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Texas Instruments SmartPA Speaker Protection Algorithm Application notes
Application Report
SLAA857 – August 2018
SmartPA Speaker Protection Algorithm
Susan Xue, Supriyo Palit, Peter Wei, Andrew Du .............................................. China HUAWEI Sales Team
ABSTRACT
SmartPA has seen increased usage in personal electronic in recent years. SmartPA is used often in smart
phones to make full use of the relatively smaller speaker and get better sound quality with maximum
volume.
SmartPA system consists of
• Power amplifier with current and voltage sensing:
• SmartPA speaker protection algorithm which protects the speaker from excursion and temperature
damage (This is based on the mechanical and electrical characteristics of the speaker)
This article discusses the speaker modeling and protection based on the TI SmartPA algorithm.
1
2
3
4
5
Contents
Speaker Basics .............................................................................................................. 2
Speaker Impedance and Excursion Model ............................................................................... 4
Speaker Model Measurement .............................................................................................. 6
SmartPA Temperature and Excursion Protection Algorithm ........................................................... 9
References .................................................................................................................. 13
List of Figures
1
Energy Transfer in Speaker ................................................................................................ 2
2
Typical Speaker Structure .................................................................................................. 2
3
Electro-Motive Model of Speaker .......................................................................................... 3
4
Speaker Characterization by PPC3 and Learning Board 2 ............................................................ 6
5
Impedance and Excursion Simulation Result with Matlab Based on Speaker Model .............................. 7
6
Impedance and Excursion Characterization Result with PPC3 and LB2............................................. 8
7
Smart amp Algorithm ........................................................................................................ 9
8
Excursion Protection System in Smart Amp Algorithm ................................................................. 9
9
Excursion Approximation in Low Frequency Range ................................................................... 10
10
Speaker Model Update Algorithm ........................................................................................ 11
11
Thermal Protection in Smart Amp Algorithm
12
13
...........................................................................
Typical Thermal Model of Speaker ......................................................................................
Thermal Characterization Method in PPc3 and Learning Board 2...................................................
11
12
12
List of Tables
1
Main Parameters in Speaker Electro-Motive Model ..................................................................... 3
2
Thiele/Small (TS) Parameter ............................................................................................... 5
3
Main Physical Parameters of Iphone 7 Speaker
4
........................................................................ 7
Main Thermal Parameters of Iphone 7 Speaker ....................................................................... 12
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Speaker Basics
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Trademarks
All trademarks are the property of their respective owners.
1
Speaker Basics
1.1
Speaker Structure
In a speaker, similar to motor driver, current flows through windings and magnetic field is created.
Windings (voice coil) move in magnetic field because of the magnetic force. The cone membrane (all the
moving parts including diaphragm, frame, suspension, and so forth) is attached firmly to the windings and
will move the same way, leading to sound. This is the basic principle of a speaker. It is a type of
electroacoustic transducer.
Electrical energy
Voice
Coil
Mechanical energy
Cone
Membrane
Sound energy
Figure 1. Energy Transfer in Speaker
F BlI
VBEMF Blv
(1)
(2)
Figure 2. Typical Speaker Structure
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Speaker Basics
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1.2
Classical Electro-Motive Model
i
u
+
Heat :
P = i 2 x Re
±
Cms
Electro Motor
Re(T)
Bl x v
+
+
F = Bl x i
±
±
x/Cms
Rms
Mms
~SPL
(accel.)
V
Figure 3. Electro-Motive Model of Speaker
Table 1. Main Parameters in Speaker Electro-Motive Model
Electro-Motive Parameter
Description
Unit
Rms
Mechanical damping factor
N × s/m
Mms
Mechanical mass
g
Cms
Mechanical compliance
mm / N
Bl
Force factor
T×m
RE
DC resistance of the speaker
Ω
u
Amplifier voltage
V
i
Voice coil current
A
v
Velocity of membrane
m/s
F
Mechanical force in magnetic field
N
X
Membrane excursion
m
Table 1 describes how the speaker converts electrical energy to mechanical energy. Speakers act as a
type of transformer. The difference from regular electro-magnetic transformer is that the secondary side is
mechanical dimension instead of electrical dimension. The primary side of the system can be taken as an
electrical circuit, where excitation signal u is audio input. In this closed circuit, part of voltage drop is
across the DC resistance, while the other part of voltage drop results from back electromotive force
(induced from windings cutting the magnetic field, for example, BackEMF).
