Feedback=20 and fidelity part 2

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Norman Koren Audio page | Home = page | Part 1

Feedback and fidelity part 2
by Norman = Koren=20
Updated Oct.=20 9, 2006 (last update December 8, 2003)
.
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

In part = 1 we=20 discussed negative feedback concepts and applied them to = preamplifiers.

Clipping=20

When an amplifier is driven to its limits=E2=80=94 into = saturation=E2=80=94 the tops and bottoms of the output waveforms flatten out. This phenomenon is known = as clipping. Because most music signals contain short-term peaks whose=20 instantaneous power is much greater than the average, most = amplifiers=E2=80=94 even=20 moderately powerful amplifiers=E2=80=94 occasionally clip during normal = operation. For=20 this reason, the behavior of an amplifier during clipping has a profound = effect on its sound quality.=20

The power amplifier of fig. 6 is an excellent platform for studying = the=20 effects of feedback on clipping. It can be built as a modified Dynaco = Mark 3, or=20 from scratch with a 4300 ohm primary impedance output transformer. Due = to the=20 limitations of the evaluation version of PSpice, simplified bias and = power=20 supplies have been shown. I have named this amplifier the "Local Hero" = because=20 of its use of local feedback (and also after one of my favorite = movies.). Since=20 it has outstanding sound quality and makes exemplary use of feedback, we = shall=20 describe its circuit in some detail.

Figure 6. The "Local Hero" amplifier: = a modified=20 Dynaco Mark III.

The Local Hero=E2=80=99s chief feature is the absence of global = negative feedback from the output transformer secondary to the input stage. Instead, = balanced feedback from the output is returned to the cathodes of the driver = (TU3, TU4)=20 and output tubes (TU5, TU6). This eliminates many of the stability = problems=20 associated with a large global loop: The fewer stages in the loop, the = easier it=20 is to control phase shifts at both frequency extremes. The amount of = feedback on=20 the drivers is controlled by voltage dividers (R3F, R3C) and (R4F, R4C). = The=20 resistance ratios may be changed to alter the amount of feedback, but if = they=20 are, the parallel resistance between the driver cathodes (nodes 3C and = 4C) and=20 ground should remain around 3300 ohms. The loop is compensated with = capacitors=20 C3M and C4M, with C34 added to extend the high frequency response. = (These=20 capacitors have the same functions as C3M and C3C in fig. 2.) They do = not=20 transmit RF interference from the output. The effects of RF interference = are=20 further reduced because the signal at the drivers is much greater than = at the=20 input. RLD and R16 are for simulation only-- they aren't physically = present. RLD=20 represents the speaker load. R16 prevents an unconnected node error. = Stability=20 is excellent: Even a 1 microfarad capacitor in shunt with the load = results in=20 little ringing.

The input stage (TU1) uses local current feedback: Gain can be = controlled by=20 adjusting R1B. It is ac-coupled to a split-load phase invertor (TU2), = which also=20 has local current feedback. The split-load phase invertor is an = excellent=20 performer when it doesn=E2=80=99t have to drive output tubes, as it does = in the classic=20 Dynaco circuits. Ac-coupling allows the plate resistors to be chosen for = equal=20 but opposite ac current in TU1 and TU2, so that no net ac current is = drawn from=20 the power supply. This reduces sonic degradation from power supply = electrolytic=20 capacitors, which are notoriously nonlinear. The original Williamson = circuit=20 (the grandfather of the Local Hero) had to be dc-coupled because there = were=20 already too many coupling capacitors in the global feedback loop; = another would=20 have undermined the low frequency stability. Ac-coupling also increases = the=20 phase invertor=E2=80=99s maximum output. A note for experimenters: If = you build this=20 circuit, you may need to make fine adjustments on C3M and C4M, and = possibly also=20 C34, for flat response and good stability.

Note: I haven't = actually built the=20 Local Hero, but I've gotten inquiries. I haven't included the = power supply=20 design. Power supplies for this type of amplifier are pretty = standard. The=20 Hammond = 372JX=20 (300-0-300V, 250 mA) and 373BX (350-0-350V, 175 mA) are good power transformer choices if you're building Local Hero as monoblocks. = The=20 372JX is more conservative, but the 373BX will should put out = about 30%=20 more power (you'll need 500V power supply = capacitors).=20

If you build it, = I recommend testing it by driving it with a square wave generator, loading it = with a=20 typical loudspeaker load (with cables), and looking at the signal = at the=20 output (and speakers) with an oscilloscope. If there is ringing, = increase the Miller capacitors, C3M and C4M. If the square waves seem = excessively rounded, you may be able to decrease C3M and C4M with no ill = effects. The voltage at test points 5C and 6C should be approximately 0.5 V = for 50 mA bias current (per tube). Remember = to be=20 careful of high voltages when you work inside tube=20 = amplifiers!

