Acknowledgments

My heartfelt thanks to:

Gareth Connor of The Signal Transfer Company for unfailing encouragement, providing the facilities with which some of the experiments in this book were done, and with much appreciation of our long collaboration in the field of audio.

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“The End . . . is the Knowledge of Causes and secret motions of things, and the enlarging of the bounds of human empire, to the effecting of all things possible.”

Francis Bacon, New Atlantis

“Another damned thick book! Always scribble, scribble, scribble! Eh, Mr. Gibbon?”

Attributed to Prince William Henry, Duke of Gloucester, in 1781 upon receiving the second volume of The History of the Decline and Fall of the Roman Empire from its author.

When the first edition of this book was published, I imagined that its rather specialised appeal might limit its sales compared with my other books on preamplifiers and power amplifiers. Rather remarkably, that has not proved to be the case, and so I am very happy to be able to offer a new and improved second edition. The book has been considerably expanded, growing from 19 to 23 chapters, and increasing in length by 30%.

The new material includes

•Amuch, much, broader palette of ready-made filter designs for crossover construction, including single-stage 4th-order Linkwitz-Riley filters, which makes it possible to build a 2-way 4th-order active crossover with one dual opamp (that’s just one stereo channel, obviously). Other additions are many new ways to make 4thand 5th-order filters, new 5thand 6th-order highpass filters, and more advanced filters such as the Tow-Thomas biquad, which allow greater precision in defining the response.

•More on notch filters, especially full design details and procedures for the extremely flexible and useful Bainter notch filter.

•Economical ways of making high-order bandwidth definition filters.

•Abig new chapter on distortion and noise in active filters, covering Sallen & Key, multiplefeedback, and Tow-Thomas filters.

•More on equalisation circuitry, including filter slopes of −3 dB and −4.5 dB/octave.

•More on different loudspeaker types and their specific crossover requirements. New stuff on speaker non-linearity and Doppler distortion, and sound absorption in air.

•Anew section on MTM (d’Appolito) Tweeter-Mid configurations.

•Afull explanation of vertical line arrays of loudspeakers, including J-arrays and amplitude and frequency tapering.

•A whole new chapter on motional feedback loudspeakers and interfacing them with active crossovers.

•Instrumentation amplifiers as low-noise balanced inputs. They have long been praised for having superb common-mode rejection, but this has been hard to exploit in audio applications.

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I demonstrate how to do it and get lower noise at the same time.Also, what I modestly call the

Self variable-gain balanced input, which gives excellent channel balance on stereo inputs without using expensive parts.

•Much more on the ingenious but little-known technology of ground-cancelling outputs, showing how they can give a noise advantage over conventional balanced interconnections. Cunning ways of substantially reducing line output transformer distortion at near-zero cost are described.

•New material on achieving awkward resistor and capacitor values.

However, what you most emphatically will not find here is any truck with the religious dogma of audio Subjectivism; the directional cables, the oxygen-free copper, the World War One vintage triodes still spattered with the mud of the Somme, and all the other depressing paraphernalia of pseudo-science and anti-science. I have spent more time than I care to contemplate in double-blind listening tests— properly conducted ones, with rigorous statistical analysis—and every time the answer was that if you couldn’t measure it you couldn’t hear it. Very often if you could measure it you still couldn’t hear it. However, faith-based audio is not going away any time soon because few people (apart of course from the unfortunate customers) have any interest in it doing so. If you want to know more about my experiences and reasoning in this area, there is a full discussion in my book Audio Power Amplifier

Design (Sixth edition).

As in the first edition of the current volume, the final implementation of each crossover design is analogue, using opamps. For the digital domain you just split off at the point where the frequencies and Q’s of the various filter stages are fixed.You then set your IIR filter coefficients and so on. Purely digital issues like word length and noise shaping are left for you to grapple with.

Also as in the first edition, you will find here the barest minimum of mathematics required to get a design job done. There is no complex algebra, no Laplace variables, and the square root of minus one is conspicuous by its absence. This approach is only possible because SPICE simulators are downloadable for free (e.g. LTspice) and can give you the frequency response, phase, and group delay of a filter before you could write down the first line of complex algebra. The design and analysis equations for 1stand 2nd-order filters are given because they are simple, but beyond that the design procedures are long and complicated and often involve solving systems of equations rather than just plugging in numbers. Explaining them would take up far too much space, and also, some of them are part of my personal stock-in-trade as a consultant in the audio business. For all those reasons, those procedures are not described here.

