book

The Design of Active Crossovers, 2nd Edition

by Douglas Self

March 2018

Intermediate to advanced

698 pages

22h 12m

English

Routledge

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What a Crossover DoesWhy a Crossover Is NecessaryBeaming and LobingPassive CrossoversActive Crossover ApplicationsBi-Amping and Bi-WiringLoudspeaker CablesThe Advantages and Disadvantages of Active CrossoversThe Advantages of Active CrossoversSome Illusory Advantages of Active CrossoversThe Disadvantages of Active CrossoversThe Next Step in Hi-FiActive Crossover SystemsMatching Crossovers and LoudspeakersA Modest Proposal: Popularising Active CrossoversMulti-Way ConnectorsSubjectivism
Sealed-Box LoudspeakersReflex (Ported) LoudspeakersAuxiliary Bass Radiator (ABR) LoudspeakersTransmission Line LoudspeakersHorn LoudspeakersElectrostatic LoudspeakersRibbon LoudspeakersElectromagnetic Planar LoudspeakersAir-Motion TransformersPlasma Arc LoudspeakersThe Rotary WooferMTM Tweeter-Mid Configurations (d’Appolito)Vertical Line ArraysLine Array Amplitude TaperingLine Array Frequency TaperingCBT Line ArraysDiffractionSound Absorption in AirModulation DistortionDrive Unit DistortionDoppler DistortionFurther Reading on Loudspeaker Design
General Crossover Requirements1 Adequate Flatness of Summed Amplitude/Frequency Response On-Axis2 Sufficiently Steep Roll-Off Slopes Between the Filter Outputs3 Acceptable Polar Response4 Acceptable Phase Response5 Acceptable Group Delay BehaviourFurther Requirements for Active Crossovers1 Negligible Extra Noise2 Negligible Impairment of System Headroom3 Negligible Extra Distortion4 Negligible Impairment of Frequency Response5 Negligible Impairment of ReliabilityLinear PhaseMinimum PhaseAbsolute PhasePhase PerceptionTarget Functions

