Years ago someone said that perception is more important than reality.  This applies equally to the audio industry, so much of the equipment designed for domestic audio reproduction focusses on the music source, the amplifier and the speakers.  Speakers have electro-mechanical issues of course, but they are not so objectionable as the electronic sins of sources and amplifiers.

The human ear seeks ‘natural’ sound in everything it hears.  This is simply primordial, our evolution;  arising from the need to avoid danger and to communicate with others.  With good hearing we can avoid most of the many dangers of modern life.  As we walk around our cities, our hearing tells us the approach and direction of fast moving vehicles and people.  While most sounds in the natural world are created by wind, people, animals, moving objects and rain, there are sounds created by chemical and electrical processes, such as controlled explosions, lightning, firearms, electrical hum and other man-made machines.  Most humans can identify many sources from the sound, just as most can perceive the sound differences between a gasoline and a diesel reciprocating engine.  When we perceive sound which is man-made, we generally recognise its source from our experience.  We easily differentiate the sounds of aeroplanes, trains and cars.  We recognise the ‘machine’ sounds immediately, even an even, slow mechanical sounds like a steam engine.  But this skill to differentiate natural from man-made noises is pivotal, and it is very much the domain of the serious audiophile who strains to hear ‘unnatural’ sounds from his system from his wide experience of music and instrument sounds.  This focusses us on the subjective;  perhaps a preferred sound system could simply be choice, the way we select clothing, food, cars, or entertainment?


So how do we make sense of this evident skill our ears deliver?  Are there measureable markers which differentiate natural from ‘non-natural’ sounds?  What is ‘distortion’?  Is low THD essential, or is it not the whole story?

As it happens, there are some markers which most people agree on.  ‘Warm’ is one of them, and people agree that tube amplifiers are warmer than SS amps.  Resolution is another;  most can hear the rain right through The Doors ‘Riders of the Storm’ in a good system, yet we do not hear the level of clarity on an iPod.  Natural sound is more difficult, but most recognise a hard, brittle sound with digital compressed music.  But more subtle aspects, like musical engagement and image depth, are much more subjective and mark the wonderful from the ‘competent’.  So, how does distortion alter the perception of sound?  Can we analyse this, and what are Fourier harmonics, and what is harmonic profiling?  Why does a tube amp with 1% THD sounds very good, yet a SS amp with 0.005% can sound sharp, strident, non-engaging and unmusical?


Amps with very low THD (less than 0.02%) generally apply heavy global negative feedback. GNFB radically alters the harmonic structure of the original signal because the fb corrects not only the output distortions, but corrects corrections as well, leading to a long train of harmonics (a Taylors Series), extending out to the 20th harmonic (H20) or even more.  These harmonics are not found in the natural environment and while they are not directly heard, the ear perceives them as objectionable and they lead to ‘listener fatigue’.  They are described as ‘machine tones’, with all the implications for ‘machine sound’ and listener fatigue.  Whilst reducing measured distortion for low low THD with GNFB changes the natural profile of the harmonics of the fundamental notes passed to the amplifier, creating and extending a train of harmonics, and altering their inter-relationships due to ‘time- smearing’.  This affects our perception of the music in subtly ways and could be described as ‘unmusical’, or ‘strident’.Two common basic topologies, single ended and push pull, have implications for sound quality (SQ). SE amplifiers tend to emphasise even orders, which are generally musical, whilst PP amplifiers, at least at the output stage, tend to cancel the even orders, revealing the odd orders (H3, H5, H7, H9 …), which are not musical.  Since PP amplifier are used commercially and domestically because they are more efficient than SE, and this has serious consequences for sound quantity of PP SS commercial amplifiers.Amps with little or no global feedback tend to have poor damping factor, poor drive (not good for slam and impact, essential for Rock and Orchestral music) but have a short profile of harmonics, often stopping at the fifth harmonic, H5. They sound natural, musical, and ‘alive’, but they are not good on percussion, and seem a little soft in presentation.  Such amps are often tube based, and the best, but smallest, are usually the single ended triodes.  GNFB works well, but with subtle penalties.The best amplifiers create a monotonic decrease of harmonics, shown below. That is, H2 is largest, H3 is 15dB down, H4 is 30dB below H2, and H5 is 45dB below H2.  This is the ideal, starting with H2 at around -85dB, but it is not easy to design for this, particularly across an entire amplifier with four stages.  Here is a single transistor emitter follower  profile at 1KHz in simulation (LTSpice) used as a buffer for a headphone amp:

THD of the buffer is 0.0213%, but more than 99.96% of this THD is attributed to H2, H3 and H4, all of which are found in the natural environment and which are musical.  The second harmonic is at -74dB, and this confers slight ‘warmth’ to the sound, and frequency is extended to 10MHz to indicate that nothing appears above the noise floor over about 5KHz.  This is an excellent profile and very like the profile created by a good single ended triode amplifier.

