ST AN3340 APPLICATION NOTE

Loudspeaker characterization and compensation

1 Introduction

The application note describes how to measure and analyze the performance of a
loudspeaker and how to compensate the frequency response using the ST Speaker Tune
software, a tool available in the APWorkbench.

Scope

Although the application note focusses on compensation using Sound Terminal® devices,
the principles can be applied to a variety of other DSPs.

AN3340

Application note

February 2011 Doc ID 18453 Rev 1 1/24

www.st.com

Contents AN3340

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 What is a loud speaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Why compensate a loud speaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 How to compensate a loud speaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Mechanical structure of a loud speaker . . . . . . . . . . . . . . . . . . . . . . . . . 5

4 Electrical model of a loudspeaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 Frequency response of a loudspeaker . . . . . . . . . . . . . . . . . . . . . . . . . . 9

6 Loudspeaker compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6.1 General procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6.2 Speaker Tune tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6.2.1 Speaker Tune tool in practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

6.2.2 An example and verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Appendix A APWorkbench information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

A.1 Frequency response data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

A.2 On-line presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

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AN3340 Overview

2 Overview

2.1 What is a loud speaker

A loudspeaker, or often called a speaker drive, is an electro-acoustic transducer. It is able to
convert an electrical signal coming from an audio power amplifier into the movement of a
diaphragm. Hence the diaphragm of the speaker moves in accordance with the variations of
the electrical signal to cause pressure waves in the air which the listener detects as sound.

A lot of speaker models and designs are available on the market. The simplest and most
diffused solution consists of a single diaphragm which is able to reproduce a large portion of
the audio frequency range. This sort of device is named a “full-range speaker”. The
frequency response of a full-range speaker and its cost are driving a lot of TV manufacturers
to select this kind solution in a considerable part of their products, mainly in low and mid
level markets.

The audio performance of a full-range speaker can be improved using a multi-way speaker
system where two or more speakers are connected via a filter so that each speaker
reproduces only a specific portion of the audio frequency range. A very diffused example of
this solution is represented by a two-way speaker system where a large diameter speaker
(woofer) reproduces the low frequencies while another speaker manages the mid and high
frequencies. A further step is made using three speakers: a woofer for the low frequencies, a
mid-range speaker for the middle frequencies and a tweeter speaker to reproduce only the
high frequencies.

Of course for, a multi-way solution each speaker must be appropriately driven with the
correct portion of the audio band. For a three-way loud-speaker system, for instance, a low­pass, a high-pass and a band-pass filter must be designed and implemented to properly
drive each loud speaker. These filters, called crossover filters, can be implemented with
passive or active components.

A passive crossover filter is made using only inductors and capacitors and it is connected
between the output of the power amplifier and the loud-speaker system. It is generally
placed in the speaker cabinet.

In the active solution the crossover filter is implemented using active components, such as
operational amplifiers or DSPs (in a digital system) and it is implemented just following the
pre-amplifier. In this solution each speaker is driven using a dedicated power amplifier. It
can be a very expensive solution.

2.2 Why compensate a loud speaker

In the flat-screen TV market the incessant tendency to reduce the thickness of the TV set
forces the speaker manufactures to design new components with very small dimensions.
The result of this process impacts negatively on the quality of the sound reproduction
because the frequency response of this sort of full-range speaker is very narrow and the
sensitivity is quite low.

In high quality flat-screen TV sets the loud-speaker system is often implemented with a

2.1-channel active solution. Here, two channels are dedicated to reproduce the mid and
high frequencies (for each left and right channel) while the lowest portion of the audio band,
usually below 200 Hz, is reproduced in mono using a single large speaker (a subwoofer)
enclosed in a suitable box. Each speaker is driven with a dedicated power amplifier (five

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Overview AN3340

amplifiers in total) and the crossover filters are implemented using the DSP already present
in the audio chain. Although this solution should provide good performance, the audio
quality which the viewer/listener perceives is not so good because the dimensions of the
speakers are very small.

Some clever and original solutions have been developed in the past, for example, speakers
with two or more coils placed side by side, but the effort was directed only to solve the
problem of the mechanical dimensions, with the sound performance being neglected.

So it seems that the simplest way to improve the overall audio performance of a loudspeaker
system is to tailor the audio signal sent to the speaker in an attempt to compensate for the
deficient speaker response.

2.3 How to compensate a loud speaker

In order to improve the overall audio performance we need to match the audio signal to the
speaker. A simple and effective way to achieve this is to use the equalization circuits often
incorporated in audio amplifiers. In this way the signal can be modified to compensate for
the poor loudspeaker response.

With the ST Sound Terminal
section of these devices is a very flexible equalizer that can be usefully programmed to
compensate the speaker frequency characteristics.

®

devices this action is very simple to perform. In the DSP

This procedure can be performed manually, for each filter adjusting the frequency, the gain
and the quality factor. However, this procedure needs time and the final result depends on
the operator ability, aptitude and experience.

Another possibility is to use the automatic feature now available in the APWorkbench
software: the ST Speaker Tune.

The final result is an equalization curve which reflects the inverse speaker frequency
response. Thus, the overall frequency response in the final application, in a flat-screen TV,
for instance, will be flatter than the uncompensated system and at the same time the
frequency bandwidth will be enlarged. But the most important effect is the viewer/listener
experience who perceives a positive improvement.