All-Pole and Non-All-Pole CrossoversSymmetric and Asymmetric CrossoversAllpass and Constant-Power CrossoversConstant-Voltage CrossoversFirst-Order CrossoversFirst-Order Solen Split CrossoverFirst-Order Crossovers: 3-WaySecond-Order CrossoversSecond-Order Butterworth CrossoverSecond-Order Linkwitz-Riley CrossoverSecond-Order Bessel CrossoverSecond-Order 1.0 dB-Chebyshev CrossoverThird-Order CrossoversThird-Order Butterworth CrossoverThird-Order Linkwitz-Riley CrossoverThird-Order Bessel CrossoverThird-Order 1.0 dB-Chebyshev CrossoverFourth-Order CrossoversFourth-Order Butterworth CrossoverFourth-Order Linkwitz-Riley CrossoverFourth-Order Bessel CrossoverFourth-Order 1.0 dB-Chebyshev CrossoverFourth-Order Linear-Phase CrossoverFourth-Order Gaussian CrossoverFourth-Order Legendre CrossoverHigher-Order CrossoversDetermining Frequency OffsetsFiller-Driver CrossoversThe Duelund CrossoverCrossover TopologyCrossover Conclusions
Elliptical Filter CrossoversNeville Thiele MethodTM (NTM) Crossovers
Subtractive CrossoversFirst-Order Subtractive CrossoversSecond-Order Butterworth Subtractive CrossoversThird-Order Butterworth Subtractive CrossoversFourth-Order Butterworth Subtractive CrossoversSubtractive Crossovers With Time DelaysPerforming the Subtraction
Active FiltersLowpass FiltersHighpass FiltersBandpass FiltersNotch FiltersAllpass FiltersAll-Stop FiltersBrickwall FiltersThe Order of a FilterFilter Cutoff Frequencies and Characteristic FrequenciesFirst-Order FiltersSecond-Order and Higher-Order FiltersFilter CharacteristicsAmplitude Peaking and QButterworth FiltersLinkwitz-Riley FiltersBessel FiltersChebyshev Filters1 dB-Chebyshev Lowpass Filter3 dB-Chebyshev Lowpass FilterHigher-Order FiltersButterworth Filters up to 8th-OrderLinkwitz-Riley Filters up to 8th-OrderBessel Filters up to 8th-OrderChebyshev Filters up to 8th-OrderMore Complex Filters—Adding ZerosInverse Chebyshev Filters (Chebyshev Type II)Elliptical Filters (Cauer Filters)Some Lesser-Known Filter CharacteristicsTransitional FiltersLinear-Phase FiltersGaussian FiltersLegendre-Papoulis FiltersLaguerre FiltersSynchronous FiltersOther Filter Characteristics
Designing Real FiltersComponent SensitivityFirst-Order Lowpass FiltersSecond-Order FiltersSallen & Key 2nd-Order Lowpass FiltersSallen & Key Lowpass Filter ComponentsSallen & Key 2nd-Order Lowpass: Unity GainSallen & Key 2nd-Order Lowpass Unity Gain: Component SensitivityFilter Frequency ScalingSallen & Key 2nd-Order Lowpass: Equal CapacitorSallen & Key 2nd-Order Lowpass Equal-C: Component SensitivitySallen & Key 2nd-Order Butterworth Lowpass: Defined GainsSallen & Key 2nd-Order Lowpass: Non-Equal ResistorsSallen & Key 2nd-Order Lowpass: OptimisationSallen & Key 3rd-Order Lowpass: Two StagesSallen & Key 3rd-Order Lowpass: Single StageSallen & Key 3rd-Order Lowpass in a Single Stage: Non-Equal ResistorsSallen & Key 4th-Order Lowpass: Two StagesSallen & Key 4th-Order Lowpass: Single-Stage ButterworthSallen & Key 4th-Order Lowpass: Single-Stage Linkwitz-RileySallen & Key 4th-Order Lowpass: Single Stage With Non-Equal ResistorsSallen & Key 4th-Order Lowpass: Single Stage With Other Filter CharacteristicsSallen & Key 5th-Order Lowpass: Three StagesSallen & Key 5th-Order Lowpass: Two StagesSallen & Key 5th-Order Lowpass: Single StageSallen & Key 6th-Order Lowpass: Three StagesSallen & Key 6th-Order Lowpass: Single StageSallen & Key Lowpass: Input ImpedanceLinkwitz-Riley Lowpass With Sallen & Key Filters: Loading EffectsLowpass Filters With AttenuationBandwidth Definition FiltersBandwidth Definition: Butterworth Versus BesselVariable-Frequency Lowpass Filters: Sallen & Key
