Beyond THD+N: Exposing Low-Level Crossover Distortion in Audio Power Amplifiers
Beyond THD+N: Exposing Low-Level Crossover Distortion in Audio Power Amplifiers
A comparative 1 kHz study of an Allen Eaton 45 Monoblock and the Dayton Audio APA150 at 2.80 V and 1.00 V output
Scope of this study
This is an academic measurement exercise focused on how distortion structure changes at low output power. It is not a generalized comparison of tube versus solid-state amplification, nor is it a controlled listening trial. The two amplifiers were deliberately chosen because their subjective presentations are very different and because the measured spectra provide a useful contrast.
Abstract. Conventional amplifier specifications usually reduce nonlinear behavior to a single value such as THD or THD+N. That number is useful, but it can conceal the harmonic structure that created it. This study compares a 45-triode Allen Eaton monoblock used as a golden reference with a Dayton Audio APA150 Class A/B amplifier at two deliberately low output levels: 2.80 V RMS (approximately 0.98 W into 8 Ω) and 1.00 V RMS (0.125 W into 8 Ω). These levels are relevant to high-sensitivity domestic loudspeakers, where normal listening often requires only a fraction of a watt. The results show a striking contrast: the Allen Eaton has substantially higher total harmonic distortion because it is dominated by second harmonic, while the APA150 shows a lower total figure but a persistent sequence of higher-order odd harmonics consistent with crossover nonlinearity. The distinction becomes especially clear at 1.00 V, where the APA150 odd-harmonic “comb” remains prominent while the Allen Eaton higher-order products collapse toward the measurement floor.
Why test at only one watt — and below?
Power-amplifier measurements are often presented near rated output, where large signal swing produces impressive signal-to-noise ratios and where some amplifiers measure at their best. That operating point is not necessarily representative of a high-sensitivity loudspeaker in a domestic room. For a nominal 8 Ω loudspeaker rated at 92 dB sensitivity at 2.83 V/1 m, a stereo pair at 2.5 m produces approximately 78 dB SPL in free-field conditions from only 1.00 V RMS per channel. The 2.80 V test corresponds to about 87 dB SPL under the same simplified assumptions. Room reinforcement will generally reduce the power required further, while musical peaks can demand more headroom.
The calculation is intentionally simple: speaker sensitivity is adjusted by 20 log10(V/2.83), approximately +3 dB is allowed for a pair of loudspeakers, and free-field distance loss is 20 log10(2.5). It is not intended as a room-acoustics model; its purpose is to show that 1.00 V is not an exotic “bench-only” condition. For a 92 dB-sensitive system, it is directly in the neighborhood of normal 75–80 dB listening levels.
Figure 1. Estimated stereo SPL at 2.5 m for a pair of 92 dB-sensitive, nominal 8 Ω loudspeakers. The 1.00 V test falls directly in the normal domestic listening window; 2.80 V represents approximately 1 W and provides useful peak-level context. Free-field estimate; no room gain included.
The two amplifiers
Allen Eaton 45 Monoblock — golden sample. The reference amplifier uses the Type 45 directly heated power triode. Historical tube data places the 45 in the very-low-power class: typical single-tube Class A operating examples are roughly 1.6–2 W depending on operating point. [1] The unit used here was selected because it is subjectively familiar and consistently produces the type of presentation I associate with very high-quality low-power amplification.
Dayton Audio APA150 — DUT. Dayton identifies the APA150 as a Class A/B amplifier using discrete output transistors. The current product page specifies 75 W per channel into 4 Ω, 150 W bridged into 8 Ω, THD below 0.01%, and an unweighted SNR above 100 dB. [2] Those published figures describe the product in conventional specification terms; the present study asks a different question: what does the distortion spectrum look like at the fractions-of-a-watt levels that may dominate real listening on sensitive loudspeakers?
Subjective listening context
My listening assessment of the Allen Eaton is a beautiful, lush, rich and dynamic presentation with excellent soundstage depth, and an ability to render instruments and vocals with lifelike realism. By contrast, I hear the APA150 as grainy and etched, with a comparatively flat soundstage. These impressions are the reason these two amplifiers were selected as deliberately contrasting examples. The measurements below correlate with those observations, but correlation is not proof of causation; a controlled, level-matched blind trial would be required to establish audibility rigorously.
