
- •Contents
- •Acknowledgments
- •Preface
- •What a Crossover Does
- •Why a Crossover Is Necessary
- •Beaming and Lobing
- •Passive Crossovers
- •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 Hi-Fi
- •Active Crossover Systems
- •Matching Crossovers and Loudspeakers
- •A Modest Proposal: Popularising Active Crossovers
- •Multi-Way Connectors
- •Subjectivism
- •Sealed-Box Loudspeakers
- •Reflex (Ported) Loudspeakers
- •Auxiliary Bass Radiator (ABR) Loudspeakers
- •Transmission Line Loudspeakers
- •Horn Loudspeakers
- •Electrostatic Loudspeakers
- •Ribbon Loudspeakers
- •Electromagnetic Planar Loudspeakers
- •Air-Motion Transformers
- •Plasma Arc Loudspeakers
- •The Rotary Woofer
- •MTM Tweeter-Mid Configurations (d’Appolito)
- •Vertical Line Arrays
- •Line Array Amplitude Tapering
- •Line Array Frequency Tapering
- •CBT Line Arrays
- •Diffraction
- •Sound Absorption in Air
- •Modulation Distortion
- •Drive Unit Distortion
- •Doppler Distortion
- •Further Reading on Loudspeaker Design
- •General Crossover Requirements
- •1 Adequate Flatness of Summed Amplitude/Frequency Response On-Axis
- •2 Sufficiently Steep Roll-Off Slopes Between the Filter Outputs
- •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
- •All-Pole and Non-All-Pole Crossovers
- •Symmetric and Asymmetric Crossovers
- •Allpass 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 1.0 dB-Chebyshev Crossover
- •Third-Order Crossovers
- •Third-Order Butterworth Crossover
- •Third-Order Linkwitz-Riley Crossover
- •Third-Order Bessel Crossover
- •Third-Order 1.0 dB-Chebyshev Crossover
- •Fourth-Order Crossovers
- •Fourth-Order Butterworth Crossover
- •Fourth-Order Linkwitz-Riley Crossover
- •Fourth-Order Bessel Crossover
- •Fourth-Order 1.0 dB-Chebyshev Crossover
- •Fourth-Order Linear-Phase Crossover
- •Fourth-Order Gaussian Crossover
- •Fourth-Order Legendre Crossover
- •Higher-Order Crossovers
- •Determining Frequency Offsets
- •Filler-Driver Crossovers
- •The Duelund Crossover
- •Crossover Topology
- •Crossover Conclusions
- •Elliptical Filter Crossovers
- •Neville Thiele MethodTM (NTM) 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
- •Active Filters
- •Lowpass Filters
- •Highpass Filters
- •Bandpass Filters
- •Notch Filters
- •Allpass Filters
- •All-Stop Filters
- •Brickwall Filters
- •The Order of a Filter
- •Filter Cutoff Frequencies and Characteristic Frequencies
- •First-Order Filters
- •Second-Order and Higher-Order Filters
- •Filter Characteristics
- •Amplitude Peaking and Q
- •Butterworth Filters
- •Linkwitz-Riley Filters
- •Bessel Filters
- •Chebyshev Filters
- •1 dB-Chebyshev Lowpass Filter
- •3 dB-Chebyshev 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
- •Laguerre Filters
- •Synchronous Filters
- •Other Filter Characteristics
- •Designing Real Filters
- •Component Sensitivity
- •First-Order Lowpass Filters
- •Second-Order Filters
- •Sallen & Key 2nd-Order Lowpass Filters
- •Sallen & Key Lowpass Filter Components
- •Sallen & Key 2nd-Order Lowpass: Unity Gain
- •Sallen & Key 2nd-Order Lowpass Unity Gain: Component Sensitivity
- •Filter Frequency Scaling
- •Sallen & Key 2nd-Order Lowpass: Equal Capacitor
- •Sallen & Key 2nd-Order Lowpass Equal-C: Component Sensitivity
- •Sallen & Key 2nd-Order Butterworth Lowpass: Defined Gains
- •Sallen & Key 2nd-Order Lowpass: Non-Equal Resistors
- •Sallen & Key 2nd-Order Lowpass: Optimisation
- •Sallen & Key 3rd-Order Lowpass: Two Stages
- •Sallen & Key 3rd-Order Lowpass: Single Stage
- •Sallen & Key 4th-Order Lowpass: Two Stages
- •Sallen & Key 4th-Order Lowpass: Single-Stage Butterworth
- •Sallen & Key 4th-Order Lowpass: Single-Stage Linkwitz-Riley
- •Sallen & Key 5th-Order Lowpass: Three Stages
- •Sallen & Key 5th-Order Lowpass: Two Stages
- •Sallen & Key 5th-Order Lowpass: Single Stage
- •Sallen & Key 6th-Order Lowpass: Three Stages
- •Sallen & Key 6th-Order Lowpass: Single Stage
- •Sallen & Key Lowpass: Input Impedance
