The Design of Active Crossovers 
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THE DESIGN OF ACTIVE CROSSOVERS by Douglas Self Chapter 1: Active crossover basics Chapter 2: How loudspeakers work Chapter 3: Crossover requirements Chapter 4: Crossover types Chapter 5: Notch crossovers Chapter 6: Subtractive crossovers Chapter 7: Lowpass and highpass filter characteristics Chapter 8: Designing lowpass and highpass filters Chapter 9: Bandpass & Notch Filters Chapter 10: Timedelay Filters Chapter 11: Equalisation Chapter 12: Passive components for active crossovers Chapter 13: Opamps for active crossovers Chapter 14: Crossover system design Chapter 15: Subwoofers and their crossovers Chapter 16: Line Inputs Chapter 17: Line Outputs Chapter 18: Power supply design Chapter 19: An active crossover design  Chapter 1: Active crossover basics What a crossover does Why a crossover is necessary Beaming and lobing Active crossover applications Biamping and biwiring Loudspeaker cables The advantages and disadvantages of active crossovers The advantages of active crossovers Some illusory advantages of active crossovers The disadvantages of active crossovers The next step in hifi Active crossover systems Matching crossovers and loudspeakers A modest proposal: popularising active crossovers Multiway connectors Subjectivism Chapter 2: How loudspeakers work Sealed box loudspeakers Vented boxes Reflex (ported) loudspeakers Auxiliary Bass Radiator (ABR) loudspeakers Transmission line loudspeakers Horn loudspeakers Diffraction Modulation distortion Further reading Chapter 3: Crossover requirements General crossover requirements 1: Adequate flatness of summed amplitude/frequency response onaxis 2: Sufficiently steep rolloff slopes between the output bands 3: Acceptable polar response 4: Acceptable phase response 5: Acceptable group delay behaviour Further requirements for active crossovers 1: Negligible extra noise 2: Negligible impairment of system headroom 3: Negligible extra distortion 4: Negligible impairment of frequency response 5: Negligible impairment of reliability Linear phase Minimum phase Absolute phase Phase perception Target functions Chapter 4: Crossover types Allpole and nonallpole crossovers Symmetrical and asymmetrical crossovers Allpass and ConstantPower crossovers Constant voltage crossovers Firstorder crossovers Firstorder Solen split crossover Firstorder crossovers: 3way Secondorder crossovers Secondorder Butterworth crossover Secondorder LinkwitzRiley crossover Secondorder Bessel crossover Secondorder 1dBChebychev crossover Thirdorder crossovers Thirdorder Butterworth crossover Thirdorder LinkwitzRiley crossover Thirdorder Bessel crossover Thirdorder 1dBChebychev crossover Fourthorder crossovers Fourthorder Butterworth crossover Fourthorder LinkwitzRiley crossover Fourthorder Bessel crossover Fourthorder 1dBChebychev crossover Fourthorder linearphase crossover Fourthorder Gaussian crossover Fourthorder Legendre crossover Higherorder crossovers Determining frequency offsets Summary of crossover properties Fillerdriver crossovers The Duelund crossover Crossover topology Crossover conclusions Chapter 5: Notch crossovers Elliptical filter crossovers Neville Thiele MethodTM (NTM) crossovers Chapter 6: Subtractive crossovers Subtractive crossovers Firstorder subtractive crossovers Secondorder Butterworth subtractive crossovers Thirdorder Butterworth subtractive crossovers Fourthorder Butterworth subtractive crossovers Subtractive crossovers with time delays Performing the subtraction Chapter 7: Lowpass and highpass filter characteristics Active filters Lowpass filters Highpass filters Bandpass filters Notch filters Allpass filters The order of a filter Filter cutoff frequencies and characteristic frequencies Firstorder filters Secondorder and higherorder filters Filter characteristics Butterworth filters LinkwitzRiley filters Bessel filters Chebyshev filters 1dBChebyschev lowpass filter 3dBChebyschev lowpass filter Higherorder filters Butterworth filters up to 8th order LinkwitzRiley filters up to 8th order Bessel filters up to 8th order Chebyshev filters up to 8th order More complex filters adding zeros Inverse Chebyshev Filters (Chebyshev Type II) Elliptical Filters (Cauer filters) Some lesserknown filter characteristics Transitional filters LinearPhase filters Gaussian filters LegendrePapoulis filters Synchronous filters Other filters Chapter 8: Designing lowpass and highpass filters Designing real filters Component sensitivity Firstorder lowpass and highpass filters Secondorder filters Sallen & Key secondorder filters Sallen & Key lowpass filter