Next graphs the FFT of a good quality SS Class AB PP amplifier (the AKSA 55 created by Aspen in 2000), at 12.5W (+20dB) into 8R.  The profile is very different to the above single transistor amplifier.  THD 0.028%, H2 -75dB, H3 -111dB, and H4 and H5 -98dB (see over page):

You see the higher orders beyond 10Khz, the train of artefacts created by feedback.  These are below -100dB, but there is some concern about ‘fatigue’.

Finally, here is the harmonic profile of my flagship amplifier, the Maya, which closely demonstrates a monotonic decrease of the harmonics, with H2 at -71dB for 12.5W (+20dB) output into 8R 1KHz.  THD is 0.028%.  Note the high, odd order harmonics are well below their contiguous, even order harmonics:

For best sound, and since we love a ‘sweet, warm sound’, we should design so that we start with highest H2, reducing evenly down to H5 and no higher orders.  This is a ‘natural’ profile which the ear ‘seems’ as ‘real’, originally noted by Jean Hiraga of France in the sixties.  If a higher harmonic is higher than the previous harmonic, it will not sound natural.  The AKSA has H4 and H5 will higher than H3, and while it is an excellent amp, it is not as ‘natural’ as the previous single transistor buffer above.  These are all simulated, but they are recreated on the testbench with fourier analysis.  In subjective terms, humans perceive tone changes, so the harmonic of a profile is profoundly important to subjectivity of music.  Tube amplifiers follow the Hiraga observations, but start at H2 around -42dB below fundamental.  This is very high ‘distortion’, creating very high THD, but many audiophiles prefer the tube sound to SS, and their preference cannot be ignored.

Depth of image is a high end quality and is not the same for different people. I identify it with my eyes closed;  can I hear the size of the orchestra, can I discern the percussion at the rear, the soloist out front, and the backing instruments left and right.  Can I place the different positions of Violin First from Second and even perceive the distances in metres which are consistent with the reality?  Imaging diminishes with higher levels of global feedback.Feedback amplifiers must be compensated, so that no gain is permitted at the frequency where the phase shift is at 180 degrees. At this frequency, the global feedback is transmuted into positive feedback, and a small input is increased quickly to destructive, oscillation which destroys the amplifier.  This is verboten, but what is not understood is that the quality and quantity of this compensation affects the sound quality in the audio spectrum.  Compensation is crucial and must be very carefully applied.Most amplifiers have at least four stages; an input stage, the voltage amplifier, the driver stage, and the output stage.  Global feedback from output stage back to the input stage can be reduced by nesting feedback inside the loop, so from third stage back to first, or even second stage back to first.  By reducing the global feedback – that fb from output stage back to input stage – we can give the image depth that tube amplifiers are well known for.The heart of an amplifier is the voltage amplifier. This is normally the second stage.  The amplifying device must deliver voltage gain AND current gain, and only one configuration – common emitter (or cathode) – can deliver this requirement.  These dual requirements make this stage critical;  the parasitics of the transistor are exacerbated.  Typically the input signal is presented to the base, and taken off at the collector.  This is often the slowest part of the amplifier, since this is normally where the compensation must be applied.  The speed of this stage and its configuration makes choosing the device critical.  With some bad choices it is possible to destroy the musicality of any SS amplifier at this point.  Any good sounding amplifier fails or succeeds on the voltage amplifier stage, the VAS.  Input stages, drivers and output devices are important, but not as significant for good sound.Crossover Distortion. I mention this issue because it is poorly understood.  It is very, very small, but tends to add H5, H7, and H9 harmonics.  It can be dialled out with good bias settings but is hugely overestimated.  Crossover is almost negligible in a well biased output stage.  Here are the currents in the two output devices (blue upper npn and red lower pnp) crossing the zero point, and the green colour is the voltage.  This is blown up, and you can see that there is very little alteration to the input signal, the transfer is very smooth (see overpage):

Here is the 1KHz crossover point at 0V magnified to a tiny range of 1.4V total:

You can see that the voltage applied to the speaker is completely linear and free of crossover glitches;  the transfer of power from the outputs is accurate and free of distortion.  Crossover is not the bogey man it is painted;  PP amplifiers do produce odd order distortion, but it is large signal distortion, not small signal distortion around the 0V crossover point.


Distortion is inevitable in amplifier design and operation.  Whilst it should be minimised, we need to pay attention to the type of distortion, in particular, the harmonic profile.  We need to go more into Fourier analysis, which reveals the type and amplitude of the harmonics.  From our subjective understanding of tube amplifiers, high levels of THD do not relate to poor sound quality, but the corollary that low THD does not ensure high sound quality.  It depends on the harmonic profile, which can only be tailored by careful choice of topology, operating points, feedback regimes and component choice.  Design for very high sound quality remains a black art and explains why people like John Curl, Charles Hansen, Julian Verecker and Nelson Pass are demi-gods in the audio community.  Few can create a killer amp which everyone loves to listen to!