Aural Harmonic Envelopes and Distortion Harmonics on the Audio Amplifiers

产品评测Product Reviews

发布日期:2013-12-04浏览次数: 1847

Introduction

Is there a correlation between subjective judgment of sound quality and THD measurement on an audio amplifier? The answer probably is no. Otherwise, audiophiles and audio enthusiasts will buy the cheap amps at consumer electronics department stores such as Best Buy, Circuit City, Sears, etc those amps usually can have relatively low THD (<< 0.1%) and retailed under $200. It seems most audiophiles has been rejecting bench specifications as an indicator of sound quality of an amplifier. How can one claim an expensive tube amp with THD above 1% has superior sound reproduction? If so, is he enhancing a subjective experience over the objective criteria for justifying a revival of the old approaches to amplification? This subject had been well studied by Cheever on his thesis work in 2001 [Ref 1]. In his paper, he reviewed the history of audio testing methodology that applied to audio amplifiers and pointed out that a universal concept emerged, one that calls for stronger weight of the higher order, more aurally discordant harmonic distortion products, over the low order, more benign harmonics. On other hand, as shown in his paper, separately a study of the psychoacoustics of the ear resulted in a mathematical derivation of the ears intrinsic aural distortion. He proposed that the two are combined and offer a methodology for weighing the harmonics based on a dimensionless figure of merit that quantifies the amplifier’s harmonic distortion envelopes departure from the ears aural masking, named Total Aural Disconsonance or T.A.D. Based on his work, we reviewed the Harmonics distortion spectrums published in the past years by Stereophile Magazine on the highly regard audio amplifiers (both integrated and power amplifiers) they had studied. We compared the results of measurements with the aural harmonic envelopes at different sound pressure level. From 130 amplifiers being studied, we found few of them has harmonic distortion pattern that follows the aural harmonic envelope. Because harmonics conformed to aural harmonic envelope are transparent to the ears (one cannot hear those harmonics), output sound from these amps is thought to have a superior neutrality and dynamics to the ear.

The Conscious of Ear’s phenomenon of masking and Aural Harmonic Envelope

The Total Harmonic Distortion (THD) is defined by the following formula:

where terms 2…N are the aptitudes of the harmonics and term 1 is the aptitude of the fundamental mode (the pure tone). Given a pure sine wave input signal (fundamental frequency), if the THD is zero for an amplifier, the amplifier then shall output a pure tone (sine wave), no harmonics. Two common ways to measure the THD are to use a Spectrum analyzer or a Fast Fourier Transform (FFT). With a Spectrum Analyzer, one can scan the output signal to detect the aptitudes of harmonics: f2 …fn…, where fn = nF, and n is harmonics order and F is fundamental frequency (pure input tone). By using FTT to analysis a signal, one also can calculate the aptitudes of Fourier components that are the aptitudes of harmonics.

It has been known that the cochlea that is the potion of the inner ear devoted to hearing creates harmonics by itself. The detailed results of studies on ear self harmonics from a single tone has been well documented in the References 2-5. The Table 1 below shows the harmonics levels down from that of fundamental tone at different Sound Pressure Levels (SPL). The data were extracted from the Figure 2-3 and 2-4 in the Ref 1, which were originally published in 1967 by Olson’s work [Ref 2 and 5].

SPL to ear	100 (dB)	90 (dB)	80 (dB)	70 (dB)	60 (dB)
(Fundamental)	0	0	0	0	0
2	-10	-12	-15	-20	-28
3	-27	-30	-35	-40	-45
4	-40	-43	-50	-53	-59
5	-50	-56	-60	-60	-65
6	-60	-66	-68	-75	-79
7	-70	-73	-85	-93	-102
8	-79	-90	-98	-108
9	-85	-95	-105

Table 1: Ear self-generated harmonics (dB down from fundamental frequency) at different sound pressure levels

We plot those data as shown in the figure 1 below. The curves from top to bottom are for SPL 100, 90, 80, 70, and 60 dB, respectively, where the SPLs are the absolute Sound Pressure Levels (A-weight) measured by ear.

Fig 1: Harmonics levels generated by ear self versus harmonics number at different SPLs (100, 90, 80, 70, and 60 dB from top to bottom, respectively).

The studies of aural harmonics shows that there was no correlation between age and sex in terms of aural harmonic envelope shown in the Fig 1 although there are significant sex and age differences on other aspects of hearing, such as frequency extension [Ref 2-5]. Table below shows harmonics levels generated by ear self in terms % of fundamental tone (converted from Table 1). Note the dominated 2n and 3rd of harmonic distortion from ear self.

