1. Power handling and power compression in loudspeakers Doug Button dougbutton@roadrunner.com

2. Ohm’s Pie Chart

3. Watts, Volts and dB Decibels are a relative scaleDecibels are a relative scale dB is a POWER RATIOdB is a POWER RATIO Sound Pressure Level is an absolute scale expressed in Decibels relative to 0dB=20μP (RMS)Sound Pressure Level is an absolute scale expressed in Decibels relative to 0dB=20μP (RMS) Sound intensity is W/m 2Sound intensity is W/m 2 dB= 10 x Log(P 1 /P 2 ) power ratiodB= 10 x Log(P 1 /P 2 ) power ratio dB= 20 x Log(E 1 /E 2 ) voltage ratiodB= 20 x Log(E 1 /E 2 ) voltage ratio dB= 20 x Log(I 1 /I 2 ) current ratiodB= 20 x Log(I 1 /I 2 ) current ratio

4. dB, Power, Volts and Amps 3 dB is 2 times the power3 dB is 2 times the power 6 dB is 4 times the power6 dB is 4 times the power 10 dB is 10 times the power10 dB is 10 times the power 20 dB is 100 times the power20 dB is 100 times the power 6dB is 2 times the voltage6dB is 2 times the voltage 6dB is 2 times the current6dB is 2 times the current 20 dB is 10 times the voltage20 dB is 10 times the voltage 20 dB is 10 times the current20 dB is 10 times the current

5. Amplifier Voltage multiplierVoltage multiplier –Input is in mV (ipod, cd player) –Output in Volts Ratio is called gain. Typically in dBRatio is called gain. Typically in dB Has maximum peak voltage (slightly less than supply rails) waveform ‘Clips’Has maximum peak voltage (slightly less than supply rails) waveform ‘Clips’ Has maximum RMS volts (3db less than peak)Has maximum RMS volts (3db less than peak) –Power rating is RMS volts into resistive load Must be able to handling [lowest] impedanceMust be able to handling [lowest] impedance Rating need not match speakerRating need not match speaker

6. AC Volts AC Volts Peak Voltage = 1 RMS Voltage =.707 (Root Mean Square) P to P = 2

7. Random Voltage Peak V = 1 RMS V=.5 Crest factor=20*Log (Peak/RMS)= 6dB

8. Impedance DC Resistance (Re)DC Resistance (Re) AC impedanceAC impedance Nominal impedanceNominal impedance 8 ohms nominal DC Resistance= 6 Ohms Resonance = 50 Hz Minimum impedance =7.5 Ohms Power handling is CALCULATED based on an RMS voltage into minimum Z

9. Complex Load Impedance Current leads, 4 th quad (capacitive) Current lags, 1st quad (inductive)

10. Power Handling Specs What voltage?What voltage? What impedance assumption?What impedance assumption? –Minimum impedance –Average impedance –Nominal impedance –Impedance under power? RMS Power? Average Power? Real Power? Music Power? Peak Power?RMS Power? Average Power? Real Power? Music Power? Peak Power? Crest factor?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?Amp power rating? –Sine wave at 1000 Hz X% THD into resistive load IEC, AES, EIA Power handling is CALCULATED based on an RMS voltage into minimum Z

11. Credible ratings IEC standard system power test: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 standardAES standard –One decade Pink noise –2 hour duration EIA 426A/BEIA 426A/B –B Based on power compression –A is like IEC 8 hours

12. Heat Dissipation Sets power handlingSets power handling Dictates power compressionDictates power compression Limits Max SPLLimits Max SPL DC resistance is linear with temperatureDC 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

13. Thermal Model Analogy Temperature rise vs. time in transducer Thermal Circuit Q= real heat power R= o C/W Voltage= temperature Current=power P ∆T 1 ∆T 2 coil magnet

14. Thermal Resistance 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 DCR (warm)= DCR (room T)* (1+(∆T*TCR))

15. Power Handling True Power max = Max ∆T / Rt Example (200 C)/(1.5 deg C/watt)= 133watts 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) )

16. 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)

17. Failure modes Thermal, electrical powerThermal, electrical power –Coil burns up, larger coils better! Shorts outShorts out Goes OpenGoes Open MechanicalMechanical –Fatigue ConeCone SpiderSpider SurroundSurround TinselsTinsels

18. Time vs. Failure Analysis Data suggests a 2 to 1 power range for 2 to 300 hr

19. Power rating Good guide for what size amp to match with a speaker.Good guide for what size amp to match with a speaker. BUT, all it really tells you is how easily the speaker will breakBUT, all it really tells you is how easily the speaker will break A 200 watt speaker will break easier than a 400 watt speakerA 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)Pay close attention to qualifiers such as peak, continuous, average, music, noise or RMS (misnomer)

20. Power compression Combination of reduced efficiency and less power delivered due to higher resistanceCombination of reduced efficiency and less power delivered due to higher resistance Rarely statedRarely stated Predictable from thermal modelPredictable from thermal model DCR doubles at 525 F (270C)DCR doubles at 525 F (270C) (approx 6dB compression in midband) (approx 6dB compression in midband)

21. Higher DCR reduces efficiency K x (BL) 2 x (Sd) 2 DCR x (Mms) 2 Efficiency = Additionally: Higher impedance pulls less power

22. Thiele-Small Parameters Higher DCR (Re) increases electrical Q Reduces damping

23. Power compression

24. Impedance change with temperatureImpedance change with temperature Power compression

25. Power compressionPower compression Power compression

26. DCR (%change) =( ∆T*TCR) or (∆T/250) ∆T= DCR (%change)* 250 DCR hot =DCR cold *(1+(∆T*TCR)) Power compression=20Log(1+ DCR (%change) ) Power compression is 6dB when DCR doubles

27. Power compression mismatch No compression Compressed tweeter

28. Power compression mismatch No compression Compressed woofer

29. Power compression matched No compression Both compressed

30. Summary Power Handling Power compression and power handling can be predicted based on a simple thermal modelPower compression and power handling can be predicted based on a simple thermal model Power ratings of speakers are not the true power (calculated).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 damagePower 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)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).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).

31. Summary Power Compression Combination of reduced efficiency and less power delivered due to higher resistanceCombination of reduced efficiency and less power delivered due to higher resistance Power compression is never speced, but can be inferred from the power ratingPower compression is never speced, but can be inferred from the power rating Power compression changes the bass alignmentPower compression changes the bass alignment Power compression causes frequency response anomalies which are worst if components don’t compress equallyPower compression causes frequency response anomalies which are worst if components don’t compress equally

32. 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