- •Linkwitz-Riley Lowpass With Sallen & Key Filters: Loading Effects
- •Lowpass Filters With Attenuation
- •Bandwidth Definition Filters
- •Bandwidth Definition: Butterworth Versus Bessel
- •Variable-Frequency Lowpass Filters: Sallen & Key
- •First-Order Highpass Filters
- •Sallen & Key 2nd-Order Filters
- •Sallen & Key 2nd-Order Highpass Filters
- •Sallen & Key Highpass Filter Components
- •Sallen & Key 2nd-Order Highpass: Unity Gain
- •Sallen & Key 2nd-Order Highpass: Equal Resistors
- •Sallen & Key 2nd-Order Butterworth Highpass: Defined Gains
- •Sallen & Key 2nd-Order Highpass: Non-Equal Capacitors
- •Sallen & Key 3rd-Order Highpass: Two Stages
- •Sallen & Key 3rd-Order Highpass in a Single Stage
- •Sallen & Key 4th-Order Highpass: Two Stages
- •Sallen & Key 4th-Order Highpass: Butterworth in a Single Stage
- •Sallen & Key 4th-Order Highpass: Linkwitz-Riley in a Single Stage
- •Sallen & Key 4th-Order Highpass: Single-Stage With Other Filter Characteristics
- •Sallen & Key 5th-Order Highpass: Three Stages
- •Sallen & Key 5th-Order Butterworth Filter: Two Stages
- •Sallen & Key 5th-Order Highpass: Single Stage
- •Sallen & Key 6th-Order Highpass: Three Stages
- •Sallen & Key 6th-Order Highpass: Single Stage
- •Sallen & Key Highpass: Input Impedance
- •Bandwidth Definition Filters
- •Bandwidth Definition: Subsonic Filters
- •Bandwidth Definition: Combined Ultrasonic and Subsonic Filters
- •Variable-Frequency Highpass Filters: Sallen & Key
- •Designing Filters
- •Multiple-Feedback Filters
- •Multiple-Feedback 2nd-Order Lowpass Filters
- •Multiple-Feedback 2nd-Order Highpass Filters
- •Multiple-Feedback 3rd-Order Filters
- •Multiple-Feedback 3rd-Order Lowpass Filters
- •Multiple-Feedback 3rd-Order Highpass Filters
- •Biquad Filters
- •Akerberg-Mossberg Lowpass Filter
- •Akerberg-Mossberg Highpass Filters
- •Tow-Thomas Biquad Lowpass and Bandpass Filter
- •Tow-Thomas Biquad Notch and Allpass Responses
- •Tow-Thomas Biquad Highpass Filter
- •State-Variable Filters
- •Variable-Frequency Filters: State-Variable 2nd Order
- •Variable-Frequency Filters: State-Variable 4th-Order
- •Variable-Frequency Filters: Other Orders of State-Variable
- •Other Filters
- •Aspects of Filter Performance: Noise and Distortion
- •Distortion in Active Filters
- •Distortion in Sallen & Key Filters: Looking for DAF
- •Distortion in Sallen & Key Filters: 2nd-Order Lowpass
- •Distortion in Sallen & Key Filters: 2nd-Order Highpass
- •Mixed Capacitors in Low-Distortion 2nd-Order Sallen & Key Filters
- •Distortion in Sallen & Key Filters: 3rd-Order Lowpass Single Stage
- •Distortion in Sallen & Key Filters: 3rd-Order Highpass Single Stage
- •Distortion in Sallen & Key Filters: 4th-Order Lowpass Single Stage
- •Distortion in Sallen & Key Filters: 4th-Order Highpass Single Stage
- •Distortion in Sallen & Key Filters: Simulations
- •Distortion in Sallen & Key Filters: Capacitor Conclusions
- •Distortion in Multiple-Feedback Filters: 2nd-Order Lowpass
- •Distortion in Multiple-Feedback Filters: 2nd-Order Highpass
- •Distortion in Tow-Thomas Filters: 2nd-Order Lowpass
- •Distortion in Tow-Thomas Filters: 2nd-Order Highpass
- •Noise in Active Filters
- •Noise and Bandwidth
- •Noise in Sallen & Key Filters: 2nd-Order Lowpass
- •Noise in Sallen & Key Filters: 2nd-Order Highpass
- •Noise in Sallen & Key Filters: 3rd-Order Lowpass Single Stage
- •Noise in Sallen & Key Filters: 3rd-Order Highpass Single Stage
- •Noise in Sallen & Key Filters: 4th-Order Lowpass Single Stage
- •Noise in Sallen & Key Filters: 4th-Order Highpass Single Stage
- •Noise in Multiple-Feedback Filters: 2nd-Order Lowpass
- •Noise in Multiple-Feedback Filters: 2nd-Order Highpass
- •Noise in Tow-Thomas 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
- •Bainter Notch Filter Design
- •Bainter Notch Filter Example
- •An Elliptical Filter Using a Bainter Highpass Notch
- •The Bridged-Differentiator Notch Filter
- •Boctor Notch Filters
- •Other Notch Filters
