Hot and Nonlinear – Loudspeakers at High Amplitudes - Klippel GmbH
Hot and Nonlinear – Loudspeakers at High Amplitudes - Klippel GmbH
Hot and Nonlinear – Loudspeakers at High Amplitudes - Klippel GmbH
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<strong>Hot</strong> <strong>and</strong> <strong>Nonlinear</strong> <strong>–</strong><br />
<strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong><br />
by Wolfgang <strong>Klippel</strong><br />
Tutorial<br />
Presented <strong>at</strong> 131st AES Convention,<br />
New York, October 2011<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 1
Abstract:<br />
<strong>Nonlinear</strong>ities inherent in electro-dynamical transducer <strong>and</strong> the he<strong>at</strong>ing of<br />
the voice coil <strong>and</strong> magnetic system limit the acoustical output, gener<strong>at</strong>e<br />
distortion <strong>and</strong> other symptoms <strong>at</strong> high amplitudes. The large signal<br />
performance is the result of a deterministic process <strong>and</strong> predictable by<br />
lumped parameter models comprising nonlinear <strong>and</strong> thermal elements.<br />
The tutorial gives an introduction into the fundamentals, shows altern<strong>at</strong>ive<br />
measurement techniques <strong>and</strong> discusses the rel<strong>at</strong>ionship between the<br />
physical causes <strong>and</strong> symptoms depending on the properties of the<br />
particular stimulus (test signal, music). Selection of meaningful<br />
measurements, the interpret<strong>at</strong>ion of the results <strong>and</strong> practical loudspeaker<br />
diagnostic is the main objective of the tutorial, which is important for<br />
designing small <strong>and</strong> light transducers producing the desired output <strong>at</strong> high<br />
efficiency <strong>and</strong> reasonable cost.<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 2
Our topic today<br />
1. Large Signal Behavior (Symptoms)<br />
2. Physical Causes <strong>and</strong> Models<br />
3. Measurement of Large Signal Parameters<br />
4. Loudspeaker Diagnostics<br />
5. Modern Loudspeaker Design<br />
6. Active Control<br />
7. Conclusion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 3
Amplitude<br />
X<br />
[mm]<br />
30<br />
10<br />
3<br />
1<br />
0,3<br />
voice-coil<br />
displacement<br />
Assessment of Sound Quality<br />
<strong>Nonlinear</strong><br />
<strong>and</strong><br />
Thermal<br />
Model<br />
Linear<br />
Model<br />
Destruction<br />
Large signal<br />
performance<br />
Small signal<br />
performance<br />
Rel<strong>at</strong>ed to size,<br />
weight, cost !!!<br />
• Maximal Output<br />
• Distortion<br />
• Power H<strong>and</strong>ling<br />
• Stability<br />
• Compression<br />
•B<strong>and</strong>width<br />
•Sensitivity<br />
•Fl<strong>at</strong>ness of Response<br />
•Impulse Accuracy<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 4
W<strong>at</strong>ch for <strong>Nonlinear</strong> Symptoms !<br />
Gener<strong>at</strong>or<br />
1. Experiment<br />
f < f s<br />
tone <strong>at</strong> f<br />
2. Experiment<br />
f � f s<br />
Resonance<br />
frequency f s<br />
pointer<br />
scale<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 5<br />
stroboscope<br />
3. Experiment<br />
f > f s
Vibr<strong>at</strong>ion Behavior<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 6<br />
<strong>Klippel</strong> <strong>GmbH</strong>
X [mm]<br />
7,5<br />
5,0<br />
2,5<br />
0,0<br />
-2,5<br />
-5,0<br />
1. Symptom: Distorted Waveform<br />
Input: sinousoidal voltage signal <strong>at</strong> 20 Hz<br />
Output: Voice coil Displacement<br />
ZOOM<br />
Y2(t)<br />
Input signal Y2(t) vs time<br />
0,00 0,05 0,10 0,15<br />
Time [s]<br />
0,20 0,25<br />
KLIPPEL<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 7<br />
Distortion in<br />
the time<br />
domain
2. Symptom: Harmonic Distortion<br />
Stimulus Response<br />
Amplitude<br />
f1<br />
frequency<br />
Amplitude<br />
DC<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 8<br />
f1<br />
harmonics<br />
A single tone gener<strong>at</strong>es harmonics <strong>and</strong> a DC component<br />
(in displacement)<br />
Distortion in<br />
the frequency<br />
domain<br />
frequency
3. Symptom: Intermodul<strong>at</strong>ion Distortion<br />
Two-tone Stimulus<br />
Amplitude<br />
f1<br />
bass tone<br />
harmonics<br />
sound pressure spectrum<br />
difference tones summed tones<br />
f2<br />
voice tone<br />
frequency<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 9
dBu (Uo = 1V)<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
-30<br />
-40<br />
-50<br />
Example: Reproduced Two-tone Signal<br />
input <strong>Nonlinear</strong> System<br />
output<br />
Response 1<br />
Frequency Domain<br />
101 102 103 f [Hz]<br />
Two-tone signal<br />
dBu (Uo = 1V)<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
-30<br />
-40<br />
-50<br />
Response 1<br />
Frequency Domain<br />
101 102 103 f [Hz]<br />
Fundamentals<br />
Harmonics<br />
Intermodul<strong>at</strong>ion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 10
X [mm]<br />
7,5<br />
5,0<br />
2,5<br />
0,0<br />
-2,5<br />
-5,0<br />
ZOOM<br />
4. Symptom: DC-Displacement<br />
Y2(t)<br />
Input signal Y2(t) vs time<br />
0,00 0,05 0,10 0,15<br />
Time [s]<br />
0,20 0,25<br />
KLIPPEL<br />
K MS(x)<br />
•Dc displacement is gener<strong>at</strong>ed dynamically by rectific<strong>at</strong>ion of ac components<br />
•Caused by asymmetrical nonlinearities<br />
DC displacement<br />
rest position of the coil<br />
•working point is shifted away from rest position<br />
•significant amplitude X DC (comparable with fundamental)<br />
• usually in displacement (not in velocity, accelar<strong>at</strong>ion, input current)<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 11<br />
x
5. Symptom: Amplitude Compression<br />
2,5<br />
Linear System<br />
X [mm] (rms)<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
0,0<br />
23.4 Hz<br />
Fundamental component<br />
| X ( f1, U1 ) |<br />
KLIPPEL<br />
0,0 2,5 5,0 7,5<br />
Voltage U1 [V]<br />
10,0 12,5 15,0<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 12
dB - [V] (rms)<br />
130<br />
125<br />
120<br />
115<br />
110<br />
105<br />
100<br />
95<br />
90<br />
85<br />
80<br />
Compression of SPL Output<br />
for a sinusoidal tone versus frequency<br />
Sound Pressure Response<br />
Long Term Response linear response<br />
Limited by peak displacement<br />
Limited by coil temper<strong>at</strong>ure<br />
20 50 200 500 2k<br />
Frequency [Hz]<br />
KLIPPEL<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 13<br />
Long term response<br />
was measured by<br />
using a stepped sine<br />
wave <strong>and</strong> cycling 1<br />
min on/1 min off
Compression of 3 rd -order Harmonic<br />
Percent<br />
80<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
Third-order harmonic distortion in percent (IEC 60268)<br />
Signal <strong>at</strong> IN1<br />
0.50 V 1.57 V 2.64 V 3.71 V 4.79 V 5.86 V 6.93 V 8.00 V<br />
Voltage<br />
4*101 6*101 8*101 102 Frequency f1 [Hz]<br />
KLIPPEL<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 14
Percent<br />
25<br />
20<br />
15<br />
10<br />
5<br />
Harmonic Distortion<br />
Second-order harmonic distortion in percent (IEC 60268)<br />
Signal <strong>at</strong> IN1<br />
3.71 V 4.79 V 5.86 V 6.93 V 8.00 V<br />
4*101 6*101 8*101 102 Frequency f1 [Hz]<br />
• <strong>Nonlinear</strong> Distortion depend on frequency <strong>and</strong> voltage<br />
• Complic<strong>at</strong>ed amplitude characteristic (compression, reduction)<br />
• Measurement versus amplitude also required (3D measurement)<br />
KLIPPEL<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 15
| X ( f1, U1 ) |<br />
Amplitude response of fundamental component in displacement<br />
10 0<br />
[mm]<br />
10 -1<br />
10 -2<br />
10 -3<br />
6. Vari<strong>at</strong>ion of Resonance Frequency<br />
caused by suspension nonlinearity K(x)<br />
6 dB<br />
steps<br />
resonance peak<br />
10 100 200<br />
Frequency [Hz]<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 16
7. Symptom: Bifurc<strong>at</strong>ion into Multiple St<strong>at</strong>es<br />
X [mm]<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
backbone curve<br />
10 100<br />
frequency f [Hz]<br />
Small signal<br />
resonance<br />
Sweeping down<br />
Large signal<br />
resonance<br />
Sweeping up<br />
unstable st<strong>at</strong>es<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 17
Occurs if:<br />
8. Symptom: Instabilities<br />
- Driver has soft linear suspension<br />
- Equal-length configur<strong>at</strong>ion<br />
(Bl(x) nonlinearity)<br />
- Sinusoidal stimulus f > fs<br />
Paket<br />
bifurc<strong>at</strong>ion caused by motor.MOV<br />
Bl(x)<br />
5,0<br />
4,5<br />
[N/A]<br />
4,0<br />
3,5<br />
3,0<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
Unstable for f > f s<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 18<br />
KLIPPEL<br />
-5 -4 -3 -2 -1 0 1 2 3 4 5<br />
[mm] x<br />
� Bifurc<strong>at</strong>ion into two stable st<strong>at</strong>es of vibr<strong>at</strong>ion
Bl(x)<br />
5,0<br />
4,5<br />
[N/A]<br />
4,0<br />
3,5<br />
3,0<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
9. Symptom: Chaotic Behavior<br />
KLIPPEL<br />
-5 -4 -3 -2 -1 0 1 2 3 4 5<br />
[mm]<br />
x<br />
� Gener<strong>at</strong>ion of subharmonics<br />
x [mm]<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
-30<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 19<br />
x(t)<br />
KLIPPEL<br />
0,0 0,1 0,2 0,3 0,4 0,5<br />
t [s]<br />
0,6 0,7 0,8 0,9 1,0<br />
� Stochastic responses for sinusoidal excit<strong>at</strong>ion<br />
How far away from chaos ?