components Sallen & Key secondorder lowpass: unitygain Sallen & Key secondorder lowpass unitygain: component sensitivity Sallen & Key secondorder lowpass: equalcapacitor Sallen & Key secondorder lowpass equalC: component sensitivity Sallen & Key secondorder Butterworth lowpass: defined gains Sallen & Key secondorder lowpass: nonequalresistors Sallen & Key thirdorder lowpass in a single stage Sallen & Key thirdorder lowpass in a single stage: nonequalresistors Sallen & Key fourthorder lowpass in a single stage Sallen & Key fourthorder lowpass in a single stage: nonequalresistors Sallen & Key fifth and sixthorder lowpass in a single stage Sallen & Key highpass filters Sallen & Key secondorder highpass: unitygain Sallen & Key secondorder highpass: equalresistors Sallen & Key secondorder Butterworth highpass: defined gains Sallen & Key secondorder highpass: nonequalcapacitors Sallen & Key thirdorder highpass in a single stage Sallen & Key fourthorder highpass in a single stage LinkwitzRiley with Sallen & Key filters: loading effects Lowpass filters with attenuation Bandwidth definition filters Bandwidth definition: Butterworth versus Bessel ultrasonic filters Bandwidth definition: subsonic filters. Bandwidth definition: combined ultrasonic & subsonic filters Distortion in Sallen & Key filters: highpass Distortion in Sallen & Key filters: lowpass Mixed capacitors in lowdistortion Sallen & Key filters Noise in Sallen & Key filters: lowpass Noise in Sallen & Key filters: highpass Multiple feedback filters Multiplefeedback lowpass filters Multiplefeedback highpass filters Distortion in multiplefeedback filters: highpass Distortion in multiplefeedback filters: lowpass Noise in multiplefeedback filters: highpass Noise in multiplefeedback filters: lowpass Statevariable filters Variablefrequency filters: Sallen & Key Variable frequency filters: statevariable secondorder Variable frequency filters: statevariable fourth order Variable frequency filters: other orders Chapter 9: Bandpass and Notch Filters Multiple feedback bandpass filters HighQ bandpass filters Notch filters The twinT notch filter The 1 bandpass notch filter The Bainter notch filter The bridgeddifferentiator notch filter Boctor notch filters Other notch filters Simulating notch filters Chapter 10: Timedelay filters The requirement for delay compensation Calculating the required delays Signal summation Physical methods of delay compensation Delay filter technology Sample crossover & delay filter specification Allpass filters in general Firstorder allpass filters Distortion & noise in firstorder allpass filters Cascaded firstorder allpass filters Secondorder allpass filters Distortion & noise in secondorder allpass filters Third order allpass filters Distortion & noise in thirdorder allpass filters Higherorder allpass filters Delay lines for subtractive crossovers Variable allpass time delays Lowpass filters for time delays Chapter 11: Equalisation The need for equalisation What equalisation can and can’t do Loudspeaker equalisation 1) Drive unit equalisation 2) 6dB/oct dipole equalisation 3) Bass response extension 4) Diffraction compensation equalisation 5) Room interaction correction Equalisation circuits HFboost and LFcut equaliser HF cut and LFboost equaliser Combined HFboost and HFcut equaliser Adjustable peak/dip equalisers: fixed frequency & low Q Adjustable peak/dip equalisers: variable centre frequency & low Q Adjustable peak/dip equalisers with high Q The bridgedT equaliser The biquad equaliser Capacitance multiplication for the biquad equaliser Equalisers with non6 dB slopes Equalisation by frequency offset Equalisation by adjusting all filter parameters Chapter 12: Passive components for active crossovers Resistors: values and tolerances Improving accuracy with multiple components: Gaussian distribution Resistance value distributions Improving accuracy with multiple components: uniform distribution Obtaining arbitrary resistance values Resistor noise: Johnson and excess noise Resistor nonlinearity Capacitors: values and tolerances Capacitor shortcomings Nonelectrolytic capacitor nonlinearity Electrolytic capacitor nonlinearity Chapter 13: Opamps for active crossovers Active devices for active crossovers Opamp types Opamp properties: Noise Opamp properties: Slewrate Opamp properties: Common mode range Opamp properties: Input offset voltage Opamp properties: Bias current Opamp properties: Cost Opamp properties: Internal distortion Opamp properties: Slewrate limiting distortion Opamp properties: Distortion due to loading Opamp properties: Commonmode distortion Opamps surveyed The TL072 opamp