SPL	100 (dB)	90 (dB)	80 (dB)	70 (dB)	60 (dB)
Harmonics in % of fundamental
2	10	6.3	3.2	1	0.16
3	0.2	0.1	0.032	0.01	0.003
4	0.01	0.005	0.001	0.0005	0.0001
5	0.001	0.00025	0.0001	0.0001	3.2E-05
6	0.0001	2.5E-05	1.6E-05	3.2E-06	1.3E-06
7	0.00001	5.0E-06	3.2E-07	5.0E-08	6.3E-09
8	1.3E-06	0.0000001	1.6E-08	1.6E-09
9	3.2E-07	3.2E-08	3.2E-09

Table 2: the harmonics levels generated by ear self in terms % of fundamental tone at different SPLs.

Most striking phenomenon from aural harmonics studies is that the ear/brain completely suppress the sound of a range of harmonics if they conform to follow the aural harmonic envelops as shown in the Fig1. Therefore, if an amplifier generates harmonics distortion transforms to a SLP from a speaker to the ear that conform as harmonically consonant envelope as shown in the Fig 1 or Table 2, these harmonics will be transparent to the ears (one cannot hear those harmonics). Output sound of such amplifier shall have a superior neutrality and dynamics to the ear.

Cheever proposed an empirical formula to fit the aural harmonic envelope data. He suggested that the aural harmonic amplitude in % of fundamental is proportional to the harmonic number in –11 power, equation 2-1 in the Ref 1. But this formula seems to fit data only from n=3 – 7 well. It dose not fit to 2nd and beyond 7th order data. He suggested that each harmonics deviation be on a relative basis (% of reading, referenced to the level of the nth aural harmonic derived from Eq 2-1 in Ref 1), rather than on the absolute percentage referenced to the fundamentals level (THD). The Eq. 2-2 in his paper so-called “Total Aural Disconsonance”, or TAD, a dimensionless figure of merit measures mean-square-root of harmonics deviated from aural harmonics. It is first method to use psycho-acoustic based data to weight the individual harmonics. However, the formula may not be practical since it contains absolute SPL to the ear, which depends on the speakers, listener’s position related to the speakers and the output power of the amp.

Initial Studies on the Spectrum Analyses of Harmonic distortion on the high-end Amplifiers by Stereophile magazine

It has been no success in the attempt to characterize sound quality of an amplifier by using specification. The amplifiers, in the past, with the most power, or the lowest IM distortion or the lowest THD, or the lowest noise have not been given as a classic status. Most of them have not been even more than a modest success in the market. Today, pricing of high-end audio components is totally de-correlated with the specification. Without an ability to completely measure the performance in an objective manner and lacking experience correlating what sounds good to knowledge of component design, one just cannot price the audio amplifier truly right. Those high priced amplifies usually are the results of individual efforts and reflect a coherent underlying some ones’ philosophy which often is in fully subjective nature on sound quality and performance. If such subjectivity is really matter, one shall take first step, apart from the intrinsic of audio components, to treat them as black boxes for audition.

We recently auditioned several Chinese-made tube (single-ended) amplifiers which are relatively inexpensive made by a company called Dared. The models we have been investigating Dared single-ended VP-300B, VP-845, MP-7 and the push-pull VP-20 integrated amplifiers. The performance of these relatively inexpensive single-ended amplifiers is surprising. The sound seems extremely clear, and much less grain than what we thought on other tube amplifiers. The resolution and imaging are excellent. We had measured THD on these amps up 15th order of harmonics at 50 Hz and 1kHz with low power. As expected, the THD is around 1%. The spectrum analyses were performed at 50 Hz and 1kHz, respectively, scanned up to 15th order of harmonics. The detail of measurements on those Dared amps will be published later. As an interesting result, we found the characteristics of harmonic distortion up to 10th order are pretty close to the aural harmonic envelope, which are thought to be a reason found a superior transparent and neutrality on those Dareds. Can intrinsic linearity and dynamics be reflected by how well the nature of harmonics produced by the amplifier follows the aural harmonic mask? We believe a such linkage. The initial studies on the Dared amplifiers inspire us to look into this further on all the amplifiers studied by Stereophile magazine.

