation (red curve), shows

that diffractions are worked out at 650Hz. Let’s name this frequency fdiffrac . Above the

frequency fdiffrac the IEC baffle measurement is equal to the infinite baffle response.

2. Comparing the IEC baffle simulation and IEC baffle measurement shows also that at a certain

frequency the measured SPL (green curve) starts deviating from the simulated SPL (blue

curve) due to non-piston behavior and breakup of the cone. We call this frequency fbreak and

it is about 800Hz for this transducer. The frequency fbreak is not the same for each

loudspeaker. In general the frequency fbreak becomes lower for larger transducer cones.

Below the frequency fbreak the TSP transducer simulation is equal to the infinite baffle

response.

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Figure 8

To visualize more the difference between the measurement and the simultion, calculating the ratio

of the IEC baffle measurement over the simulated IEC baffle response of the TSP model shows this

non-piston and break up behavior, see Figure 9. The response of TSP transducer model is equal to

the measurement starting from 150Hz up to 800Hz, the frequency fbreak. This curve is a good guide to

model cone breakup.

Figure 9

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2.2.2 The final Leap infinite baffle transducer model

A final transducer model is created in Leap. The created model is the pink curve in Figure 10. For

low frequencies the TSP transducer model response is used. At the frequency fbreak the model starts

following the measurement in the best way. Mapping a model on a measurement in Leap is not so

powerful. Only a mean value of the measurement can be created as a model. Nevertheless the

created model can be used for the application simulations. As a correction on the SPL, a frequency

response error will be calculated (see next chapter) and applied later in the application simulations.

Figure 10

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2.2.3 Frequency response correction on the Leap transducer model

The measured transducer IEC baffle response is equal to the infinite baffle response above fdiffrac ,

which is equal to 650Hz in our setup. This means that a frequency response error correction can be

determined as the ratio of the IEC baffle measured response over the Leap transducer model

response, for frequencies higher than fdiffrac. In figure 11 the frequency response correction is show

for the transducer model of figure 10. This correction can be applied on the Leap transducer model

response to create a accurate infinite baffle response. It can be used also after a simulation in an

enclosure is done using the Leap transducer model.

In Figure 12 an accurate infinite baffle frequency response (red curve) is created, multiplying the

Leap transducer model response (pink curve) and the frequency response correction for this

transducer.

Figure 12

Figure 11

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2.3 “Transducer in enclosure” response

2.3.1 “Transducer in enclosure” simulation

Once the transducer model is defined in Leap, it can be simulated in an enclosure. After the

enclosure is modeled and the transducer is placed in the enclosure, the response can be simulated in

different domains. Also the impedance response of the transducer in the enclosure is simulated. See

in Figure 13 an example of a modeled enclosure in Leap EnclosureShop with the Accuton C90

transducer mounted in it.

In Figure 14 the blue curve shows the simulated response in enclosure. The pink curve is the

transducer infinite baffle response. The influence on the response by the enclosure compared with

infinite baffle response can be seen.

Figure 14

Figure 13

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2.3.2 Frequency response correction on the “transducer in enclosure response”

To create a more accurate response of the “transducer in enclosure” at higher frequencies, the

frequency response correction like described in chapter 2.2.3 is applied on the simulated response.

This results in the red curve. This curve can be exported to be used for further design like the

crossover network.

Figure 15

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2.4 Design of the speaker system crossover filter in Leap

CrossoverShop

2.4.1 Import the transducer in enclosure responses

After all transducers used in an actual speaker system are simulated in their enclosure in Leap

EnclosureShop and updated with the frequency response correction, they can be imported in Leap

CrossoverShop or another simulation tool for the crossover filter design. Also the simulated

impedances in the enclosure are imported. As an illustration example, a three way system with 2 x

Eton 8-402 parallel for the low section, the Accuton C90 7-624 for the midrange and the Berylium

Scanspeak D3004-664000 for the tweeter is shown. See the enclosure in Figure 16, the simulated and

corrected SPL of the speaker units in the enclosure in Figure 167 and the simulated impedances of

the speaker units in the enclosure in Figure 18

Figure 16

Figure 17

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2.4.2 Creating targets for the individual transducers responses in enclosure

Before starting the design of the crossover filter, SPL targets for each transducer are created. One

must make a choice which crossover filter topology is preferred. In many cases the classical

Butterworth and Linkwitz Riley filters are chosen. But also filters like elliptical filters are an option.

For this example we choose the Linkwitz Riley 4th order filtering at 350 and 3500Hz. See Figure 19.

Figure 18

Figure 19

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2.4.3 Crossover filter design

A crossover is designed for the best mapping of the filtered transducer responses on the targets. An

example with a passive filter is shown in Figure 20. The individual filtered transducer responses are

presented in color, the sum response in black and the targets in light grey.

Figure 20

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