Measurement setup and procedure
A 1 kHz sine wave was used so that individual harmonics could be resolved cleanly and compared directly. The signal source was an SMSL D300 DAC. SMSL specifies the D300 around a ROHM BD34301EKV converter and quotes THD+N as low as -116 dB, making it a suitably low-distortion source for this type of experiment. [3] The amplifier output was terminated in an 8 Ω dummy load.
A physical oscilloscope was connected across the load and used to establish output voltage from the measured peak-to-peak waveform. For a sine wave, Vrms = Vpp / (2√2), so the nominal setpoints are approximately 7.92 Vpp for 2.80 V RMS and 2.83 Vpp for 1.00 V RMS. The amplifier output was then captured with an E1DA Cosmos ADC and analyzed in Virtins Multi-Instrument.
Within Virtins, the Spectrum Analyzer and DDP Array Viewer were used. The report selected was “A-Harmonic Frequencies, RMS, Phases,” which provides harmonic order, frequency, RMS magnitude and phase for each component. Virtins documents this report explicitly and also describes using harmonic magnitudes and phases to synthesize a distortion residual after removing the fundamental. [4][5] The exported arrays were used here through H20.
Measurement signal chain
| SMSL D300 1 kHz source |
Amplifier under test |
8 Ω dummy load |
E1DA Cosmos ADC |
Virtins Multi-Instrument |
Oscilloscope connected across the 8 Ω load to set the required Vpp before each capture.
Why the harmonic distribution matters more than one THD number
THD is the root-sum-square of the harmonic components. It deliberately discards their identity. A spectrum containing mostly H2 can therefore return a larger THD number than another spectrum containing a ladder of H3, H5, H7, H9 and higher products. The two conditions are mathematically different and potentially perceptually different, yet a single THD figure cannot explain why.
This limitation is not merely philosophical. Geddes and Lee reported that, for the nonlinear-distortion stimuli in their 2003 AES study, conventional THD and IMD metrics did not show a significant relationship with subjective ratings, while a perceptually weighted metric did. [6] More recent AES work has likewise examined how conventional nonlinear-distortion indicators can omit or obscure components that matter to the overall distortion picture. [7] These studies should not be read as “THD is useless”; rather, they support the narrower point that THD is incomplete when used without spectral context.
Low-level testing is particularly relevant for Class A/B output stages because crossover nonlinearity occurs around the handoff between complementary devices. Audio measurement literature has long used low-power tests, including the conventional 2.83 V into 8 Ω condition, specifically because non-ideal crossover behavior can become easier to see when the amplifier is not operating near full output. [8]
Results at 2.80 V RMS: approximately one watt
At 2.80 V RMS, the two amplifiers already look fundamentally different. The Allen Eaton is dominated by H2 at approximately -37.4 dBc and H3 at about -56.4 dBc. Above that, the spectrum drops rapidly: H5 is around -84 dBc, H7 about -96.5 dBc, and most of the higher products are near or below -100 dBc.
The APA150 shows the opposite pattern. H2 is very low, around -79.5 dBc, but H3 through H19 form a persistent odd-order sequence. H3 is roughly -66.1 dBc, H5 -67.5 dBc, H7 -68.6 dBc, H9 -69.5 dBc, H11 -70.3 dBc, and the series continues only slowly downward through H19. The even-order components between them are typically far lower, producing the visually obvious alternating comb associated with a relatively symmetrical nonlinearity.
Figure 2. Harmonic spectrum at 2.80 V RMS nominal output. Levels are recalculated from the Virtins percentage column and expressed in dBc relative to the 1 kHz fundamental. The Allen Eaton is dominated by low-order even distortion; the APA150 develops a persistent higher-order odd-harmonic sequence.
The aggregate numbers are counter-intuitive if viewed without the spectrum:
| 2.80 V metric | Allen Eaton 45 | Dayton APA150 | Interpretation |
|---|---|---|---|
| H2–H20 harmonic sum (THD) | 1.365% | 0.102% | The tube amplifier has the larger total number. |
| Odd-only harmonic sum | 0.151% | 0.101% | The totals are similar, but their order distribution is not. |
| Even-only harmonic sum | 1.356% | 0.0109% | Allen Eaton distortion is overwhelmingly even-order. |
This is the central lesson of the first test: a simple ranking by THD would declare the Allen Eaton “worse” by more than an order of magnitude. Yet that ranking throws away the most interesting information — the Allen Eaton’s distortion is primarily a smooth second-harmonic component, whereas the APA150 distributes a much smaller total amount of energy across a long series of odd harmonics.
