Tube sound (or valve sound) is the characteristic sound associated with a vacuum tube-based audio amplifier. After introduction of solid state amplifiers, tube sound appeared as the logical complement of transistor sound, which had some negative connotations due to crossover distortion of early transistor amplifiers. Transistor sound has evolved vastly after the early days of transistor amplifiers, and transistor sound has become the norm, while tube sound was left without a clear definition. The audible significance of tube amplification on audio signals is a subject of continuing debate among audio enthusiasts.
- 1 History
- 2 Sound reproduction
- 3 Musical instrument amplification
- 4 Audible differences
- 5 Harmonic content and distortion
- 6 Design comparison
- 7 Intentional distortion
- 8 Tube sound enthusiasts
- 9 See also
- 10 Notes
- 11 References
Before the commercial introduction of transistors in the 1950s, electronic amplifiers used vacuum tubes (known in Great Britain as "valves"). By the 1960s, solid state (transistorized) amplification had become more common because of its smaller size, lighter weight, lower heat production, and improved reliability. Tube amplifiers have retained a loyal following amongst some audiophiles and musicians. Some tube designs command very high prices, and tube amplifiers have been going through a revival since Chinese and Russian markets have opened to global trade—tube production never went out of vogue in these countries.
Audiophiles may agree or disagree on the relative merits of tube vs solid state amplification. Some say they prefer the sound produced from tube amplifiers on the grounds that it is more natural and satisfying than the sound from transistor amplifiers. Otherwise this preference or difference is far too generalised or even vague without taking amplifier designs into consideration, and there are many. Certainly these audible differences are due to distortion types: harmonic, distribution, level and many other factors.
Those who subscribe to measurement and scientifically-based approaches to high fidelity note that in general, solid state designs can be manufactured without output transformers and are therefore immune to speaker-dependent impedance mismatches and other transformer effects which alter the system spectral response. On the other hand, ruler flat frequency response does not necessarily mean a good sounding amplifier. The loudspeaker itself (regardless of price) will likely produce more distortions (non-linearity and uneven frequency response) than any other part of the system. Typically, in sound reproduction systems, accurate reproduction of the sound of the original recording is the goal; distortion and uneven spectral response within the audible frequency band is something designers deliberately seek not to introduce.
Musical instrument amplification
Some musicians also prefer the distortion characteristics of tubes over transistors for electric guitar, bass, and other instrument amplifiers. In this case, generating deliberate (and sometimes considerable, in the case of electric guitars) audible distortion or overdrive is usually the goal. The term can also be used to describe the sound created by specially-designed transistor amplifiers or digital modeling devices that try to closely emulate the characteristics of the tube sound.
The tube sound is often subjectively described as having a "warmth" and "richness", but the source of this is by no means agreed on. It may be due to the non-linear clipping that occurs with tube amps, or due to the higher levels of second-order harmonic distortion, common in single-ended designs resulting from the characteristics of the tube interacting with the inductance of the output transformer.
The sound of a tube amplifier is partly a function of the circuit topologies typically used with tubes versus the topologies typically used with transistors, as much as the gain devices themselves. Beyond circuit design, there are other differences such as the differing electronic characteristics of triode, tetrode, and pentode vacuum tubes, along with their solid-state counterparts such as bipolar transistor, FET, MOSFET, IGBT, etc. These can be further divided into differences among various models of the said device type (e.g. EL34 vs. 6L6 tetrodes). In many cases circuit topologies need to account these differences to either homogenize their widely varying characteristics or to establish a certain operating point required by the device.
The low frequency roll-off can be explained by many tube amplifiers having high output impedance compared to transistor designs, due to the combination of both higher device impedance itself and typically reduced feedback margins (more feedback results in a lower output impedance).
Harmonic content and distortion
Triodes (and MOSFETs) produce a monotonically decaying harmonic distortion spectrum.[clarification needed] Even-order harmonics and odd-order harmonics are both natural number multiples of the input frequency.