The 5532 and 5534 opamps The 5532 with shunt feedback 5532 output loading in shunt feedback mode The 5532 with series feedback Commonmode distortion in the 5532 Reducing 5532 distortion by output stage biasing Which 5532? The 5534 opamp The LM4562 opamp Commonmode distortion in the LM4562 The LME49990 opamp Commonmode distortion in the LME49990 The AD797 opamp Commonmode distortion in the AD797 The OP27 opamp Opamp selection Chapter 14: Crossover system design Crossover features Input level controls Subsonic filters Ultrasonic filters Output level trims Output mute switches, Output phasereverse switches Control protection Features usually absent Metering Relay output muting Switchable crossover modes Noise, headroom, and internal levels Circuit noise and LowImpedance Design Using raised internal levels Placing the output attenuator The amplitude/frequency distribution of musical signals, & internal levels Gain structures Noise gain Active gaincontrols Filter order in the signal path Output level controls Mute switches Phaseinvert switches Distributed peakdetection Power amplifier considerations Chapter 15: Subwoofers and their crossovers Subwoofer applications Subwoofer technologies Sealed (Infinite baffle) subwoofers Reflex (ported) subwoofers Auxiliary Bass Radiator (ABR) subwoofers Transmission line subwoofers Bandpass subwoofers Isobaric subwoofers Dipole subwoofers Hornloaded subwoofers Subwoofer drive units Hifi subwoofers Home entertainment subwoofers Lowlevel inputs (unbalanced) Lowlevel inputs (balanced) Highlevel inputs Highlevel outputs Mono summing LFE input Level control Crossover in/out switch (LFE/normal) Crossover frequency control (lowpass filter) Highpass subsonic filter Phase switch (normal/inverted) Variable phase (delay) control Signal activation out of standby Home entertainment crossovers Fixed frequency Variable frequency Multiple Variable Power amplifiers for home entertainment subwoofers Subwoofer integration Soundreinforcement subwoofers Line or area arrays Cardioid subwoofer arrays Auxfed subwoofers Automotive audio subwoofers Chapter 16: Line inputs External signal levels Internal signal levels Input amplifier functions Unbalanced inputs Balanced interconnections The advantages of balanced interconnections The disadvantages of balanced interconnections Balanced cables and interference Balanced connectors Balanced signal levels Electronic vs transformer balanced inputs Common mode rejection ration (CMRR) The basic electronic balanced input Commonmode rejection ratio: opamp gain Commonmode rejection ratio: opamp frequency response Commonmode rejection ratio: opamp CMRR Commonmode rejection ratio: Amplifier component mismatches A practical balanced input Variations on the balanced input stage Combined unbalanced and balanced inputs The Superbal input Switchedgain balanced inputs Variablegain balanced inputs High inputimpedance balanced inputs The instrumentation amplifier Transformer balanced inputs Input overvoltage protection Noise and balanced inputs Lownoise balanced inputs Lownoise balanced inputs in real life Ultralownoise balanced inputs Chapter 17: Line outputs Unbalanced outputs Zeroimpedance outputs Groundcancelling outputs Balanced outputs Transformer balanced outputs Output transformer frequency response Transformer distortion Reducing transformer distortion Chapter 18: Power supply design Opamp supply rail voltages Designing a ±15V supply Designing a ±17V supply Using variablevoltage regulators Improving ripple performance Dual supplies from a single winding Power supplies for discrete circuitry Mutual shutdown circuitry Chapter 19: An active crossover design Design principles Example crossover specification The gain structure Resistor selection Capacitor selection The balanced line input stage The bandwidth definition filter The HF path: 3 kHz LinkwitzRiley highpass filter The HF path: time delay compensation The MID path: topology The MID path: 400 Hz LinkwitzRiley highpass filter The MID path: 3 kHz LinkwitzRiley lowpass filter The MID path: time delay compensation The LF path: 400 Hz LinkwitzRiley lowpass filter The LF path: no time delay compensation Output attenuators and level trim controls Balanced outputs Crossover programming Noise analysis: input circuitry Noise analysis: HF path Noise analysis: MID path Noise analysis: LF path Improving the noise performance: the MID path Improving the noise performance: the input circuitry The noise performance: comparisons with power amplifier noise Conclusion Appendix 1: Crossover design references Appendix 2: Loudspeaker design references Douglas Self London Jan 2011