Book Review: Introduction to Electroacoustics & Audio Amplifier Design, by Prof Marshall Leach (with notes on gyrators)

Book Review: Introduction to Electroacoustics & Audio Amplifier Design, by Prof Marshall Leach (with notes on gyrators)



Writing this book review for Introduction to Electroacoustics & Audio Amplifier Design [ISBN 978-0-7575-7286-9] is a bittersweet task, as the author was the very popular Georgia Tech Electrical Engineering Professor W Marshall Leach Jr, who was taken from us at just 70 in November 2010 (obituary).¹

Electroacoustics is the part of of acoustics that pertains to the conversion of sound waves into  electrical signals, such as with microphones, phono pickup cartridges and vibration sensors; and electric signals into sound waves, such as in loudspeakers and hearing aids. The beauty of electroacoustics is that  the electrical, mechanical and acoustical portions are modeled together using straightforward electrical circuit techniques, very often with just linear “lumped” elements (resistors, inductors, capacitors and transformers), where the entire system behavior can be accurately designed or analyzed.

The Table of Contents shows comprehensive coverage of the material, and when followed in sequence, is quite an impressive audio engineering textbook.

1. Basic Principles of Sound
2. Fundamentals of Acoustics
3. Analogous Circuits of Acoustical Systems
4. Analogous Circuits of Mechanical Systems
5. Microphones
6. Moving-Coil Loudspeakers
7. Closed-Box Loudspeaker Systems
8. Vented-Box Loudspeaker Systems
9. Acoustic Horns
10. Crossover Networks
11. A Loudspeaker Potpourri — This chapter alone is worth the price of the book.
12. Audio Power Amplifiers

The first chapter on Basic Principles of Sound is rather straightforward, covering what sound is, how it’s generated, it’s characteristics; plus it also goes into human hearing, introducing equal loudness contours and a basic loudness compensation volume control using a tapped potentiometer circuit.

The second chapter adequately discusses the fundamentals of acoustics, assuming the reader has knowledge of partial differential equations and surface & volume integrals; while the 3rd & 4th chapters cover analogous acoustical & mechanical systems (i.e. mass, resistance & compliance), tying everything together into relatively simple electrical circuit models that can be easily solved to accurately predict the properties.

Chapter 8 goes into the details of vented box analysis & synthesis; and presents the 4th order Butterworth & Chebyshev and the 3rd order quasi-Butterworth QB3 alignments, basically expanding on Neville Thiele’s 1971 seminal papers on the subject. However, the reader needs to go to section 5.3 of Chapter 11 to find out about the very handy 6th order assisted vented-box alignment, which uses a 2nd order high-pass filter in the amplifier circuit, which is used to lower the cutoff frequency while containing voice coil motion below that point.

One minor disappointment is in chapter 9 and elsewhere: The lack of the use of a gyrator  model for the voice coil, which “eliminates the confusing parallel-element mobility and admittance circuits from the analysis.” Go to figure 2 of Leach’s 1979 seminal paper On the Specification of Moving-Coil Drivers for Low-Frequency Horn-Loaded Loudspeakers and you’ll see the gyrator with a gyration resistance of Bl between the electrical and mechanical network segments.³ Although introduced for horn-loaded loudspeakers, in fact it has broad use across electroacoustics, including for conventional piston loudspeakers of all varieties, and also for hearing aids. In this final edition before his death in November 2010, Dr Leach did not include his groundbreaking use of the gyrator, because parallel reactive network elements are now easily handled in SPICE; however we believe it should have been included, as it makes pencil & paper calculations much easier when SPICE is not available.  Interestingly, in chapter 4’s problem #4 (p.65) the gyrator is introduced; but it’s not even mentioned in the index.

Chapter 11, A Loudspeaker Potpourri, is worth the price of the book alone: Oftentimes in both acoustics and (especially) audio engineering you’ll see all sorts of “cookbook recipes” that have significant errors; but here you’ll find the correct information for your loudspeaker designs, including step-by-step instructions on measuring the Thiele-Small electroacoustic parameters of any moving coil loudspeaker driver in sections 11.7 & 11.8. Section 11.5.3 has the recipe for the valuable 6th-order Butterworth and Chebyshev assisted vented box alignment using a second order active high pass filter in the preamp, the latter being this author’s EE3900 Junior Design Project.²

One annoyance this author and former student of Professor Leach’s has, however, is in section 11.4 on passive radiator (“drone-cone”) systems. Although passive radiators look sexy, in fact they are no more than performance-sapping decorations that compensate for the laziness of the designer. Specifically, the compliance Cap and resistance Rap of the passive radiator are non-zero, and have a negative impact on the performance. Also, although equation 11.60 is correct, the value for ωs derived in equation 11.61 is not, as Mac is not approximately the same as Mas, i.e. the acoustic mass of the diaphragm and its air load is not the same as for an infinite baffle. Although it’s readily apparent from the equations that using a passive radiator would sap performance, this author believes it should be explicitly stated in section 11.4.1.