A=20 pleasant surprise! Jorn Loe of Norway built a Local Hero. It took = him a=20 long time (he isn't experienced at building tube amplifiers), but = it's=20 working and sounding fine. You can reach him at n (dot) craft (at) = c2i=20 (dot) net.
=20

A = comment from=20 Jorn, Oct. 8, 2006: I did a small correction in the = Local=20 Hero after oscilloscope measurements showed some oscillation. My = layout=20 made the C3M and C4M paths too long. When I connected = C3M and=20 C4M directly to anodes 3P and 4P the amplifiers went silent. I=20 talked to other tube builders, and they said that this was a = good=20 change. (Sounds fine to = me. =E2=80=94NLK)=20

The results of driving the amplifier into saturation are shown in = figures 7=20 (without feedback) and 8 (with feedback). Since the gain with an 8 ohm = load is=20 9.46dB lower (a factor of 0.3365) with feedback than without it, the = input=20 signals have been adjusted for the same degree of saturation. The actual = amount=20 of feedback is the difference in gain without the load: 15.4dB. = This is a=20 moderate amount: much more than most single-ended tube amplifiers, = slightly less=20 than classic push-pull tube amplifiers, and much less than mid-fi = solid-state=20 amplifiers.

Fig. 7. Sine wave = clipping with no=20 negative feedback.

When feedback is applied, clipping at the amplifier output ( lower = curve, fig. 8) becomes more severe: its onset becomes more abrupt and the tops = and=20 bottoms of the waveforms become flatter. Since no signal is fed back = during=20 clipping, voltage spikes appear at the grid of the output tubes (upper = curve,=20 fig. 8). The difference between figures 7 and 8 is modest because only = 15.4 dB=20 of feedback has been employed: Had more been applied to emphasize the = effects of=20 clipping, the sound quality would have suffered, and the Local Hero = would not=20 have been such a good example of proper use of feedback. In a mid-fi = solid-state=20 amplifier, with 40 dB or more feedback, the tops and bottoms would have = been=20 cleanly chopped off.

Fig. 8. Sine wave = clipping with 15.4 dB=20 negative feedback.

Hard clipping is the direct cause of the constricted dynamics and = much of the=20 sonic harshness attributed to feedback. The audible degradation can only = be=20 determined by ear: there is no hard and fixed rule, but much can be = learned by=20 correlating SPICE results with careful listening. Sonic degradation is a = strong=20 function of amplifier power and loudspeaker efficiency: the higher the = sound=20 pressure level at the onset of clipping, the less offensive it will be. = That,=20 along with the stability/frequency response issue described above, is = the reason=20 that low powered SE amplifiers have limited tolerance for feedback.

Clipping is rarely a problem in preamplifiers. The figure 2 = preamplifier has=20 enough headroom to drive any commercial power amplifier well beyond = saturation=E2=80=94=20 10 to 30 dB, depending on its sensitivity and input impedance.

Despite its drawbacks in power amplifiers, negative feedback offers = one=20 significant advantage: It reduces the output impedance. High output = impedance=20 can cause irregular frequency response under realistic loudspeaker loads = [8] as=20 well as poor woofer damping, audible as mushy ill-defined bass. The = optimum=20 output impedance and feedback level depends on a number of factors that=20 ultimately reduce to a tradeoff between mushy bass at one extreme (no = feedback)=20 and harsh clipping at the other (too much feedback). Several aspects of = this=20 tradeoff are discussed in the sidebar.

Despite negative feedback=E2=80=99s disadvantages in single-ended = tube power amplifiers, two local experimenters have chosen to use a small amount = of it=E2=80=94=20 around 3 to 4dB. Without it, the bass was just too sloppy. They did not = take=20 this step lightly: They listened extensively, perhaps obsessively, = before adding=20 feedback, and they wouldn't have done so had they duplicated Martin = Colloms=E2=80=99=20 observation, made on the Cary 805C, that even the smallest amount of = feedback=20 compromises musicality.

