July 2008

Challenges in Faithful Reproduction of Musical Peaks
A Power Amplifier Designer's Perspective
Article by Simon Thacher, Ph.D. Of Spectron Audio 

Real Life Speaker Loads

The ability of an amplifier to produce undistorted dynamic passages of music is frequently mistaken as its continuous (rms) power output rating. However, this specification is useful only to approximate the amplifier's ability to reach the desired loudness of the sound at the listening position — and no more. Alan Lofft from Axiom Audio has shown in Enjoy the Music.com ⁽¹⁾ that if you want to reproduce the illusion in your living room of standing next to a grand piano, then peaks of 109dB would be required. To reproduce realistically a peak loudness of 109dB using the speaker with a sensitivity of 88dB to 89dB located 12 feet from the listening chair, the amplifier must produce about 400 watts peak power. To reproduce realistic peaks of a rock band, the amplifier must produce 4000 watts of peak power. Nearly the same power capabilities are needed to approximate the realistic experience of a symphonic conductor at the podium.

These projections are accurate only if the speaker in question has purely resistive impedance. However, loudspeaker loads comprise complex impedances with both resistive and reactive (capacitive and inductive) components. Such impedance can be depicted as a vector with its magnitude (modulus) and angle (phase), and both vary with frequency. In general, the voltage and current waveforms, in complex impedance load, are out of phase with each other and therefore, to characterize accurately a speaker's load impedance, both modulus versus frequency and phase versus frequency plots must be known. Frequently, the phase angle is much more crucial to the speaker load than the modulus alone. Their peaks and dips, as a rule, do not coincide with each other. Because of those disparities, the resulting actual load can be very severe at frequencies that would not be intuitively obvious from looking at the separate plots.

To deal with this phenomenon, Keith Howard ⁽²⁾ introduced the figure of merit he has labeled Equivalent Peak Dissipation Resistance (EPDR). This is, simply, the resistive load that would give rise to the same peak power device dissipation as the speaker itself. Using EPDR as a figure of merit, the speakers can be compared directly with each other. It is an excellent idea, and John Atkinson of Stereophile has supported its use ⁽³⁾. However, speaker manufacturers are not utilizing it, and amplifier manufacturers are not demanding it.

Using the B&W 805 speaker, with 87.5dB/W/m sensitivity, and the powerful Music Fidelity amplifier, Howard did a number of measurements of produced peak SPL from a few recorded classical pieces. He found that peak SPL can be as high as 120dB at 10 feet from the speakers. The measured peak power at this peak was 3.4 kW. While this output is extremely  difficult to achieve we still should remember that B&W 805 is only a bookshelf speaker (albeit an excellent one) and the comparison with more difficult-to-drive speakers would be most instructive. For example, the estimate for B&W 803D for the same recordings is that its peak power requirement would be as high as 7 kW. Many speakers have even more reactive loads making truly enormous demands of the amplifier power delivery.

Power Supplies: Peak Voltage

While perhaps a very few amplifiers can deliver such a peak power, that does not mean that they can reproduce an undistorted musical event. Headroom is the more accurate measure of the amplifier's ability to reproduce large transients. These large transients can be in the form of a very loud event — e.g., the cannons in the 1812 Overture — or, more commonly, in a loud piano chord, or the rim strike of a snare drum, often heard in jazz. It is true that power is the product of voltage times current. But any amplifier's voltage headroom is limited by the power supply voltage, which thus limits the peak voltage. Spectron's amplifiers deliver among the very highest voltages in the audiophile world, using a +/- 120V supply. By comparison, most amplifiers use power supply voltages in the order of +/- 65V or even lower. (Regular non-OTL tube amplifier's power supplies have a large voltage to handle the tube plate but, as a rule, it does not translate into the large output voltage). The high voltage also yields higher energy storage (its proportional to the voltage in square) which in turn allows much better swing capability and bass performance.

An engineer evaluating an amplifier to determine the required headroom would look at the output voltage of the amplifier with an oscilloscope while playing the loudest music he would reasonably anticipate would be listened to. At Spectron we have done that. We have found that it is common in high-quality recordings to see voltages above 100V peak, with medium-efficiency speakers.

This is easy to understand if we take the example of a regular CD player with typical output of 2.2V rms (i.e., peak 3V). If we use XLR balanced output, the player's peak voltage doubles to 6V. For simplicity, let us assume that we are using a passive preamp with a gain setting at unity: 1.0. Finally, let us take a typical amplifier with common gain of 26dB (x20). You would then expect your amplifier to have this output peak voltage: 6V x 1.0 x 20 = 120V; and indeed this was what we measured. That means that when listening to the same music with most other amplifiers, the signal would be "clipped." Those amplifiers would be unable to deliver the necessary transient voltage to the speaker. The effect is that the music loses some of its lifelike qualities; the signal is distorted and the dynamics are clearly compressed.