We found a few among the 130 amplifiers under studied by Stereophile [Ref 10] that consist of harmonic distortions measured at 50 Hz or 1000 Hz to seem close to the Aural Harmonic mask. Table below lists these 20 amplifiers that are considered to be “best”. The ranks provided in the table are suggestive since most measurement results were given on either fundamental 50 Hz or 1000 Hz. More measurements are needed in order to consistently rank them. Three ranks, 1 – 3, are used here. Comparing the measurements from Ref 10 to the Fig 1, if the Harmonics profile is close to but under the envelope of 60 dB SPL Aural Harmonics in Fig 1, the amp is ranked as 1 (good). If the Harmonics profile found close to or above the envelope of 80 dB SPL Aural Harmonics in Fig 1, the amp is ranked as 3 (best). Otherwise we rank it as 2 (very good).

rand/model of amps (links to measurement results)

ink to review

Rank by how close of the harmonic distortion to follow Aural Harmonic Envelope (1 – 3, where 3 is best, 2 is very good and 1 is good)

MB 175 Signature monoblock power amplifier

http://www.stereophile.com/amplificationreviews/160/index.html

Sapphire power amplifier

http://www.stereophile.com/amplificationreviews/535/index.html

MB750 monoblock power amplifier

http://www.stereophile.com/amplificationreviews/152/index.html

ST-85 power amplifier

http://www.stereophile.com/amplificationreviews/149/index.html

CAD-300SEI integrated amplifier

http://www.stereophile.com/amplificationreviews/398/index.html

EA-2101 power amplifier

http://www.stereophile.com/amplificationreviews/875/index.html

Model Eighty Eight monoblock power amplifier

http://www.stereophile.com/amplificationreviews/843/index.html

MC2000 power amplifier

http://www.stereophile.com/amplificationreviews/283/index.html

Kora Electronic Concept Cosmos monoblock power amplifier

http://www.stereophile.com/amplificationreviews/1201kora/index.html

Aleph 3 power amplifier

http://www.stereophile.com/amplificationreviews/674/index.html

Cardinal XS monoblock amplifier

http://www.stereophile.com/amplificationreviews/196wavelength/index.html

Starlet integrated amplifier

http://www.stereophile.com/amplificationreviews/310/index.html

Stingray integrated amplifier

http://www.stereophile.com/amplificationreviews/1299manley/index.html

Avatar integrated amplifier

http://www.stereophile.com/amplificationreviews/400vac/index.html

Premier Eleven power amplifier

http://www.stereophile.com/amplificationreviews/403/index.html

ATM-211 tube monoblock power amplifier

http://www.stereophile.com/amplificationreviews/687/index.html

CAD-280SA V12 power amplifier

http://www.stereophile.com/amplificationreviews/601cary/index.html

CAD-805 monoblock power amplifier

http://www.stereophile.com/amplificationreviews/740/index.html

SH-833 monoblock power amplifier

http://www.stereophile.com/amplificationreviews/704wavac/index.html

Prima Luna Prologue One integrated amplifier

http://www.stereophile.com/amplificationreviews/205prima/index.html

References

“A New Methodology for Audio Frequency Power Amplifier testing based psychoacoustic Data that better correlates with sound quality” by Daniel H. Cheever, MS Thesis In Electrical and Computer Engineering, University of New Hampshire, December 2001.

Olsen, Harry F. “Music, Physics and Engineering” Dover Publications, Inc. N.Y., 2nd ed., 1967

Newman, Edwin Broomell. “Factors in the Production of Aural Harmonics and combination tones” Lancaster, PA, Lancaster Press, 1937 (Reprinted from The Journal of the Acoustical Society of America, Vol. 9, No. 2, October, 1937.

Fletcher “Speech and Hearing”, 1924, D.Van Nostrand Company, Inc., and Bell Telephone Laboratories.

Olson, Harry F., Massa, Frank. F. “Applied Acoustics”, 1934 Van Nostrand Co.

W. Marshall Leach, Jr. “SPICE Models for Vacuum-Tube Amplifiers” J. Audio Eng. Soc., Vol. 43, No. 3, 1995 March.

MITHAT F. KONAR “Vacuum Tube Parameter Identification Using Computer Methods”, 1996 Biro Technology.

James Boyk and Gerald Jay Sussman. “Small-Signal Distortion in Feedback Amplifiers for Audio” April, 2003, Dept. of EE and CS at California Institute of Technology, and Dept of Music in EE and Music Lab at Massachusetts Institute of Technology.