I can only speculate on the reasons for this discrepancy. At first I = thought=20 the sound pressure level at the onset of clipping would be slightly = higher for=20 the experimenter=E2=80=99s systems, which use Svetlana SV811-10 output = tubes operated in=20 class A2, driving loudspeakers with 93 and 96dB efficiency in rather = small=20 rooms. But the clipping level of the Cary 805C driving the 93 dB = efficient=20 Wilson WITT should be at least as high. Perhaps the discrepancy can be = explained=20 by differences in the room size and acoustics, amplifier clipping = signature, or=20 loudspeaker damping requirements. But there is another intriguing = possibility.=20

Since I don=E2=80=99t have access to the Cary 805C=E2=80=99s = schematic diagram, I can only=20 speculate that when feedback is switched on, the traditional = compensation technique=E2=80=94 a capacitor in shunt with the feedback = resistor=E2=80=94 may be employed. If=20 this is so, then all the RF picked up from the speaker cables will be transmitted back to the input stage, even for the smallest amount of = feedback, but none will be transmitted if there is no feedback. This could well = explain Martin Colloms=E2=80=99 observation.

The great harmonic distortion scam=20

Any circuit technique that improves an amplifier=E2=80=99s = linearity at power=20 levels below saturation, i.e., reduces total harmonic distortion (THD), = will=20 result in more abrupt, harder clipping. Negative feedback is only one of = several such techniques. The relationship between linearity and clipping can be examined with the transfer and linearity curves in figures 9 and 10. = These curves are derived from the same PSpice simulations as figures 7 and 8 = for=20 saturated 200Hz sine waves, but instead of using time as the independent variable (x-axis), they use the input voltage, V(INPUT).=20

Figure 9. Transfer and = linearity curves=20 for the "Local Hero" amplifier without feedback=20

Fig. 10. Transfer and = linearity curves=20 with 15.4dB negative feedback.

The transfer curve is simply the output voltage, V(SPKR), as a = function of=20 the input voltage. For small input signals, it rises along a relatively = straight=20 line. As it approaches saturation, it deviates from the straight line to = a=20 greater or lesser degree, depending on how well the circuit is = linearized. At=20 saturation, it flattens out. Since it can be difficult to see the = deviation from=20 the straight line, we introduce the linearity curve.

The linearity curve is the slope, or rate of change, of the transfer = curve.=20 In the language of differential calculus, it is the derivative of the = output=20 voltage with respect to the input, dV(SPKR)/dV(INPUT). For small input = signals,=20 it is a relatively straight horizontal line whose value equals the gain = of the=20 amplifier. As it approaches saturation, it starts to drop. This drop is = much=20 more visible than the corresponding change in the slope of the transfer = curve.=20 At saturation, it drops to zero.

We must now explain the multiple traces in the transfer and linearity = curves.=20 To obtain these curves, we drive the output tubes (via computer = simulation, of=20 course) into hard saturation=E2=80=94 hard enough to drive the voltage = on the grid of=20 output tube positive with respect to the cathode for a portion of the = cycle.=20 This causes grid current to be drawn, alternately charging coupling = capacitors=20 C3P and C4P. These capacitors can charge quite rapidly, but their = discharge is=20 governed by the RC time constant that includes the grid resistor: = C4P=EF=BF=BDR6G=20 or C3P=EF=BF=BDR5G =3D 0.05 seconds, = corresponding to a -3dB=20 frequency of 3.2Hz. Since the simulation starts with no signal, and = hence no=20 charge, the charge that accumulates whenever one of the output tube = grids=20 conducts causes the multiple traces.

This is no mere artifact of SPICE simulation: It is a real effect in = any=20 amplifier where the grids of the output tubes are capacitively coupled. = In hard=20 saturation, continuous waveforms behave very differently from a single = transient=20 pulse: They can build enough charge across the coupling capacitors to = drive the=20 output tubes deep into cutoff. This leads to an overload recovery time, = governed=20 by the above-mentioned RC time constant, that can be quite audible. = Overload=20 recovery is eliminated in class A2 or AB2 amplifiers, where the output = tube=20 drivers can source grid current. This can be accomplished either with=20 transformer-coupling or dc-coupled cathode followers [7], either of = which are=20 costly. An additional advantage of class A2 or AB2 power amplifiers is = that they=20 can put out much more power when the output stage is triode-connected. =

Now, back to the transfer and linearity curves. Fourier analysis = tells us=20 that signals on straight line portions of the curves have no appreciable distortion. Signals on portions of the curves with sharp kinks or = abrupt changes generate lots of high order harmonic distortion. Depending on = your viewpoint, either the kinks or the high-order harmonics are the source = of sonic=20 degradation. Signals on portions of the curves with gradual curvature or = gentle=20 rounding generate mostly low (second and third) order harmonic = distortion.