We were also a bit disappointed that transmission line loudspeakers were not covered, especially since when you go to  Dr Leach’s Amplifier and Speaker Projects page we find the following:

In fact, we cited this very paper in our previous article titled Rarefaction and condensation… or should it be compression?; and also it should be noted that Dr Leach was Robinson’s advisor. The upshot of all this is that if you want to design & build a transmission line loudspeaker — and are willing to wade through 150 pages — then this thesis is for you.


1) Dr Leach was my professor at Georgia Tech for  Audio Engineering (EE4026) in Spring 1981, Low-Noise Amplifiers (EE4084) in Fall 1982, and was my faculty advisor for my Junior Design Project (EE3900) of a subwoofer system. It is in memory of my former Professor and Mentor to whom I dedicate this book review.

2) My EE3900 Junior Design Project subwoofer system consisted of an Electro-Voice EVM-18B 18 inch driver in an 18 ft³ vented cabinet, and  included an active VCVS (non-inverting left channel) and MFB  (inverting right channel) 2nd order  Chebyshev response bandpass crossover network. When I put this all  together, I achieved a 6th order Chebyshev high-pass response with a lower -3dB (cut-off) frequency response of 24.5 Hz with a 36dB/octave rolloff & upper cutoff of 85Hz. If you go to §11.3 (pp 206-211) in the Loudspeaker Potpourri section, you’ll see the entire design rationale for the 2nd order high pass auxiliary filtering. The theory of operation, and  reason for the voltage-controlled voltage source (VCVS) and multiple feedback (MFB) topologies is that (a) the sound in both channels of a stereo recording below ≈100 Hz is the same, and (b) by having non-inverted & inverted signals fed into the two channels of my BGW 750B (class AB1) amplifier, and floating the outputs in a bridged mono configuration, I was able to squeeze 800 watts RMS out of it, which, in the days before class D PWM amplifiers were commonplace, was a lot of power

3)  On the Specification of Moving-Coil Drivers for Low-Frequency Horn-Loaded Loudspeakers (Journal of the Audio Engineering Society, vol. 27, no. 12, pp. 950-959, December 1979); also posted here on the Georgia Tech website. A gyrator is a passive, linear, lossless, two-port electrical network element proposed by by Bernard DH Tellegen in his 1948 paper  The gyrator, a new electric network element  by Bernard DH Tellegen (click for the mirror copy here on The Hearing Blog).  as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer. Unlike the four conventional elements, the gyrator is non-reciprocal.  An important property of a gyrator is that it inverts the current-voltage characteristic of an electrical component or network; and in the case of linear elements, the impedance is also inverted; or in other words, a gyrator can make a capacitive circuit behave inductively, a series LC circuit behave like a parallel LC circuit, and so on…

Annotated Tellegen gyrator schematic

Annotated Tellegen gyrator schematic. The gyration resistance (or equivalently its reciprocal the gyration conductance) has an associated direction indicated by an arrow on the schematic diagram. By convention, the given gyration resistance or conductance relates the voltage on the port at the head of the arrow to the current at its tail. The voltage at the tail of the arrow is related to the current at its head by minus the stated resistance. Reversing the arrow is equivalent to negating the gyration resistance, or to reversing the polarity of either port.

Cascaded gyrator equivalent circuit

An ideal gyrator is similar to an ideal transformer in being a linear, lossless, passive, memoryless two-port device. However, whereas a transformer couples the voltage on port 1 to the voltage on port 2, and the current on port 1 to the current on port 2, the gyrator cross-couples voltage to current and current to voltage. Cascading two gyrators achieves a voltage-to-voltage coupling identical to that of an ideal transformer.


 …And it was this principal Dr Leach cleverly leveraged in 1979:

Figures 1 & 2 on page 952 (page 3 of PDF) of ‘On the Specification of Moving-Coil Drivers for Low-Frequency Horn-Loaded Loudspeakers’ by Dr W Marshall Leach. Note the use of the gyrator between the electrical and mechanical networks with gyration resistance equal to the Bl motor product. (Click to view enlarged image in a new window)

Gyrators permit network realizations of two-(or-more)-port devices which cannot be realized with just the conventional four elements. Unlike Tellegin’s then-hypothetical circuit element, gyrators today make possible network realizations of isolators and circulators; and  is primarily used in active filter design and miniaturization today, including in audio filters such as equalizers and analog hearing aids, replacing bulky inductors with small precision capacitors. Gyrators do not, however, change the range of one-port devices that can be realized: Although Tellegen conceived it as a fifth linear element, its adoption makes both the ideal transformer and either the capacitor or inductor redundant; thus the number of necessary linear elements is in fact reduced to three.

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Typo corrected and subscripts reformatted on 14 August 2013

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About the author

Dan Schwartz

Electrical Engineer, via Georgia Tech


  1. Saugat Roy
    October 18, 2015 at 3:08 am

    @ DS can you please add me up for your blogs. Thanks

    • Dan Schwartz
      October 18, 2015 at 3:14 am

      You just did when you registered and checked the box to receive updates!

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