Power handling and power compression in loudspeakers

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Power handling and power compression in
loudspeakers

• Doug Button
• JBL Professional, Northridge CA
• button_at_usc.edu

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Ohms Pie Chart
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Watts, Volts and dB

• Decibels are a relative scale
• dB is a POWER RATIO
• Sound pressure level is an absolute scale
  expressed in Decibels
• dB 10 x Log(P1/P2) power ratio
• dB 20 x Log(E1/E2) voltage ratio

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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
• Twice the voltage is 6dB
• Twice the amps is 6 dB
• 10 times the voltage is 20 dB
• 10 times the amps is 20 dB

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Amplifier

• Voltage multiplier
• Source 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 (square wave, high
  distortion)
• Power rating is RMS volts into resistive load
• Must be able to handling lowest impedance
• Rating need not match speaker

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AC Volts
(Root Mean Square)
RMS Voltage .707
Peak Voltage 1
P to P 2
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Random Voltage
Peak V 1
RMS V .5
Crest factor20Log (Peak/RMS) 6dB
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Impedance

• DC resistance
• AC impedance
• Nominal impedance

Resonance 50 Hz
8 ohms nominal
DC 6 Ohms
Minimum impedance 7.5 Ohms
Power handling is calculated based on an RMS
voltage into minimum Z
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Complex Load Impedance
Current lags, 1st quad (inductive)
Current leads, 4th quad (capacitive)
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Heat Dissipation

• Sets power handling
• Dictates power compression
• Limits Max SPL
• DC resistance is linear with temperature

DCR(warm)DCR(room T)(1(?TTCR))
TCR Thermal Coefficient of Resistivitychange in
DCR/C TCR for Cu and Al .004 ?/C or 1/250
100 change in DCR (double) ?T of 250 C
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Topologies
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Thermal Implications
Thermal FEA of Tall coil thin top plate
Tips of over hung coil run hotter Maximum T
516K243C
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Thermal Implications
With thicker top plate T479K206C Tips much
cooler Temperature across coil more even
Thermal FEA of shorter coil thicker top plate
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Thermal pictures
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Thermal Model Analogy
Voltage temperature
Currentpower
magnet
coil
P
Q real heat power
?T2
?T1
R oC/W
Thermal Circuit
Temperature rise vs. time in transducer
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Power Handling
DCR(warm)DCR(room T)(1(?TTCR))
DCR(change)(?TTCR) or (?T/250) ?TDCR(change)
250 30 change in DCR0.3250 75 Deg C Coil
Temperature 7520 90 Deg C R?T/Q (Qtrue
power)
Example if above was at 50 watts of
power R75/50 1.5 deg C/watt
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Power Handling
True Pmax Max ?T / Rt Example (200 C)/(1.5 deg
C/watt) 133watts AES(calculated)Power Vmax2 /
Min Z (room T) Min Z(full power) Min Z (room T)
? DCR Power(AES)Power (true)(Min Z(full
power) /Min Z(room T))
Example Min Z8 DCR6 Max T220 C
Rt1.5 True power 200/1.5133 watts Calculated
133(8((200/250)6)213watts
VmaxSQRT(Power(AES)min Z(rT))SQRT(2138)41.3Vr
ms
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Power Handling Specs

• What voltage?
• What impedance assumption?
• Minimum impedance
• Average impedance
• Nominal impedance
• 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

AES and IEC Power handling is calculated based on
an RMS voltage into minimum Z
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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)

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Thiele-Small parameters

• Electro-dynamic lumped parameters
• Mass
• Compliance
• Piston size
• BL
• B Magnetic field strength
• L Length of the wire in the coil
• DCR
• Rme (BL)2/DCR
• Motor strength

Resonance Fs
Vas equivalent acoustic spring
Qtsdamping
K x (BL)2 x (Sd)2 DCR x (Mms)2
No
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Relationships
(air mass load)
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Power compression

• Rarely stated
• JBL Spec is 5 minutes, Nobody specs long-term
  free air or in Box.
• Predictable from thermal model
• DCR doubles at 525 F (270C) ( approx 6dB
  compression)
• Thermal rating of coil sets power handing in most
  cases
• JBL sets power rating based on coil temp (typ 500
  F at full power long term)

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Power compression
300 Hz to 3000 Hz pink noise at rated power
Power compression comparison between single gap
(JBL 2123) and Dual Coil Drive (JBL 2251)
transducers.
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Power compression

• Impedance change with temperature

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Power compression

• Power compression

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Power compression
DCRhotDCRcold(1(?TTCR))
DCR(change)(?TTCR) or (?T/250) ?T
DCR(change) 250
Power compression20Log(1 DCR(change)) Power
compression is 6dB when DCR doubles
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Maximum Output

• Found by combining the efficiency of a speaker
  with its power rating
• A speaker with an efficiency/sensitivity of 100
  dB for 1 watt with a 100 watt rating can play 120
  dB maximum output, right.

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Maximum SPL

• Published values do not include power compression
• Predictable based on thermal model
• Best measured with noise
• Varies with spectrum choice
• 6dB is often added for Peak output

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Maximum SPL
Maximum output comparison between single gap (JBL
2123) and Dual Coil Drive (JBL 2251) transducers.
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Noise testing
SPL of 18 drivers 2.83 volts 30 to 300 Hz
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Noise testing
Power compression of 18 drivers 30 to 300 Hz
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Noise testing
Maximum SPL of 18 drivers 30 to 300 Hz
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Power Test Design

• IEC standard system power test
• Pink noise from 50Hz to 3250Hz slow roll off in
  HF more rapid at LF
• 6dB crest factor
• AES standard
• One decade Pink noise
• 2 hour duration
• JBL Professional design qualification
• IEC spectrum
• AES spectrum
• Up to 300 hour duration

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Failure modes

• Thermal, electrical power
• Coil burns up, larger coils better!
• Shorts out
• Goes Open
• Mechanical
• Fatigue
• Cone
• Spider
• Surround
• Tinsels

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Time vs. Failure Analysis
Data suggests a 2 to 1 power range for 2 to 300 hr
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Power compression mismatch
No compression
Compressed tweeter
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Power compression mismatch
No compression
Compressed woofer
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Power compression matched
Both compressed
No compression
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Summary

• Power compression and power handling can be
  predicted based on a simple thermal model
• Power ratings are not the true power (calculated)
• Power rating of Amp and Power rating of speaker
  do not need to match, however matching them will
  yield the most possible output
• The amp simply needs to be able to handle the
  load
• Be very wary of power handling claims, check for
  qualifiers. Or misnomers.
• Power compression is never speced, but can be
  inferred from the power rating
• Power rating tells you nothing about the fidelity
  of the speaker or how loud it will play.
• Power compression causes frequency response
  anomalies which are worst if components dont
  compress equally