VBEMF
Blv
u
1u R e T
(3)
Similar to a transformer, the power delivered to secondary is:
P1
VBEMF u i Blv u i
(4)
Corresponding impedance is:
R1
Blv
i
(5)
The secondary side is a mechanical system. The power is proportional to ampere force and velocity of
membrane.
P2
Fuv
Bli u v
P1
(6)
Take v as voltage and F as current, the equivalent mechanical resistance is:
R2
v
F
v
Bl u i
(7)
The equivalent turns ratio is:
TR
Bl u v
v
Bl
(8)
According to principle of transformer, ratio of R1 and R2 is:
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Speaker Impedance and Excursion Model
R1
R2
TR 2
Bl
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2
(9)
For a transformer, turns ratio is the most important parameter. It describes how the voltage and power is
transferred from one side to the other side. Get back to the speaker “transformer system”, the “turns ratio”
Bl is the most important parameter to determine the sensitivity from electrical system to mechanical
system. In other words, Bl decides how fast Mms will be moving. So obtaining Bl is a critical step for the
characterization of a speaker.
Now let’s try to focus on the mechanical system alone. Take the moving part (voice coil and membrane)
as an object, and the mass of this moving part is Mms.
Three kinds of forces are imposed on Mms:
1. Elastic force FC (measured by compliance Cms, the higher Cms, the smaller elastic force)
2. Viscous resistance force FR measured by Rms (a higher Rms indicates larger resistance and damping)
3. Outside force from ampere force F (Bl × i according to electro-magnetic principle)
FC
FR
F
x
C ms
(10)
R ms v
(11)
Bl u i
(12)
According to Newton’s Second Law,
M ms a
F
FC
Bl u i
2
FR
x
C ms
R ms v
(13)
Speaker Impedance and Excursion Model
For certain input level and frequency, impedance and excursion (excursion doesn’t mean absolute
excursion, it describes transfer function from input voltage to excursion, with a unit of mm/V) of speaker
are dependent on first five parameters in Table 1. See Equation 14 and Equation 15 for details.
Bl
Bl
sM ms
Z exc s
R ms
Bl
sR E §
¨ sM
ms
¨
©
s
2
Z BMEF s
2
M ms
1
sC ms
s2
s
R ms
M ms
1
§
¨R
¨ ms
©
Bl ·
¸
RE ¸
¹
2
·
1 ¸
sC ¸
¹
1
M msC ms
Bl
M msR E §
¨
¨ 2
¨s
¨
¨¨
©
(14)
1
Bl
Rms
RE
s
Mms
2
·
¸
¸
1
¸
M msC ms ¸
¸¸
¹
(15)
Above the electrical and mechanical parameters are basic physical parameters in a speaker. However,
they are not easy to measure once speaker is manufactured. Also, they still can’t describe clearly enough
to help us to understand how the system works. T/S parameters are introduced to better describe the
resonance system as a whole.
Take speaker as an oscillation system and equations above can be rewritten as below:
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Bl
Z BMEF s
2
s
Zs
M ms § 2
·
s
Z s2 ¸
¨s
¨
¸
Q ms
©
¹
Bl
s
M msR E § 2
·
Zs
s
Z s2 ¸
¨s
¨
¸
Q ms
©
¹
Z exc s
(16)
(17)
This system oscillates at certain frequency, resonance frequency
fs
Zs
1
2S
2S M msC ms
(18)
Impedance transfer function is also limited by mechanical quality factor:
Q ms
1
R ms
M ms
C ms
(19)
Equation 19 shows how each element in mechanical system has effect on the mechanical quality factor.
Higher Qms causes the bandwidth to narrow, which causes the system to oscillates with less damping.
The lower Qms leads to an opposite effect.
While impedance is influenced mainly by mechanical part, excursion value is measured by both electrical
and mechanical system. Total quality factor Qts is introduced here.
M ms
1
Q ts
Bl
R ms
2
C ms
RE
(20)
Qts reveals quality factor of the combination of electrical and mechanical system. Since they are in series,
and electrical quality factor is introduced as Qes,
Q ts
Q esQ ms
Q es
Q ms
(21)
We have Qes as below:
Q es
RE
Bl
M ms
2
C ms
(22)
Table 2. Thiele/Small (TS) Parameter
Driver model parameter (Thiele/Small)
Description
Unit
fs
Resonance frequency of electro-motive
system
Hz
Qts
Total quality factor
/
Qms
Quality factor of mechanical system
/
Qes
Quality factor of electrical system
/
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Speaker Model Measurement
3
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Speaker Model Measurement
Based on speaker model specified above, we use the characterization tool in PPC3 (PurePath Console 3)
to measure each parameter. (Details about PPC3 is available in Smart Amp Quick Start Guide provided in
the Reference section.)