First-Order Highpass FiltersSallen & Key 2nd-Order FiltersSallen & Key 2nd-Order Highpass FiltersSallen & Key Highpass Filter ComponentsSallen & Key 2nd-Order Highpass: Unity GainSallen & Key 2nd-Order Highpass: Equal ResistorsSallen & Key 2nd-Order Butterworth Highpass: Defined GainsSallen & Key 2nd-Order Highpass: Non-Equal CapacitorsSallen & Key 3rd-Order Highpass: Two StagesSallen & Key 3rd-Order Highpass in a Single StageSallen & Key 4th-Order Highpass: Two StagesSallen & Key 4th-Order Highpass: Butterworth in a Single StageSallen & Key 4th-Order Highpass: Linkwitz-Riley in a Single StageSallen & Key 4th-Order Highpass: Single-Stage With Other Filter CharacteristicsSallen & Key 5th-Order Highpass: Three StagesSallen & Key 5th-Order Butterworth Filter: Two StagesSallen & Key 5th-Order Highpass: Single StageSallen & Key 6th-Order Highpass: Three StagesSallen & Key 6th-Order Highpass: Single StageSallen & Key Highpass: Input ImpedanceBandwidth Definition FiltersBandwidth Definition: Subsonic FiltersBandwidth Definition: Combined Ultrasonic and Subsonic FiltersVariable-Frequency Highpass Filters: Sallen & Key
Designing FiltersMultiple-Feedback FiltersMultiple-Feedback 2nd-Order Lowpass FiltersMultiple-Feedback 2nd-Order Highpass FiltersMultiple-Feedback 3rd-Order FiltersMultiple-Feedback 3rd-Order Lowpass FiltersMultiple-Feedback 3rd-Order Highpass FiltersBiquad FiltersAkerberg-Mossberg Lowpass FilterAkerberg-Mossberg Highpass FiltersTow-Thomas Biquad Lowpass and Bandpass FilterTow-Thomas Biquad Notch and Allpass ResponsesTow-Thomas Biquad Highpass FilterState-Variable FiltersVariable-Frequency Filters: State-Variable 2nd OrderVariable-Frequency Filters: State-Variable 4th-OrderVariable-Frequency Filters: Other Orders of State-VariableOther Filters
Aspects of Filter Performance: Noise and DistortionDistortion in Active FiltersDistortion in Sallen & Key Filters: The Distortion Aggravation FactorDistortion in Sallen & Key Filters: Looking for DAFDistortion in Sallen & Key Filters: 2nd-Order LowpassDistortion in Sallen & Key Filters: 2nd-Order HighpassMixed Capacitors in Low-Distortion 2nd-Order Sallen & Key FiltersDistortion in Sallen & Key Filters: 3rd-Order Lowpass Single StageDistortion in Sallen & Key Filters: 3rd-Order Highpass Single StageDistortion in Sallen & Key Filters: 4th-Order Lowpass Single StageDistortion in Sallen & Key Filters: 4th-Order Highpass Single StageDistortion in Sallen & Key Filters: SimulationsDistortion in Sallen & Key Filters: Capacitor ConclusionsDistortion in Multiple-Feedback Filters: The Distortion Aggravation FactorDistortion in Multiple-Feedback Filters: 2nd-Order LowpassDistortion in Multiple-Feedback Filters: 2nd-Order HighpassDistortion in Tow-Thomas Filters: 2nd-Order LowpassDistortion in Tow-Thomas Filters: 2nd-Order HighpassNoise in Active FiltersNoise and BandwidthNoise in Sallen & Key Filters: 2nd-Order LowpassNoise in Sallen & Key Filters: 2nd-Order HighpassNoise in Sallen & Key Filters: 3rd-Order Lowpass Single StageNoise in Sallen & Key Filters: 3rd-Order Highpass Single StageNoise in Sallen & Key Filters: 4th-Order Lowpass Single StageNoise in Sallen & Key Filters: 4th-Order Highpass Single StageNoise in Multiple-Feedback Filters: 2nd-Order LowpassNoise in Multiple-Feedback Filters: 2nd-Order HighpassNoise in Tow-Thomas Filters
Multiple-Feedback Bandpass FiltersHigh-Q Bandpass FiltersNotch FiltersThe Twin-T Notch FilterThe 1-Bandpass Notch FilterThe Bainter Notch FilterBainter Notch Filter DesignBainter Notch Filter ExampleAn Elliptical Filter Using a Bainter Highpass NotchThe Bridged-Differentiator Notch FilterBoctor Notch FiltersOther Notch FiltersSimulating Notch Filters