Wh<strong>at</strong> Limits the Acoustical Output?<br />
Limiting factors:<br />
1. Maximal temper<strong>at</strong>ure of the voice coil<br />
2. Maximal voice coil displacement (e.g. in suspension)<br />
3. Maximal acceler<strong>at</strong>ion, forces (e.g. in the cone)<br />
4. Maximal sound pressure (e.g. in the horn)<br />
Those factors depend on<br />
• Properties of the transducer (linear, nonlinear <strong>and</strong> thermal<br />
parameters)<br />
• Properties of the enclosure (sealed or vented box)<br />
• Properties of the stimulus <strong>at</strong> the terminals (spectral <strong>and</strong><br />
amplitude distribution, vari<strong>at</strong>ion over time)<br />
• Ambient condition (temper<strong>at</strong>ure, air convection, …)<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 20
dB - [V] (rms)<br />
Maximal Sound Pressure Output<br />
for a sinusoidal input with different On/Off Cycle<br />
140<br />
135<br />
130<br />
125<br />
120<br />
115<br />
110<br />
105<br />
100<br />
95<br />
90<br />
SOUND PRESSURE LEVEL<br />
Maximal SPL (short term)<br />
Cycled sine wave 1 s on, 1 min off<br />
20 50 100 200 500 1k 2k 5k<br />
Limited by displacement<br />
Maximal SPL (long term)<br />
Cycled sine wave 1 min on, 1 min off<br />
Frequency [Hz]<br />
Limited by coil temper<strong>at</strong>ure<br />
Limited by acceler<strong>at</strong>ion<br />
KLIPPEL<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 21
Agenda<br />
1. Large Signal Behavior (Symptoms)<br />
2. Physical Causes <strong>and</strong> Models<br />
3. Measurement of Large Signal Parameters<br />
4. Loudspeaker Diagnostics<br />
5. Modern Loudspeaker Design<br />
6. Active Control<br />
7. Conclusion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 22
<strong>Loudspeakers</strong> - a nonlinear <strong>and</strong> time-varying system<br />
Amplitude<br />
X<br />
[mm]<br />
30<br />
10<br />
3<br />
1<br />
0,3<br />
voice-coil<br />
displacement<br />
Working range<br />
Destruction<br />
Large signal domain<br />
Small signal domain<br />
MODELING<br />
<strong>Nonlinear</strong> Model<br />
Thermal Model<br />
Linear Model<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 23
How to Structure the Model ?<br />
Domains <strong>and</strong> interfaces passed by the audio signal<br />
Input power<br />
Coil temper<strong>at</strong>ure<br />
digital<br />
D<strong>at</strong>a compression<br />
Sample r<strong>at</strong>e<br />
conversion,<br />
AD conversion<br />
Voltage<br />
electrical<br />
Amplifier<br />
Crossover<br />
Motor<br />
He<strong>at</strong> transfer<br />
Convection cooling<br />
Time constants<br />
thermal<br />
Coil<br />
displacement<br />
velocity<br />
mechanical<br />
Suspension<br />
Cone<br />
Cone<br />
displacement<br />
Sound<br />
pressure in<br />
ear channel<br />
acoustical<br />
Radi<strong>at</strong>ion,<br />
Diffraction<br />
Propag<strong>at</strong>ion,<br />
Room Influence<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 24<br />
psychoacoustical<br />
Perception,<br />
Evalu<strong>at</strong>ion
Power density:<br />
Audio<br />
signal<br />
Power Distributed by the Loudspeaker<br />
Amplifier<br />
Crossover<br />
EQ<br />
linear<br />
u(t)<br />
10 W / cm 3 1 W / cm 3 1 W / m 3 1 mW / m 3<br />
Electromechanical<br />
Transducer<br />
i(t)<br />
x(t)<br />
nonlinear<br />
Mechanoacoustical<br />
Transducer<br />
(Cone)<br />
Radi<strong>at</strong>ion<br />
Radi<strong>at</strong>ion<br />
Radi<strong>at</strong>ion<br />
Sound<br />
Propag<strong>at</strong>ion<br />
Sound<br />
Propag<strong>at</strong>ion<br />
Sound<br />
Propag<strong>at</strong>ion<br />
linear<br />
Room<br />
Acoustics<br />
Room<br />
Interference<br />
Room<br />
Interference<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 25<br />
p(r 1 )<br />
p(r 2 )<br />
sound<br />
field<br />
p(r 3 )
estoring<br />
force<br />
Stiffness K ms (x) of Suspension<br />
F � Kms<br />
( x)<br />
x<br />
displacement<br />
F<br />
F<br />
x<br />
x<br />
K<br />
6<br />
N/mm<br />
5<br />
4<br />
3<br />
2<br />
1<br />
spider<br />
-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0<br />
Kms(x) determined by<br />
• suspension geometry<br />
• impregn<strong>at</strong>ion<br />
surround<br />
diplacement x mm<br />
• adjustment of spider <strong>and</strong> surround<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 26<br />
total<br />
suspension
Das verknüpfte Bild kann nicht angezeigt werden. Möglicherweise wurde die D<strong>at</strong>ei verschoben, umbenannt oder gelöscht. Stellen Sie sicher, dass die Verknüpfung auf die korrekte D<strong>at</strong>ei und den korrekten Speicherort zeigt.<br />
Mechanical Stress in a Spider<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 27
Symmetrical Limiting of Spider<br />
K_MS [N/mm]<br />
4,0<br />
3,5<br />
3,0<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
0,0<br />
-x_max < x < x_max<br />
stiffness K_MS(x)<br />
KLIPPEL<br />
-10 -5 0 5 10<br />
><br />
spider<br />
diaphragm<br />
voice coil<br />
former<br />
Requirements:<br />
• geometry of inner corrug<strong>at</strong>ion roll is important<br />
• sufficient numbers of corrug<strong>at</strong>ion rolls<br />
• number of grooves equals numbers of ridges<br />
• symmetrical feet<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 28<br />
frame
Distortion Gener<strong>at</strong>ed by K ms(x)<br />
simplified signal flow chart<br />
fs<br />
Voltage pressure<br />
distortion<br />
multiplier<br />
Displacement x<br />
� ( x)<br />
� K ( 0)<br />
�<br />
Kms ms Re<br />
�<br />
Bl<br />
fs<br />
lowpass<br />
highpass<br />
Bass tone<br />
� Multiplic<strong>at</strong>ion of displacement time signals x(t)*Kms(x(t))<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 29<br />
pass b<strong>and</strong>
Symptom of Kms: Amplitude Compression<br />
Fundamental coil displacement in a vented-box System<br />
linear<br />
nonlinear<br />
X [mm] (rms)<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
Fundamental component<br />
| X ( f1, U1 ) |<br />
1.00 V 2.00 V 3.00 V<br />
4.00 V LINEAR MODEL<br />
Compression<br />
101 102 Frequency f1 [Hz]<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 30
<strong>Nonlinear</strong> Stiffness K ms(x)<br />
Symptoms:<br />
- Compression of the fundamental (f
ack pl<strong>at</strong>e<br />
F<br />
magnet<br />
Φ dc<br />
Force Factor Bl(x)<br />
pole pl<strong>at</strong>e<br />
B-field<br />
0 mm<br />
F � Bl(<br />
x)<br />
i<br />
U � Bl(<br />
x)<br />
v<br />
coil<br />
pole piece<br />
displacement<br />
Electro-dynamical driving force Voice coil current<br />
Back EMF Voice coil velocity<br />
x<br />
Bl(x) determined by<br />
• Magnetic field distribution<br />
• Height <strong>and</strong> overhang of the coil<br />
• Optimal voice coil position<br />
3.5<br />
3.0<br />
2.5<br />
2.0<br />
1.5<br />
1.0<br />
0.5<br />
0.0<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 32<br />
5.0<br />
N/A<br />
Bl(x)<br />
N S<br />
-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5<br />
><br />
F<br />
i<br />
F �<br />
Bli
Motor with Equal-length Configur<strong>at</strong>ion<br />
magnet<br />
pole piece<br />
h coil<br />
h<br />
gap<br />
Coil height h coil � gap height h gap<br />
x<br />
pole pl<strong>at</strong>e<br />
voice coil<br />
Properties:<br />
3,0<br />
50%<br />
b [N/A]<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 33<br />
3,5<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
0,0<br />
-x_max < x < x_max<br />
force factor b(x)<br />
h coil<br />
KLIPPEL<br />
-7,5 -5,0 -2,5 0,0 2,5 5,0 7,5<br />
><br />
• Sensitive to offset in rest position<br />
• Sensitive to instabilities f>fs • Low-order distortion <strong>at</strong> low amplitudes<br />
• Low inductance <strong>and</strong> flux modul<strong>at</strong>ion<br />
�
magnet<br />
pole piece<br />
Motor with Overhang Coil<br />
h coil<br />
h<br />
gap<br />
Coil height h coil > gap height h gap<br />
x<br />
pole pl<strong>at</strong>e<br />
voice coil<br />
Properties:<br />
b [N/A]<br />
5,5<br />
5,0<br />
4,5<br />