- •Simulating Notch Filters
- •The Requirement for Delay Compensation
- •Calculating the Required Delays
- •Signal Summation
- •Physical Methods of Delay Compensation
- •Delay Filter Technology
- •Sample Crossover and Delay Filter Specification
- •Allpass Filters in General
- •First-Order Allpass Filters
- •Distortion and Noise in 1st-Order Allpass Filters
- •Cascaded 1st-Order Allpass Filters
- •Second-Order Allpass Filters
- •Distortion and Noise in 2nd-Order Allpass Filters
- •Third-Order Allpass Filters
- •Distortion and Noise in 3rd-Order Allpass Filters
- •Higher-Order Allpass Filters
- •Delay Lines for Subtractive Crossovers
- •Variable Allpass Time Delays
- •Lowpass Filters for Time Delays
- •The Need for Equalisation
- •What Equalisation Can and Can’t Do
- •Loudspeaker Equalisation
- •1 Drive Unit Equalisation
- •3 Bass Response Extension
- •4 Diffraction Compensation Equalisation
- •5 Room Interaction Correction
- •Equalisation Circuits
- •HF-Cut and LF-Boost Equaliser
- •Combined HF-Boost and HF-Cut Equaliser
- •Adjustable Peak/Dip Equalisers: Fixed Frequency and Low Q
- •Adjustable Peak/Dip Equalisers With High Q
- •Parametric Equalisers
- •The Bridged-T Equaliser
- •The Biquad Equaliser
- •Capacitance Multiplication for the Biquad Equaliser
- •Equalisers With Non-Standard Slopes
- •Equalisers With −3 dB/Octave Slopes
- •Equalisers With −3 dB/Octave Slopes Over Limited Range
- •Equalisers With −4.5 dB/Octave Slopes
- •Equalisers With Other Slopes
- •Equalisation by Filter Frequency Offset
- •Equalisation by Adjusting All Filter Parameters
- •Component Values
- •Resistors
- •Through-Hole Resistors
- •Surface-Mount Resistors
- •Resistors: Values and Tolerances
- •Resistor Value Distributions
- •Obtaining Arbitrary Resistance Values
- •Other Resistor Combinations
- •Resistor Noise: Johnson and Excess Noise
- •Resistor Non-Linearity
- •Capacitors: Values and Tolerances
- •Obtaining Arbitrary Capacitance Values
- •Capacitor Shortcomings
- •Non-Electrolytic Capacitor Non-Linearity
- •Electrolytic Capacitor Non-Linearity
- •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 NE5532 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
- •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
- •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
- •Subwoofer Applications
- •Subwoofer Technologies
- •Sealed-Box (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
- •Hi-Fi 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
- •Crossover Frequency Control (Lowpass Filter)
- •Highpass Subsonic Filter
- •Phase Switch (Normal/Inverted)
- •Variable Phase 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
- •Motional Feedback Loudspeakers
- •History
- •Feedback of Position
- •Feedback of Velocity
- •Feedback of Acceleration
- •Other MFB Speakers
- •Published Projects
- •Conclusions
- •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 Ratio (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
- •The Self Variable-Gain Balanced Input
- •High Input Impedance Balanced Inputs
- •The Instrumentation Amplifier
- •Instrumentation Amplifier Applications
- •The Instrumentation Amplifier With 4x Gain
- •The Instrumentation Amplifier at Unity Gain
- •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
- •Unbalanced Outputs
- •Zero-Impedance Outputs
- •Ground-Cancelling Outputs
- •Balanced Outputs
- •Transformer Balanced Outputs
- •Output Transformer Frequency Response
- •Transformer Distortion
- •Reducing Transformer Distortion
- •Opamp Supply Rail Voltages
- •Designing a ±15 V Supply
- •Designing a ±17 V Supply
- •Using Variable-Voltage Regulators
- •Improving Ripple Performance
- •Dual Supplies From a Single Winding
- •Mutual Shutdown Circuitry
- •Power Supplies for Discrete Circuitry
- •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
- •Index

Passive Components for Active Crossovers 447
Table 15.15: Relative cost of polyester and polypropylene capacitors, relative to 100 nF polyester.