Psychoacoustic phenomena include the effect that high-order harmonics are more offensive than low. Thus, in distortion measurements this should be taken into consideration to weight audible high-order harmonics more than low. The importance of high-order harmonics suggests that distortion should be regarded in terms of the complete series or of the composite wave-form that this series represents. It has been shown that weighting the harmonics by the square of the order correlates well with subjective listening tests. Weighting the distortion wave-form proportionally to the square of the frequency gives a measure of the reciprocal of the radius of curvature of the wave-form, and is therefore related to the sharpness of any corners on it. Based on said discovery, highly sophisticated methods of weighting of distortion harmonics have been developed. Since they concentrate in the origins of the distortion, they are mostly useful for the engineers who develop and design audio amplifiers, but on the other hand they may be difficult to use for the reviewers who only measure the output.
A huge issue is that measurements of objective nature (for example, those indicating magnitude of scientifically quantifiable variables such as current, voltage, power, THD, dB, and so on) fail to address subjective preferences. Especially in case of designing or reviewing instrument amplifiers this is a considerable issue because design goals of such differ widely from design goals of likes of HiFi amplifiers. HiFi design largely concentrates on improving performance of objectively measurable variables while instrument amplifier design largely concentrates on subjective issues, such as "pleasantness" of certain type of tone. Fine examples are cases of distortion or frequency response: HiFi design tries to minimize distortion and focuses on eliminating "offensive" harmonics. It also aims for ideally flat response. Musical instrument amplifier design deliberately introduces distortion and great non-linearities in frequency response. Former "offensiveness" of certain types of harmonics becomes a highly subjective topic, along with preferences towards certain types of frequency responses (whether flat or un-flat).
Push-pull amplifiers use two nominally identical gain devices "back to back". One consequence of this is that all even-order harmonic products cancel, leaving odd order products to dominate. A push-pull amplifier is said to have a symmetric (odd symmetry) transfer characteristic, and accordingly produces only odd harmonics.
A single-ended amplifier has an asymmetric transfer characteristic, and produces both even and odd harmonics. As tubes are often run single-ended, and semiconductor amplifiers are often push-pull, the types of distortion are incorrectly attributed to the devices (or even the amplifier class) instead of the topology. Push-pull tube amplifiers can be run in class A, AB, or B. Also, a class B amplifier may have crossover distortion that will be typically high order and thus sonically very undesirable indeed.
Another factor is that the distortion content of class A circuits (SE or PP) typically monotonically reduces as the signal level is reduced, asymptotic to zero during quiet passages of music. For this reason class A amplifiers are especially desired for classical and acoustic music etc. cf. class B and AB amplifiers, for which the amplitude of the crossover distortion is more or less constant, and thus the distortion relative to signal in fact increases as the music gets quieter. Class A amplifiers measure best at low power, class AB and B amplifiers measure best just below max rated power.
Loudspeakers present a reactive load to an amplifier (capacitance, inductance and resistance). This impedance may vary in value with signal frequency and amplitude. This variable loading affects the amplifier's performance both because the amplifier has finite output impedance (it cannot keep its output voltage perfectly constant when the speaker load varies) and because the phase of the speaker load can change the stability margin of the amplifier. The influence of the speaker impedance is different between tube amplifiers and transistor amplifiers, principally because tube amplifiers normally use output transformers, and cannot use as much negative feedback due to phase problems in transformer circuits. Notable exceptions are various "OTL" (output-transformerless) tube amplifiers, pioneered by Julius Futterman in the 1950s, or somewhat rarer tube amplifiers that replace the impedance matching transformer with additional (often transistorized) circuitry (such as Berning's unique tube-transformerless "ZOTL" circuit). In addition to that, many solid-state amplifiers, designed specifically to amplify electric instruments such as guitars or bass guitars, employ current feedback circuitry that increases the amplifier's output impedance, resulting into response similar to that of tube amplifiers.