50%<br />
4,0<br />
3,5<br />
3,0<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
0,0<br />
-x_max < x < x_max<br />
force factor b(x)<br />
�h � h �<br />
h coil<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 34<br />
�<br />
�<br />
coil<br />
KLIPPEL<br />
-10,0 -7,5 -5,0 -2,5 0,0 2,5 5,0 7,5 10,0<br />
><br />
• Insensitive to offset <strong>at</strong> rest position<br />
• Low distortion for x < (h coil-h gap)<br />
• <strong>High</strong> distortion for x > (h coil-h gap)<br />
• <strong>High</strong> voice coil inductance<br />
• Sensitive to flux modul<strong>at</strong>ion<br />
gap
Adjusting Coil‘s Rest Position<br />
Bl [N/A]<br />
5,0<br />
4,5<br />
4,0<br />
3,5<br />
3,0<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
0,0<br />
magnet<br />
pole piece<br />
x=0<br />
pole pl<strong>at</strong>e<br />
Induction B<br />
voice coil<br />
displacement<br />
Force factor Bl vs. displacement X<br />
Bl(X)<br />
-10,0 -7,5 -5,0 -2,5 0,0 2,5 5,0 7,5 10,0<br />
Displacement X [mm]<br />
Bl [N/A]<br />
5,0<br />
4,5<br />
4,0<br />
3,5<br />
3,0<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
0,0<br />
magnet<br />
pole piece<br />
x=x b<br />
pole pl<strong>at</strong>e<br />
Induction B<br />
voice coil<br />
Force factor Bl vs. displacement X<br />
Bl(X)<br />
displacement<br />
-10,0 -7,5 -5,0 -2,5 0,0 2,5 5,0 7,5 10,0<br />
Displacement X [mm]<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 35
Gener<strong>at</strong>ion of Bl(x) Distortion<br />
1 st nonlinear effect: Parametrical Excit<strong>at</strong>ion<br />
Voice tone<br />
Bass tone<br />
1. Motor force F=Bl(x)*i<br />
2. Multiplic<strong>at</strong>ion of displacement x(t) <strong>and</strong> current i(t)<br />
3. <strong>High</strong> distortion (f 1 ≤ f s, f 2 > f s)<br />
fs<br />
fs<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 36<br />
pass b<strong>and</strong><br />
Voltage fs pressure<br />
distortion<br />
impedance highpass<br />
multiplier<br />
current<br />
x<br />
lowpass
Bl(x)<br />
5,0<br />
[N/A]<br />
4,5<br />
4,0<br />
3,5<br />
3,0<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
Symmetrical<br />
Force factor<br />
Bl(x)<br />
Amplitude Modul<strong>at</strong>ion<br />
KLIPPEL<br />
-5 -4 -3 -2 -1 0 1 2 3 4 5<br />
[mm]<br />
two-tone stimulus f 1 < f s, f 2 > f s<br />
Pfar [ N / m^2 ]<br />
5,0<br />
2,5<br />
0,0<br />
-2,5<br />
-5,0<br />
Sound pressure Pfar(t) in far field vs time<br />
Pfar(t)<br />
x peak<br />
Bottom<br />
Rest position<br />
Mean<br />
Cycle<br />
0,05 0,10 0,15<br />
Time [s]<br />
0,20 0,25 0,30<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 37
Third-order intermodul<strong>at</strong>ion distortion in percent (IEC 60268)<br />
Pressure Pfar in far field<br />
125<br />
100<br />
75<br />
50<br />
25<br />
Symptoms of Bl(x)<br />
Intermodul<strong>at</strong>ion Distortion<br />
intermodul<strong>at</strong>ion in same<br />
order of magnitude as<br />
harmonics for f < fs<br />
U = 1.5 U = 3 U = 4.5 U = 6 U = 7.5<br />
U = 9 U = 10.5 U = 12 U = 13.5 U = 15<br />
4*102 6*102 8*102 103 Frequency [Hz]<br />
KLIPPEL<br />
(constant bass tone f 1 =0.5f s <strong>and</strong> varying voice tone).<br />
magnet<br />
pole piece<br />
x=x b<br />
pole pl<strong>at</strong>e<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 38<br />
Induction B<br />
voice coil<br />
displacement<br />
Parametric excit<strong>at</strong>ion<br />
F=Bl(x)*i
X dc<br />
5 mm -<br />
0<br />
Bl-maximum<br />
dc-displacement (X dc )<br />
Symptoms of Bl(x)<br />
dc displacement<br />
unstable<br />
fs 2fs frequency<br />
for f < f s : small X dc towards maximum of Bl-curve<br />
for f = f s (resonance): no dc-part gener<strong>at</strong>ed (X dc = 0)<br />
for f > f s : X dc away from Bl-maximum<br />
for f � 1.5fs: high values of X dc (� may become unstable)<br />
UNIQUE SYMPTOM<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 39
(x)<br />
Instability of the <strong>Nonlinear</strong> Motor<br />
5,0<br />
4,5<br />
[N/A]<br />
4,0<br />
3,5<br />
3,0<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
Unstable for f > f s<br />
KLIPPEL<br />
-5 -4 -3 -2 -1 0 1 2 3 4 5<br />
[mm] x<br />
145.0<br />
U [V]<br />
20<br />
15<br />
Effects:<br />
• Reduced acoustical output<br />
• Substantial Distortion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 40<br />
10<br />
5<br />
Fundamental<br />
| Pfar( f1, U1 ) |<br />
100<br />
200<br />
300<br />
f [Hz]<br />
400<br />
0.75<br />
0.50<br />
0.25<br />
0.00<br />
500<br />
Pfar [N/m^2]
Bl [N/A]<br />
5,5<br />
5,0<br />
4,5<br />
4,0<br />
3,5<br />
3,0<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
0,0<br />
Curve 1<br />
Effect of a <strong>Nonlinear</strong> Motor<br />
KLIPPEL<br />
-15 -10 -5 0 5 10 15<br />
Displacement X [mm]<br />
• Parametric excit<strong>at</strong>ion<br />
F=Bl(x)*i<br />
• <strong>Nonlinear</strong> damping<br />
F=Bl(x) 2 /Re*v<br />
mm<br />
8<br />
7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
driver with<br />
• dominant Bl(x)-nonlinearity<br />
• linear suspension<br />
• constant inductance<br />
Fundamental component<br />
| X ( f1, U1 ) |<br />
U = 1.5 U = 3 U = 4.5 U = 6 U = 7.5<br />
U = 9 U = 10.5 U = 12 U = 13.5 U = 15<br />
KLIPPEL<br />
displacement<br />
102 103 Frequency [Hz]<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 41
Force Factor Bl(x)<br />
Symptoms:<br />
- Compression of the fundamental (f
Φ coil(-9 mm)<br />
U ind<br />
Φ counter<br />
Reluctance<br />
force<br />
shorting ring<br />
d ( x,<br />
i)<br />
� �<br />
dt<br />
�<br />
F rel<br />
Voice Coil Inductance L e(x)<br />
-9 mm<br />
d<br />
�L( x)<br />
i�<br />
dt<br />
0 mm<br />
2<br />
i ( t)<br />
dL(<br />
x)<br />
� �<br />
2 dx<br />
Φ coil(+9 mm)<br />
9 mm<br />
Differenti<strong>at</strong>ed<br />
Magnetic flux<br />
voice coil displacement<br />
x<br />
L e(x) determined by<br />
With with shorting rings ring<br />
• geometry of coil, gap, magnet<br />
• optimal size <strong>and</strong> position of short cut ring<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 43<br />
4.0<br />
Le<br />
[mH]<br />
2.5<br />
2.0<br />
1.5<br />
1.0<br />
0.5<br />
0.0<br />
Without without shorting rings ring<br />
-15 -10 -5 0 5 10 15<br />
[mH<br />
0,30<br />
0,25<br />
0,20<br />
0,15<br />
0,10<br />
0,05<br />
0,00<br />
Effect of <strong>Nonlinear</strong> Inductance L e(x)<br />
Le(X)<br />
[Ohm]<br />
25<br />
20<br />
15<br />
10<br />
5<br />
0<br />
KLIPPEL<br />
-4 -3 -2 -1 -0 1 2 3 4<br />
><br />
X=-4 mm X=4 mm<br />
Le(x) nonlinearity causes vari<strong>at</strong>ion of<br />
electrical input impedance<br />
Magnitude of electric impedance Z(f)<br />
x= 0 mm x = - 4 mm x = + 4 mm<br />
Coil is clamped<br />
X=-4 mm<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 44<br />
KLIPPEL<br />
X=4 mm<br />
101 102 103 104 Frequency [Hz]
Distortion caused by L e(x)<br />
6dB/oct<br />
pass b<strong>and</strong><br />
fs<br />
Voltage pressure<br />
distortion<br />
differenti<strong>at</strong>or<br />
multiplier<br />
L(<br />
x)<br />
1� L(x) L(<br />
0)<br />
current<br />
Voice tone<br />
f 2<br />
Bass tone<br />
f 1<br />
1. Multiplic<strong>at</strong>ion of x(t) <strong>and</strong> i(t)<br />
2. Differenti<strong>at</strong>ion of distortion + <strong>High</strong>-pass filtering<br />
� <strong>High</strong> intermodul<strong>at</strong>ion distortion (f 1 ≤ f s, f 2 > f s)<br />
i<br />
x<br />
displacement<br />
impedance<br />
fs<br />
fs<br />
lowpass<br />
highpass<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 45
Remedies for L e(x)<br />
Symptoms:<br />
- Intermodul<strong>at</strong>ion distortion (f 1 < f s , f 2 > f s)<br />
- dc displacement (f>f s)<br />
Remedies:<br />
1. Reduce magnetic ac-flux<br />
• by using a smaller coil with less windings<br />
• by increasing the voice coil resistance<br />
• Using shorting m<strong>at</strong>erial<br />
2. Make Le(x)=constant<br />
• By placing shorting m<strong>at</strong>erial <strong>at</strong> right position<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 46