In a circuit with high linearity=E2=80=94 the result of large amounts = of negative feedback=E2=80=94 the transfer curve is a straight line up to = saturation, where is=20 abruptly levels off. The linearity curve is a horizontal line up to = saturation,=20 where it "hits a brick wall" and abruptly drops to zero. There will be = very=20 little harmonic distortion below saturation, but as soon as the = amplifier=20 saturates, serious high-order harmonic distortion is generated.

Amplifiers are traditionally specified for total harmonic distortion = at the=20 rated power, typically around 1dB below saturation (roughly 90% of = saturation=20 voltage or 80% of saturation power). The difference between the rated = power and=20 the saturation level is the "headroom." An amplifier with relatively = soft=20 clipping, such as the Local Hero without feedback (fig. 9), must start = rounding=20 off the signal at amplitudes well below saturation. At the rated power=20 therefore, it can have considerable THD, but this distortion is mostly = low order=20 (second and third) harmonics. At power levels above saturation, high = order=20 harmonic distortion components will remain much lower than for a highly = linear=20 amplifier.

The problem of hard clipping is not limited to feedback amplifiers. I = once=20 had an amplifier=E2=80=94 obtained in a trade, without careful = auditioning=E2=80=94 that=20 featured a circuit called "super-feedforward," intended to eliminate the = vices=20 of feedback. It put out 120 watts per channel at 0.005% THD (one of the = lowest=20 in the 1980 Audio Annual Equipment Directory), had response to = 250kHz,=20 and had sound that can only be described as hateful and irritating, even = though=20 it had no obvious flaws. The only suspicious measurement was the = saturated sine=20 waves: They didn=E2=80=99t just clip; they dipped! I didn=E2=80=99t keep = the amplifier long=20 enough to find out why.

Modest levels of low order harmonic distortion do not seem to harm = sound quality. In SE tube amplifiers, most of which have little or no = feedback, the=20 predominant distortion component is the second harmonic. Push-pull = amplifiers=20 cancel even order harmonic distortion components, resulting in lower = THD. The=20 second harmonic distortion in SE amplifiers may well be responsible for = their=20 alluring sound. It has given rise to the theory that even order harmonic = distortion components are more benign than odd. My own view is that the = real=20 culprit is high order distortion components. Second harmonic distortion = may=20 actually enhance sound quality by adding harmonic = content=E2=80=94 some call it=20 "euphonic distortion"=E2=80=94 that increases the perception of richness = and detail. In=20 all fairness, I haven=E2=80=99t persuaded my experimenter friends that = this is the case.=20

In the 1950s and early 1960s, high fidelity tube amplifiers had 0.5 = to 1.5%=20 THD at rated power output. In the 1970s, a distortion race took place = that=20 paralleled the automotive horsepower race of the 1950s: If 1% THD was = OK, 0.1%=20 was better, and 0.001% would be really awesome. The more leading zeros, = the=20 merrier. These low THD levels were primarily accomplished by increasing = negative=20 feedback to levels well beyond 40dB. We all know the results: amplifiers = that=20 sounded so bad that=E2=80=94 a real silver lining on a dark cloud = =E2=80=94 they gave birth to=20 the high-end audio industry we know today.

That brings us to the ultimate audio paradox: In a well-designed = high=20 fidelity power amplifier, the lower the total harmonic distortion at = rated=20 power, the harder the clipping; hence the worse the sound. This runs = exactly=20 counter to the popular belief of the past, a belief still widely held in = segments of the audio industry outside the high-end. Within the high-end = community, the predominant belief has been that THD has little to do = with sound=20 quality, even though most of us have experienced evidence of the inverse = correlation: mid-fi amplifiers with low THD but mediocre sound and old = tube=20 amplifiers much higher THD but wonderful sound.

To minimize the likelihood of misunderstanding=E2=80=94 inevitable = when the above=20 statement is quoted out of context=E2=80=94 let me emphasize that the = power amplifier=20 must have no serious design flaws (like low-level crossover distortion) = and must=20 be working properly. Extremely high levels of THD, over 5 or 10%, = probably=20 indicate trouble. Low harmonic distortion is still desirable in = preamplifiers=20 and line level amplifiers that have at least 10dB of headroom (a factor = of ten=20 in power) between their rated output and saturation. Low harmonic = distortion at=20 rated output only degrades the sound quality of power amplifiers.