|
Manufacturer A |
Manufacturer B |
Manufacturer C |
Manufacturer A |
|
|
|
|
|
Dielectric |
Polyester |
Polyester |
Polyester |
Polypropylene |
100 nF |
1.00 |
1.00 |
1.00 |
9.42 |
220 nF |
1.18 |
1.76 |
1.55 |
25.66 |
470 nF |
1.55 |
2.25 |
2.38 |
31.58 |
|
|
|
|
|
slowly than proportionally. Therefore, making up a capacitance with two equal values, as in our example of 440 nF = 2 × 220 nF, is going to cost more than using a single 470 nF capacitor. The table also demonstrates that polypropylene capacitors cost a lot more than polyester, so the cost difference is much greater. In making your design decisions you will of course be working with prices from your intended supplier.
Polypropylene capacitors are much more expensive than polyester, but their great advantage is that they do not generate distortion (see later). In many filter types only one of the capacitors needs to be polypropylene for capacitor distortion to be eliminated, and this can save some serious money. This intriguing state of affairs is described in detail in Chapter 11.
Capacitor Shortcomings
Capacitors fall short of being an ideal circuit element in several ways, notably leakage, equivalent series resistance (ESR), equivalent series inductance (ESL), dielectric absorption, and non-linearity:
Capacitor leakage is equivalent to a high value resistance across the capacitor terminals, which allows a trickle of current to flow when a DC voltage is applied. Leakage is usually negligible for nonelectrolytics, but is much greater for electrolytics. It is not normally a problem in audio design.
Equivalent series resistance (ESR) is a measure of how much the component deviates from a mathematically pure capacitance. The series resistance is partly due to the physical resistance of leads and foils and partly due to losses in the dielectric. It can also be expressed as tan-δ (tan-delta), which is the tangent of the phase angle between the voltage across and the current flowing through the capacitor. Once again it is rarely a problem in the audio field, the values being small fractions of an ohm and very low compared with normal circuit resistances.
Equivalent series inductance (ESL) is always present. Even a straight piece of wire has inductance, and any capacitor has lead-out wires and internal connections. The values are normally measured in nanohenries and have no effect in normal audio circuitry.
Dielectric absorption is a well-known effect; take a large electrolytic, charge it up, and then fully discharge it. Over a few minutes the charge will partially reappear. This “memory effect” also occurs in non-electrolytics to a lesser degree; it is a property of the dielectric and is minimised by using polystyrene, polypropylene, NP0 ceramic, or PTFE dielectrics. Dielectric absorption is invariably
modelled by adding extra resistors and capacitances to an ideal main capacitor, such as Figure15.9 for a 1

448 Passive Components for Active Crossovers
Figure 15.9: A model of dielectric absorption in a 1 uF polystyrene capacitor. All components are linear.
uF polystyrene capacitor, which does not hint at any source of non-linearity. [12] However, the dielectric absorption mechanism does seem to have some connection with capacitor distortion, since the dielectrics that show the least dielectric absorption also show the lowest non-linearity. Dielectric absorption is
a major consideration in sample-and-hold circuits but of no account in itself for normal linear audio circuitry; you can see from Figure15.9 that the additional components are relatively small capacitors with very large resistances in series, and the effect these could have on the response of a filter is microscopic, and far smaller than the effects of component tolerances. Note that the model is just an approximation and is not meant to imply that each extra component directly represents some part of a physical process.