Counter flux<br />
� C<br />
L E(x)<br />
L_E [mH]<br />
Remedy for L e(x): Shorting Ring<br />
1,75<br />
1,50<br />
1,25<br />
1,00<br />
0,75<br />
0,50<br />
0,25<br />
0,00<br />
magnet<br />
pole piece<br />
-x_max < x < x_max<br />
inductance L_E(x)<br />
pole pl<strong>at</strong>e<br />
Coil flux � A<br />
voice coil<br />
KLIPPEL<br />
Reduced<br />
value<br />
Less vari<strong>at</strong>ion versus x<br />
-5,0 -2,5 0,0 2,5 5,0<br />
><br />
short cut ring<br />
x<br />
i<br />
R E (T V )<br />
u<br />
L E (x)<br />
R RING<br />
Effect depends on<br />
b(x)v b(x) b(x)i<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 47<br />
L 2 (x)<br />
R 2 (x)<br />
v<br />
CMS (x) MMS RMS Electro-mechanical Equivalent Circuit<br />
• Geometry (Ring or Cap)<br />
• M<strong>at</strong>erial (Aluminum or Copper)<br />
• Size, position, distance to the coil<br />
F m (x,i)
<strong>Nonlinear</strong>ities of Loudspeaker Ports<br />
Air plug Air plug<br />
• Usual modeling the air flow by a lumped mass (air plug) is a<br />
simplific<strong>at</strong>ion !<br />
jet stream in loudspeaker ports .MOV<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 48
• V < V Crit<br />
Flow Resistance R A(v) of a Port<br />
<strong>at</strong> Medium <strong>Amplitudes</strong><br />
• Gener<strong>at</strong>ing an air jet<br />
• energy dissip<strong>at</strong>ed in the far field<br />
• Harmonics <strong>at</strong> low frequencies<br />
R A(v)<br />
• R A(v) ~ |v|*m v<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 49
Asymmetrical Flow Resistance R A(v)<br />
p box<br />
• R A(v 0) > R A(-v 0)<br />
p 0<br />
x DC<br />
• DC component in pressure p box<br />
• dynamical voice coil offset x<br />
R A(v)<br />
p box<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 50<br />
v<br />
x DC
Symptoms:<br />
Vented Box System<br />
• Q-factor of port decreases with amplitude (port closes !!)<br />
• Harmonics (not critical !!)<br />
• Gener<strong>at</strong>es modul<strong>at</strong>ed air noise (critical !!)<br />
• dc component in sound pressure in enclosure <strong>and</strong> a dynamic offest in<br />
voice coil working point (critical !!)<br />
Remedies:<br />
• Keep velocity in port low (< 10 m/s)<br />
• Keep port geometry symmetrical !!<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 51
<strong>Nonlinear</strong> Sound Propag<strong>at</strong>ion<br />
Wave Steepening<br />
Speed of sound depends on sound pressure c(p)<br />
Sound pressure maxima travel faster than minima<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 52
Wave Steepening in Horns<br />
Symptoms:<br />
• dominant second order harmonic <strong>and</strong> intermodul<strong>at</strong>ion distortion<br />
• Distortion rises by 6dB/oct. to higher frequencies<br />
• Distortion rises with distance from thro<strong>at</strong><br />
Remedies:<br />
� Reduce propag<strong>at</strong>ion where sound pressure is high<br />
� <strong>High</strong> Flare r<strong>at</strong>e of the horn<br />
� Short horn length<br />
� Low pressure <strong>at</strong> thro<strong>at</strong><br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 53
<strong>Nonlinear</strong> Mechanical Resistance R ms(v)<br />
Air flow<br />
magnet<br />
Pole piece<br />
v<br />
dome<br />
gap<br />
spider<br />
R ms(v)<br />
R ms(v) depends on velocity v of the coil due to air flow <strong>and</strong> turbulences <strong>at</strong> vents <strong>and</strong><br />
porous m<strong>at</strong>erial (spider, diaphragm)<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 54<br />
v
Remedies for <strong>Nonlinear</strong> Mechanical Damping<br />
Problem:<br />
• Air Flow in vents, holes, leakages or porous m<strong>at</strong>erial in enclosures<br />
• Dissip<strong>at</strong>ion depends on velocity (turbulences, energy is moved into the<br />
far field)<br />
Occurs in:<br />
• Microspeaker, Headphones, Tweeter<br />
• Horn compression driver<br />
Remedy:<br />
• Increase electrical damping by increasing Bl or decreasing Re<br />
• better sealing of the enclosure<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 55
Which nonlinearities are important ?<br />
Criteria for dominant <strong>Nonlinear</strong>ities:<br />
• limits acoustical output<br />
• gener<strong>at</strong>es audible distortion,<br />
• indic<strong>at</strong>es an overload situ<strong>at</strong>ion<br />
• causes unstable behavior<br />
• rel<strong>at</strong>ed with cost, weight, volume, efficiency<br />
• affects speaker system alignment<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 56
Ranking List of<br />
Transducer <strong>Nonlinear</strong>ities<br />
1. Force Factor Bl(x)<br />
2. Compliance Cms(x) � tweeter<br />
3. Inductance Le(x) 4. Flux Modul<strong>at</strong>ion of Le(i) 5. Mechanical Resistance Rms(v) 6. <strong>Nonlinear</strong> Sound Propag<strong>at</strong>ion c(p)<br />
7. Doppler Distortion �(x)<br />
8. Flux Modul<strong>at</strong>ion of Bl(i)<br />
9. <strong>Nonlinear</strong> Cone Vibr<strong>at</strong>ion<br />
10. Port <strong>Nonlinear</strong>ity RA(v) 11. many others ...<br />
� microspeaker<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 57<br />
� woofers<br />
� microspeaker<br />
� horns
Electro-mechanical Equivalent Circuit<br />
<strong>Nonlinear</strong> parameters:<br />
• Force factor Bl(x) of the motor<br />
• Compliance C MS(x, t) of the suspension<br />
• Voice coil inductance L E(x), L 2(x)<br />
• resistance R 2(x) due to eddy currents<br />
• DC-resistance R E(T V)<br />
• Reluctance force F M(x)<br />
• Compliance C r (p rear ) of rear enclosure<br />
• Compliance C ab (p box ) of vented enclosure<br />
• Losses in port R ap(q p)<br />
• Time delay t(x) due to Doppler effect<br />
i<br />
Re (Tv)<br />
Le(x)<br />
L2(x)<br />
R2(x)<br />
Mms Rms(v) Cms(x)<br />
U Bl(x,I)V Bl(x,I) Bl(x,I)I<br />
Sd<br />
V<br />
Fm (x,I)<br />
are not constant parameters but<br />
depend on st<strong>at</strong>e variables:<br />
• Displacement x<br />
• Voice coil temper<strong>at</strong>ure T V<br />
•Time t due to ageing<br />
• volume velocity q p in port<br />
• pressure p rear rear enclosure<br />
• pressure p box in vented enclosure<br />
Cab(pbox)<br />
Cr(prear)<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 58<br />
SdV<br />
pbox<br />
prear<br />
Ral<br />
qp<br />
Rap(qp)<br />
Map<br />
radi<strong>at</strong>ion
Signal Flow Chart of the Transducer<br />
simplified by assuming a linear impedance for the mechanical load<br />
Feedback<br />
<strong>Nonlinear</strong> differential equ<strong>at</strong>ion<br />
Based on lumped parameter modeling<br />
Linear system modeled by transfer function H(f,r a)<br />
Feed-forward<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 59
Source of the <strong>Nonlinear</strong> Distortion<br />
considering dominant nonlinearities in electrodynamical loudspeakers<br />
Loudspeaker<br />
u<br />
input<br />
uD<br />
<strong>Nonlinear</strong><br />
distortion<br />
<strong>Nonlinear</strong><br />
System<br />
H(s,r1)<br />
H(s,ri) p(ri)<br />
H(s,rN)<br />
p(r1)<br />
sound<br />
...<br />
... field<br />
...<br />
...<br />
...<br />
...<br />
p(rN)<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 60
Voice Coil He<strong>at</strong>ing depends on the<br />
Spectral Properties of the Stimulus<br />
100<br />
90<br />
80<br />
70<br />
50<br />
30<br />
20<br />
10<br />
0<br />
-1 0<br />
KLIPPEL<br />
[K ] [W ]<br />
40<br />
t 1<br />
t 2<br />
0 250 500 750 1000 1250 1500 1750 2000 2250<br />
t [s e c ]<br />
t 3<br />
P RE<br />
P Re<br />
� T V<br />
Delta Tv<br />
Music: Classic<br />
Pop<br />
Vocal<br />
Thermal resistance<br />
�T v/P re=<br />
6,8 K/W 4,6 K/W 7,5 K/W<br />
<strong>High</strong> voice coil displacement gives<br />
high Convection cooling<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 61<br />
30<br />
25<br />
15<br />
10<br />
is not constant !!<br />
5<br />
0
P coil<br />
T v<br />
�T v<br />
<strong>Nonlinear</strong> Thermal Model<br />
C tv<br />
P tv<br />
P con<br />
R tc (v)<br />
Air<br />
convection<br />
cooling<br />
Rta (x)<br />