Each filter is given as an example, usually with a cutoff frequency of 1 kHz. Full instructions are given in Chapter 8 for scaling the component values to give the desired frequency. Nothing more complicated than multiplication is required.

There is unquestionably a need for high-quality analogue circuitry. For example, a good microphone preamplifier needs a gain range from 0 to +80 dB if it is to get any signal it is likely to encounter up to a workable nominal value; there is little prospect of ever being able to connect an A-to-D converter directly to a microphone. If you are starting at line level and have an analogue power amplifier, and all you need is a relatively simple but high-quality active crossover, there is little incentive to convert to digital via an expensive ADC, perform the very straightforward arithmetic manipulations in the digital domain, then go back to analogue via an expensive DAC. Certainly you can do just about anything in the digital domain just by writing code, but you first have to get the signal safely into the

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digital domain.Alittle while ago I was involved in a telemetry project where sophisticated analogue processing, including allpass filters for time compensation, was required before the signal could be accurately digitised.

Therefore analogue circuitry is often the way to go. This book describes how to achieve high performance without spending a lot of money.As was remarked in a review of the first edition of

Active Crossover Design, duplicating the performance attained here in the digital domain is not at all a trivial business.

In the pursuit of high quality at low cost, there are certain principles that pervade this book:

•Low-impedance design. This reduces the effects of Johnson noise and current noise without making voltage noise worse; the only downside is that a low impedance requires an opamp capable of driving it effectively, and sometimes more than one. This is a small price to pay; since an active crossover is an extra piece of equipment inserted into the signal path, it needs to be as transparent as possible, and low noise is an important aspect of this.

•Asophisticated approach to implementing awkward component values.Active crossover design— and filter design in general—is a prime example of a requirement for non-standard component values (RIAAnetworks for phono preamplifiers, as well as variable equalisers, are some other important applications in the audio business). Very often in filter design, only one component can be chosen to be a preferred value from the widely used E24 resistor series. While resistors are freely available in the E96 series, if you are faced with a required value that is effectively random, you will do much better by using two E24 values in series, or, preferably, in parallel.

The nominal value will on average be three times more accurate than for E96. If you go a little further and use three E24 values combined, the accuracy of the nominal value is further improved by ten times. This may appear a bit profligate with components, but resistors are cheap. There is another advantage to the multiple component approach that is less obvious: the effective tolerance is reduced. By how much depends on how much the values vary; the maximum advantage with

2xE24 is √2 times and with 3xE24 is √3 times. The problem is more acute with capacitors as they are not often available in a closely spaced series like E24. They are also more expensive.

•The principle of optimisation. This may sound grand, but what it comes down to is closely scrutinising each circuit block is to see if it is possible to improve it by doing a bit more thinking rather than a bit more spending.

And now a little about the nuts and bolts of this book:

Phrases describing filter order such as “second-order” and “third-order” recur over and over again in this book. To save space and make them stand out better, they have been rendered as “2ndorder” and “3rd-order”.All other ordinal numbers are spelt out fully. The active elements are called “amplifiers” though most of the time they will be opamps; however the Sallen & Key filter configuration in particular can be easily implemented with discrete emitter-followers if desired, so I have used the more general term “amplifiers”.

All measurements were performed with an Audio Precision SYS-2702.

So far as I am aware, no supernatural assistance was received in the making of this book.All suggestions for its improvement that do not involve combustion or a baying crowd will be gratefully

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received.You can find my email address on the front page of my website at douglas-self.com, where I will be adding supplementary material on active crossover design as it occurs.

Further information, and PCBs, kits and built circuit boards of some of my designs, such as phono input stages and complete preamplifiers, can be found at: www.signaltransfer.freeuk.com.

Agood deal of thought and experiment has gone into this book, and I dare to hope that I have moved analogue audio design a bit further forward. I hope you find it useful, and I hope you enjoy it too.

Douglas Self

London, September 2017

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