Feedback and fidelity part 1

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Norman Koren Audio page | Home = page | Part 2

Feedback and fidelity part 1
by Norman = Koren=20
Updated August 18, 2001
Negative feedback can be a wonderful thing when done=20 well,

but it's often done badly. Here's how to use it=20 properly.

Table=20
of contents

Introduction=20

I've seen negative feedback attacked, reviled, denounced, and = defamed for so long I can no longer stand idly by. Feedback may be as stylish as a = =E2=80=9863=20 Dodge Dart, but it=E2=80=99s a dear friend who=E2=80=99s brought beauty = and joy to my life. It=20 may not be a saint, but we don=E2=80=99t expect Marilyn Monroe to be = Mother Theresa, do=20 we? It=E2=80=99s just misunderstood=E2=80=94 often as much by its = supporters as by its=20 detractors. In the ten years I=E2=80=99ve been designing and building = amplifiers I=E2=80=99ve=20 learned how to bring out its best while respecting its limitations. The = time has=20 come to share that knowledge.=20

In his January 1998 Stereophile article "A Future Without = Feedback ,"=20 Martin Colloms asserts that "measurements do not fully describe sound = quality,"=20 and goes on to suggest that "corrective feedback is fundamentally = unmusical." He=20 poses the question, "has anyone explored the implications of negative = feedback=20 for reproduced sound quality in the absolute sense?" What follows is the = results=20 of such an exploration. We shall describe new measurements that provide = improved=20 insight into the origins of audio quality, and we shall use these = measurements=20 to determine when and where to apply feedback to best advantage. = Although we=20 will use vacuum tube circuits as examples, all observations apply = equally well=20 to solid-state. We shall also revisit traditional measurements. One of = them=E2=80=94=20 harmonic distortion at rated power output=E2=80=94 has an unexpected = correlation with=20 sound quality.

Sometimes it seems that so much has been written about = feedback=E2=80=99s harmful effects that it=E2=80=99s easy to forget its benefits. Why do engineers = love it? Improved frequency response, reduced harmonic distortion, better gain = control, increased input impedance (in many circuits), and decreased output = impedance (in circuits with voltage feedback). So why do audiophiles hate it? = Harsh, gritty, grainy, glaring sound. Reason enough.

Now for the BIG question: Are these qualities intrinsic to negative = feedback=20 or do they arise from its improper application? From my experience = it=E2=80=99s mostly=20 the latter. Mostly. There are a few places where feedback runs = into=20 unavoidable problems, and it shouldn=E2=80=99t be a big surprise that = one of them is the=20 single-ended vacuum tube power amplifier. How can we know this? We have = an=20 instrument for looking deep into the heart of amplifiers=E2=80=94 an = instrument that may=20 be within your reach this very moment.

Computer modeling=20

The idea of using the computer=E2=80=94 the ultimate digital = machine=E2=80=94 to design old-fashioned vacuum tube circuits may seem more than a little = incongruous. So=20 it may be, but in the computer we have powerful tool that wasn=E2=80=99t = available in=20 the glory days of Dynaco, McIntosh, and Marantz; an affordable tool for = anyone=20 interested in high-end audio, and usable by anyone with modest = engineering=20 skill. More precisely, our tool is a computer program called = SPICE=E2=80=94 acronym for=20 Simulation Program with Integrated Circuit Emphasis, originally = developed at the=20 University of California Berkeley.=20

SPICE is widely used in industry to prove integrated circuit designs = before=20 they are cast in silicon, where fixing errors is far more costly than in = concrete. There are several commercial versions of SPICE, all of which = start=20 with the Berkeley algorithms and add user-friendly front-ends and = outputs.=20 Probably the best-known of them is PSpice from Cadence Design Systems = (http://www.orcad.= com/Product/Analog/analog.asp). A free = evaluation version that can simulate up to fifty parts is available on CD ROM = or can=20 be downloaded from the web. Fifty parts won=E2=80=99t get you far with = semiconductors, but it=E2=80=99s sufficient for the design of surprisingly = sophisticated vacuum tube=20 circuits. Full versions of PSpice are very expensive. Another excellent = program=20 is Electronics Workbench from Interactive Image Technologies = (1-800-263-5552; http://www.interactiv.com/), = which comes=20 in a $299 package (sometimes on sale) that can do some serious = simulation. Each=20 of these programs has its learning curve, and since I=E2=80=99ve taken = the trouble to=20 learn PSpice, I=E2=80=99m stuck with it. I love it.