R tv<br />
R tt (v)<br />
C ta<br />
T a<br />
P eg<br />
Direct he<strong>at</strong><br />
transfer<br />
T g<br />
�T g<br />
�T m<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 62<br />
P g<br />
C tg<br />
R tg<br />
P mag<br />
T m<br />
C tm<br />
R tm
Agenda<br />
1. Large Signal Behavior (Symptoms)<br />
2. Physical Causes <strong>and</strong> Models<br />
3. Measurement of Large Signal Parameters<br />
4. Loudspeaker Diagnostics<br />
5. Modern Loudspeaker Design<br />
6. Active Control<br />
7. Conclusion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 63
Identific<strong>at</strong>ion of the Driver Model<br />
Three Tasks:<br />
Abstraction<br />
i<br />
R E (T V )<br />
u<br />
L E (x)<br />
L 2 (x)<br />
R 2 (x)<br />
b(x)v b(x) b(x)i<br />
Lumped Parameter Model<br />
Identific<strong>at</strong>ion<br />
v<br />
CMS (x) MMS RMS • prove th<strong>at</strong> the model is adequ<strong>at</strong>e for the particular driver<br />
• measure the free parameters (C ms, Bl, M ms, ...) of the model<br />
• measure instantaneous st<strong>at</strong>e variables (displacement x, ...)<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 64<br />
F m (x,i)<br />
2<br />
� dLe<br />
( x)<br />
� d x dx<br />
�Bl(<br />
x)<br />
� i�i<br />
� Mms<br />
� Rms<br />
� Kms(<br />
x)<br />
x<br />
2<br />
� dx � dt dt<br />
dx d(<br />
Le(<br />
x)<br />
i)<br />
u � Rei<br />
� Bl(<br />
x)<br />
�<br />
dt dt<br />
Differential Equ<strong>at</strong>ion
Large Signal Model & Parameters<br />
He<strong>at</strong> transfer<br />
Convection cooling<br />
Stimulus<br />
Amplifier<br />
Crossover<br />
Linear<br />
System<br />
H el(s)<br />
R tv, R tm,<br />
� tv, � tm,<br />
Bl(x), L(x),<br />
L(i)<br />
T/S Parameter<br />
Thermal<br />
Model<br />
<strong>Nonlinear</strong><br />
System<br />
Kms(x)<br />
Z m(s)<br />
Motor Suspension Cone<br />
Linear<br />
System<br />
H a(s)<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 65<br />
Sound<br />
pressure<br />
output<br />
Enclosure, Horn room
Measurement of Large Signal Parameters<br />
St<strong>and</strong>ard IEC 62458<br />
defines<br />
1. St<strong>at</strong>ic (quasi-st<strong>at</strong>ic) method<br />
2. Incremental dynamic method<br />
3. Full dynamic method<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 66
Method:<br />
1. Select a working point<br />
2. Excite with DC stimulus<br />
St<strong>at</strong>ic Measurement<br />
3. Measure associ<strong>at</strong>ed st<strong>at</strong>e signals<br />
4. Calcul<strong>at</strong>e instantaneous parameters<br />
5. Repe<strong>at</strong> the measurement <strong>at</strong> other<br />
working points<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 67<br />
F<br />
secant<br />
x<br />
K MS(x)= F DC<br />
x DC
Example: St<strong>at</strong>ic Measurement of Stiffness<br />
Ringlstetter Harman Becker Straubing 2004<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 68
Incremental dynamic Measurement<br />
Method:<br />
1. Select a working point<br />
2. Excite with a dc stimulus<br />
3. Add a small AC-signal<br />
4. Measure st<strong>at</strong>e variables XAC <strong>and</strong> FAC 5. Calcul<strong>at</strong>e gradient Kgrad (XDC) 6. Repe<strong>at</strong> <strong>at</strong> other working points<br />
7. Parameter Transform<strong>at</strong>ion<br />
F DC FAC<br />
K grad(x)= F AC<br />
X AC<br />
Transform<strong>at</strong>ion<br />
K MS(x)= F<br />
X<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 69<br />
tangent<br />
x DC<br />
x AC
First available product: DUMAX<br />
incremental dynamic method<br />
Photo courtesy by D. Clark<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 70
Method:<br />
Full dynamic Measurement<br />
1. Excite speaker with audio-like signal<br />
2. Measure instantaneous st<strong>at</strong>e variables<br />
3. Estim<strong>at</strong>e free model parameters<br />
� first applic<strong>at</strong>ion of system<br />
identific<strong>at</strong>ion to loudspeakers<br />
(Knudsen 1993)<br />
F AC(t)<br />
K MS(x)= F<br />
X<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 71<br />
F<br />
secant<br />
x<br />
X AC(t)
Full Dynamic Measurement of<br />
Loudspeaker <strong>Nonlinear</strong>ities<br />
Suspension Part<br />
Measurement<br />
(SPM)<br />
Large Signal<br />
Identific<strong>at</strong>ion (LSI)<br />
Long-term Power<br />
Testing (PWT)<br />
Motor-Suspension<br />
Check QC (MSC)<br />
Advantages:<br />
• Loudspeaker under normal<br />
working conditions<br />
• Audio-like stimulus<br />
• On-line measurement<br />
Disadvantage:<br />
• Large Signal Idenific<strong>at</strong>ion requires<br />
nonlinear signal processing<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 72
Adaptive Identific<strong>at</strong>ion Principle<br />
full dynamic method based on current & voltage measurement<br />
audio-like,<br />
persistent<br />
Signal<br />
Source<br />
protection<br />
Detection<br />
working range<br />
normal<br />
working<br />
conditions<br />
Model<br />
precise,<br />
robust<br />
sensor<br />
St<strong>at</strong>e<br />
Measurement<br />
optimal fitting<br />
Parameter<br />
Estim<strong>at</strong>ion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 73
Stimulus<br />
Noise,<br />
Audio signals<br />
(music, noise)<br />
Multi-tone<br />
complex<br />
Linear Parameters<br />
• T/S parameters <strong>at</strong> x=0<br />
• Box parameters fb,Qb<br />
• Impedance <strong>at</strong> x=0<br />
Dynamic Measurement<br />
of Motor <strong>and</strong> Suspension <strong>Nonlinear</strong>ities<br />
Voltage & current<br />
<strong>Nonlinear</strong><br />
System<br />
Identific<strong>at</strong>ion<br />
<strong>Nonlinear</strong> Parameters<br />
• nonlinearities Bl(x), Kms(x), Cms(x),<br />
Rms(v), L(x), L(i)<br />
• Voice coil offset<br />
• Suspension asymmetry<br />
• Maximal peak displacement (Xmax)<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 74<br />
St<strong>at</strong>e Variables<br />
• peak displacement during measurement<br />
• voice coil temper<strong>at</strong>ure<br />
• eletrical input power,<br />
Thermal Parameters<br />
• Thermal resistances Rtv, Rtm<br />
• Thermal capacity Ctv, Ctm<br />
• Air convection cooling
Controlling the Production Process<br />
Corrected<br />
Rest Position<br />
B field<br />
voice<br />
coil<br />
Shift coil 0.6 mm to backpl<strong>at</strong>e<br />
Action<br />
Failure:<br />
Coil Offset<br />
B field<br />
Fail<br />
voice<br />
coil<br />
Targets:<br />
•Detection of motor <strong>and</strong><br />
suspension problem as fast<br />
as possible (when first<br />
device arrives <strong>at</strong> the end of<br />
line)<br />
•Simplify interpret<strong>at</strong>ion of<br />
results (voice coil offset in<br />
mm)<br />
•Single-valued parameter<br />
can be directly be used for<br />
adjustment<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 75
Delta Tv [K]<br />
[mm]<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
125<br />
100<br />
75<br />
50<br />
25<br />
0<br />
Measurement of Thermal Parameters<br />
within the Large Identific<strong>at</strong>ion Module (LSI)<br />
0 Delta 2500 Tv 5000 7500 P real 10000 12500P Re 15000<br />
t [sec]<br />
KLIPPEL<br />
nonlinear<br />
r V<br />
0 2500 5000 7500<br />
t [sec]<br />
10000 12500 15000<br />
R TV ,� V<br />
�<br />
Xpeak Xbottom<br />
Voice coil displacement<br />
Power dissep<strong>at</strong>ed in Re<br />
R TM ,� M<br />
Thermal identific<strong>at</strong>ion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 76<br />
KLIPPEL<br />
Voice coil temper<strong>at</strong>ure<br />
Real input power<br />
225<br />
200<br />
175<br />
150<br />
125<br />
100<br />
75<br />
50<br />
25<br />
0<br />
P [W]
Agenda<br />
1. Large Signal Behavior (Symptoms)<br />
2. Physical Causes <strong>and</strong> Models<br />
3. Measurement of Large Signal Parameters<br />
4. Loudspeaker Diagnostics<br />
5. Modern Loudspeaker Design<br />
6. Active Control<br />
7. Conclusion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 77
Small Signal Performance<br />