The design of speaker crossover networks and other electro-mechanical properties may result in a speaker with a very uneven impedance curve, for a nominal 8 Ω speaker, being as low as 6 Ω at some places and as high as 30–50 Ω elsewhere in the curve. An amplifier with little or no negative feedback will always perform poorly when faced with a speaker where little attention was paid to the impedance curve.
There has been considerable debate over the characteristics of tubes versus bipolar junction transistors. Triodes and MOSFETs have certain similarities in their transfer characteristics, whereas later forms of the tube, the tetrode and pentode, have quite different characteristics that are in some ways similar to the bipolar transistor. Despite this, e.g. MOSFET amplifier circuits typically do not reproduce tube sound any more than typical bipolar designs, due to the circuit topology differences between a typical tube design and a typical MOSFET design. But there are exceptions, for example designs such as the Zen series by Nelson Pass.
A characteristic feature of most tube amplifier designs is the high input impedance (typically 100 kΩ or more) in modern designs and as much as 1 MΩ in classic designs. The input impedance of the amplifier is a load for the source device. Even for some modern music reproduction devices the recommended load impedance is over 50 kΩ. This implies that the input of an average tube amplifier is a problem-free load for music signal sources. By contrast, some transistor amplifiers for home use have lower input impedances, as low as 15 kΩ. Since it is possible to use high output impedance devices due to the high input impedance, other factors may need to be accounted for, such as cable capacitance and microphonics in such cases.
Audio amplifiers are usually loaded by loudspeakers and in the history nearly all loudspeakers have been electrodynamic loudspeakers, while there exists also minority of electrostatic loudspeakers and some other even more exotic loudspeakers. Electrodynamic loudspeakers transform electric current to force and force to acceleration of the diagraphm which causes sound pressure. Due to the principle of an electrodynamic speaker, most loudspeaker drivers ought to be driven by an electric current signal. The current signal drives the electrodynamic speaker more accurately, causing less distortion than a voltage signal. In an ideal current or transconductance amplifier the output impedance approaches infinity, while practically all commercial audio amplifiers are voltage amplifiers, and their output impedances have been intentionally developed to approach zero. Due to the nature of vacuum tubes and audio transformers, the output impedance of an average tube amplifier is usually considerably higher than of the modern audio amplifiers produced completely without vacuum tubes or audio transformers. Thus, most tube amplifiers with their higher output impedance are less ideal voltage amplifiers than the solid state voltage amplifiers with their smaller output impedance.
Soft clipping is a very important aspect of tube sound especially for guitar amplifiers, although a Hi-fi amplifier should not normally ever be driven into clipping. The harmonics added to the signal are of lower energy with soft clipping than hard clipping. However, soft clipping is not exclusive to tubes, it can be simulated in transistor circuits (below the point that real hard clipping would occur). (See "Intentional distortion" section).
Large amounts of negative feedback are not available in tube circuits, due to phase shift in the output transformer, and lack of sufficient gain without large numbers of tubes. With lower feedback, distortion is higher and predominantly of low order. The onset of clipping is gradual. Large amounts of feedback, allowed by transformerless circuits with many active devices, leads to numerically lower distortion but with more high harmonics, and harder clipping—as input increases, the feedback uses the extra gain to ensure that the output follows it accurately until the amplifier has no more gain to give and the output saturates.