The above example represents the situation when the preamplifier gain is unity and relatively efficient speakers are used. When the speakers (or music) demand preamplifier gain exceeding unity, even Spectron stereo amplifiers will clip. (Fortunately, the Spectron Musician III can operate in both stereo and fully balanced bridged mono modes. Fully balanced bridged operation will at least triple the rms power, and double the headroom to +/- 240 volts, delivering a staggering 7000 watts of peak power).

Power Supplies: Peak Current

Let us turn our attention to current, the other important aspect of headroom. High current is required to deliver power into a low-impedance speaker, or a medium-impedance speaker that has a dip in its impedance curve. (It is important to note that most speakers have some dips in their impedance curves. Current demands are associated with the lower music frequencies. Speakers are assigned a rated impedance — e.g., 4 or 6 ohms. However, few speakers stay within 25 percent of this value throughout the frequency range. Many well regarded speakers' impedances dip down, sometimes even lower than one ohm. When a musical note is played at the frequencies where the impedance dips, the current demands skyrocket. When this happens with amplifiers that lack large output current capability, the amplifier "current clips." Those transients will be both attenuated and quite distorted, and as a rule high frequency and bass performance will be degraded.

Duration Of The Peaks

The third very important attribute of headroom is duration. The amplifiers should not only deliver very high peak current, but also continue that current delivery long enough to play loud passages cleanly. Some 16 years ago, NAD investigated maximum power output versus duration capability before clipping; they found that musical signals demand hundreds of milliseconds of power burst for accurate reproduction of musical peaks ⁽⁴⁾.These periods of increased power demand can exceed a half-second. These results are particularly important in showing that even small degrees of clipping are clearly audible on tone burst of only 2msec duration ⁽²⁾.

Thus sufficient peak power duration is paramount to fully experiencing the complete burst of crescendo passages. This is achieved in the Spectron amplifiers by the ability to deliver peak output of 120V indefinitely, and 65 amperes for the extraordinary duration of 500 msec.

Waveforms At Clipping

When an amplifier is unable to deliver required voltage or current, by using a sensitive oscilloscope at its output, we would see that the waveform peaks are clipped. This clipping, in turn, generates harmonic distortion. This harmonic distortion contains only odd-order harmonics if the clipping is symmetrical and even-order harmonics if clipping is asymmetrical. As a rule, all amplifiers when clipping produce both odd and even harmonic output. However, transistor amplifiers produce largely odd-order harmonics, while tube amplifiers  produce largely even-order harmonics. All these harmonics increase in amplitude with higher degrees of clipping, resulting in more and more audible distortion of the audio signal. While amplifiers based on semiconductors, with increased odd harmonics, produce ear piercing sound, many tube amplifiers, when driven above their capabilities, have so called "soft" clipping which still is extremely unpleasant for people used to live concerts.

Output Stage: Heat Handling Capability

The fourth important characteristic of the amplifier's ability to reproduce required peak power is its output devices' heat handling capability. As we described above, Howard measured 3400 watts peak power to produce sound peaks of 120dB with the B&W 805 speakers. The estimate for the B&W 803 was 7000 watts. Its easy to extrapolate, that real-life speakers with more difficult loads than the B&W 803, can make huge demands of amplifier output-device heat dissipation. In such circumstances, a great deal of heat is generated very rapidly. However, if output devices can't handle these instantaneous high-power conditions they will be pushed beyond the safe operating area and without protection circuitry they will fail. On the other hand, if the amplifier's protection is activated, its output will be clipped. This is even though the speaker's voltage and current demands may be within its power supply capability. Therefore, the heat dissipating capability of the amplifier output stage is paramount in the delivery of required peak voltage and current, frequently over the periods of hundreds of milliseconds ⁽⁴⁾.

Output Stage: Thermal and Other Distortions

Rising temperature of the output devices will also cause thermal distortions, which add to the harmonic distortions caused by clipping. These distortions are particularly harmful at low frequencies, where output devices can heat and cool during a single cycle.