Specific<strong>at</strong>ions for Active <strong>and</strong> Passive Loudspeaker Systems<br />
180°<br />
90°<br />
90°<br />
270°<br />
-90°<br />
�<br />
�<br />
0°<br />
All inform<strong>at</strong>ion are provided by a complex 3D far<br />
field response H(f,�, �) measured with sufficient<br />
angular resolution<br />
Most important responses:<br />
• SPL on-axis amplitude response<br />
� under anechoic conditions (IEC 60268-5)<br />
• Directivity<br />
� Directivity index D i(f) or sound power response P a(f) (IEC 60268-5 Sec. 22.1)<br />
• Group delay<br />
� l<strong>at</strong>ency<br />
� vari<strong>at</strong>ion vs. Frequency,<br />
� vari<strong>at</strong>ion between channels<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 78
Large Signal Performance<br />
Specific<strong>at</strong>ions for Active <strong>and</strong> Passive Loudspeaker Systems<br />
• Maximal SPL max <strong>at</strong> 1 m, on-axis anechoic conditions, in frequency range<br />
• Effective frequency range (Upper <strong>and</strong> lower limits f lower,l < f < f upper,l )<br />
• Fl<strong>at</strong>ness of on-axis response (maximal devi<strong>at</strong>ion of SPL on-axis response from<br />
mean SPL)<br />
• Harmonic distortion (Equivalent input distortion)<br />
• Intermodul<strong>at</strong>ion distortion (voice <strong>and</strong> bass sweep)<br />
• Impulsive distortion (peak, crest) indic<strong>at</strong>ing rub&buzz, loose particles<br />
• Modul<strong>at</strong>ed noise (MOD) indic<strong>at</strong>ing air leakage<br />
• Durability verified in acceler<strong>at</strong>ed life test<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 79
How to interprete Harmonic Distortion<br />
2 nd harmonic<br />
asymmetry<br />
2 nd , 3 rd <strong>and</strong> higher-order harmonics<br />
(amplitude <strong>and</strong> phase inform<strong>at</strong>ion)<br />
3 rd harmonic<br />
symmetry<br />
THD<br />
magnitude<br />
Characteristics of the nonlinearity<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 80<br />
Important for<br />
irregular defects<br />
„rub & buzz“<br />
CHD<br />
Crest factor<br />
smoothness
dB - [V] (rms)<br />
130<br />
120<br />
110<br />
100<br />
90<br />
80<br />
70<br />
60<br />
50<br />
Interpret<strong>at</strong>ion of THD in SPL<br />
Kms(x)<br />
Bl(x)<br />
L(x)<br />
Fundamental<br />
Fundamental<br />
Fundamental THD<br />
50 100 200 500 1k 2k 5k<br />
Frequency [Hz]<br />
THD<br />
L(i)<br />
Cone Vibr<strong>at</strong>ion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 81<br />
KLIPPEL
dB - [V]<br />
0<br />
-5<br />
-10<br />
-15<br />
-20<br />
-25<br />
-30<br />
-35<br />
-40<br />
-45<br />
Transform Distortion to the Source<br />
Sinusoidal<br />
sweep<br />
Distortion in Voltage<br />
3rd harmonic distortion in voltage<br />
Signal <strong>at</strong> IN1<br />
nearfield 30 cm 60 cm 1 m distance<br />
KLIPPEL<br />
Independent of room<br />
50 100 200<br />
Frequency [Hz]<br />
500 1k<br />
U(f)<br />
D<br />
<strong>Nonlinear</strong><br />
<strong>Nonlinear</strong><br />
System<br />
System<br />
H(f,r1)<br />
H(f,r2)<br />
Inverse filtering<br />
with H(f,r)<br />
p(r1)<br />
sound<br />
field<br />
p(r2)<br />
3rd harmonics absolute<br />
Signal <strong>at</strong> IN1<br />
1 m distance 60 cm distance 30 cm distance nearfield<br />
KLIPPEL<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 82<br />
dB - [V]<br />
90<br />
85<br />
80<br />
75<br />
70<br />
65<br />
60<br />
55<br />
50<br />
45<br />
40<br />
Sound pressure<br />
measurement<br />
50 100 200<br />
Frequency [Hz]<br />
500 1k
Interpret<strong>at</strong>ion of Multi-tone Distortion<br />
[dB]<br />
120<br />
110<br />
100<br />
90<br />
80<br />
70<br />
60<br />
50<br />
Kms(x)<br />
Fundamental Multi-tone Distortion<br />
Fundamental<br />
50 100 200 500 1k 2k 5k 10k<br />
Frequency [Hz]<br />
Bl(x)<br />
Distortion<br />
L(x)<br />
L(i)<br />
Doppler Effect<br />
Cone Vibr<strong>at</strong>ion<br />
KLIPPEL<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 83
How to cope with nonlinearities<br />
• Measure nonlinear distortion in the near field<br />
� ensure sufficient SNR<br />
• Transform distortion to the loudspeaker input<br />
� concept of equivalent input distortion<br />
• Be aware of interactions between nonlinearities<br />
� no compens<strong>at</strong>ion of Kms(x), Bl(x), L(x)<br />
• Check for dc-displacement<br />
� instability<br />
• Use numerical simul<strong>at</strong>ion tool<br />
� predict THD, Xmax, SPLmax, IMD, Pmax, T<br />
• Separ<strong>at</strong>e regular nonlinearities from irregular defects<br />
� measure Crest Factor of Distortion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 84
Thermal Parameters<br />
alpha 0.375914 He<strong>at</strong>ing of voice coil by eddy currents<br />
Rtv 0.932822 K/W thermal resistance coil ==> pole tips<br />
rv 0.192945 Ws/Km air convection cooling depending on velocity<br />
Rtm 0.372579 K/W thermal resistance magnet ==> environment<br />
tau m 67 min thermal time constamt of magnet<br />
Ctm 10796.289063 Ws/K thermal capacity of the magnet<br />
tau v 131.063660 s thermal time constant of voice coil<br />
Ctv 140.502304 Ws/K thermal capacity of the voice coil<br />
Can be directly be pasted into the Simul<strong>at</strong>ion module (SIM) to<br />
make a thermal analysis (predict temper<strong>at</strong>ures <strong>and</strong> power flow)<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 85
P coil<br />
P RE +<br />
0.3 (P real <strong>–</strong>P RE)<br />
T v<br />
�T v<br />
C tv<br />
Thermal Analysis<br />
single tone <strong>at</strong> 65 Hz with 40 V rms<br />
P con<br />
Air<br />
convection<br />
cooling<br />
P tv<br />
R tc (v)<br />
1/r tv V rms<br />
R tv<br />
0.93 K/ W<br />
Direct he<strong>at</strong><br />
transfer<br />
T a<br />
P eg<br />
�T m<br />
C tm<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 86<br />
P g<br />
0.7 (P real <strong>–</strong>P RE)<br />
T m<br />
0.37 K/ W<br />
R tm
P coil<br />
167 W<br />
T v<br />
�T v<br />
C tv<br />
Thermal Analysis<br />
single tone <strong>at</strong> 65 Hz with 40 V rms<br />
146 W<br />
Rtv 196 K P T g 163 W m 60 K<br />
P tv<br />
P con<br />
Air<br />
convection<br />
cooling<br />
21 W<br />
R tc (v)<br />
Direct he<strong>at</strong><br />
transfer<br />
T a<br />
P eg<br />
17 W<br />
�T m<br />
C tm<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 87<br />
R tm
70 W<br />
P coil<br />
T v<br />
�T v<br />
C tv<br />
Thermal Analysis<br />
single tone <strong>at</strong> 1000 Hz with 40 V rms<br />
69 W<br />
P tv<br />
P con<br />
R tc (v)<br />
R tv<br />
99 K 34 K<br />
1 W<br />
T a<br />
P eg<br />
22 W<br />
Direct he<strong>at</strong><br />
transfer<br />
�T m<br />
C tm<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 88<br />
P g<br />
91 W<br />
T m<br />
R tm
P coil<br />
134 W<br />
T v<br />
�T v<br />
Thermal Analysis<br />
two-tone <strong>at</strong> 1000 Hz <strong>and</strong> 50 Hz with 30 V rms<br />
C tv<br />
118 W<br />
R tv<br />
160 K 50 K<br />
P tv<br />
P con<br />
16 W<br />
R tc (v)<br />
Direct he<strong>at</strong><br />
transfer<br />
T a<br />
P eg<br />
16 W<br />
�T m<br />
C tm<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 89<br />
P g<br />
134 W<br />
T m<br />
R tm
P coil<br />
Tv Rtv Tm<br />
�T v<br />
C tv<br />
Power Bypass Factor<br />
The power P tv should be minimal !<br />
P tv<br />
P con<br />
R tc (v)<br />
T a<br />
118 W<br />
16 W<br />
16 W<br />
P eg<br />
P mag<br />
�T m<br />
C tm<br />
R tm<br />
� �<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 90<br />
The bypass<br />
factor � should<br />
be maximal !<br />
P � P<br />
con eg<br />
P � P<br />
Re R2<br />
Total input power
Optimal Thermal Design<br />
Investig<strong>at</strong>ion of Design Choices<br />
dome<br />
vent<br />
gap<br />
Vented pole piece<br />
Av<br />
dome<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 91<br />
vent<br />
Av<br />
gap<br />
Sealed pole piece<br />
Which design Choice provides a better he<strong>at</strong> transfer ?
