The Design of Active Crossovers

By Douglas Self

Page updated:
22 July 2011

Out now

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My latest book is on the design of active crossovers for multi-way loudspeaker systems. It is, to the best of my knowledge, the first book that concentrates wholly on the subject. It is a unique collection of detailed information on crossover design. It will contain a lot of wholly original information that I have worked out over the last twelve months. A detailed synopsis of the chapter contents is given below.

The book comprises about 580 pages; that is a lot of information.

Out now.

From any good/big bookshop, from Elsevier or Amazon.

You can order from Amazon: Amazon UK

I try to make sure everything I write is wholly free from errors. I sometimes fail. There are a couple of typos which are listed here: Errata


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: 	Time-delay 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

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Chapter 1: 	  Active crossover basics
What a crossover does
Why a crossover is necessary
Beaming and lobing
Active crossover applications
Bi-amping and bi-wiring
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
Multi-way 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 on-axis
	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
All-pole and  non-all-pole crossovers
Symmetrical and asymmetrical  crossovers
All-pass and  Constant-Power crossovers
Constant voltage crossovers
First-order crossovers
First-order Solen split crossover
First-order crossovers:  3-way
Second-order crossovers
	Second-order Butterworth crossover
	Second-order Linkwitz-Riley crossover
	Second-order Bessel crossover
	Second-order 1dB-Chebychev crossover
Third-order crossovers
	Third-order Butterworth crossover
	Third-order Linkwitz-Riley crossover
	Third-order Bessel crossover
	Third-order 1dB-Chebychev crossover
Fourth-order crossovers
	Fourth-order Butterworth crossover
	Fourth-order Linkwitz-Riley crossover
	Fourth-order Bessel crossover
	Fourth-order 1dB-Chebychev crossover
	Fourth-order linear-phase crossover
	Fourth-order Gaussian crossover
	Fourth-order Legendre crossover
Higher-order crossovers
Determining frequency offsets
Summary of crossover properties
Filler-driver 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
First-order subtractive crossovers
Second-order Butterworth subtractive crossovers
Third-order Butterworth subtractive crossovers
Fourth-order 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
All-pass filters
The order of a filter
Filter cutoff frequencies and characteristic frequencies
First-order filters
Second-order and higher-order filters
Filter characteristics
	Butterworth filters
	Linkwitz-Riley filters
	Bessel filters
	Chebyshev filters
	1dB-Chebyschev lowpass filter
	3dB-Chebyschev lowpass filter
Higher-order filters
	Butterworth filters up to 8th order
	Linkwitz-Riley 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 lesser-known  filter characteristics
	Transitional filters
	Linear-Phase filters
	Gaussian filters
	Legendre-Papoulis filters
	Synchronous filters
Other filters



Chapter 8: 	  Designing lowpass and highpass filters
Designing real filters
Component sensitivity
First-order lowpass and highpass filters
Second-order filters
Sallen & Key second-order filters
Sallen & Key lowpass filter components
Sallen & Key second-order lowpass:  unity-gain
Sallen & Key second-order lowpass unity-gain:  component sensitivity
Sallen & Key second-order lowpass: equal-capacitor
Sallen & Key second-order lowpass equal-C:  component sensitivity
Sallen & Key second-order Butterworth lowpass:  defined gains
Sallen & Key second-order lowpass: non-equal-resistors
Sallen & Key third-order lowpass in a single stage
Sallen & Key third-order lowpass in a single stage: non-equal-resistors
Sallen & Key fourth-order lowpass in a single stage
Sallen & Key fourth-order lowpass in a single stage: non-equal-resistors
Sallen & Key fifth and sixth-order lowpass in a single stage

Sallen & Key highpass filters
Sallen & Key second-order highpass:  unity-gain
Sallen & Key second-order highpass:  equal-resistors
Sallen & Key second-order Butterworth highpass:  defined gains
Sallen & Key second-order highpass:  non-equal-capacitors
Sallen & Key third-order highpass in a single stage
Sallen & Key fourth-order highpass in a single stage
Linkwitz-Riley 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 low-distortion Sallen & Key filters
Noise in Sallen & Key filters:  lowpass
Noise in Sallen & Key filters:  highpass
Multiple feedback filters
Multiple-feedback lowpass filters
Multiple-feedback highpass filters
Distortion in multiple-feedback filters:  highpass
Distortion in multiple-feedback filters:  lowpass
Noise in multiple-feedback filters:  highpass
Noise in multiple-feedback filters:  lowpass
State-variable filters
Variable-frequency filters:  Sallen & Key
Variable frequency filters:  state-variable second-order
Variable frequency filters:  state-variable fourth order
Variable frequency filters:  other orders