Better measurements=20

The one conventional measurement that provides some indication of = an=20 amplifier=E2=80=99s saturation behavior=E2=80=94 THD+noise as a function = of power level=E2=80=94 has=20 several shortcomings. It emphasizes harmonic distortion at levels below=20 saturation and lacks sufficient detail above saturation to describe = actual=20 clipping. Furthermore, it measures total harmonic distortion; = hence it=20 gives far too much weight to the relatively benign second and third = order=20 distortion components.=20

The transfer and linearity curves (figures 9 and 10) are more direct indicators of audio quality and saturation behavior. The transfer curve = is easy=20 to obtain on any oscilloscope with X-Y input capability. The linearity = curve is=20 trickier because it involves differentiating the output voltage with = respect to=20 the input. This requires a digital oscilloscope. A number of issues need = to be=20 resolved before this measurement becomes a standard: How far should the=20 amplifier be overdriven? What is the ideal waveform for this = measurement? We=20 chose a 200Hz sine wave because, with a 1kHz sine wave, the = amplifier=E2=80=99s high=20 frequency limitations smoothed the curves. Would a 100Hz sine wave or a = single=20 sawtooth pulse have been any better? It would be worthwhile to publish = these=20 curves in equipment reviews, even before a standard is established, to = see what=20 can be learned.

Measurements made inside the circuit, examples of which are found in = figures=20 3-5, have great value for the equipment designer, but little value for = the=20 reviewer because different amplifiers have such different circuit = topologies.=20 There is a real need for measurements that indicate sensitivity to RF=20 interference. Paul Miller made a good first step by inserting = noise-modulated RF=20 signals into amplifiers and measuring the audible noise spectrum [5], = but his=20 descriptions were incomplete, and I am unaware of any follow-up work. =

Feedback = forever?=20

To feedback=E2=80=99s opponents, a well-designed amplifier without = feedback is preferable a similar amplifier with it. Presumably, this also includes individual devices like tubes or transistors. There is an important, = though not=20 obvious, exception that casts doubt on this view. The triode=E2=80=94 = the favorite of=20 audiophiles=E2=80=94 has built-in local negative feedback.=20

In a plate-follower triode gain stage, as the grid voltage (the input = signal)=20 increases, the plate current increases. This causes the plate voltage = (the=20 output signal) to drop. Since the plate current depends on the plate = voltage, it=20 will be lower than it would have been had the plate voltage remained = constant.=20 This, by definition, is degenerative, i.e., negative feedback: It could = be=20 eliminated by making the plate current independent of the plate voltage. = This=20 could be done inside the tube by adding a second grid, connected to a = constant=20 high voltage, between the control grid and plate. To keep the electrons = that=20 bounce off the plate and getting absorbed by the second grid, a third = grid,=20 connected to a low voltage, would have to be added between the second = grid and=20 the plate.

What would such a tube be called? A pentode, of course! With no = negative feedback, its gain and output impedance are much higher and its = linearity is=20 poorer. The sound of the triode is almost universally preferred. = Considered in=20 this light, feedback shouldn=E2=80=99t look so bad. For a tube amplifier = to be called=20 truly feedback-free=E2=80=94 in the local as well as the global = sense=E2=80=94 it would have to=20 be built entirely of pentodes. Any takers?

Feedback without fear=20

By incorporating engineering theory into computer simulation, we = have been able learn a great deal=E2=80=94 some of it new and unexpected=E2=80=94 = about the origins of=20 audio quality. The old theory was fine as far as it went; it just = couldn=E2=80=99t handle the complexity of audio amplifiers, where the devil is truly in = the=20 details.=20

The use of computer simulation to study subjective sound quality is = still in=20 its infancy. As it progresses, amplifier designs will become simpler, = more=20 elegant, and better sounding. Best of all, amateurs are now in a = position to=20 make real contributions to the art, much as they did in the early days = of radio.=20 Some excellent simulation tools are available for free, including the = evaluation=20 version of PSpice from MicroSim, and Duncan Munro=E2=80=99s excellent = web page,=20 http://duncanamps.simplenet.com/. Relevant articles appear in Glass = Audio=20 and Audio Electronics.