Bypass Power Factor �<br />
dome<br />
vent<br />
Av<br />
(vented <strong>and</strong> sealed pole piece)<br />
gap<br />
60<br />
50<br />
��������� ���������<br />
40<br />
[%]<br />
30<br />
20<br />
10<br />
00<br />
1 10 100 1000 1000<br />
frequency [Hz]<br />
Closing the vent in the pole piece:<br />
50 percent of the power will bypass the coil !<br />
vent sealed<br />
vent open<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 92
Agenda<br />
1. Large Signal Behavior (Symptoms)<br />
2. Physical Causes <strong>and</strong> Models<br />
3. Measurement of Large Signal Parameters<br />
4. Loudspeaker Diagnostics<br />
5. Modern Loudspeaker Design<br />
6. Active Control<br />
7. Conclusion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 93
Steps in Loudspeaker System<br />
Design<br />
1. Definition of target performance <strong>and</strong> constraints<br />
2. Defining the interface between the components<br />
(DSP, amplifier, transducers)<br />
3. Specific<strong>at</strong>ion of the components<br />
4. Selecting the components<br />
5. Building the first prototype<br />
6. Verific<strong>at</strong>ion of the performance<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 94
Modeling<br />
Measurement<br />
Applic<strong>at</strong>ion<br />
Parts<br />
(cone, spider,<br />
motor parts)<br />
Loudspeaker Development<br />
Distributed Parameter<br />
Models<br />
(FEA, BEA)<br />
Geometry<br />
M<strong>at</strong>erial<br />
Parameter<br />
Driver<br />
(woofer,<br />
tweeter)<br />
Thermal<br />
Parameters<br />
Linear T/S<br />
Parameters<br />
Lumped<br />
Parameter<br />
Models<br />
Cone<br />
Vibr<strong>at</strong>ion<br />
Parameters independent of stimulus<br />
<strong>Nonlinear</strong><br />
Parameters<br />
Definition of Target Performance<br />
Selection of Components & Design<br />
System<br />
(driver + Xover + room)<br />
Evalu<strong>at</strong>ion of the First Prototype<br />
End-of-line Testing<br />
System-oriented<br />
Models<br />
<strong>Nonlinear</strong><br />
Distortion<br />
Power<br />
H<strong>and</strong>ling<br />
Loudness<br />
density<br />
Small Signal<br />
Performance<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 95<br />
Listener<br />
Psychoacoustical<br />
Models<br />
Symptoms dependent on stimulus<br />
R&D<br />
Sound<br />
Attributes<br />
Quality<br />
Metrics<br />
QC
How to define the Target Performance<br />
Auraliz<strong>at</strong>ion using the large signal model<br />
Development<br />
Manufacturing<br />
Objective Evalu<strong>at</strong>ion<br />
• Distortion, Maximal Output<br />
• Displacement, Temper<strong>at</strong>ure<br />
• Evalu<strong>at</strong>ion of Design Choices<br />
• Indic<strong>at</strong>ions for Improvements<br />
Marketing<br />
Management<br />
Subjective Evalu<strong>at</strong>ion<br />
• Personal Impression<br />
• Sufficient Sound Quality<br />
• Tuning to the target market<br />
• Performance/Cost R<strong>at</strong>io<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 96
Auraliz<strong>at</strong>ion - System<strong>at</strong>ic Listening Tests<br />
using Simul<strong>at</strong>ion <strong>and</strong> Decomposition Techniques<br />
Stimulus<br />
H el(s)<br />
Linear<br />
System<br />
Transfer function<br />
Thermal<br />
Parameters<br />
R tv, R tm<br />
Power<br />
varied parameter<br />
Thermal<br />
Model<br />
Lumped<br />
Parameters<br />
<strong>Nonlinear</strong><br />
System<br />
Bl(x), L(x).<br />
Cms(x) Re, Mms<br />
Temper<strong>at</strong>ure<br />
Y(s)<br />
Mechancial<br />
Cone<br />
Admittance<br />
Linear<br />
System<br />
H a(s)<br />
Electrical Transfer<br />
Function<br />
Amplifier Crossover Motor Suspension Cone Enclosure, Horn Room<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 97<br />
Listening test<br />
Sens<strong>at</strong>ions<br />
Psychoacoustical<br />
Model
Music<br />
Test signals<br />
<strong>Nonlinear</strong> Auraliz<strong>at</strong>ion Technique<br />
Force factor Bl (X)<br />
-Xprot < X < Xprot Xp- < X < Xp+<br />
Stiffness of suspension Kms (X)<br />
6<br />
KLIPPEL<br />
5<br />
4<br />
3<br />
2<br />
2,25<br />
-Xprot < X < Xprot<br />
2,00<br />
1,75<br />
Xp- < X < Xp+<br />
KLIPPEL<br />
1<br />
1,50<br />
0<br />
-7,5 -5,0 -2,5 0,0 2,5 5,0 7,5<br />
X [mm]<br />
1,25<br />
1,00<br />
0,75<br />
0,50<br />
0,25<br />
0,00<br />
-7,5 -5,0 -2,5 0,0 2,5<br />
X [mm]<br />
5,0 7,5<br />
Bl [N/A]<br />
Parameters<br />
Kms [N/mm]<br />
Loudspeaker<br />
Model<br />
Coil displacement,<br />
Power, Temper<strong>at</strong>ure<br />
Linear Signal<br />
SLIN<br />
SDIS<br />
Plin<br />
PDIS<br />
Distortion<br />
Separ<strong>at</strong>ion of the nonlinear<br />
distortion components<br />
Perceptual<br />
Signal Quality<br />
Analyzer<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 98<br />
Sound pressure<br />
output
Ideal Speaker (Linear)<br />
Real Speaker<br />
Perceptual Sound Quality Evalu<strong>at</strong>ion<br />
OPERA/PEAQ<br />
Total signal<br />
distortion<br />
Perceptional <strong>at</strong>tributes<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 99
How to Specify the Optimal Transducer ?<br />
Parameters give a<br />
comprehensive<br />
set of d<strong>at</strong>a !!<br />
Should be<br />
transformed into<br />
parameters<br />
1. Parameters (independent of stimuli)<br />
• Acoustical transfer functions<br />
• Mechanical transfer functions<br />
• Small signal parameter T/S<br />
• Large signal parameters (thermal, nonlinear)<br />
2. Stimulus-based Characteristics<br />
• Maximal SPL<br />
• <strong>Nonlinear</strong> distortion (THD, IMD, XDC)<br />
• Symptoms of irregular defects (rub, buzz, leakage,...)<br />
• Coil temper<strong>at</strong>ure, compression, Pmax<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 100
Transform<strong>at</strong>ion of Symptoms into Parameters<br />
Intermodul<strong>at</strong>ion distortion IMD @ SPL MAX � force factor BL(x)<br />
[Percent]<br />
40<br />
35<br />
30<br />
25<br />
20<br />
15<br />
10<br />
5<br />
0<br />
Two- tone<br />
Stimulus<br />
Rel<strong>at</strong>ive third-order intermodul<strong>at</strong>ion distortion ( d3 )<br />
Pfar - pressure in far field<br />
1.00 V 2.15 V 4.64 V 10.00 V<br />
KLIPPEL<br />
4*102 6*102 8*102 103 2*103 Frequency f1 [Hz]<br />
Loudspeaker<br />
Model<br />
(SIM Module)<br />
Target:<br />
change WIDTH in nonlinear<br />
curve editor of Bl(x) curve<br />
IMD<br />
Distortion<br />
• Check<br />
• 3rd order IMD @ SPLMAX using two-tone<br />
signal f2 >> fs <strong>and</strong> f1 < fs<br />
• Displacement limit XBl Bl [N/A]<br />
5,0<br />
4,5<br />
4,0<br />
3,5<br />
3,0<br />
2,5<br />
2,0<br />
1,5<br />
1,0<br />
0,5<br />
Force factor Bl(X) vs displacement<br />
50 % Bl<br />
5 mm 10 mm<br />
Coíl Height<br />
0,0<br />
-10,0 -7,5 -5,0 -2,5 0,0 2,5 5,0 7,5 10,0<br />
Displacement X [mm]<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 101
u<br />
Tv<br />
Magnetic<br />
FEA<br />
Motor<br />
(coil,gap,<br />
magnet)<br />
Thermal<br />