I=E2=80=99m not the only one who values SPICE. When I escaped from = Silicon Valley in=20 1985, I had a neighbor who was developing a version (HSpice) in his = garage.=20 While I was tinkering with tubes, he was quietly taking over the market = for=20 large-scale integrated circuit simulation. In August 1997 I read that he = had=20 sold his company=E2=80=94 Meta Software=E2=80=94 for one hundred and = sixty million dollars.=20 (That was before the dot com boom, when hardware still got some = respect.) Can=20 there be a lesson here? I suppose we tube lovers must be content to = receive our=20 reward in heavenly sound. None of us will become another Bill Gates. = Besides,=20 the only reproduced sound he ever hears is digital.

Many readers may wonder how well digital simulation can unlock the = secrets of=20 analog electronics. In my experience it can do so astonishingly well. I = never=20 cease to be amazed by how closely measurements match SPICE simulations. =

Models and measurements=20

No matter how strongly you believe that measurements don=E2=80=99t = or can=E2=80=99t=20 correlate with sound quality, you must agree that electrical signals = inside=20 circuits obey the laws of physics. If a computer program has accurate = enough=20 device models, it will simulate the signals with precision. If you = examine the details of those signals with enough care, you may begin to find = patterns that=20 shed light on sound quality.=20

What is wrong with conventional measurements? Two things. The first = is that=20 most of them are made in frequency domain. The real world happens in = time=20 domain. Frequency domain measurements are derived from a mathematical = construct=20 called the Fourier transform, which is defined for linear systems. When = a system=20 becomes seriously nonlinear=E2=80=94 as an amplifier does when it = saturates=E2=80=94 frequency=20 domain measurements their meaning. Time domain measurements, such as = pictures of=20 clipped sine waves, are needed to tell the real story. The one time = domain=20 measurement frequently seen in equipment reviews is the 10kHz square = wave. This=20 measurement is usually made with a small signal=E2=80=94 far from = saturation=E2=80=94 and=20 provides the same information as the frequency response curve. SPICE = produces=20 output in both time and frequency domain.

The second problem is that conventional measurements are taken only = at an=20 amplifier=E2=80=99s external connections: A signal is fed into the input = terminals and=20 measured at the output terminals. What happens inside the circuit can = make the=20 difference between sonic mediocrity and distinction. With SPICE, you can = probe=20 deep inside of circuits. I=E2=80=99ve made measurements that would be = difficult,=20 expensive, and time-consuming with hardware instruments; measurements = rarely if=20 ever seen in equipment reviews; measurements that correlate much more = closely=20 with sound quality than such old standbys as harmonic distortion and = frequency=20 response. We=E2=80=99ve known for a long time they didn=E2=80=99t hold = the secrets.

A program=E2=80=99s performance is only as good as its = models=E2=80=94 sets of equations that=20 simulate device behavior=E2=80=94 and SPICE does not have built-in = models for vacuum=20 tubes. External models must be added. For many years tubes were modeled = by the=20 Langmuir-Childs law [1,2], which represents a tube as a = voltage-controlled=20 current source whose current is proportional to the three-halves power = of the=20 voltage on the controlling elements. This model approximates tube = performance=20 fairly well in the middle of the operating range, but fails miserably = near=20 cutoff, a region particularly critical to the performance of class AB = push-pull=20 amplifiers. It works well for calculating frequency response but not for = distortion.

A new set of models, accurate enough to match experimental tube = behavior in=20 all critical regions, has recently been published [3] and applied to the = design=20 of a modified Dynaco PAS preamplifier [4] with stunning sonic results. = We shall=20 use the old and new PAS line amplifiers (figures 1 and 2) as examples of = problems and solutions related to feedback.

To you non-technical readers, I offer an apology. Feedback cannot be discussed intelligently without getting somewhat technical. I shall try = to keep=20 this exposition as readable as possible=E2=80=94 There will be no heavy = formulas, and=20 you may safely skip over circuit descriptions and references to = resistors and=20 capacitors.

Before we proceed, a few definitions are needed: There are two types = of=20 negative feedback, or degenerative feedback as it is sometimes called: = local and=20 global. Local feedback is connected within or around a single gain = stage; global=20 feedback is connected around several gain stages, usually from the = amplifier=E2=80=99s=20 output to its input. Local feedback is generally regarded as benign, and = with=20 this view I concur. The amount of feedback, expressed in decibels (dB), = is the=20 ratio of the gains without and with feedback (the open and closed-loop = gains):=20 6dB is a factor of 2 in voltage (4 in power); 20dB is a factor of 10 in = voltage=20 (100 in power), etc.

