Power handling and power
compression in loudspeakers
Doug Button
dougbutton@roadrunner.com
Ohm’s Pie Chart
Watts, Volts and dB
• Decibels are a relative scale
• dB is a POWER RATIO
• Sound Pressure Level is an absolute scale expressed
in Decibels relative to 0dB=20μP(RMS)
• Sound intensity is W/m2
• dB= 10 x Log(P1/P2) power ratio
• dB= 20 x Log(E1/E2) voltage ratio
• dB= 20 x Log(I1/I2) current ratio
dB, Power, Volts and Amps
•
•
•
•
3 dB is 2 times the power
6 dB is 4 times the power
10 dB is 10 times the power
20 dB is 100 times the power
• 6dB is 2 times the voltage
• 6dB is 2 times the current
• 20 dB is 10 times the voltage
• 20 dB is 10 times the current
Amplifier
• Voltage multiplier
– Input is in mV (ipod, cd player)
– Output in Volts
• Ratio is called gain. Typically in dB
• Has maximum peak voltage (slightly less than supply
rails) waveform ‘Clips’
• Has maximum RMS volts (3db less than peak)
– Power rating is RMS volts into resistive load
• Must be able to handling [lowest] impedance
• Rating need not match speaker
V 1 2  ...Vn 2
RMS  
n
(Root Mean Square)
AC Volts
Voltage vs Time
1.5
RMS Voltage = .707
Peak Voltage = 1
1
Voltage
0.5
P to P
=2
0
-0.5
-1
-1.5
0
10
20
30
40
50
Time
60
70
80
90
100
Random Voltage
RMS V= .5
Peak V = 1
Noise or music voltage wave from
1.5
1
Voltage
0.5
0
-0.5
-1
-1.5
0
10
20
30
40
50
60
70
80
90
Time
Crest factor=20*Log (Peak/RMS)= 6dB
100
•
•
•
DC Resistance (Re)
AC impedance
Nominal impedance
Impedance
Impedance of a loudspeaker
100
Resonance = 50 Hz
Ohms
8 ohms nominal
Minimum impedance =7.5 Ohms
DC Resistance= 6 Ohms
1
1
100
Frequency
10000
Power handling is CALCULATED based on an RMS voltage into minimum Z
Complex Load Impedance
woofer impedance
40.00
Ohms
30.00
20.00
10.00
0.00
10.00
Woofer phase
1000.00
freq
90.00
60.00
Current lags, 1st quad (inductive)
Phase angle
30.00
0.00
-30.00
Current leads, 4th quad (capacitive)
-60.00
-90.00
10.00
1000.00
Freq
Power Handling Specs
• What voltage?
• What impedance assumption?
– Minimum impedance
IEC, AES, EIA Power handling is
– Average impedance
CALCULATED based on an RMS
– Nominal impedance
voltage into minimum Z
– Impedance under power?
• RMS Power? Average Power? Real Power? Music Power? Peak
Power?
• Crest factor?
– Sine is 3dB
– Noise is 6dB or greater (often 12dB)
– Music is 6dB or greater (as high as 25 to 30dB)
• Amp power rating?
– Sine wave at 1000 Hz X% THD into resistive load
Credible ratings
• IEC standard system power test:
– Pink noise from 50Hz to 3250Hz
slow roll off in HF more rapid at LF
– 6dB crest factor
– 100 hours
• AES standard
– One decade Pink noise
– 2 hour duration
• EIA 426A/B
– B Based on power compression
– A is like IEC 8 hours
Heat Dissipation
•
•
•
•
Sets power handling
Dictates power compression
Limits Max SPL
DC resistance is linear with temperature
DCR
(warm)=
DCR
(room T)*
(1+(∆T*TCR))
TCR= Thermal Coefficient of Resistivity=change in DCR/C
TCR for Cu and Al ~ .004 ∆/C or 1/250
100% change in DCR (double)= ∆T of 250 C
Thermal Model Analogy
Voltage= temperature
Current=power
magnet
coil
P
∆T1
∆T2
Q= real heat power
R= oC/W
Thermal Circuit
Temperature rise vs. time in transducer
Thermal Resistance
DCR
(warm)=
DCR
(room T)*
(1+(∆T*TCR))
DCR(%change)=(∆T*TCR) or (∆T/250)
∆T=DCR(%change)* 250
30% change in DCR=0.3*250 = 75 Deg C
Coil Temperature = 75+20 = 95 Deg C
R=∆T/Q (Q=true power)
Example: Q = 50 watts of power
R=75/50= 1.5 deg C/watt
Power Handling
True Power max = Max ∆T / Rt
Example (200 C)/(1.5 deg C/watt)= 133watts
Min Z
(full power)=
Min Z
(room T)
+ ∆ DCR
Power(calc)=Power (true)*(Min Z(full power) /Min Z(room T))
Power Handling Example
Min Z(roomT) = 8 Ω DCR = 6 Ω
Max T = 220 C Rt = 1.5 °C/W
True power =200/1.5=133 watts
Change in DCR = 200/250 x 6ohms=4.8 Ω
Min Z(full) = 8+4.8 = 12.8 Ω
Power(calculated) = 133 x (12.8/8) = 213 Watts
V(rated P)=SQRT(Power(Calc)*min Z) = SQRT(213*8) = 41.3
V(RMS)
Failure modes
• Thermal, electrical power
– Coil burns up, larger coils better!