Dynamics<br />
Thermal<br />
FEA<br />
Design of the Transducer<br />
P<br />
F<br />
coil<br />
former<br />
v<br />
Mechanical<br />
System<br />
(suspension,<br />
cone,<br />
diaphragm)<br />
Coupled mechano-acoustical analysis<br />
FEA<br />
X(rc)<br />
Radi<strong>at</strong>or<br />
Acoustical<br />
System<br />
(enclosure,<br />
horn)<br />
near field<br />
F(rc)<br />
v(r)<br />
p(r)<br />
BEA<br />
Sound<br />
Propag<strong>at</strong>ion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 102<br />
p(ra)<br />
Far-Field
Progress:<br />
• Processing time, h<strong>and</strong>ling<br />
• Asymmetries in the shape<br />
• Geometrical nonlinearities<br />
(“vari<strong>at</strong>ion of the geometry”)<br />
• Acoustical-mechanical coupling<br />
Problems:<br />
• (<strong>Nonlinear</strong>) M<strong>at</strong>erial parameters<br />
• visco-elastic properties<br />
(Hyperelasticity, creep,<br />
Relax<strong>at</strong>ion)<br />
FEA Modeling<br />
by A. Svobodnik<br />
NADwork<br />
Pacsys<br />
ANSYS<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 103<br />
FineCone<br />
By P. Larsen<br />
Comsol
Agenda<br />
1. Large Signal Behavior (Symptoms)<br />
2. Physical Causes <strong>and</strong> Models<br />
3. Measurement of Large Signal Parameters<br />
4. Loudspeaker Diagnostics<br />
5. Modern Loudspeaker Design<br />
6. Active Control<br />
7. Conclusion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 104
u<br />
u D<br />
Equivalent Input Distortion<br />
<strong>Nonlinear</strong><br />
System<br />
H(f,r 1 )<br />
H(f,r 2 ) p(r 2 )<br />
H(f,r 3 )<br />
p(r ) 1<br />
sound<br />
field<br />
p(r 3 )<br />
9<br />
[V]<br />
rms<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
Equivalent Input Fundamental <strong>and</strong><br />
Distortion in Volt<br />
Compression<br />
3 rd -order Harmonic<br />
2 nd -order Harmonic<br />
Fundamental<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 105<br />
KLIPPEL<br />
50 100 200 500 1k<br />
Frequency [Hz]
Active Speaker Lineariz<strong>at</strong>ion<br />
Active Control Loudspeaker<br />
z<br />
<strong>Nonlinear</strong><br />
System<br />
-<br />
u D<br />
u<br />
u D<br />
<strong>Nonlinear</strong><br />
System<br />
H(f,r 1 )<br />
H(f,r 2 )<br />
H(f,r 3 )<br />
p(r1 )<br />
sound<br />
field<br />
Only the equivalent input distortion (EID) can be<br />
compens<strong>at</strong>ed by an active control system !!<br />
p(r 2 )<br />
p(r 3 )<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 106
New Degrees of freedom<br />
Controller Design Adjustment<br />
sound quality<br />
(linear <strong>and</strong> nonlinear<br />
distortion)<br />
Active Speaker System<br />
Passive Speaker<br />
Design<br />
cost,weight<br />
directivity<br />
enclosure volume<br />
max. sound pressure<br />
efficiency<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 107
Force Factor Bl(x)<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 108
Curing Loudspeaker Defects by DSP ?<br />
Coil hitting<br />
backpl<strong>at</strong>e<br />
Waveform is<br />
completely<br />
reproducible<br />
Buzzing loose<br />
joint<br />
vibr<strong>at</strong>ion<br />
Rubbing<br />
voice coil<br />
Envelope is<br />
reproducible<br />
(Waveform is not)<br />
Flow noise <strong>at</strong> air<br />
leak<br />
Waveform is not<br />
reproducible<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 109<br />
Loose particle<br />
hitting<br />
membrane<br />
Semi‐r<strong>and</strong>om<br />
Deterministic R<strong>and</strong>om<br />
(mixed characteristic)<br />
Loose particle
gap<br />
Loudspeaker Defect: Voice Coil Rubbing<br />
• signal contains reproducible <strong>and</strong><br />
stochastic components<br />
Voice coil<br />
voice coil rubbing<br />
distortion signal<br />
Cause: rocking mode <strong>at</strong> 328 Hz<br />
one period<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 110<br />
time
Loudspeaker Defect: Air Noise<br />
• stochastic signal<br />
• air pressure is changed by coil displacement<br />
• synchronized with stimulus <strong>–</strong> signal envelope<br />
one period<br />
Air noise<br />
gap<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 111<br />
cone<br />
leakage<br />
dust cap<br />
time
Loudspeaker Defect: Loose Particles<br />
• r<strong>and</strong>om process<br />
• impulsive<br />
• particles are acceler<strong>at</strong>ed by cone displacement<br />
• not synchronized with stimulus<br />
• constant output power<br />
bouncing<br />
distortion signal<br />
bouncing<br />
one period<br />
gap<br />
Voice<br />
coil<br />
former<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 112<br />
cone<br />
dust cap<br />
Loose Particle<br />
time
Loudspeaker Defect: Voice Coil Bottoming<br />
Voice coil Voice coil<br />
Voice coil<br />
backpl<strong>at</strong>e backpl<strong>at</strong>e backpl<strong>at</strong>e backpl<strong>at</strong>e<br />
distortion signal<br />
Short impulse, deterministic symptom<br />
one period<br />
Voice coil<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 113<br />
time
Protection of the Driver<br />
audio<br />
signal<br />
Ptrotection<br />
System<br />
parameter<br />
vector<br />
st<strong>at</strong>e<br />
vector<br />
Mirror Filter<br />
-<br />
Adaptive<br />
Detector<br />
voltage<br />
current<br />
Benefits:<br />
• Access to critical st<strong>at</strong>e variables (displacement, temper<strong>at</strong>ure)<br />
• autom<strong>at</strong>ic adjustment to particular speaker (Xmax, Tv)<br />
• full mechanical protection due to prediction of envelope<br />
• minimal impact on sound quality<br />
• no additional time delay<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 114
Summary<br />
Thermal <strong>and</strong> nonlinear properties of the loudspeaker<br />
• limit the maximal acoustical output<br />
• cause a smooth compression of the fundamental<br />
• cause additional signal component (distortion)<br />
• indic<strong>at</strong>e an overload situ<strong>at</strong>ion<br />
• can be described by lumped parameters<br />
• can be predicted by FEM<br />
• are directly rel<strong>at</strong>ed with cost, weight <strong>and</strong> size<br />
• can be be identified by voltage <strong>and</strong> current monitoring<br />
• have to be considered by electrical protection systems<br />
• can be compens<strong>at</strong>ed by adaptive control<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 115
Thank you !<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 116
Loudspeaker <strong>Nonlinear</strong>ities <strong>–</strong><br />
Causes, Parameters, Symptoms<br />
• Get a free poster giving a<br />
summary on this topic<br />
• Detailed discussion on<br />
practical examples in the<br />
Journal of Audio Eng. Soc.,<br />
Oct. 2006.<br />
• Poster on cone vibr<strong>at</strong>ion <strong>and</strong><br />
sound rad<strong>at</strong>ion<br />
<strong>Klippel</strong>, Tutorial: <strong>Loudspeakers</strong> <strong>at</strong> <strong>High</strong> <strong>Amplitudes</strong>, 117