Capacitor non-linearity is the least known but by far the most troublesome of capacitor shortcomings.
An RC lowpass filter to demonstrate the effect can be made with a series resistor and a shunt polyester capacitor, as in Figure 15.10, and if you examine the output with a distortion analyser, you will find to your consternation that the circuit is not linear. If the capacitor is a non-electrolytic type with a dielectric such as polyester, then the distortion is relatively pure third harmonic, showing that the effect is symmetrical. For a 10 Vrms input, the THD level may be 0.001% or more. This may not sound like much, but it is substantially greater than the midband distortion of a good opamp. The definitive work on capacitor distortion is a magnificent series of articles by Cyril Bateman in Electronics World. [13] The authority of this is underpinned by Cyril’s background in capacitor manufacture.
Capacitors are used in audio circuitry for four main functions, where their possible non-linearity has varying consequences:
1.Coupling or DC-blocking capacitors. These are usually electrolytics, and if properly sized have a negligible signal voltage across them at the lowest frequencies of interest. The non-linear properties of the capacitor are then unimportant unless current levels are high; power amplifier
output capacitors can generate considerable midband distortion. [14] This makes you wonder what sort of non-linearity is happening in those big non-polarised electrolytics in passive crossovers.
A great deal of futile nonsense has been talked about the mysterious properties of coupling capacitors, but it is all total twaddle. How could a component with negligible voltage across it put its imprint on a signal passing through it? For small-signal use, as long as the signal voltage across the coupling capacitor is kept low, non-linearity is not detectable by the best THD methods. The capacitance value is non-critical, as it has to be, given the wide tolerances of electrolytics.
2.Supply filtering or decoupling capacitors. Electrolytics are used for filtering out supply rail ripple, etc, and non-electrolytics, usually around 100 nF, are used to keep the supply impedance low at high frequencies and thus keep opamps stable. The capacitance value is again non-critical.

Passive Components for Active Crossovers 449
3.For active crossover purposes, by far the most important aspect of capacitors is their role in active filtering. This is a much more demanding application than coupling or decoupling, for first, the capacitor value is now crucially important, as it defines the accuracy of the frequency response. Second, there is by definition a significant signal voltage across the capacitor, and so its nonlinearity can be a serious problem. Non-electrolytics are always used in active filters, though sometimes a time-constant involving an electrolytic is ill-advisedly used to define the lower end of the system bandwidth; this is a very bad practice, because it is certain to introduce significant distortion at the bottom of the frequency range.
4.Small value ceramic capacitors are used for opamp compensation purposes, and sometimes in active filters in the HF path of a crossover. So long as they are NP0 (C0G) ceramic types, their non-linearity should be negligible. Other kinds of ceramic capacitor, using the XR7 dielectric, will introduce copious distortion and must never be used in audio paths. They are intended for highfrequency decoupling, where their linearity or otherwise is irrelevant.
Non-Electrolytic Capacitor Non-Linearity
It has often been assumed that non-electrolytic capacitors, which generally approach an ideal component more closely than electrolytics and have dielectrics constructed in a totally different way, are free from distortion. It is not so. Some non-electrolytics show distortion at levels that is easily measured and can exceed the distortion from the opamps in the circuit. Non-electrolytic capacitor distortion is essentially third harmonic, because the non-polarised dielectric technology is basically symmetrical. The problem is serious, because non-electrolytic capacitors are commonly used to define time-constants and frequency responses (in RIAAequalisation networks, for example) rather than simply for DC blocking.