Extensive computer simulation and listening have led me to conclude = that=20 feedback amplifiers can have flawless sound quality, without a trace of=20 muddiness or grayness, provided that the three dangers of = feedback=E2=80=94 instability,=20 RF susceptibility, and sharpened clipping=E2=80=94 can be eliminated or = minimized. This=20 can be always be accomplished in well-designed vacuum tube = preamplifiers, but=20 there will always be a tradeoff between clipping and output impedance in = power=20 amplifiers. Because this tradeoff involves many factors=E2=80=94 = amplifier saturation=20 level, open loop output impedance, loudspeaker efficiency and damping, = etc. =E2=80=94=20 one solution will never fit all needs. The industry-wide trend towards = lower=20 negative feedback may well continue, but I will hazard the guess that it = won=E2=80=99t=20 go all the way to zero.

Although I cannot prove that feedback has no audible = drawbacks=E2=80=94 no such proof=20 is possible when the issue is subjective quality=E2=80=94 I can offer = the fig. 2=20 preamplifier line stage as evidence. When implemented with a high = quality power=20 supply, its superb sound should equal anything on the market, with or = without=20 feedback. Details of its construction (as a modified Dynaco PAS) have = been=20 published in Glass Audio [4]. The entire project, which includes = a moving=20 magnet phono stage, can be built for around $300 in parts.

In high fidelity amplifiers, the magic is in the circuit. Premium = components and skilled layout may improve the sound of a good circuit, but they = cannot save a poor one. With the knowledge gained by correlating SPICE = simulations with careful listening, we can confidently apply the right amounts = feedback to=20 the right places=E2=80=94 sparingly in power amplifiers, more generously = in preamplifiers=E2=80=94 without fear of degrading the sound. Advertising = claims of "no=20 negative feedback" should be treated with the usual skepticism. A = well-designed=20 amplifier can have excellent sound whether or not it has feedback. The = ultimate=20 judge of audio quality is, and always will be, the ear.=20

Output connections: impedance and power=20 tradeoffs

In a power amplifier with pentode output tubes (6L6GC, EL34, = 6550,=20 etc.), output impedance and power depend on the screen grid = connection.=20 The three standard connections are:

Pentode: The screen grids are connected to a constant = high=20 voltage source.
Triode: The screen grids are connected to the plates. = Its=20 performance characteristics are those of a triode; hence it is a = triode=20 in all but name.
Ultra-linear (UL): The screen grids are connected to = output=20 transformer taps intermediate (about 40% of the way) between the = center=20 and plate taps.

The following table compares = conventional=20 expectations with PSpice simulations for the Local Hero amplifier, = changing only the output tube screen grid connections.

TABLE=20 1. PROPERTIES OF OUTPUT TUBE=20 CONNECTIONS
Connection=20 (mode)	PENTODE	UL	TRIODE
Conventional=20 understanding
Output=20 power	highest	close to = pentode	1/3=20 pentode
Output=20 impedance	highest	1/3=20 pentode	1/10=20 pentode
Voltage=20 gain	highest	intermediate	lowest
PSpice simulation of Local Hero = amplifier
Output power=20 (Watts RMS)	76	68	33
Feedback=20 (dB)	20-44=20 (0.1-10kHz)	15.4	9.5
Output impedance=20 no NFB	25-370W	11.7W	4.9W
Output impedance=20 NFB	2.3W	1.9W	1.5W

Power output is measured at clipping for 50mA bias current per = tube and=20 a 480V power supply. Normal rated power output is about 20% lower. =

The UL connection is popular in classic designs because it = offers a good tradeoff between output power and impedance. Changing an = amplifier from UL to triode mode is a common modification. Triode mode has = lower output impedance, less sensitivity to loudspeaker loads, and less = feedback (hence softer clipping) if the circuit is unchanged, but = also=20 lower power. If the Local Hero is wired in triode mode, reduce C3M = and C4M=20 to 150pF. A class A2 or AB2 triode output stage [7], which can = operate=20 with grid current, would have much greater output power. It's the = best of=20 both worlds, but it comes at a price: The output stage grid must = be driven=20 by a transformer-coupled gain stage (limited bandwidth and = don=E2=80=99t even=20 think of feedback) or by direct-coupled cathode followers, which = greatly=20 complicates the power supply. This has been accomplished in The=20 Emperor's New = Amplifier.

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=20 Koren, a native of Rochester, NY, received a BA in physics from Brown = University=20 in 1965 and an MA in physics from Wayne State University in 1969. His = destiny as=20 a 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 1.=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 = amplifiers was=20 his passion between about 1990 to 1998.

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