Natural Music Reproduction
Ideally, a pair of loudspeakers reproducing stereophonic music should be inaudible, meaning the music should be projected three-dimensionally into the listening room and not "stick" to the loudspeakers. To achieve this, in multi-way systems, the phase frequency responses of the individual speakers must be congruent for at least ±2 octaves around the crossover frequencies, the crossover frequencies must be low enough for homogeneous sound radiation with only one main radiation lobe, the power amplifiers must not produce audible distortions, and, last but not least, the bass dynamics must be sufficient to create an authentic musical experience.
1. Phase-Parallel Active Crossover
The sound quality of a multi-way speaker system is not primarily determined by the quality of the individual speakers but by the most perfect interaction of all components. Even a budget yet properly constructed tweeter can reproduce high frequencies better than the most expensive full-range speaker, and a mid-bass driver with large linear excursion and a torsionally stiff diaphragm is superior to the full-range speaker in bass reproduction. However, if the tweeter is poorly coupled to the mid-bass driver, the two-way system will sound awful, while the full-range speaker can deliver music at a relatively high level. The key factor is the crossover.
The current state of the art in passive, active analog, and active digital crossovers is explained in these four PDF files:
Analog-Audio-Passive-Crossover
Analog-Audio-Active-Crossover
Digital-Audio-IIR-Crossover
Digital-Audio-FIR-Crossover
The acoustic transfer functions of the individual speakers, which in first approximation each correspond to a second-order high-pass filter, are already taken into account in the crossover development to achieve a linear amplitude frequency response of the acoustic sum with as flat a phase frequency response as possible. This is referred to as "phase linear" or "time correct." However, the "phase linearity" (which assumes massless diaphragms, which do not exist) of the sum signal is of secondary importance because the ear is somewhat tolerant of the absolute phase frequency response of the sum. The only prerequisite is that the phase frequency responses of both stereo channels are identical; a continuous phase shift of up to 1400° from 20 Hz to 20 kHz remains practically inaudible! Far more important is the phase parallelism of the individual paths (i.e., between the tweeter, midrange, and woofer of a multi-way system), as the ear is highly sensitive to the relative phase between the individual speakers in the crossover range. Even a 10° phase difference is audible as coloration when using the best individual speakers and amplifiers. Phase parallelism has rarely been considered until now, neither with conventional analog nor digital active crossovers – and with passive crossovers, exact phase parallelism is impossible! Therefore, "soft-sounding" amplifiers are often preferred for passive multi-way speakers (which is often interpreted as the "musicality" of an amplifier) to minimize the unpleasant effects of phase errors.
While not the sole factor, the exact phase parallelism of the individual paths is generally the most important factor for the sound quality of a multi-way speaker, not the "phase linearity" of the sum. For example, if a passive 2-way speaker with the legendary "6dB crossover of 1st order" (which it actually is not, since the individual speakers themselves are second-order high-pass filters, resulting in a convoluted third-order high-pass in the high frequencies) tends to sound better than one with a "12dB passive crossover of 2nd order" (which in the high frequencies results in a convoluted fourth-order high-pass), this is not due to "linear phase" but because the overall flatter phase frequency response also improves the phase parallelism. Without sufficient phase parallelism, natural music reproduction is impossible; the sound becomes colored. Even a phase difference between the midrange and tweeter of, say, 16°, which causes only an unmeasurable dip of -0.14 dB in the crossover range, is clearly audible as coloration, and with passive systems, common phase differences of 30/40/50°, whose equivalent dips of -0.5/-0.9/-1.4 dB are still hidden within the real speaker chassis’ pressure fluctuations, color the sound even more. This leads to the oddity that full-range speakers mounted in exponential horns, even if their amplitude frequency response is significantly less balanced, still sound more natural than many conventional multi-way systems.
In the above four PDFs, the phase frequency responses of the individual paths are not shown or simply ignored. The following graphic shows the complete simulation of a typical 3-way system with a second-order passive crossover, including the transfer functions of the individual speakers and all phase frequency responses:
With conventional analog or digital active crossovers, this could hardly be improved; the resulting sound quality was more or less a matter of luck. Depending on how the individual phase frequency responses run chaotically, there are always sound colorations and spatial reproduction distortions that are not apparent from the amplitude frequency response of the sum. With the same individual speakers and, within the measurement accuracy, an identical amplitude frequency response, almost any number of multi-way systems can be built, each sounding different but never natural, because the individual phase frequency responses are always different and never exactly parallel!