In the recording industry and especially with microphone amplifiers it has been shown that amplifiers are often overloaded by signal transients. Russell O. Hamm, an engineer working for Walter Sear at Sear Sound Studios, wrote in 1973 that there is a major difference between the harmonic distortion components of a signal with greater than 10% distortion that had been amplified with three methods: tubes, transistors, or operational amplifiers. Mastering engineer R. Steven Mintz wrote a rebuttal to Hamm's paper, saying that the circuit design was of paramount importance, more than tubes vs solid state components. Hamm's paper was also countered by Dwight O. Monteith Jr and Richard R. Flowers in their article "Transistors Sound Better Than Tubes", which presented transistor mic preamplifier design that actually reacted to transient overloading similarly as the limited selection of tube preamplifiers tested by Hamm. Monteith and Flowers said: "In conclusion, the high voltage transistor preamplifier presented here supports the viewpoint of Mintz: 'In the field analysis, the characteristics of a typical system using transistors depends on the design, as is the case in tube circuits. A particular 'sound' may be incurred or avoided at the designer's pleasure no matter what active devices he uses.'"
Early tube amplifiers often had limited response bandwidth, in part due to the characteristics of the inexpensive passive components then available. In power amplifiers most limitations come from the output transformer; low frequencies are limited by primary inductance and high frequencies by leakage inductance and capacitance. Another limitation is in the combination of high output impedance, decoupling capacitor and grid resistor, which acts as a high-pass filter. If interconnections are made from long cables (for example guitar to amp input), a high source impedance with high cable capacitance will act as a low-pass filter.
Modern premium components make it easy to produce amplifiers that are essentially flat over the audio band, with less than 3 dB attenuation at 6 Hz and 70 kHz, well outside the audible range.
Typical (non-OTL) tube power amplifiers amplifiers could not use as much negative feedback (NFB) as transistor amplifiers due to the large phase shifts caused by the output transformers and their lower stage gains. While the absence of NFB greatly increases harmonic distortion, it avoids instability, as well as slew rate and bandwidth limitations imposed by dominant-pole compensation in transistor amplifiers. However, the effects of using low feedback principally apply only to circuits where significant phase shifts are an issue (e.g. power amplifiers). In preamplifier stages high amounts of negative feedback can easily be employed and such designs are commonly found from many tube-based applications aiming to higher fidelity.
Since the alleged phenomenon of transient intermodulation distortion was believed to be mainly caused by negative feedback, tube sound never suffered much of that kind of distortion.
On the other hand, the dominant pole compensation in transistor amplifiers is precisely controlled: exactly as much of it can be applied as needed to strike a good compromise for the given application.
The effect of dominant pole compensation is that gain is reduced at higher frequencies and therefore there is in fact increasingly less NFB at high frequencies due to the reduced loop gain. This is why amplifiers exhibit increased distortion for higher frequency components of a signal. In effect, transistor amplifiers start to become more "tube like" (employ less negative feedback and distort more) at higher frequencies.
In audio amplifiers, the bandwidth limitations introduced by compensation are still far beyond the audio frequency range, and the slew rate limitations can be configured such that full amplitude 20 kHz signal can be reproduced without the signal encountering slew rate distortion, which is not even necessary for reproducing actual audio material.
Early tube amplifiers had power supplies based on rectifier tubes. These supplies were unregulated, which is a practice which continues to this day in transistor amplifier designs. The typical anode supply was a rectifier, perhaps half-wave, a choke (inductor) and a filter capacitor. When the tube amplifier was operated at high volume, due to the high impedance of the rectifier tubes, the power supply voltage would dip as the amplifier drew more current (assuming class AB), reducing power output and causing signal modulation. The dipping effect is known as "sag", which may be desirable effect for some electric guitarists when compared with hard clipping. As the amplifier load or output increases this voltage drop will increase distortion of the output signal. Sometimes this sag effect is desirable for guitar amplification.
Some instrument tube amplifier designs use a vacuum tube rectifier instead of silicon diodes, and some designs offer the choice of both rectifiers via a switch. Such ah amplifier was introdued in 1989 by Mesa/Boogie, called "Dual Rectifier", and the rectifier switching is the subject of a patent.
A solid state rectifier arrangement could introduce audible noise (switching noise) into the amplifier, but only if poorly implemented, this may be audible as a buzzing sound at typically twice mains supply frequency. The voltage sag of a tube rectifier can be emulated with silicon rectifiers, by adding a resistance in series with the high voltage supply. This resistance can be switched in when required.
