Hephaestus Audio

Total Harmonic Distortion (THD) is the standard measurement for the accuracy of audio equipment, particularly audio amplifiers.  Unfortunately, it is a poor metric for audio amplifiers for one simple reason: they are intended to be listened to.  If the amplifier were intended to drive a precision actuator for an industrial process, for example, then perhaps THD would be a good metric, along with bandwidth, slew rate, settling time, etc.

Lower-order harmonic distortion tends to be perceived much more favorably than higher-order harmonic distortion (the ear naturally generates low-order harmonic distortion).  This leads one immediately to at least consider a harmonically weighted distortion metric.  In fact, such a metric was proposed as early as 1937 by the Recording Manufacturers’ Association of America, however such metrics have seen little, if any, practical application.  No doubt this is due in part to the many different choices for harmonic weighting functions, frequency dependent factors, etc. – there are no such choices with THD.

Fairly recently a metric has been proposed that seems to have very good correlation with subjective impression.  This is the “GedLee Metric” by Earl Geddes and Lidia Lee of GedLee LLC.  Here are the first and second parts of the relevant AES papers.  There is a tremendous amount of momentum to overcome for a metric such as this to ever gain traction in the audio industry.  Especially resistant will be any manufacturers that stand to have their specifications suffer by it.  For example, low THD linear amplifiers that have made use of large amounts of global feedback, with little attention given to the linearity of the open-loop transfer function, may look poor in the light of this new metric.

An amplifier’s damping factor is a rating that gives a feel for the amplifiers control over a load.  It is essentially a measure of the output impedance of the amplifier – a value that would be zero for an ideal amplifier (i.e. the ideal amplifier would be load-independent).

Like many measurements of an amplifier’s performance, this one is the victim of misinterpretation and measurement trickery:

First, the exact measurement point has a huge impact on the resulting value.  For example, taking a measurement right at the feedback points of the amplifier tends to give a high damping factor, as this is the actual point the amplifier is attempting to regulate.  Unfortunately, this is rarely where the user connects the load!  The user generally uses the externally accessible speaker connector, so this is the chain that results: the wires/traces from feedback nodes, the contact resistance of the speaker connector, and the external cables that connect to the load.  When this more realistic chain is considered, much more modest damping factors result, however they are much more representative and useful for the user.

Second, the bottom line is that if the amplifier’s effective output impedance is much lower than the minimum impedance of the loudspeaker being driven, there is little to be gained from further increasing the damping factor.  In fact, it may very well be detrimental, given that the typical means of increasing the damping factor is by increasing feedback.  If the feedback is increased excessively it may impact stability and result in lower-amplitude, but more objectionable, harmonics – this will be the topic of a future entry.

Every once in a while it is important to take those dusty tomes down off the top shelf, or out of those boxes behind the furnace in the basement, and remind ourselves exactly what makes all this stuff tick.  Periodically I plan to post a little something about these fundamentals – “Physics Friday”.

This Friday the topic is one that is crucial for electronics: Maxwell’s equations.  There are a few different ways of presenting these equations, the most common one is in integral form.  This is a great form for introducing the topic, but there are only a handful of highly symmetric problems that you can attack with this.  The next most common is in differential form using the del operator with either the dot product or cross product.  This is a very useful form, although it only holds for Cartesian coordinates, which is rarely the coordinate system of choice for E&M problems.  Another differential form uses the “div” and “curl” operators, which are not only coordinate system independent, they are also very intuitive.  The “div” operator is just that – a diverging field (one that tends to move outward to infinity) and the “curl” operator is a curling field (think of the “right hand rule“).

$$div\mathbf{E}=\frac{\rho }{\varepsilon_{0}}$$

A charge density produces a diverging electric field (Gauss’s Law).

$$div\mathbf{B}=0$$

No magnetic monopoles means there is no diverging magnetic field (Gauss’s law for magnetism).

$$curl\mathbf{E}=-\frac{\partial }{\partial t}\mathbf{B}$$

A time-varying magnetic field generates a curling electric field that tends to oppose it (Faraday’s Law).

$$curl\mathbf{B}=\mu _{0}\mathbf{J}+\mu _{0}\varepsilon _{0}\frac{\partial }{\partial t}\mathbf{E}$$

A curling magnetic field is generated by either a current density or a time-varying electric field (Ampere’s Law).