The Requirement for Delay CompensationCalculating the Required DelaysSignal SummationPhysical Methods of Delay CompensationDelay Filter TechnologySample Crossover and Delay Filter SpecificationAllpass Filters in GeneralFirst-Order Allpass FiltersDistortion and Noise in 1st-Order Allpass FiltersCascaded 1st-Order Allpass FiltersSecond-Order Allpass FiltersDistortion and Noise in 2nd-Order Allpass FiltersThird-Order Allpass FiltersDistortion and Noise in 3rd-Order Allpass FiltersHigher-Order Allpass FiltersDelay Lines for Subtractive CrossoversVariable Allpass Time DelaysLowpass Filters for Time Delays
The Need for EqualisationWhat Equalisation Can and Can’t DoLoudspeaker Equalisation1 Drive Unit Equalisation2 6 dB/octave Dipole Equalisation3 Bass Response Extension4 Diffraction Compensation Equalisation5 Room Interaction CorrectionEqualisation CircuitsHF-Boost and LF-Cut EqualiserHF-Cut and LF-Boost EqualiserCombined HF-Boost and HF-Cut EqualiserAdjustable Peak/Dip Equalisers: Fixed Frequency and Low QAdjustable Peak/Dip Equalisers: Variable Centre Frequency and Low QAdjustable Peak/Dip Equalisers With High QParametric EqualisersThe Bridged-T EqualiserThe Biquad EqualiserCapacitance Multiplication for the Biquad EqualiserEqualisers With Non-Standard SlopesEqualisers With −3 dB/Octave SlopesEqualisers With −3 dB/Octave Slopes Over Limited RangeEqualisers With −4.5 dB/Octave SlopesEqualisers With Other SlopesEqualisation by Filter Frequency OffsetEqualisation by Adjusting All Filter Parameters
Component ValuesResistorsThrough-Hole ResistorsSurface-Mount ResistorsResistors: Values and TolerancesImproving Accuracy With Multiple Components: Gaussian DistributionResistor Value DistributionsImproving Accuracy With Multiple Components: Uniform DistributionObtaining Arbitrary Resistance ValuesOther Resistor CombinationsResistor Noise: Johnson and Excess NoiseResistor Non-LinearityCapacitors: Values and TolerancesObtaining Arbitrary Capacitance ValuesCapacitor ShortcomingsNon-Electrolytic Capacitor Non-LinearityElectrolytic Capacitor Non-Linearity
Active Devices for Active CrossoversOpamp TypesOpamp Properties: NoiseOpamp Properties: Slew RateOpamp Properties: Common-Mode RangeOpamp Properties: Input Offset VoltageOpamp Properties: Bias CurrentOpamp Properties: CostOpamp Properties: Internal DistortionOpamp Properties: Slew Rate Limiting DistortionOpamp Properties: Distortion Due to LoadingOpamp Properties: Common-Mode DistortionOpamps SurveyedThe TL072 OpampThe NE5532 and 5534 OpampsThe 5532 With Shunt Feedback5532 Output Loading in Shunt-Feedback ModeThe 5532 With Series FeedbackCommon-Mode Distortion in the 5532Reducing 5532 Distortion by Output Stage BiasingWhich 5532?The 5534 OpampThe LM4562 OpampCommon-Mode Distortion in the LM4562The LME49990 OpampCommon-Mode Distortion in the LME49990The AD797 OpampCommon-Mode Distortion in the AD797The OP27 OpampOpamp Selection
Crossover FeaturesInput Level ControlsSubsonic FiltersUltrasonic FiltersOutput Level TrimsOutput Mute Switches, Output Phase-Reverse SwitchesControl ProtectionFeatures Usually AbsentMeteringRelay Output MutingSwitchable Crossover ModesNoise, Headroom, and Internal LevelsCircuit Noise and Low-Impedance DesignUsing Raised Internal LevelsPlacing the Output AttenuatorThe Amplitude/Frequency Distribution of Musical Signals and Internal LevelsGain StructuresNoise GainActive Gain ControlsFilter Order in the Signal PathOutput Level ControlsMute SwitchesPhase-Invert SwitchesDistributed Peak DetectionPower Amplifier Considerations
Subwoofer ApplicationsSubwoofer TechnologiesSealed-Box (Infinite Baffle) SubwoofersReflex (Ported) SubwoofersAuxiliary Bass Radiator (ABR) SubwoofersTransmission Line SubwoofersBandpass SubwoofersIsobaric SubwoofersDipole SubwoofersHorn-Loaded SubwoofersSubwoofer Drive UnitsHi-Fi SubwoofersHome Entertainment SubwoofersLow-Level Inputs (Unbalanced)Low-Level Inputs (Balanced)High-Level InputsHigh-Level OutputsMono SummingLFE InputLevel ControlCrossover In/Out SwitchCrossover Frequency Control (Lowpass Filter)Highpass Subsonic FilterPhase Switch (Normal/Inverted)Variable Phase ControlSignal Activation Out of StandbyHome Entertainment CrossoversFixed FrequencyVariable FrequencyMultiple VariablePower Amplifiers for Home Entertainment SubwoofersSubwoofer IntegrationSound-Reinforcement SubwoofersLine or Area ArraysCardioid Subwoofer ArraysAux-Fed SubwoofersAutomotive Audio Subwoofers