Electric guitar amplifiers often use a class AB1 amplifier. In a class A stage the average current drawn from the supply is constant with signal level, consequently it does not cause supply line sag until the clipping point is reached. Other audible effects due to using a tube rectifier with this amplifier class are unlikely.
One possible practical advantage of tube rectification is that the rectifier tube takes some time to warm up before it begins to conduct. This will allow a little time for the output tube heaters to warm up somewhat and allow them to start conducting before the high voltage (HT) reaches full potential allowing a soft start, possibly extending their lifespan. Some say[who?] that if the full high voltage supply (HT) is present during the warm up process, on output tubes, cathode damaged may result.
Some high end manufacturers, such as Welborne Labs in their premium kits, use silicon diodes on the basis that the cost and power required to operate a vacuum tube rectifier does not yield any measurable improvement in the sound.
The benefit of all Class A amplifiers is the absence of crossover distortion. This crossover distortion was found especially annoying after the first silicon-transistor Class B and Class AB transistor amplifiers arrived on the consumer market; earlier germanium-based designs with the much lower turn-on voltage of this technology and the non-linear response curves of the devices had not shown large amounts of cross-over distortion. Although crossover distortion is very fatiguing to the ear and perceptible in listening tests, it is also almost invisible (until looked for) in the traditional Total harmonic distortion (THD) measurements of that epoch.
A Class A push-pull amplifier produces low distortion for any given level of applied feedback, and also cancels the flux in the transformer cores, so this topology is often seen by HIFI-audio enthusiasts and do-it-yourself builders as the ultimate engineering approach to the tube Hi-fi amplifier for use with normal speakers. Output power of as high as 15 watts can be achieved even with classic tubes such as the 2A3 or 18 watts from the type 45. Classic pentodes such as the EL34 and KT88 can output as much as 60 and 100 watts respectively. Special types such as the V1505 can be used in designs rated at up to 1100 watts. See "An Approach to Audio Frequency Amplifier Design", a collection of reference designs originally published by G.E.C.
Single-Ended Triode (SET) amplifiers
SET amplifiers typically show poor measurements for distortion with a resistive load, have low output power, are inefficient, have poor damping factors and high measured harmonic distortion. But they perform somewhat better in dynamic and impulse response.
The triode, despite being the oldest signal amplification device, also can (depending on the device in question) have a more linear no-feedback transfer characteristic than more advanced devices such as beam tetrodes and pentodes.
Audiophiles who prefer SET-amplifiers state that measured sound performance is a poor indicator of real world sound performance and distortion level is not the only criterion for good sound reproduction. There are measurements not using resistive load but actual loudspeakers to back this up. In the 1970s, designers started producing transistor amps with higher open loop gain to support a greater value of negative feedback. In the following years, amplifiers were built with modest gain but good open loop linearity, deployed with only minimal levels of NFB.
All amplifiers distort, so do SETs. This for the most part harmonic distortion is a distortion with a unique pattern of simple and monotonically decaying series of harmonics, dominated by modest levels of second harmonic. The result is like adding the same tone one octave higher. The added harmonic tone is lower, at about 1–5% or less in a no feedback amp at full power and rapidly decreasing at lower levels. It has been also claimed that a single-ended power amplifier's second harmonic distortion could reduce similar harmonic distortion in a single driver loudspeaker, if their harmonic distortions were equal and amplifier was connected to the speaker so that the distortions would neutralize each other.
SETs usually only produce about 2 watt (W) for a 2A3 tube amp to 8 W for a 300B up to the practical maximum of 40 W for a 805 tube amp. The resulting sound pressure level depends on the sensitivity of the loudspeaker and the size and acoustics of the room as well as amplifier power output. Their low power also makes them ideal for use as preamps. SET amps have a power consumption of a minimum of 8 times the stated stereo power. For example a 10 W stereo SET uses a minimum of 80 W, and typically 100 W.