In the next chapters the speaker compensation process using ST Speaker Tune is explained
and acoustic improvements are shown.

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AN3340 Mechanical structure of a loud speaker

3 Mechanical structure of a loud speaker

Figure 1. Cross section of a speaker

Diaphragm
or Cone

Spider

Surround

Dust Cup
or Dome

Permanent
Magnet

Voice Coil
Assembly

Voice Coil

Frame
or
Basket

A basic loudspeaker is made from a diaphragm or cone connected to a metal basket or a
rigid structure, via a flexible suspension. This suspension constrains the voice coil, which is
connected to the diaphragm, to move axially through a cylindrical magnetic gap.

The audio signal from the power amplifier is applied to the voice coil. This generates a
variable electric current which interacts with the static magnetic field in the cylindrical gap
between the poles of a permanent magnet to move the diaphragm, which is mounted on the
voice-coil former. The diaphragm suspension must be elastic and must operate in its linear
region to ensure that the diaphragm is displaced according to the amplitude of the input
signal.

The diaphragm movement generates a variable sound pressure which is proportional to the
drive signal applied, that is, the output of the power amplifier.

The surround and the spider keep the diaphragm mechanically centered and maintain the
voice coil in the neutral position when no signal is applied.

The voice coil is usually made with a copper winding on a cylindrical former and oriented
coaxially inside the cylindrical air gap within which the magnetic field is uniform over the
range of travel of the coil.

In special designs, more cones can be combined in a single enclosure to make a multi-way
coaxial speaker, as shown in Figure 2.

Another approach is to design the speaker to enlarge the frequency bandwidth rather than
to achieve a full-range speaker. Such a speaker could have a non-unity aspect ratio as
shown in Figure 3. Although the frequency range is quite large the frequency response is
generally not flat.

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Mechanical structure of a loud speaker AN3340

Figure 2. Coaxial speaker (2 way)

Figure 3. Figure 3: LED LCD speaker

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AN3340 Electrical model of a loudspeaker

4 Electrical model of a loudspeaker

As described in the previous chapter the electrical, magnetic and mechanical parts of the
speaker work together to convert an electrical signal into air pressure waves. The speaker
can be represented by an electrical equivalent circuit to simulate the effect of its individual
components.

Figure 4 depicts the simplest electrical model of a speaker in a perfect infinite baffle to

decouple front and rear air-pressure waves.

Figure 4. Simple electrical model of a loudspeaker

Electrical part

Mechanical part

In this simple model the electrical parts and the mechanical parts are separate. In detail the
components present in this model are:

z For the electrical part:

– Rdc simulates the DC resistance of the voice coil

– Ls is the inductance of the voice coil

z For the mechanical part:

– Cr represents the cone and is mostly linked to the cone mass

– Lr represents the surround and is related to the suspension compliance

– Rr represents the suspension losses.

The impedance of this equivalent circuit is given by:

Z(ω) Rdc jω Ls

-----------------------------------------------++=

1

----- - j ωCr
Rr

1

⎛⎞

+

⎝⎠

1

--------- -–

ωLr

It is quite easy to calculate or measure the parameters Rdc and Ls but it is not so simple to
determine the values of the mechanical parts. Parameters Cr, Lr and Rr can be measured
only with specific mechanical tests.

The task can be simplified by using the above equation for impedance. Measurements can
be performed by driving the voice coil with a AC voltage generator with fixed amplitude and
reading the modulus and phase of the current.

By measuring the impedance at five different frequencies a set of five linear simultaneous
equations can be written and solved for the five unknown parameters.

A intelligent selection of the five frequencies can simplify the calculation.

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Electrical model of a loudspeaker AN3340

A

Rdc can be identified immediately considering the impedance at very low frequencies, for
example, at 20Hz or even at DC.

The effect of Ls is predominant at high frequencies and so this parameter can be measured
at a frequency around 20 kHz.

The remaining three parameters can be calculated considering the property of a parallel
resonant circuit. Rr is the mathematical difference between the peak impedance measured
at the resonant frequency and Rdc, assuming that the term with Ls is negligible.

The last two parameters Cr and Lr can be calculated considering the value of the resonant
frequency and the quality factor of the parallel resonator or simply using two other
frequencies.

The impedance characteristic is important because it provides useful information:

z to identify potential overload situations

z to optimize the output filter design

z to identify the resonant frequency.

The last point is important when the speaker compensation procedure is applied. Due to the
nature of the speaker, the resonant frequency represents the lower limit of the frequency
range that the speaker is able to reproduce efficiently, that is, with good sensitivity.

Figure 5 shows the trace of the impedance of a typical loudspeaker. The impedance peak at

the resonant frequency can be clearly seen in the red trace. The blue trace shows the phase
which is 0° at the resonant frequency.

Figure 5. Speaker impedance vs frequency

30

28

26

24

Z

22

20

O

h

18

m

16

14

12

10

10

20k20 50 100 200 500 1k 2k 5k 10k

f Hz

+100

+80

+60

+40

+20

+0

-20

-40

-60

-80

-100

P
H

S
E

d
e
g

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