Very small capacitances present no great problem. Simply make sure you are using the C0G (NP0) type, and so long as you choose a reputable supplier, there will be no distortion. I say “reputable supplier” because I did once encounter some allegedly C0G capacitors from China that showed significant non-linearity. [15]
Middle-range capacitors, from 1 nF to 1 uF, present more of a problem. Capacitors with a variety of dielectrics are available, including polyester, polystyrene, polypropylene, polycarbonate, and polyphenylene sulphide, of which the first three are the most common (note that what is commonly called “polyester” is actually polyethylene terephthalate, PET).
Figure 15.10 shows a simple lowpass filter circuit which, with a good THD analyser, can be used to measure capacitor distortion. The values shown give a measured pole frequency, or −3 dB roll-off
Figure 15.10: Simple lowpass test circuit for non-electrolytic capacitor distortion; −3 dB at 723 Hz.

450 Passive Components for Active Crossovers
point, at 723 Hz. We will start off with polyester, the smallest, most economical, and therefore the most common type for capacitors of this size.
The THD results for a microbox 220 nF 100 V capacitor with a polyester dielectric are shown in
Figure 15.11, for input voltages of 10, 15 and 20 Vrms. They are unsettling.
The distortion is all third-harmonic. It peaks at around 300 to 400 Hz, well below the −3 dB frequency, and even with the input limited to 10 Vrms will exceed the non-linearity introduced by opamps such as the 5532 and the LM4562. Interestingly, the peak frequency changes with applied level. Below the peak, the voltage across the capacitor is roughly constant, but distortion falls as frequency is reduced, because the increasing impedance of the capacitor means it has less effect on a circuit node at a 1 kΩ impedance. Above the peak, distortion falls with increasing frequency because the lowpass circuit action causes the voltage across the capacitor to fall.
The level of distortion varies with different samples of the same type of capacitor; six of the type in Figure 15.11 were measured, and the THD at 10 Vrms and 400 Hz varied from 0.00128% to
0.00206%. This puts paid to any plans for reducing the distortion by some sort of cancellation method.
The distortion can be seen in Figure 15.11 to be a strong function of level, roughly tripling as the input level doubles. Third-harmonic distortion normally quadruples for doubled level, so there may well
be an unanswered question here. It is however clear that reducing the voltage across the capacitor reduces the distortion. This suggests that if cost is not the primary consideration, it might be useful to put two capacitors in series to halve the voltage and the capacitance, and then double up this series
combination to restore the original capacitance, giving the series-parallel arrangement in Figure 15.12. The results are shown in Table 15.16, and once more it can be seen that halving the level has reduced distortion by a factor of three rather than four.
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Figure 15.11: Third-harmonic distortion from a 220 nF 100 V polyester capacitor, at 10, 15, and 20 Vrms input level, showing peaking around 400 Hz.

Passive Components for Active Crossovers 451
Figure 15.12: Reducing capacitor distortion by series-parallel connection.
Table 15.16: The reduction of polyester capacitor distortion by series-parallel connection.
Input level Vrms |
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The series-parallel arrangement has obvious limitations in terms of cost and PCB area occupied but might be useful in some cases. It has the advantage that, as described earlier in the chapter, using multiple components improves the average accuracy of the total value.
An unexpected complication in these tests was that every time a polyester sample was remeasured, the distortion was lower than before. I found a steady reduction in distortion over time; if a test signal was applied continuously, 9 Vrms at 1 kHz would roughly halve the THD over 11 hours. This change consists of both temporary and permanent components. When the signal is removed, over days the distortion increases again but never rises to its original value. When the signal is reapplied, the distortion slowly falls again. This self-improvement effect is therefore of little practical use, but if nothing else it demonstrates that polyester capacitors are more complicated than you might think. I do not believe this has anything to do with dim-witted audio commentators claiming that circuitry has to be left switched on for months or years before it attains its optimum sound; for one thing, nothing happens unless you also continuously apply a signal of much higher amplitude than normal, which would be hard to arrange and has never been touted as a good way to run-in equipment. For fuller details of this strange self-improvement business, see my Linear Audio article. [16]
Clearly polyester capacitors can generate significant distortion, despite their extensive use in audio circuitry of all kinds. The next dielectric we will try is polystyrene. Capacitors with a polystyrene dielectric are extremely useful for some filtering and RIAAequalisation applications because they can be obtained at a 1% tolerance at up to 10 nF at a reasonable price. They can be obtained in larger sizes but at much higher prices.