By the nature of its construction, a MOSFET has a built-in anti-parallel diode – this is refered to as the intrinsic “body diode”.  It is generally very slow, unless the MOSFET is optimized to have a fast body diode, which unfortunately often has the side effect of increasing the Rds(on) of the MOSFET.

It is usually easier to find fast body diodes in lower voltage MOSFETs than in higher voltage ones, so the body diode tends to be less of an issue with lower power amplifiers (i.e. lower voltage) than with higher power amplifiers (i.e. higher voltage).  IXYS has a notable exception with their “PolarHV™ HiPerFETs” – a series of high voltage MOSFETs with fast intrinsic body diodes.

This article explores the issue of the slow body diode in greater detail and also gives some example means for dealing with it.

MOSFETs and IGBTs each have their own set of strengths and weaknesses when used in switching audio amplifiers.

MOSFETs only employ “majority carriers“.  For an N-channel MOSFET (the most commonly used due to the much higher mobility of electrons versus holes) the carriers are electrons.  This is a great advantage from a switching speed point of view, as the MOSFET may be turned off very quickly since there are no “minority carriers” to remove from the conducting channel, in order to return it to a non-conducting state.  However, the downside is that no “conductivity modulation” takes place – i.e. the presence of increasing numbers of minority carriers tends to decrease the effective resistance of the conducting channel, much as happens with diodes, or BJTs, or…

IGBTs utilize both majority and minority carriers.  From a switching speed point of view this is a disadvantage because the minority carriers must now be swept from the conducting channel before the IGBT can return to a non-conducting state.  The is the often referred to “current tail” of IGBTs.  Conversely, IGBTs do enjoy the benefits of conductivity modulation, so while MOSFETs are suffering Rds(on)·I² losses, the IGBT suffers only Vce(sat)·I losses.  Even better, the Vce(sat) of the IGBT tends to be roughly constant with temperature (sometimes even decreasing a bit), while the Rds(on) of a MOSFET can increase by up to 2.5 times with increasing temperature.

What does this mean for audio?  Given the high peak-to-average ratio of audio program material, the IGBT is a natural choice, since the losses are roughly proportional to current, instead of proportional to the square of current, as with a MOSFET.  The only problem is the higher switching frequency of switching amplifiers results in extra dissipation due to the minority charge of the IGBT.  This may not be an issue at all in the power supply portion of the switching amplifier, but in the amplifier section it is a little more tricky.  However, with a little ingenuity it is possible to combine the strengths of both devices in the amplifier section as well.  This promises to provide amazingly high efficiency in higher power switching amplifiers.

The audio industry is a small one, but luckily there are much larger industries that can be drawn upon both for inspiration and for the components particular to that industry.  For example, many of the MOSFETs and IGBTs available have been driven by the automotive and telecom industries, but they are also well-suited to audio.

Robotics is a good example of a field that can be used for inspiration.  For example, one particularly useful and powerful conecpt is that of “subsumption architecture” developed by Rodney Brooks.  This approach builds a robot up in functional layers: the innermost dealing primarily with functions such as movement and safety, and the outermost dealing primarily with high-level functions, such as path-planning or communication, that are sometimes able to override the lower-level functions.  As applied to audio amplifiers, this concept leads one to build a robust amplifier core that can drive the required load, protect against a short, etc. and then to augment it with layers of higher-level functionality and protection.

One of the earliest lessons I learned in amplifier design was the very fine line between reliability and usability.  If an amplifier is designed to protect aggressively against any possible deviation from the norm, then it is likely a user will trigger a protective measure during legitimate use.  Conversely, if the amplifier is designed solely with the idea that “the show must go on”, then it is likely the user will at some point do something the amplifier really should protect against.  If subsumption architecture is applied, then it allows for the best of both worlds: an amplifier that can protect itself from legitimate abuse via the inner layers, and an amplifier that allows the show to go on via the intelligence located in the outer layers.