Single-ended pentode and tetrode amplifiers
The special feature among tetrodes and pentodes is the possibility to obtain ultra-linear or distributed load operation with an appropriate output transformer. Ultra-linear connection is a negative feedback method, enabling less harmonic distortion.
The majority of modern commercial Hi-fi amplifier designs have until recently used Class AB topology (with more or less pure low-level Class A capability depending on the standing bias current used), in order to deliver greater power and efficiency, typically 12–25 watts and higher. Modern designs normally include at least some negative feedback, although in the old times of High fidelity use of feedback was totally out of question.However, Class D topology (which is vastly more efficient than Class B, and has garnered some respect from audiophiles) is more and more frequently applied where traditional design would use Class AB.
Class AB push-pull topology is nearly universally used in tube amps for electric guitar applications that produce power of more than about 10 watts. Whereas audiophile amps are primarily concerned with avoiding distortion, a guitar amp embraces it. When driven to their respective limits, tubes and transistors distort quite differently. Tubes clip more softly than transistors, allowing higher levels of distortion (which is sometimes desired by the guitarist) whilst still being able to distinguish the harmonies of a chord. This is because the soft profile of the tube amplifier's distortion means that the intermodulation products of the distortion are generally more closely related to the harmonies of the chord. All sides of the question are inclined to agree about valve guitar amplifiers offering a very useful sound, though there are also some well-respected solid-state designs.
Tube sound from transistor amplifiers
Some individual characteristics of the tube sound, such as the waveshaping on overdrive, are straightforward to produce in a transistor circuit or digital filter. For more complete simulations, engineers have been successful in developing transistor amplifiers that produce a sound quality very similar to the tube sound. Usually this involves using a circuit topology similar to that used in tube amplifiers.
In 1982, Tom Scholz, a graduate of MIT and a member of Boston, introduced the Rockman, which used JFET/BJT-based operational amplifiers and diode-based clipping circuits, but achieved a distorted sound adopted by many well known musicians. Advanced digital signal processing offers the possibility to simulate tube sound. Computer algorithms are currently available that transform digital sound from a CD or other digital source into a distorted digital sound signal.
Using modern passive components, and modern sources, whether digital or analogue, and wide band loudspeakers, it is possible to have tube amplifiers with the characteristic wide bandwidth and "fast" sound of modern transistor amplifiers, including using push-pull circuits, class AB, and feedback. Some enthusiasts, such as Nelson Pass, have built amplifiers using transistors and MOSFETs that operate in class A, including single ended, and these often have the "tube sound".
Tubes are often used to impart characteristics that many people find audibly pleasant to solid state amplifiers, such as Musical Fidelity's use of Nuvistors, tiny triode tubes, to control large bi-polar transistors in their NuVista 300 power amp. In America, Moscode and Studio Electric use this method, but use MOSFET transistors for power, rather than bi-polar. Pathos, an Italian company, has developed an entire line of hybrid amplifiers.
To demonstrate one aspect of this effect, one may use a light bulb in the feedback loop of an infinite gain multiple feedback (IGMF) circuit. The slow response of the light bulb's resistance (which varies according to temperature) can thus be used to moderate the sound and attain a tube-like "soft limiting" of the output, though other aspects of the "tube sound" would not be duplicated in this exercise.
Tube sound enthusiasts
||This section possibly contains original research. (September 2011)|
Different uses of tube amplifiers can be found due to the different personal preferences of the enthusiasts. From those who opt to restrict their use as active devices to those who opt to include them in the audio circuit, accepting the use of semiconductor gain devices in the power supply or as constant current sources. Others, still, will use tubes for the main amplification circuit but add semiconductors (such as solid-state diodes) for clipping purposes, particularly in the preamp section, which is often debated in advertised vintage instrument amplifiers such as the Marshall JCM900 or the Vintage Modern as to their integrity due to their utilization of solid-state devices in the tone-generation circuit. Other schisms concern the use of triodes vs. tetrodes and pentodes, and the use of directly heated tubes vs. indirectly heated tubes.