The trouble with feedback=20

Despite its advantages, negative feedback can degrade amplifier = sound=20 quality in three ways: First, it can lead to instabilities that appear = as=20 response peaks or even oscillations at an amplifier=E2=80=99s frequency = extremes.=20 Second, it can increase susceptibility to RF interference. Third, it = makes=20 clipping more abrupt: This rarely affects preamplifiers, which have = plenty of=20 headroom, but it is always a concern in power amplifiers. With proper = design,=20 the first two problems can be eliminated and the third can be = controlled. We shall examine each of them closely with the help of SPICE.=20

Instability=20

Negative feedback operates by subtracting a portion of an = amplifier=E2=80=99s=20 output signal from its input. This is quite straightforward for the = middle=20 frequencies where an amplifier=E2=80=99s open-loop gain is relatively = flat. Bode=E2=80=99s=20 theorem tells us that there is very little phase shift in this region. = But=20 things can get ugly at the frequency extremes. Every RC = (resistor-capacitor)=20 network that contributes to an amplifier=E2=80=99s rolloff adds up to = 6dB per octave to the rolloff and up to 90 degrees to the phase shift. Not all of these = RC networks are obvious in the schematic: Many involve stray capacitances = within=20 the tubes. If the total phase shift exceeds 180 degrees at any frequency = where=20 the loop gain (A/G-1, where A is the open-loop gain = and=20 G is the closed-loop gain) is greater than one, the amplifier = will=20 oscillate [5]. If it merely approaches 180 degrees, a peak will appear = in the=20 frequency response curve that corresponds to ringing in the time-domain. = This=20 will definitely degrade sound quality.=20

To make matters worse, capacitance in shunt with the load increases = the phase=20 shift. Interconnect cables have around 20pF per foot, and electrostatic loudspeakers are nothing more than big honking capacitors-- as large as = 2=20 microfarads-- that know how to move. So load capacitance is = always present. An amplifier that performs nicely with a purely resistive load = (widely=20 used in equipment reviews) may misbehave in the real world. Amplifiers = have a=20 property called phase margin=E2=80=94 the difference between the = maximum phase=20 shift and 180 degrees=E2=80=94 that indicates how well they can tolerate = capacitive=20 loads. A qualitative estimate of phase margin may be obtained by = measuring the=20 response with capacitance in shunt with the load. This is particularly = easy with=20 SPICE.

To keep phase shift under control, a single RC network must dominate = the=20 rolloff. For global feedback loops, this usually involves adding a = capacitor to=20 the circuit. This is accomplished in the original PAS line amplifier = (fig. 1)=20 with 33pF capacitor CLFB connected in parallel with feedback resistor = RLFB, and=20 in the new design (fig. 2), with 7pF capacitor C3M in the input circuit. = Although these capacitors reduce the high frequency cutoff (-3dB point), = it is=20 still around 100kHz in both circuits=E2=80=94 well beyond the limits of = human hearing.=20 Most well-designed preamplifiers achieve good frequency response and = stability=20 at the same time=E2=80=94 but this is not always the case for power = amplifiers with=20 output transformers.

Figure 1. The original PAS line=20 amplifier.

The line amplifier of fig. 2 differs in just = one respect=20 from the previously published version [4]: the addition of 150 ohm = resistor ROUT=20 in series with the output. I had always objected to such a resistor = because it=20 increases the output impedance, worsening the high frequency rolloff in = the=20 presence of shunt capacitance from cables. But with negative feedback, = phase=20 shift due to shunt capacitance boosts the high frequency response = up to=20 the resonant peak, just over 100kHz. In extreme cases, this can even = result in=20 oscillation. Increasing the compensation capacitor fixes this problem at = the=20 expense of high frequency rolloff for short cables with low capacitance. = ROUT=20 solves the problem by isolating the amplifier from the load capacitance. = If the=20 correct value is chosen (easily done by trial-and-error with SPICE), the = high=20 frequency loss due to the increased output impedance will balance the = boost due=20 to feedback, making the response below the resonant peak nearly = independent of=20 the load capacitance=E2=80=94 even for cables as long as 100 meters. = This neat little=20 trick cannot be accomplished without negative feedback.

Figure 2. The modified PAS line=20 amplifier.