James Boyk. “There’s Life Above 20 Kilohertz! A Survey of Musical Instrument Spectra to 102.4 kHz” Pianist in Residence, Lecturer in Music in Electrical Engineering, and Director of the Music Lab, California Institute of Technology, 1997.

Spectrum analyses of Harmonic distortions on the high-end amplifiers by Stereophile Magazine (click following links to see the details):

V-3 power amplifier by Wes Phillips Vol.19 No.8 August, 1996

ML1 monoblock power amplifier by Jonathan Scull Vol.23 No.5 May, 2000

MB 175 Signature monoblock power amplifier by Michael Fremer Vol.20 No.6 October, 1997

Sapphire power amplifier by Michael Fremer Vol.25 No.3 March, 2002

2 HC power amplifier by John Atkinson Vol.17 No.1 January, 1994

MB750 monoblock power amplifier by Brian Damkroger Vol.20 No.12 December, 1997

250 Neo-Classic monoblock power amplifier by Paul Bolin Vol.25 No.9 September, 2002

VK-150SE monoblock power amplifier by Jonathan Scull Vol.25 No.3 March, 2002

C370 integrated amplifier by Chip Stern Vol.25 No.1 January, 2002

Horn Mono monoblock power amplifier by Robert Deutsch Vol.25 No.5 May, 2002

ST-85 power amplifier by Lonnie Brownell Vol.22 No.2 February, 1999

C370 integrated amplifier by Chip Stern Vol.25 No.1 January, 2002

VS110 power amplifier & SP16L line preamplifier by Robert Deutsch Vol.26 No.8 August, 2003

KBA-280 power amplifier by Thomas J. Norton Vol.21 No.3 March, 1998

2X150VT power amplifier by Michael Fremer Vol.25 No.1 January, 2002

HCA-2 power amplifier : Page 10 of 11 by Sam Tellig & Kalman Rubinson Vol.25 No.10 October, 2002

Premier Eleven power amplifier by Wes Phillips Vol.17 No.10 October, 1994

Cary Audio Design CAD-300SE LX20 monoblock power amplifier by Martin Colloms Vol.22 No.8 August, 1999

5350SE integrated amplifier by Robert J. Reina Vol.24 No.3 March, 2001

Starlet integrated amplifier by Chip Stern Vol.23 No.12 December, 2000

Full Power Balanced 350mc monoblock amplifier by Jonathan Scull Vol.23 No.8 August, 2000

Model Eighty Eight monoblock power amplifier by Robert Deutsch Vol.26 No.5 May, 2003

BC21 preamplifier & BC22 power amplifier by Kalman Rubinson Vol.24 No.2 February, 2001

dm58 monoblock power amplifier by Paul Bolin Vol.25 No.10 October, 2002

DiVA A85 integrated amplifier by Chip Stern Vol.25 No.2 February, 2002

Nu-Vista 300 power amplifier by Michael Fremer Vol.22 No.12 December, 1999

CAD-572SE monoblock power amplifier by Martin Colloms Vol.21 No.10 October, 1998

Lamm Industries M1.2 Reference monoblock amplifier by Paul Bolin Vol.28 No.2 February, 2005

CAD-805 monoblock power amplifier by Dick Olsher & Various Vol.17 No.1 January, 1994

CAD-300SEI integrated amplifier by Robert Harley Vol.18 No.9 September, 1995

Klimax 500 Solo monoblock power amplifier by Jonathan Scull Vol.22 No.10 October, 1999

No.334 power amplifier by Larry Greenhill Vol.22 No.9 September, 1999

EA-2101 power amplifier by Dick Olsher Vol.15 No.9 September, 1992

8008 power amplifier by Thomas J. Norton Vol.19 No.6 June, 1996

CAD-300SEI integrated amplifier by Robert Harley Vol.18 No.9 September, 1995

V10 integrated amplifier by Michael Fremer Vol.27 No.5 May, 2004

Passion 1000 monoblock power amplifier : Page 6 of 6 by Jonathan Scull Vol.22 No.1 January, 1998

Model Eighty Eight monoblock power amplifier : Page 7 of 8 by Robert Deutsch Vol.26 No.5 May, 2003

1 Alpha HC power amplifier : Page 6 of 6 by Robert Deutsch Vol.19 No.6 June, 1996

Premier Twelve monoblock amplifier : Page 6 of 6 by Michael Fremer Vol.22 No.2 February, 1999