However, when phase parallelism between the individual paths is not just approximated but mathematically exact within the accuracy of all frequency-determining components of the active crossover, multi-way systems behave acoustically like "ideal full-range systems" with completely natural music reproduction:
Such a result could not even be simulated until now and can be heard at Audio Optimum: The individual phase frequency responses of bass, midrange, treble, and acoustic sum are exactly congruent and no longer recognizable as separate lines. The three speakers work perfectly together, meaning in the crossover ranges, the involved diaphragms always swing in sync with the music signal, so the individual speakers are no longer audible as such, nor do they stand out from the sound image.
The Audio Optimum fully active systems show an almost perfect match between theory and practice, meaning for the first time, there is a coherent theory for multi-way systems, according to which the resulting sound quality can be specifically optimized. Previous "listening and measuring marathons," which laboriously wrung "pleasant" but not necessarily precise music reproduction from conventional high-end systems, are unnecessary for achieving the best possible sound quality. Digital sound processors are also unnecessary. To avoid producing a "digital sound" and to meet the highest standards, exact phase parallelism is achieved with an analog Linkwitz-Riley fourth-order crossover in combination with a second-order all-pass matrix and a Linkwitz transformation for each individual speaker of the multi-way system. The circuit is more complex than conventional active crossovers but represents the simplest way to make a 3-way system sound truly natural:
Simpler circuit designs do not yet allow for exact phase parallelism and therefore lead to audible sound colorations and spatial reproduction distortions. The solution is to integrate the acoustic second-order high-pass filters of the individual speakers into the LR4 high-pass functions of the crossover and the Bu6 high-pass function of the bass correction via Linkwitz transformations and to compensate the phase frequency responses of the individual paths with a second-order all-pass matrix to achieve congruence. The additional Bessel all-pass filters labeled T-Delay and MT-Delay, which are not yet dimensioned in the simulation, provide frequency-proportional phase shifts for ±2 octaves around the crossover frequencies, creating frequency-independent signal delays that can electronically shift the acoustic centers of the individual speakers. The Bessel all-pass filters are dimensioned by acoustic measurement on the real system.
2. Homogeneous Sound Radiation
Most multi-way loudspeakers still have a passive crossover, and the simple rule applies (here referred to as the "high-frequency rule") that a tweeter should be used at least one octave (factor 2) – better yet, one and a half to two octaves – above its resonance frequency. The more the high-frequency rule is violated, the more the tweeter stands out from the sound image and starts to become really annoying. This has little to do with an assumed overload, as the tweeter is also annoying at low volumes. Why and how to fix it will be explained shortly, but with the limited means of a passive crossover, this cannot be changed anyway; the high-frequency rule must at least be followed, which leads to another problem: To prevent the tweeter from becoming annoying, the crossover frequency is usually chosen so high that homogeneous sound radiation from the multi-way system is sacrificed. The only exception is a coaxial system, which, however, presents other problems, as either the coaxial tweeter is built into the woofer's magnet, causing its larger diaphragm to act as an unfavorable horn for the high frequencies, or the coaxial tweeter is mounted on a bridge in front of the woofer's acoustic center, requiring a delay correction that is hardly achievable passively. Decent coaxial systems that work reasonably well with a passive crossover are rare, so the tweeter is usually mounted above the woofer on the baffle. For homogeneous sound radiation, the sound wavelength equivalent to the crossover frequency must be at least 1.5 times the distance between the centers of the mid-woofer and tweeter diaphragms. However, this is difficult to achieve if the high-frequency rule must also be followed. For example, in a typical 2-way system consisting of an 18cm mid-woofer and a tweeter with a 10cm front plate, the crossover frequency should not be much above 1.5 kHz; otherwise, there is no homogeneous radiation (just one main lobe), but instead, three radiation lobes form due to interference in the crossover range, with the first lobe pointing at the floor, the second as desired forward, and the third, as unwanted as the first, toward the ceiling. At the often-chosen crossover frequency of 2.5 kHz for a typical 2-way system, the unwanted sound radiation in the crossover range – where the ear is particularly sensitive – is already significantly more energetic than the desired radiation.