If we observe the response of the original PAS line amplifier (fig. = 3;=20 simulated with Evaluation PSpice 6.3, which tolerates more components = than the=20 newer evaluation versions), we find that the output signal is fairly = flat to=20 below 1Hz, but the signal at the plate of the first gain stage plate = (node 3P)=20 has a huge resonant peak at 0.4Hz=E2=80=94 35dB above the mid-frequency = level. This peak=20 is present because there is no feedback at dc: It is blocked from = reaching the=20 output terminal by coupling capacitor C4P.

Fig. 3. Original PAS line amplifier = frequency=20 response (first plate 3P and output LINE_OUT).

Now you might ask what effect a resonant peak far below the limits of = human=20 hearing and loudspeakers=E2=80=94 a peak that doesn=E2=80=99t even = appear at the preamplifier=20 output=E2=80=94 can have on sound quality. Quite a lot, it turns out. To = begin with, 33=20 RPM turntables rotate at a frequency close to 0.4Hz. Signals from = mechanical=20 perturbations at this frequency will be greatly exaggerated inside the=20 preamplifier. Then there is tube-generated 1/f noise, also called = flicker=20 or pink noise=E2=80=94 noise whose power spectral density is inversely = proportional to=20 frequency (f). 1/f noise can be very significant at 0.4Hz. = These=20 two noise sources perturb the bias levels of tubes inside the = preamplifier.=20 Since the tubes aren=E2=80=99t perfectly linear, this leads to = envelope=20 modulation=E2=80=94 small variations in signal amplitude at the = output that muddy=20 the sound and blur the imaging.

This problem has been solved in the modified PAS line amplifier (fig. = 2) with=20 a dc-coupled negative feedback loop: Cathode resistor R6C of the cathode-follower also functions as the feedback resistor. It took quite = a bit=20 of trial-and-error with SPICE to get the input tube operating current to = the=20 correct level (0.7mA; much higher than the original). A resonant peak = (fig. 4)=20 is still present in the new circuit, but it is now 3dB below the = mid-frequency=20 signal level=E2=80=94 38dB better than the original. This is a perfect = example of how=20 external measurements can be misleading: The original design has much = more=20 extended low frequency response, but the new design has cleaner bass and = better=20 overall sound.

Fig. 4. Modified PAS line amplifier = frequency=20 response (first plate 3P and output LINE_OUT).

Feedback and output transformers=20

Reduced to its essentials, an output transformer is a device = comprising two=20 electrical windings=E2=80=94 a primary with N_P turns = and a secondary=20 with N_S turns=E2=80=94 coupled by a magnetic core, and = used to match=20 the high impedance of output tubes to relatively low impedance of = loudspeakers.=20 In simulations, transformers are modeled as devices that multiply the = signal=20 voltage by N_S/N_P, and have a small = series=20 inductance called leakage inductance (L_SP), a large = shunt=20 inductance (L_P), and a shunt capacitance (C_IP). This terminology is from "Transformers and = Tubes in=20 Power Amplifiers" by Menno Van der Veen, available from Plitron = (1-800-754-8766; http://www.plitron.com)=E2=80=94 strongly recommended to anyone who = wishes to pursue this subject further.=20

Van der Veen defines the quality factor of an output transformer as = the ratio=20 of shunt to leakage inductance, Q_F =3D=20 L_P/L_SP. Q_Fis roughly=20 proportional to the ratio of the upper to lower cutoff frequencies. = Leakage=20 inductance L_SP arises from imperfect coupling between = the=20 primary and secondary windings, and is a strong function of the type of=20 transformer. There are three broad categories:

Push-pull EI transformers (named after the shape of the core): = used in most of the classic designs. Typical cutoff frequencies are between = 25 and=20 70kHz. Can be thought of as occupying the middle ground between SE and = toroidal transformers.
Single-ended (SE) transformers: must tolerate the large dc current = drawn by SE triodes operating in class A. They have EI cores with air gaps = to keep=20 them from saturating. The air gap increases leakage inductance=20 L_SP. Q_F is lower than for the = other types.=20 Cutoff frequencies can dip into the audio range.
Push-pull toroidal (bagel-shaped) transformers: Have the largest=20 Q_F: Cutoff frequencies can exceed 200kHz. They are = sensitive=20 to dc-imbalance in push-pull circuits, but techniques are available to = maintain balance.