The phase data adds another useful perspective. Using the Virtins harmonic magnitudes and phases, the H2–H20 components can be re-synthesized after removing the fundamental. The resulting residual is not a direct oscilloscope capture; it is a phase-aware reconstruction of the measured harmonic content with broadband noise excluded. That makes waveform shape easier to interpret.
Figure 3. Phase-aware synthesized distortion residual at 2.80 V RMS, reconstructed from H2–H20 and aligned to the fundamental. The Allen Eaton residual is predominantly smooth and sinusoidal because H2 dominates. The APA150 residual contains a narrow feature around the fundamental zero crossing, consistent with the spectral signature of crossover nonlinearity.
Results at 1.00 V RMS: the normal-listening test
The 1.00 V condition is arguably the more important measurement for the loudspeaker scenario considered here. Into 8 Ω it is only 0.125 W. With a pair of 92 dB-sensitive loudspeakers at 2.5 m, the simplified free-field estimate is about 78 dB SPL — almost exactly the normal listening range that motivated the study.
At this lower output, the Allen Eaton becomes cleaner in the higher orders. H2 falls to about -46.3 dBc, H3 to -69.3 dBc, H5 to roughly -93.6 dBc, and most products from H7 upward sit around -100 dBc or lower. Its distortion is even more clearly concentrated in H2.
The APA150 does not follow that pattern. Its odd-harmonic comb remains strong: H3 is approximately -62.9 dBc, H5 -65.5 dBc, H7 -67.6 dBc, H9 -69.6 dBc, H11 about -71.4 dBc, and the sequence remains visible through H19. In other words, the distortion mechanism does not simply disappear as output power falls into the region most relevant to sensitive loudspeakers.
Figure 4. Harmonic spectrum at 1.00 V RMS (0.125 W into 8 Ω). The Allen Eaton higher-order products fall sharply, while the APA150 maintains a broad odd-order harmonic comb across the audible band.
Again, the total harmonic number alone gives a misleadingly simple ranking:
| 1.00 V metric | Allen Eaton 45 | Dayton APA150 | Interpretation |
|---|---|---|---|
| H2–H20 harmonic sum (THD) | 0.488% | 0.113% | Allen Eaton still has the larger total. |
| Odd-only harmonic sum | 0.0342% | 0.1128% | APA150 now has over 3× the odd-order RMS sum. |
| Even-only harmonic sum | 0.486% | 0.0119% | Allen Eaton remains overwhelmingly H2/even-order. |
Figure 5. Phase-aware synthesized distortion residual at 1.00 V RMS. The Allen Eaton residual remains smooth and dominated by H2. The APA150 retains a concentrated feature around the zero crossing, now occurring at an operating level directly representative of normal listening on high-sensitivity loudspeakers.
What changes as the level is reduced?
Looking only at the odd-order products makes the trend easier to see. The Allen Eaton higher-order odd products generally move downward as the amplifier is reduced from 2.80 V to 1.00 V. The APA150 retains a much flatter odd-order slope, with H3 and H5 becoming more prominent relative to the fundamental at the lower level. This is the behavior that makes crossover distortion particularly relevant at low power: a small transfer discontinuity can represent an increasingly important fraction of a small audio waveform.
Figure 6. Odd-order harmonic structure at both output levels. The APA150 maintains a slowly descending H3–H19 series at both 2.80 V and 1.00 V. The Allen Eaton higher-order odd products fall much more rapidly, particularly at 1.00 V.
Interpreting the result in the context of crossover distortion
The Dayton APA150 is a conventional Class A/B design. In an ideal complementary output stage, the positive and negative devices hand the signal to one another without a discontinuity. In a real circuit, insufficient bias, device transfer-function curvature, thermal conditions and finite feedback correction can leave a small kink around the zero crossing. A reasonably symmetrical kink naturally favors odd-order harmonics. The sharper the feature in the time domain, the farther its spectral energy extends into higher harmonic orders.
That is precisely the qualitative pattern seen here: comparatively weak even harmonics, a long sequence of odd harmonics, and a phase-aware residual whose energy is concentrated around the fundamental zero crossing. The evidence therefore supports crossover nonlinearity as the dominant explanation for the APA150 pattern under these test conditions. This does not imply that every APA150 sample will measure identically, nor that Class A/B amplifiers inherently sound this way. High-quality Class A/B designs can suppress crossover artifacts to extremely low levels through careful biasing, device matching, topology and error correction.