RM-200 power amplifier : Page 8 of 9 by Michael Fremer Vol.25 No.4 April, 2002

Power Drive DNA-1 power amplifier : Page 10 of 11 by Robert Harley Vol.15 No.4 April, 1992

Power Drive DNA-1 power amplifier : Page 7 of 11 by Robert Harley Vol.15 No.4 April, 1992

CAM 350 monoblock power amplifier : Page 8 of 8 by Brian Damkroger Vol.24 No.1 January, 2001

MC2000 power amplifier : Page 7 of 8 by Jonathan Scull Vol.23 No.3 March, 2000

Omega power amplifier : Page 6 of 7 by Jonathan Scull Vol.22 No.3 March, 1999

Kora Electronic Concept Cosmos monoblock power amplifier : Page 5 of 5 by Michael Fremer Vol.24 No.12 December, 2001

Cosmos monoblock power amplifier : Page 5 of 5 by Michael Fremer Vol.24 No.12 December, 2001

Aleph 3 power amplifier : Page 10 of 10 by Muse Kastanovich Vol.20 No.4 April, 1997

V-1 power amplifier : Page 6 of 6 by Michael Fremer Vol.22 No.9 September, 1999

Citadel monoblock amplifier : Page 6 of 6 by Jonathan Scull Vol.25 No.5 May, 2002

M150 monoblock power amplifier : Page 7 of 9 by Michael Fremer Vol.24 No.3 March, 2001

MC1201 monoblock power amplifier : Page 9 of 11 by Jonathan Scull Vol.24 No.3 March, 2001

IT-85 integrated amplifier : Page 7 of 7 by Chip Stern Vol.24 No.2 February, 2001

5350SE integrated amplifier : Page 8 of 9 by Robert J. Reina Vol.24 No.3 March, 2001

No.383 integrated amplifier : Page 8 of 9 by Larry Greenhill Vol.23 No.7 July, 2000

Cardinal XS monoblock amplifier : Page 5 of 6 by Jonathan Scull Vol.19 No.1 January, 1996

Starlet integrated amplifier : Page 7 of 9 by Chip Stern Vol.23 No.12 December, 2000

CAM 350 monoblock power amplifier : Page 4 of 8 by Brian Damkroger Vol.24 No.1 January, 2001

No.33H monoblock power amplifier : Page 6 of 6 by Wes Phillips Vol.21 No.1 January, 1998

Stingray integrated amplifier : Page 5 of 5 by Chip Stern Vol.22 No.12 December, 1999

CAV50 integrated amplifier : Page 3 of 5 by Martin Colloms Vol.21 No.8 August, 1998

Enterprise monoblock power amplifier : Page 5 of 6 by Michael Fremer Vol.27 No.3 March, 2004

Radia power amplifier : Page 5 of 6 by Paul Bolin Vol.27 No.3 March, 2004

Avatar integrated amplifier : Page 5 of 6 by Chip Stern Vol.23 No.4 April, 2000

Power 3 monoblock power amplifier : Page 5 of 6 by Brian Damkroger Vol.23 No.4 April, 2000

KAV-300i integrated amplifier : Page 6 of 6 by Martin Colloms Vol.19 No.7 July, 1996

2050 monoblock amplifier : Page 6 of 6 by Jonathan Scull Vol.21 No.9 September, 1998

PA80/80 power amplifier : Page 6 of 6 by Wes Phillips Vol.19 No.3 March, 1996

VPA monoblock power amplifier : Page 7 of 7 by Jonathan Scull Vol.22 No.4 April, 1999

M300 monoblock power amplifier : Page 9 of 11 by J. Gordon Holt & Martin Colloms Vol.10 No.9 December, 1987

DNA-225 power amplifier : Page 2 of 6 by Kalman Rubinson Vol.23 No.11 November, 2000

DNA-225 power amplifier : Page 5 of 6 by Kalman Rubinson Vol.23 No.11 November, 2000

Power Drive DNA-1 power amplifier : Page 2 of 11 by Robert Harley Vol.15 No.4 April, 1992

2 HC power amplifier : Page 6 of 8 by John Atkinson Vol.17 No.1 January, 1994

Premier Eleven power amplifier : Page 6 of 11 by Wes Phillips Vol.17 No.10 October, 1994

Gemini monoblock power amplifier : Page 8 of 11 by Robert Deutsch Vol.24 No.5 May, 2001

M3 Nu-Vista integrated amplifier : Page 5 of 5 by Michael Fremer Vol.24 No.2 February, 2001