An output transformer=E2=80=99s high = frequency rolloff is=20 dominated by the LC (inductor-capacitor) network consisting of=20 L_SP and C_IP. This type of network = has a=20 second order rolloff=E2=80=94 up to 12dB per octave at = frequencies above cutoff,=20 with a phase shift of up to 180 degrees. As a result of this phase = shift, even a=20 few dB of feedback can cause trouble=E2=80=94 response peaks or = oscillations with=20 capacitive loads=E2=80=94 unless the loop is carefully compensated. The = compensation=20 techniques are the same ones used in the line stages of figures 1 and 2. = The=20 high frequency cutoff of the RC network must be well below that of the=20 transformer=E2=80=94 the higher the feedback, the lower it must be.=20

For this reason, feedback cannot be used to extend the frequency = response of=20 an amplifier with an output transformer. Sad to say, not all tube = amplifiers apply feedback correctly. Frequency response peaks above 20kHz and = ringing in=20 response to 10kHz square waves have appeared in several = Stereophile equipment reviews, even for some extremely expensive amplifiers. Such=20 amplifiers can misbehave badly if there is much capacitance in the load. =

Feedback is particularly touchy in single-ended circuits because the = output=20 transformer cutoff frequency is so close to the top of the audible = range. A=20 feedback loop must be compensated with extreme care: Too much = compensation rolls=20 off the highs very audibly; too little risks a response peak. Even just = the=20 right balance may have poor phase margin: It might sound wonderful with = one=20 speaker-cable combination but poor with others. This is one of two = reasons that=20 SE amplifiers are poorly suited for feedback. The other=E2=80=94 = hardened clipping=E2=80=94 will=20 be discussed below.

Radio Frequency (RF) Interference=20

Feedback=E2=80=99s least-known side-effect is that it can increase = an amplifier=E2=80=99s susceptibility to RF interference. This is so because the circuit = technique most often employed to stabilize a feedback loop=E2=80=94 a capacitor = in shunt with the=20 feedback resistor (CLFB in fig. 1)=E2=80=94 allows RF signals picked up = by the=20 output cable to be fed back into the amplifier=E2=80=99s input = virtually without attenuation. Cables are antennas, albeit poor ones, and = vary widely=20 in their sensitivity to RF pickup. Premium interconnect cables should be = exceptionally well shielded to minimize this sensitivity. Speaker = cables, which=20 are usually unshielded, are much better antennas than interconnect = cables.=20

I am convinced that RF interference is a major culprit because every = circuit=20 change I=E2=80=99ve ever made to reduce the RF entering an amplifier has = improved the=20 sound=E2=80=94 made it sweeter, smoother, cleaner, and more generally = listenable. It is=20 the apparent cause of the grittiness, graininess, harshness, and = listener=20 fatigue =E2=80=94 what Martin Colloms calls "sand in the tweeter" = =E2=80=94 that can plague=20 amplifiers with otherwise excellent specifications. The sonic = degradation caused=20 by RF interference is far worse than harmonic distortion.

RF interference comes from a wide variety of sources: radio, TV, = digital cellular phones, microwave ovens, lamp dimmers, flourescent lights, and = digital=20 appliances such as computers and CD players. (It is particularly = difficult to=20 eliminate inside CD players, where it may be as responsible as jitter = for=20 "digititis.") It is virtually omnipresent in urban, suburban, and all = but the=20 most remote rural areas. It varies from time-to-time and place-to-place, = and may=20 be responsible for many of the discrepancies in published amplifier = reviews.=20

The exact mechanism by which RF interference degrades audio quality = is not=20 well-understood. The most likely cause is intermodulation distortion. = Paul=20 Miller [6] described a series of experiments in which he inserted strong = RF=20 signals modulated with random audio noise into several amplifiers and = measured=20 the resulting audio noise spectra (the result of intermodulation). He = claimed to=20 find a strong correlation with the subjective sound quality.

There is a very simple test for determining if an amplifier is overly sensitive to RF interference: Turn the volume up and listen for a pop = when you=20 turn on a nearby appliance. A well-designed amplifier will remain = silent.

The RF problem was solved in the modified PAS line amplifier (fig. 2) = by=20 compensating the feedback loop with an RC network in the input = stage=E2=80=94 R3GS and=20 C3M. Due to the Miller effect, the effective capacitance C3M is = its=20 intrinsic capacitance (7pF) multiplied by the gain of tube TU3 after = feedback is=20 applied (not its intrinsic gain). Calculating this gain can be tricky: = Global=20 feedback reduces the gain of the first stage only; all others operate at = full=20 gain. SPICE eliminates the need for tricky calculations. The correct = value of=20 C3M can be quickly determined by trial-and-error. This technique, which = we shall=20 call Miller compensation, has poorer high frequency response than the=20 traditional technique, but the response can be extended=E2=80=94 made as = good as the=20 traditional technique without compromising stability=E2=80=94 by adding = shunt capacitor=20 C3C to the input stage cathode circuit. C3C also provides a bit of extra = RF=20 suppression.