The Allen Eaton behaves very differently. Its residual is smooth and its distortion is concentrated overwhelmingly in H2, with the higher harmonics falling quickly. Even though the arithmetic THD is much higher, the waveform is not showing the narrow zero-crossing feature or persistent odd-order comb that characterizes the APA150 result.
How this relates to the listening observations
The measured contrast is consistent with the subjective descriptions that motivated the experiment. The Allen Eaton is heard as lush, rich, dynamic and spatially deep; the APA150 is heard as grainy, etched and comparatively flat. The measurements provide a plausible technical distinction that a single THD+N specification would not reveal: one amplifier concentrates its nonlinearity in low-order components, while the other produces a broad ladder of higher-order odd harmonics at the same low listening-level output.
It is important not to overstate this relationship. A harmonic spectrum is not a direct “sound-quality meter.” Audibility depends on signal content, masking, listening level, loudspeaker distortion, room acoustics and the listener. The present measurements also use a steady 1 kHz sine wave into a resistive load rather than music into a complex loudspeaker impedance. The correct conclusion is therefore not that these spectra prove the subjective adjectives. The stronger conclusion is that the two amplifiers are measurably nonlinear in very different ways, and those differences remain highly visible precisely at the low powers used in the listening system.
Why the published THD specification is not the same test
Dayton publishes a THD figure below 0.01% for the APA150. [2] The present harmonic sums are higher at these low output conditions. That should not be interpreted automatically as a contradiction or specification failure. Manufacturer figures are meaningful only with their complete test conditions: output power, load, frequency, measurement bandwidth, channel configuration, warm-up state and the exact definition of the metric. A Class A/B amplifier can also exhibit a different distortion minimum at a higher output level than it does around a fraction of a watt. The point of this article is that the normal headline specification does not describe the spectral shape at the operating point being studied.
Limitations and useful next tests
This study intentionally isolates one narrow question. Several extensions would make the picture more complete:
- Repeat the level sweep at additional voltages below 1 V (for example 0.5 V and 0.25 V RMS) to map how the odd-harmonic comb changes as the signal approaches the crossover region.
- Perform SMPTE IMD and 19+20 kHz CCIF measurements. Harmonic tests show static transfer nonlinearity well; intermodulation tests reveal how that nonlinearity creates non-harmonically related products with multi-tone signals.
- Capture a direct distortion residual in the time domain, in addition to the harmonic-synthesized residual used here, to confirm the zero-crossing feature without relying on spectral reconstruction.
- Repeat the measurements into a representative loudspeaker or simulated complex impedance. A resistive dummy load is ideal for repeatability, but real loudspeakers impose frequency-dependent magnitude and phase.
- Conduct a level-matched, preferably blind listening comparison if the goal is to establish the audibility of the measured difference rather than simply document correlation.
Conclusion
At 2.80 V and especially at 1.00 V RMS, the Allen Eaton 45 Monoblock and Dayton Audio APA150 demonstrate why amplifier distortion should not be reduced to a single THD or THD+N number. The Allen Eaton produces the larger total harmonic figure, but the distortion is overwhelmingly low-order and dominated by H2. The APA150 produces a much lower total at the 2.80 V test, yet its spectrum contains a persistent series of higher-order odd harmonics extending through the audible band. At 1.00 V — a level directly relevant to roughly 78 dB stereo listening with 92 dB-sensitive loudspeakers at 2.5 m — the contrast becomes even more consequential: the Allen Eaton’s higher orders largely disappear while the APA150 retains the odd-order crossover signature.
For high-sensitivity loudspeaker systems, the practical lesson is simple: measure amplifiers where they will actually be used. A one-watt test is useful; a one-eighth-watt test may be even more revealing. And when the goal is to understand why two amplifiers behave or sound different, inspect the harmonic spectrum and residual waveform rather than stopping at the headline THD+N figure.
References
1. RCA Type 45 tube data / historical operating data
2. Dayton Audio APA150 product specifications
3. SMSL D300 user manual and specifications
4. Virtins Multi-Instrument manual — DDP Array Viewer and harmonic reports
9. Allen Eaton Amplifiers — manufacturer information for the 45 Monoblock amplifier used in this study
Data note: All plotted amplifier data in Figures 2–6 is derived from the Virtins DDP Array Viewer exports supplied for the two devices at the two test levels. Harmonic levels shown in dBc are calculated from the report’s percentage values relative to the fundamental. Synthesized residuals use H2–H20 magnitudes and phases, with harmonic phases time-aligned to the measured fundamental.