Figure 4. Speaker Characterization by PPC3 and Learning Board 2
First, Sweep speaker with a certain range of frequencies (usually 3KHz). Get the impedance curve. Fitting
the impedance curve into model as shown in Equation 16:
Z s
RE
Z BEMF s
a
k
s2
s
bus
c
(23)
As the DC resistance, RE can be obtained directly:
RE
a
(24)
According to the relation between T/S and physical parameters,
Bl
2
k
M ms
Zs
(25)
1
c
M msC ms
Zs
R ms
Q ms
M ms
(26)
b
(27)
There are three formulas, but 4 parameters Mms, Cms, Rms and Bl are unknown. Bl should be input
before all the other 3 parameters are derived. It can be either from speaker vendor or from laser
measurement. Once Bl is known, Mms, Cms and Rms can be derived from Equation 25, Equation 26, and
Equation 27.
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Bl
M ms
C ms
2
k
(28)
1
c u M ms
k
c u Bl
Bl
R ms
b u R ms
bu
2
(29)
2
k
(30)
Then according to Equation 17, excursion curve can be fit based on the five physical parameters of
speaker.
For Iphone 7 speaker, below in Table 3 is the characterization result of different physical parameters:
Table 3. Main Physical Parameters of Iphone 7 Speaker
Driver model parameter
(physical)
Description
Unit
Value
Rms
Mechanical damping factor
N × s/m
0.305
Mms
Mechanical mass
g
0.116
Cms
Mechanical compliance
mm / N
0.21
Bl
Force factor
T×m
0.841
RE
DC resistance of the speaker
Ω
7.35
And according to Equation 14 and Equation 15, impedance and excursion simulated with matlab. Figures
as below Figure 5:
Figure 5. Impedance and Excursion Simulation Result with Matlab Based on Speaker Model
TS parameters can be derived based on the five physical parameters:
fs
1
2S M ms Cms
1
2S 0.116 u 0.21 u 10
1020 Hz
6
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(31)
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Speaker Model Measurement
Q ms
Q ts
Q ts
Q es
1
R ms
www.ti.com
M ms
C ms
1
0.116
0.305 0.21
(32)
1
0.8412
0.305
7.35
Q msQ es
Q ms Q es
Q msQ ts
Q ms
Q ts
2.43
0.116
0.21
1.85
(33)
(34)
2.43 u 1.85
2.43 1.85
7.75
(35)
The calculation of TS parameters and simulation curves of impedance and excursion match with
characterization results well.
Figure 6. Impedance and Excursion Characterization Result with PPC3 and LB2
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SmartPA Temperature and Excursion Protection Algorithm
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4
SmartPA Temperature and Excursion Protection Algorithm
A block diagram of the SmartPA algorithm is shown below:
Input
Output
Power/Excursion
Protection
+
SmartPA
Amplifier
ZEXC(S)
P(T)
Pilot
Tone
Xmax
Thermal
Controller
I/V
Thermal
Estimator
Tmax
Speaker
Model
SmartPA Algorithm
Figure 7. Smart amp Algorithm
The speaker temperature and the speaker model is derived from I/V sense. This is used to adaptively
modify the input signal in the Power/Excursion protection block so that the output provided to the speaker
is within the excursion and thermal limit of the speaker. The excursion and thermal protection algorithm is
discussed in detail in the following sections.
4.1
Excursion Protection Algorithm
For excursion protection, excursion is first calculated from the input signal based on the speaker model.
Then the excursion will be compared with the maximum excursion before deciding if protection kicks in. If
the excursion exceeds limit Xmax, input will be attenuated otherwise the input signal will pass through
unchanged. Since over excursion could possibly damage the system in a short time, a time delay is
inserted in feedforward signal chain, to make sure excursion estimation and comparison are finished
before signal is fed to protection.
Feedforward (input attenuation)
Delay
Output
Input
ZExc (s)
excursion
Excursion
limiter
Xmax
Figure 8. Excursion Protection System in Smart Amp Algorithm
Equation 15 is the excursion model when input voltage is 1 V. So total excursion Exc(s) should be,
Exc s
u s u Z Exc s
(36)
If switched to time domain by doing inverse Laplace transform on ZExc(s), final excursion is convolution of
input signal and L–1(ZExc(s))
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x t u L 1 Z Exc s
Exc t
(37)
Figure 9. Excursion Approximation in Low Frequency Range
This is how excursion is calculated and protected.
As the speaker keeps working, speaker model can change, which will have effect on the estimation
accuracy. So the speaker model should be updated dynamically to ensure proper protection. Figure 9
shows how speaker model is updated. This update is finished in feedback module.