The improvement brought about by this technique is illustrated in = fig. 5,=20 which shows the signal on the plate of the first gain stage (node 3P) = when input=20 signal VIN is applied to the line amplifier output terminal, = LINE_OUT. In=20 the critical region above 20kHz, the response of the modified amplifier = averages=20 18dB below that of the original. The actual improvement is even greater = because,=20 with VIN applied to the line amplifier input, the signal at node = 3P=20 (figures 3, 4) is 6dB larger in the modified line amplifier. This is so = because=20 local current feedback decreases the gain of the second stage (TU4), = allowing=20 the first stage to operate at increased gain. The signal-to RF noise = ratio of=20 the modified amplifier is therefore 24dB better than the = original=E2=80=94 a really=20 significant improvement.

Fig. 5. RF susceptibility from line = amplifier=20 output (signal amplitude at the
first gain stage plate with = an input=20 signal injected at the preamp output).

The Parts Connection Catalog & Resource Guide (1-800-769-0747; http://www.sonicfrontiers.com/= tpc) contains an excellent collection of schematic diagrams of classic tube preamplifiers and power amplifiers. Nearly every amplifier with = feedback=E2=80=94 and=20 that=E2=80=99s almost all of them=E2=80=94 uses the traditional = compensation technique with the=20 capacitor in parallel with the feedback resistor. In all fairness, this=20 technique is easy to apply and provides good stability with minimum = frequency=20 response loss. The new technique, Miller compensation in the input = stage,=20 requires two capacitors (C3M and C3C in fig. 2) to achieve good = frequency=20 response extension. With the proper component values, difficult to = obtain=20 without SPICE, the new technique has improved stability, i.e., less of a = response peak with capacitance in shunt with the load. Compensating a = feedback=20 loop at the input stage also reduces response peaks at intermediate gain = stages=20 that can occasionally cause such problems as unexpected saturation.

In part 2 we discuss feedback in power = amplifiers.

References

Scott Reynolds, "Vacuum-tube models for PSPICE simulations," Glass = Audio, vol. 5, no. 4, 4/93 p. 17.
W. Marshall Leach, Jr., "SPICE models for vacuum-tube amplifiers," = J.=20 Audio Eng. Soc. Vol 43, No. 3, March 1995, p. 117.
Norman L. Koren, "Improved Vacuum-Tube Models for SPICE = Simulations,"=20 Glass Audio, Vol. 8, No. 5, 1996, p. 18.
Norman L. Koren, "SPICE and the Art of Preamplifier Design," (in = two=20 parts), Glass Audio, Vol. 8, No. 2, p. 1 and No. 4, p. 38, = 1997.
Paul Miller, "Resonances and Repercussions," Hi Fi News & = Record Review, June 1989, p. 35.
Paul W. Tuinenga, "SPICE, A Guide to Circuit Simulation & = Analysis using PSpice," Prentice-Hall, 1992 or 1995.
Scott Frankland, "The Magic of Design and Synergy, Part I: The = Wavestream V-8 Triode," Positive Feedback, Vol. 5, No. 5, 1995, p. = 23.
John Atkinson, "Real-life measurements," Stereophile, August 1995, = p.=20 168.

About the=20 author

Norman Koren, a=20 native of Rochester, NY, received a BA in physics from Brown University = in 1965=20 and an MA in physics from Wayne State University in 1969. His destiny as = a=20 high-tech nomad has taken him to Boston, Philadelphia, Silicon Valley, = San=20 Diego, and most recently to Colorado, where he worked in research and=20 development of digital magnetic recording channels through = 2001.=20

E-mail | Norman=20 Koren Audio page | Part 2.=20

This page was created
December 8,=20 2003

Images and text copyright (C) 2000-2012 by Norman Koren. Norman Koren lives in Boulder, Colorado. Since = 2003 most=20 of his time has been devoted to the development of Imatest. He=20 has been involved with photography since = 1964. Designing vacuum = tube audio=20 amplifiers was his passion between about 1990 to = 1998.

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