Therefore, high-powered solid-state amplifiers usually have large numbers of output transistors, with associated increases in heat sink size, adding to their weight. High-power tube amplifiers require large numbers of output tubes. A large number of tubes placed in parallel will decrease output impedance (resulting in widening of the bandwidth) and simultaneously increase high current delivery to the speaker. To handle the large output current, as a rule, a very large output transformer must be utilized. However, a coupling between the primary and secondary windings can decrease the efficiency of the current transfer; hysteresis loss, series inductance, distributed capacitance in the windings of the large transformer as well as other challenges create additional audible distortion such as degraded bass and top frequency performance capability. On the other hand, OTL amplifier does not have any of these problems. Moreover, it has the high voltage output helping its dynamic headroom. However, even very high power OTL tube amplifiers have a great difficulties to control loads below 3 to 4 Ohms.  This is because OTL amps lack the impedance matching advantage of an output transformer, which effectively turns its high voltage output into the high current required by medium to low impedance speakers, especially for bass drive.

Because switching amplifiers are highly efficient, only a small percentage of output power is converted into heat. Therefore, from that perspective, a switching amplifier is ideal for generating high output power. There are very few very high-powered tube amplifiers, and true high-powered solid-state amplifiers are enormously heavy and generate heat mercilessly. However, switching amplifiers, even with linear power supplies, weigh much less. For example, Spectron's stereo amplifier weighs only 52 pounds and produces negligible heat.

Negative Feedback

Additionally, when an amplifier has difficulty in delivering required power peaks, other forms of distortions will occur. For example, in transistor amplifiers the increased current drawn by speakers will cause a small voltage drop across the source — i.e., the amplifier itself — which will heavily contribute to the unpleasant so-called "transistor sound.”  In that regard, regulated power supplies can be extremely helpful. Many transistor amplifiers use global negative feedback to reduce distortions and widen the bandwidth. The crucial factor in negative feedback is transit time, the amount of time it takes from when an error is detected at the input until it is corrected at the output. For example, a typical transistor power amplifier has three primary sections: a low-noise high-gain differential input stage, feeding a differential-to-single-ended conversion driving a high-current output stage. Each of these three stages is designed for low distortion and noise, but those attributes typically come at the sacrifice of speed. The typical transit time of linear amplifiers is about 2000 to 3000 nanoseconds, which is too slow for effective implementation of global feedback and error correction. This lagging results in ringing artifacts and enhances odd-order harmonics, which are particularly annoying to the human hearing ⁽⁵⁾ so even the smallest amounts of these distortions are highly noticeable. Long delays in feedback also introduces transient and phase discrepancies, susceptibility to transient overload and vulnerability to disturbances at the output such as reactive speaker interactions.

In contrast, many switching amplifiers do not use low-distortion circuits. Instead, they use much faster digital logic circuits. The Spectron Musician III transit time is 200 nanoseconds. Such an ultra-short transit time allows the amplifier to correct for many small errors; and the control loop can follow the input much more accurately. These characteristics result in a more detailed, transparent sound with less noise and louder yet cleaner musical reproduction.

A properly designed amplifier will have power supplies capable of producing both adequate high voltage and high current capability, of holding transients for sufficiently long duration to ensure that whatever the speaker load is, the amplifier will deliver the full dynamics of the recording. In parallel, its large output devices must handle the heat and produce minimal thermal and other distortions. Such an amplifier can drive everything from conventional speakers to complex loads such as ribbon or electrostatic speakers and represent effortlessly the fury of a symphonic crescendo!

Undistorted Musical Peak:  Should We Care?

The exploration of the origin of "listener fatigue" is extremely interesting, at least, for this writer. We believe that when our subconscious mind detects a small unnatural trace of distortion in reproduced acoustic music (which is not recognized yet as a very low level irritant by the analytical part of our brain) it activates a subtle alarm. This forces the listener into the tense or alert mode. Indirectly supporting this hypothesis is the common description we hear from Spectron users who utilize the two powerful monoblock amplifiers (7 kW peak power, each): "how relaxing" is my listening now.

Footnotes

1-  Alan Lofft's writing as seen at www.enjoythemusic.com/magazine/manufacture/0907

2 - Keith Howard  "How Much Power Do I Need?" Hi Fi News July-Sept, Nov 2007

3 - Keith Howard  "Heavy Load: How Loudspeakers Torture Amplifiers " Stereophile issue July, 2007

4 - Mitchell PW "A Musically Appropriate Dynamic Headroom Test For Power Amplifiers" Audio Eng. Soc. Preprint 2504,   Convention 83, 1987-10

5 - Ralph Karsten's writing at www.enjoythemusic.com/magazine/manufacture/0707/

Company Information

Spectron Audio
9334 Oso Avenue, Unit E
Chatsworth, CA 91311

Voice: (818) 435-2090
E-Mail: info@spectronaudio.com
Website: www.spectronaudio.com