The speaker model update is mainly based on impedance model. If speaker output voltage and current is
V(s) and I(s) for frequency domain, respectively, then:
I s
VBEMF s
Z BEMF s
VBEMF s
V s
(38)
I s RE
(39)
And VBEMF(s) is the backemf.
Equation 38 is converted into time domain by inverse Laplace transform as below,
VBEMF t
I t u L 1 Z BEMF s
(40)
As is shown in Figure 9, an adaptive filter is used to update the speaker impedance model. Output voltage
and current of the speaker are detected as V(t) and I(t), respectively using the sensing circuit of the
SmartPA amplifier. Back-EMF is estimated as VBEMF_est(t) based on original impedance model according to
Equation 40, and VBEMF_est(t) is compared to the actual backemf VBEMF_est(t) (=V(t) — I(t)RE) from detection
and the error e(t) is obtained:
e t
VBEMF _est t
VBEMF t
(41)
The speaker model parameters are modified dynamically till e(t) is small enough to be close to zero, which
means the model is accurate enough to forecast the impedance and excursion.
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Speaker Model
Parameters
I(t)
VBEMF_est(t)
VBEMF(t)
L-1(ZBEMF(s))
= V (t) ± I (t) RE
e(t)
Figure 10. Speaker Model Update Algorithm
TS parameters are calculated using updated physical parameters. For actual backemf we need to
measure RE. At very low frequencies, the backemf is almost zero so Equation 39 becomes,
0
V s
I s RE
(42)
hence,
v t
RE
I t
(43)
A pilot tone at low frequency (for example 60Hz.) is used to estimate RE × RE is also used for thermal
protection which is discussed in the next section.
4.2
Thermal Protection Algorithm
Thermal protection algorithm is divided into three main parts. Thermal estimator, thermal controller and
power protection. Temperature T is first estimated from I/V feedback using pilot tone based on the relation
between DC resistance and temperature, as is shown in Equation 43 and Equation 44. Then T is
compared with temperature limit Tmax to decide if it has exceeded the limit.
Power Protection
I/V
T
Thermal Controller
Thermal
Model
Tmax
Thermal Estimator
D
Figure 11. Thermal Protection in Smart Amp Algorithm
R T
R e TA
D T
TA R T
(44)
R R e TA
T
TA
R
D
(45)
The second important part is thermal controller. It controls the power protection block based on
temperature. This is done using a thermal model of the speaker. For the speaker, thermal model is shown
in Figure 11. Voice coil and magnet pole are both included. Thermal resistance and thermal capacitance
are introduced to model the transient temperature behavior and it can predict how temperature changes
as time goes by under different input power.
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SmartPA Temperature and Excursion Protection Algorithm
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TA
Pin
Rtv
Tv
Tm
Rtm
Ctv
Ctm
voice coil
magnet
Figure 12. Typical Thermal Model of Speaker
Using Iphone 7 speaker as an example, thermal resistance and capacitance (shown in Table 4) can be
calculated from the characterization result shown in below curve in Figure 12 by learning board 2.
Figure 13. Thermal Characterization Method in PPc3 and Learning Board 2
Table 4. Main Thermal Parameters of Iphone 7 Speaker
Thermal parameter
Description
Unit
Value
Rtv
Thermal resistance of voice
coil
K/W
76.9
Ctv
Thermal capacitance of voice
coil
J/K
0.0549
Rtm
Thermal resistance of magnet
pole
K/W
495
Ctm
Thermal capacitance of
magnet pole
J/K
0.832
From Figure 11, Power flows to the voice coil and magnet system, each with a time constant, denoting the
temperature rising speed respectively. This time constant can be calculated from thermal models shown in
Table 4.
Time constant for voice coil is:
Wv
R tv C tv
76.9 u 0.0549
4.22 s
(46)
Time constant for magnet part is:
Wm
R tmC tm
495 u 0.832
411.8 s
(47)
This means, temperature of voice coil can rise much faster than the magnet as the power increases. Also
for this case, temperature of voice coil is our main concern. Algorithm take s advantage of the time
constant and decides how to allocate power properly to make system work nearly the thermal limit while
ensure safety.
In power protection module, signals are attenuated according to the power output from the thermal
controller. This keeps the voice coil temperature within the thermal limit.
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References
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5
References
•
•
•
Thiele/Small Parameters
Smart Amp Quick Start Guide
W. Marshall Leach Jr, Introduction to electro-acoustics and audio amplifier design, published by
Kendall Hunt
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