The high-frequency rule results from the fact that a tweeter, like any second-order high-pass filter, rotates the phase by 180° around its resonance frequency f0. Far below f0, the phase is +180°, at f0 it is exactly +90°, and only far above f0 does the phase approach 0°. The steepness of the transition from +180° to 0° is determined by the quality factor Qtc. If the tweeter is operated too close to its resonance frequency, the phase alignment between the mid-woofer and tweeter is completely off, resulting in cancellation at the lower end of the crossover range, making the tweeter sound unpleasantly prominent. When operated with a passive crossover, the tweeter always sounds somewhat unpleasant, only to varying degrees. Moving the tweeter backward relative to the mid-woofer (stepped baffle) does not help either, as the phase shifts due to mechanical displacement of the acoustic centers of the individual speakers, the phase rotations of the crossover, and the phase rotations of the speakers due to their mass-spring system are three different issues. These three causes of insufficient phase parallelism cannot compensate for each other, but each must be addressed separately – and this can only be done completely with the phase-parallel active crossover described here!
3. SINCOS Full-Bridge Amplifier
The Sinus-Cosinus Modulator (US Patent 9,287,826) comes closer to the ideal audio amplifier than any other known circuit principle. As self-oscillating PWM (Pulse Width Modulation) amplifiers with a switching frequency independent of the modulation degree, the SINCOS® full-bridge amplifiers used exclusively by Audio Optimum are fundamentally superior to all classic analog power amplifiers, whether built with transistors or tubes. There are no significant heat losses, and no audible distortions occur up to maximum power. The driven speakers have no chance to develop a life of their own because the PWM full-bridge amplifiers control the back-EMF induced in the voice coil and feed it back into the supply voltage. Unlike lossy Class-A or Class-AB amplifiers, which sound "strained" at high volumes, SINCOS® amplifiers can reveal the finest musical details and reproduce even extreme volume levels effortlessly because the ultra-fast switching power transistors with minimal on-resistance do not even notice the load, no matter how complex.
When multi-way speakers with insufficient phase parallelism are operated with high-resolution SINCOS® full-bridge amplifiers, the phase errors become clearly audible. The tonal "hardness" arises precisely when operated with a maximally linear amplifier! To make a passive multi-way speaker sound "pleasant," it can be driven by a non-linear "soft" amplifier, whose second harmonic distortion K2 predominates over the higher and non-harmonic distortion components. Depending on the spectral distribution of the distortion components, the "softness" of the sound changes, which, in combination with the specific phase errors of conventional multi-way speakers, defines the "character" of a passive amplifier-speaker combination. What this has to do with "high-end" remains questionable, but it answers the question of why studio monitors and hi-fi speakers were developed in different directions, even though they are both supposed to do the same thing: reproduce music – and in the case of film sound, also speech and sound effects – as authentically as possible.
A classic studio monitor is meant to be analytical and neutral (so the sound engineer hears what they are producing) and is developed primarily through measurement/theory, while a classic hi-fi speaker is meant to be pleasant and engaging (so it doesn’t sound "unpleasant") and is therefore developed aurally/practically (or predominantly empirically). To a sound engineer, a conventional hi-fi speaker is "inaccurate" and "too flattering," while the hi-fi enthusiast finds a conventional studio monitor "unmusical" and "rather boring." In both cases, the cause is insufficient phase parallelism and the resulting discrepancy between the theoretical and practical development of conventional multi-way speakers, with exceptions proving the rule.
It’s a different story with the phase-parallel active crossover. Now, with various recordings (music and film sound), the qualities of the individual speakers and power amplifiers can be aurally assessed correctly, and conversely, with the best individual speakers and power amplifiers, the true quality of the recording can be heard.
4. Actively Filtered 6th Order Bass Reflex System
Anyone who has heard the compact Audio Optimum MS-8 with only 24.5 liters of net volume must wonder why large floor-standing speakers still exist at all, and in not-too-large rooms, this question can already arise with the ultra-compact MS8E with only 14.5 liters of net volume. In both cases, an actively filtered 6th order bass reflex system is used, the most effective and, with skillful tuning, also the most precise method for producing deep bass.
In combination, the phase-parallel active crossover, the SINCOS® amplifier, and the actively filtered 6th order bass reflex system enable natural music reproduction for the first time, even in a size that fits in any studio and can be integrated into any modern living room on the matching acrylic glass stand. With the greatest possible consistency between theory and practice, Audio Optimum fully active systems guarantee previously unattainable analytical accuracy and neutrality in the studio, as well as a whole new audiophile listening experience in the living room.