Many of the explanations relate to the circuit topologies pioneered using tubes, and traditionally associated with them ever since, regardless of whether they are built using tubes today, notably the directly heated single-ended triode amplifier circuit, which operates in class A and often has no external negative feedback; this topology is a classic source of the tube sound.
Feedback paths coupled through the secondary of the output transformer reduce distortion because they compensate for the transformer's distortion to some extent. However only limited NFB can be used around the transformer, as there is phase lag caused by the transformer, and this causes instability if NFB is incorrectly (without any phase / frequency correction) used.
- Audio system measurements
- British Valve Association
- European triode festival
- Virtual Valve Amplifier
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- Self, Douglas (2013). "10. Output Stage Distortions". Audio Power Amplifier Design (6th ed.). Focal Press. p. 270. ISBN 978-0-240-52613-3. "Unusually, there is something of a consensus that audible crossover distortion was responsible for the so-called ʻtransistor soundʼ of the 1960s."
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- For example, Robert Walser Running with the Devil: power, gender, and madness in heavy metal music, Wesleyan University Press, 1993 ISBN 0-8195-6260-2 pages 43-44 discusses the "tube sound" sought by Eddie Van Halen
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- Meriläinen, Esa (February 2010). "5.7 The Secret of Tube Amplifiers". Current-Driving of Loudspeakers. Createspace. pp. 111–112. ISBN 1-4505-4400-2. "The most significant differences are, however, found in the output impedance. The output impedance of transistor amplifiers is typically less than 0.1 Ω, which denotes pure voltage feed for the speaker. In tube amplifiers, instead, the output impedance varies rather widely; from tenths of an ohm to even more than five ohms (with 8 Ω loading). A source impedance of even a couple of ohms is able to weaken the speaker's EMF currents so that the effects are observable; and as the value exceeds 5 Ω, the speaker may function at some frequencies even halfly current-driven."
- "The Caged Frog -- A Pentode Based Transconductance Amplifier for Headphones". ecp.cc. 22 August 2010. Retrieved 14 October 2012. "But, as I was about to disassemble it and put the parts away, I wondered what the circuit would sound like without any feedback. That is, just a pentode with a transformer load. I figured it was going to be awful, so I was not prepared for what I heard, which was near sonic bliss. From note one, this was something special. Turns out, I had built a transconductance amp more or less by accident."
- Self, Douglas (2002) [First published 1996]. "Damping factor". Audio Power Amplifier Design Handbook (3rd ed.). Newnes. p. 25. ISBN 0-7506-56360. "Audio amplifiers, with a few very special exceptions, approximate to perfect voltage sources; i.e., they aspire to a zero output impedance across the audio band."
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- Pete Millett's DIY Audio pages. Tube data. RCA 2A3 Power Triode.
- About distortion behavior between SE amplifiers and speakers, Eduardo de Lima
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- Olsher, Dick (July 2001). "The Volksamp Aleph 30 SE Power Amplifier (product review)". Enjoy the Music.com. 5th paragraph. "It effectively bridges the gap between solid-state and tube sound, blending tube and transistor virtues into a musically satisfying whole."
- Barbour, Eric. The Cool Sound of Tubes in IEEE Spectrum Online.
- Hamm, Russell O. (September 14, 1972). "Tubes vs. Transistors: Is There An Audible Difference?". Presented at the 43rd convention of the Audio Engineering Society, New York.
- Reisch, George. Scientists vs Audiophiles 1999 in Stereophile, March, 1999.
- Tube Data Archive - Massive collection (many gigabytes) of scanned original tube data sheets and technical information.