452 Passive Components for Active Crossovers
Figure 15.13: The THD plot with three samples of 4n7 2.5% polystyrene capacitors, at 10 Vrms input level. The reading is entirely noise.
The distortion test results are shown in Figure 15.13 for three samples of a 4n7 2.5% capacitor; the series resistor R1 has been increased to 4.7 kΩ to keep the −3 dB point inside the audio band, and it is now at 7200 Hz. Note that the THD scale has been extended down to a subterranean 0.0001%, because if it was plotted on the same scale as Figure 15.11 it would be bumping along the bottom of the graph. Figure 15.13 in fact shows no distortion at all, just the measurement noise floor, and the apparent rise at the HF end is simply due to the fact that the output level is decreasing because of the lowpass action, and so the noise floor is relatively increasing. This is at an input level of 10 Vrms, which is about as high as might be expected to occur in normal opamp circuitry. The test was repeated at 20 Vrms, which might be encountered in discrete circuitry, and the results were the same, yielding no measurable distortion.
The tests were done with four samples of 10 nF 1% polystyrene from LCR at 10 Vrms and 20 Vrms, with the same results for each sample. This shows that polystyrene capacitors can be used with confidence; this finding is in complete agreement with Cyril Bateman’s results. [17]
Having resolved the problem of capacitor distortion below 10 nF, we need now to tackle it for larger capacitor values. Polyester having proven unsatisfactory, the next most common capacitor type is polypropylene, and I am glad to report that these are effectively distortion free in values up to 220 nF. Figure 15.14 shows the results for four samples of a 220 nF 250 V 5% polypropylene capacitor from RIFA. The plot shows no distortion at all, just the noise floor, with the apparent rise at the HF end being increasing relative noise due to the lowpass roll-off, as in Figure 15.13. This is also in agreement with Cyril Bateman’s findings. [18] Rerunning the tests at 20 Vrms gave the same result—
no distortion. This is very pleasing, but there is a downside. Polypropylene capacitors of this value and voltage rating are much larger physically than the commonly used 63 or 100 V polyester capacitor, and more expensive.

Passive Components for Active Crossovers 453
Figure 15.14: The THD plot with four samples of 220 nF 250 V 5% polypropylene capacitors, at 10 Vrms input level. The reading is again entirely noise.
It was therefore important to find out if the good distortion performance was a result of the 250 V rating, and so I tested a series of polypropylene capacitors with lower voltage ratings from different manufacturers.Axial 47 nF 160 V 5% polypropylene capacitors from Vishay proved to be THD-free at both 10 Vrms and 20 Vrms. Likewise, microbox polypropylene capacitors from 10 nF to 47 nF with ratings of 63 V and 160 V from Vishay and Wima proved to generate no measurable distortion, so the voltage rating appears not to be an issue. This finding is particularly important, because the Vishay range has a 1% tolerance, making them very suitable for precision filters and equalisation networks. The 1% tolerance is naturally reflected in the price.
The higher values of polypropylene capacitors (above 100 nF) appear to be currently only available with 250 V or 400 V ratings, and that means a physically big component. For example, the EPCOS 330 nF 400 V 5% part has a footprint of 26 mm by 6.5 mm, with a height of 15 mm, and capacitors like that take up a lot of PCB area. One way of dealing with this is to use a smaller capacitor in a capacitance multiplication configuration, so a 100 nF 1% component could be made to emulate 330 nF. It has to be said that this is only straightforward if one end of the capacitor is connected to ground; see
Chapter 14 for an example of this concept applied to a biquad equaliser.
When I first started looking at capacitor distortion, I thought that the distortion would probably be lowest for the capacitors with the highest voltage rating. I therefore tested some RF-suppression X2 capacitors, rated at 275 Vrms, equivalent to a peak or DC rating of 389 V. The dielectric material is unknown.An immediate snag is that the tolerance is 10 or 20%, not exactly ideal for precision filtering or equalisation. A more serious problem, however, is that they are far from distortion free. Four samples of a 470 nF X2 capacitor showed THD between 0.002% and 0.003% at 10 Vrms.Ahighvoltage rating alone does not mean low distortion.
For more information on how capacitor non-linearity affects filters see Chapter 11.