Motional Feedback LoudspeakersHistoryFeedback of PositionFeedback of VelocityFeedback of AccelerationOther MFB SpeakersPublished ProjectsConclusions
External Signal LevelsInternal Signal LevelsInput Amplifier FunctionsUnbalanced InputsBalanced InterconnectionsThe Advantages of Balanced InterconnectionsThe Disadvantages of Balanced InterconnectionsBalanced Cables and InterferenceBalanced ConnectorsBalanced Signal LevelsElectronic vs Transformer Balanced InputsCommon-Mode Rejection Ratio (CMRR)The Basic Electronic Balanced InputCommon-Mode Rejection Ratio: Opamp GainCommon-Mode Rejection Ratio: Opamp Frequency ResponseCommon-Mode Rejection Ratio: Opamp CMRRCommon-Mode Rejection Ratio: Amplifier Component MismatchesA Practical Balanced InputVariations on the Balanced Input StageCombined Unbalanced and Balanced InputsThe Superbal InputSwitched-Gain Balanced InputsVariable-Gain Balanced InputsThe Self Variable-Gain Balanced InputHigh Input Impedance Balanced InputsThe Instrumentation AmplifierInstrumentation Amplifier ApplicationsThe Instrumentation Amplifier With 4x GainThe Instrumentation Amplifier at Unity GainTransformer Balanced InputsInput Overvoltage ProtectionNoise and Balanced InputsLow-Noise Balanced InputsLow-Noise Balanced Inputs in Real LifeUltra-Low-Noise Balanced Inputs
Unbalanced OutputsZero-Impedance OutputsGround-Cancelling OutputsBalanced OutputsTransformer Balanced OutputsOutput Transformer Frequency ResponseTransformer DistortionReducing Transformer Distortion
Opamp Supply Rail VoltagesDesigning a ±15 V SupplyDesigning a ±17 V SupplyUsing Variable-Voltage RegulatorsImproving Ripple PerformanceDual Supplies From a Single WindingMutual Shutdown CircuitryPower Supplies for Discrete Circuitry
Design PrinciplesExample Crossover SpecificationThe Gain StructureResistor SelectionCapacitor SelectionThe Balanced Line Input StageThe Bandwidth Definition FilterThe HF Path: 3 kHz Linkwitz-Riley Highpass FilterThe HF Path: Time-Delay CompensationThe MID Path: TopologyThe MID Path: 400 Hz Linkwitz-Riley Highpass FilterThe MID Path: 3 kHz Linkwitz-Riley Lowpass FilterThe MID Path: Time-Delay CompensationThe LF Path: 400 Hz Linkwitz-Riley Lowpass FilterThe LF Path: No Time-Delay CompensationOutput Attenuators and Level Trim ControlsBalanced OutputsCrossover ProgrammingNoise Analysis: Input CircuitryNoise Analysis: HF PathNoise Analysis: MID PathNoise Analysis: LF PathImproving the Noise Performance: The MID PathImproving the Noise Performance: The Input CircuitryThe Noise Performance: Comparisons With Power Amplifier NoiseConclusion

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Appendix 2 US Crossover Patents

These US patents concentrate on both active and passive crossover design, but they also have much information on loudspeaker design in general. This list does not pretend to be complete, but following the references in each patent should give a comprehensive overview of the field. Dates are for publication, not filing.

2 771 518	Sziklai	Frequency band separation amplifier	November 1956
2 802 054	Corney	Sound reproducing apparatus	August 1957
3 457 370	Boner	Impedance correcting networks	July 1969
3 657 480	Cheng et al	Multi channel audio system with crossover network feeding separate amplifiers for each channel with direct coupling to low-frequency loudspeaker	April 1972
3 727 004	Bose	Loudspeaker system ...