Analog class-D amplifiers at some point convert a small analog signal to a large one.  There may be a DAC up front to allow for digital input, but the bottom line is that the gain is performed in the analog realm.  Digital class-D amplifiers never convert the signal to a small analog signal: the signal remains in the digital realm until the output stage, at which time it becomes a large analog signal.  Also, It is important not to confuse “digital” and “PWM”.  The amplitude of a digital signal is not important as long as it is sufficient to meet the noise margin requirements of the system interpreting it.  The amplitude of a PWM signal is important, because at some point something is going to integrate it – whether the feedback network of the amplifier or the output filter/loudspeaker combination.

One downside to digital class-D amplifiers is that they have no analog feedback.  This means that unless alternate means are used, the amplifier exhibits 0dB PSRR (i.e. any noise in the power supply will find its way to the output).  Some solutions have made use of a well-regulated power supply to reduce this effect, however this is simply “sweeping the dirt under the rug”, by offloading the analog feedback to another part of the circuit.  Other designs use a 1-bit ADC to measure the output signal and provide some means of feedback.  A more elegant solution is to use the DSP that is invariably present to provide feed-forward error correction of the digital signal, based on measured parameters.

Overall, despite the downsides, digital class-D amplifiers are the way the industry is heading, if for no other reason that this one: manufacturability.  Corrections to analog circuitry are difficult during the development process and may be next to impossible once production starts, especially for larger volume products.  However, firmware changes are much easier by comparison and this may be all that is needed to fix problems in a digital amplifier.  When time-to-market is critical, the faster, more efficient solution often wins out.

The maximum theoretical efficiency for a linear amplifier is about 78.5%.  This assumes zero idle losses and static supply rails (i.e. not a class-G or class-H amplifier).  The maximum theoretical efficiency of a switching amplifier is 100%.  This assumes zero idle losses and “perfect” switching devices.  Of course you can never really achieve 100% efficiency – the second law of thermodynamics forbids this – but you can achieve 90%, 99%, 99.9% and 99.99% as the technology improves to allow for it.

The determination of efficiency is a fairly straightforward measurement for a given product.  Unfortunately, marketing sometimes gets a hold of it and the following scenario occurs:

Worldly marketing type:  “Hey Bob, sweet amp.”

Innocent engineering type:  “Gee Fred, ya think so?  Thanks!”

Worldly marketing type:  “Yah, but we could really improve our position against XYZ if the efficiency were higher than 75%…”

Innocent engineering type:  “But I’m giving the end-to-end efficiency and XYZ is claiming an efficiency of 99.5% by only including the losses in the power cord!”

Worldly marketing type:  “Uh-huh.”

Innocent engineering type:  [Exasperated] “Okay, fine.  I’ll work on it after I take my Honda in for an oil change at lunch.  How’s the Bimmer working out for ya?”

Worldly marketing type:  “Fine, just fine.”

The bit about the car types was inspired by Guy Kawasaki.

The following are wonderful examples of audio companies using their websites both for commercial and for educational purposes.  My hope is to live up to the standard they set by helping to expand the body of knowledge in audio and by providing the sort of products my customers love.

Elliott Sound Products

Linkwitz Lab

Pass Labs

Rane

The following websites do not have a commercial angle to them, but they are indispensable resources.  They have been tremendously helpful to me in my products, projects, and overall audio knowledge.

Nutshell High Fidelity

Art Ludwig’s Sound Page

It is difficult to relate the intricacies of one’s approach to audio design, but these three articles do a reasonable job of summing up my design philosophy:

One of the most important requirements for designing a really good switching amplifier is Solid Execution.

A general critieria for designing good sounding audio equipment is given by the concept of Disappearing Derivatives.

Objectivists versus Subjectivists and the Engineering Perspective.