• Shorts out
• Goes Open
• Mechanical
– Fatigue
•
•
•
•
Cone
Spider
Surround
Tinsels
Time vs. Failure Analysis
VGC Transducers
Hours until failure
1000
100
10
1
500
600
700
800
900
1000
1100
1200
1300
Watts
1996 1.5% warranty rate
1992 3.4% warranty rate
1990 5% warranty rate
Data suggests a 2 to 1 power range for 2 to 300 hr
Power rating
• Good guide for what size amp to match with a speaker.
• BUT, all it really tells you is how easily the speaker will
break
• A 200 watt speaker will break easier than
a 400 watt speaker
• Pay close attention to qualifiers such as peak,
continuous, average, music, noise or RMS (misnomer)
Power compression
• Combination of reduced efficiency and
less power delivered due to higher
resistance
• Rarely stated
• Predictable from thermal model
• DCR doubles at 525 F (270C)
(approx 6dB compression in midband)
Higher DCR reduces efficiency
2
K x (BL) x (Sd)
Efficiency =
2
DCR x (Mms)
2
Additionally: Higher impedance pulls less power
Thiele-Small Parameters
Re
Qes 
2B 2 L2CmsFs
1
Fs 
2
1
MmsCms
Higher DCR (Re) increases electrical Q
Reduces damping
Power compression
Output vs Input power
Sound pressure level @ 1 m
120
115
110
Real
Ideal
105
100
1
10
Input power, Watts.
100
Power compression
Impedance Magnitude vs. Freq, as Temperature changes
Impedance Magnitude (Ohms)
100
• Impedance change with temperature
Z 20deg C
Z 70 deg C
Z 120 deg C
10
Z 170 deg C
Z 220 deg C
Z 270 deg C
1
10
100
Frequency (Hz)
1000
Power compression
On Axis SPL vs. Freq showing compression vs temperture and frequency
100
95
Magnitude SPL (dB)
90
• Power compression
85
SPL 20deg C
SPL 70 deg C
SPL 120 deg C
80
SPL 170 deg C
SPL 220 deg C
SPL 270 deg C
75
70
65
60
10
100
Frequency (Hz)
1000
Power compression
DCR =DCR *(1+(∆T*TCR))
hot
cold
DCR(%change)=(∆T*TCR) or (∆T/250)
∆T= DCR(%change)* 250
Power compression=20Log(1+ DCR(%change))
Power compression is 6dB when DCR doubles
Total acoustic magnitude
Total acoustic magnitude
100
Power compression mismatch
dB, 1 watt
90
80
70
60
10
No compression
1000
1000
Compressed tweeter
100000
Total Load
Impedance
Frerquency
Total Load
Impedance
Frerquency
50
45
40
35
Z, ohms
30
25
20
15
10
5
1000
freq
0
10
100000
1000
freq
Total acoustic magnitude
Total acoustic magnitude
100
Power compression mismatch
dB, 1 watt
90
80
70
60
No compression
1000
10
Compressed woofer
100000
1000
Total Load Impedance
Total Load
Impedance
Frerquency
Frerquency
50
45
40
35
Z, ohms
30
25
20
15
10
5
1000
freq
0
10
100000
1000
freq
Total acoustic magnitude
Total acoustic magnitude
100
Power compression matched
dB, 1 watt
90
80
70
60
10
No compression
1000
100000
1000
Both compressed
Frerquency
Total Load
Impedance
Total Load
Impedance
Frerquency
50
45
40
35
Z, ohms
30
25
20
15
10
5
1000
freq
0
10
100000
1000
freq
Summary Power Handling
• Power compression and power handling can be
predicted based on a simple thermal model
• Power ratings of speakers are not the true power
(calculated).
• Power rating of Amplifier and Power rating of speaker
do not need to match, however matching them will yield
the most possible output without damage
• The amp simply needs to be able to handle the load
(most amps can handle impedances down to 4 ohms)
• Be very wary of power handling claims, check for
qualifiers. Or misnomers (such as RMS power, Music
power, Peak power, should be AVERAGE or
CONTINUOUS).
Summary Power Compression
• Combination of reduced efficiency and less power
delivered due to higher resistance
• Power compression is never speced, but can be
inferred from the power rating
• Power compression changes the bass alignment
• Power compression causes frequency response
anomalies which are worst if components don’t
compress equally
Measurements
http://www-classes.usc.edu/engr/ee-ep/
499/423L/Power lecture April 2011/
Power rating and Power compression calculator 2011.xls
Measure the DCR of your transducers