Chapter 9: 	  Bandpass and Notch Filters
Multiple feedback bandpass filters
High-Q bandpass filters
Notch filters
The twin-T notch filter
The 1- bandpass notch filter
The Bainter notch filter
The bridged-differentiator notch filter
Boctor notch filters
Other notch filters
Simulating notch filters



Chapter 10:  Time-delay 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
All-pass filters in general
First-order allpass filters
Distortion & noise in first-order allpass filters
Cascaded first-order allpass filters
Second-order allpass filters
Distortion & noise in second-order allpass filters
Third order allpass filters
Distortion & noise in third-order allpass filters
Higher-order 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
HF-boost and LF-cut equaliser
HF cut and LF-boost equaliser
Combined HF-boost and HF-cut 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 bridged-T equaliser
The biquad equaliser
Capacitance multiplication for the biquad equaliser
Equalisers with non-6 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 non-linearity
Capacitors:  values and tolerances
Capacitor shortcomings
Non-electrolytic capacitor non-linearity
Electrolytic capacitor non-linearity


Chapter 13:	Opamps for active crossovers
Active devices for active crossovers
Opamp types
Opamp properties:  Noise
Opamp properties:  Slew-rate
Opamp properties:  Common mode range
Opamp properties:  Input offset voltage
Opamp properties:  Bias current
Opamp properties:  Cost
Opamp properties:  Internal distortion
Opamp properties:  Slew-rate limiting distortion
Opamp properties:  Distortion due to loading
Opamp properties:  Common-mode 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
	Common-mode distortion in the 5532
	Reducing 5532 distortion by output stage biasing
	Which 5532?
	The 5534 opamp
	The LM4562 opamp
	Common-mode distortion in the LM4562
The LME49990 opamp
	Common-mode distortion in the LME49990
The AD797 opamp
	Common-mode 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 phase-reverse switches
	Control protection
Features usually absent
	Metering
	Relay output muting
Switchable crossover modes
Noise, headroom, and internal levels
Circuit noise and Low-Impedance Design
Using raised internal levels
Placing the output attenuator
The amplitude/frequency distribution of musical signals, & internal levels

Gain structures
Noise gain
Active gain-controls
Filter order in the signal path
Output level controls
Mute switches
Phase-invert switches
Distributed peak-detection
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
	Horn-loaded subwoofers
Subwoofer drive units
Hifi subwoofers
Home entertainment subwoofers
Low-level inputs (unbalanced)
Low-level inputs (balanced)
High-level inputs
High-level 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
Sound-reinforcement  subwoofers
	Line or area arrays
	Cardioid subwoofer arrays
Aux-fed 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
Common-mode rejection ratio: opamp gain
Common-mode rejection ratio: opamp frequency response
Common-mode rejection ratio: opamp CMRR
Common-mode rejection ratio: Amplifier component mismatches
A practical balanced input
Variations on the balanced input stage
	Combined unbalanced and balanced inputs
	The Superbal input
	Switched-gain balanced inputs
	Variable-gain balanced inputs
	High input-impedance balanced inputs
	The instrumentation amplifier
Transformer balanced inputs
Input overvoltage protection
Noise and balanced inputs
Low-noise balanced inputs
Low-noise balanced inputs in real life
Ultra-low-noise balanced inputs


Chapter 17:	  Line outputs
Unbalanced outputs
Zero-impedance outputs
Ground-cancelling 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 variable-voltage 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 Linkwitz-Riley highpass filter
The HF path:   time delay compensation
The MID path:   topology
The MID path:   400 Hz Linkwitz-Riley highpass filter
The MID path:   3 kHz Linkwitz-Riley lowpass filter
The MID path:   time delay compensation
The LF path:  400 Hz Linkwitz-Riley 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
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