If it's similar to their guitar amps the power amplifier actually models some most distinctive characteristics of a generic push-pull, class-AB tube (power) amplifier. So depending on design it may introduce some degree of "coloration" to the signal reproduction chain, even when not particularly overdriven. At least their related patent describes a scheme to model high output impedance, and resulting weaker "damping factor", of generic tube (musical instrument) power amps, which in turn introduces "non-linearity" to overall frequency response because gain of power amplifier with low damping factor is effectively somewhat dependent on load impedance that varies with frequency. Frequency-dependent gain characteristics will enhance all resonant frequencies and frequencies that otherwise present a higher-impedance load. Usual effects are low end boost due to speaker's resonant frequency near their low frequency limit and gradually increasing enhancement of upper mid-range and higher frequencies due to inductivity of voice coils in general. Crossover networks, piezo tweeters and alike will introduce more "complex loads" where load impedance may peak at various different frequencies. Power amplifier with low damping factor will enhance all such peak frequency bands .
Additionally the patent describes means to emulate certain ovedrive characteristics that - at least by generic acknowledgment - are traditionally introduced by such aforementioned tube power amps: Clipping distortion is similarly somewhat gradual and "soft", and the dynamically changing clipping threshold due to "power supply sag" characteristics is also effectively modeled. Power tube grid overdrive and resulting dynamic effects like bias shifts, related introduction of crossover distortion under sustained loading, and related "blocking distortion" characteristics are also modeled.
So if it's anything like the design in their guitar amps it should be a power amplifier with characteristics and performance very similar to aforementioned tube (musical instrument) power amps. ...Particularly those aimed for guitar rigs because many "classic" tube power amplifier designs for bass amplification actually tried to - in great degree - reduce or eradicate effects of many aforementioned characteristics, particularly "sponginess" of amps with sagging power supplies, "fizzyness" and "farting out" of amps that introduce bias shifting during sustained overdrive, and excessively enhanced low end, overall signal "coloration", "flabbyness" and poor transient response of power amps with low damping factors.
I realize it's solely a matter of preference, but many bass guitar players - especially those employing more "modern" playing techniques and tonal landscapes overall - tend to prefer more "sterile" power amplification (whether tube or SS) when it comes to bass guitars. Distinct warmth, coloration, distortion, dynamic variance et cetera that works when you amplify an electric guitar may be too excessive and disturbing when one amplifies a bass guitar. The trend to prefer solid-state amplification is much more prominent with bass guitar players than it is with guitar players, and to very large degree due to generic "solid-state" characteristic of having no particular distinct characteristic, just amplifying the signal accurately and without coloration. Designs with "stiff" power supplies and high damping factors introduce characteristics perhaps more favourable to bass amplification, like overall frequency response linearity (even to complex loads like x-way bass cabs with passive X-overs) and improved definition of signal transients.
So, no disrespect to Quilter and his/theirs designs intented, but if one has interest in these amps because they are solid-state (and because traditional "linear" solid-state-ish performance is therefore expected), then it might be worthwhile to acknowledge that these amps most likely are not quite similar to such but rather categorize under label of musical instrument power amplifier, which loosely means something along the lines of: "I'm actually a signal processor / effect unit disguised as a power amplifier, and I WILL color the signal while I amplify it. That's the sole purpose of my design.". So if your preference was actually higher fidelity, more linear and accurate signal production, - the solid-state cliché - then you most likely want to steer away from employing (power-amplifying) effect units that had totally different design goals. They made this solid-state amp intentionally perform similarly to certain tube power amps.
On the other hand, there are bass guitarists who do prefer and enjoy such signal coloration effects, generally considered "tubey". For them these kinds of (intentionally signal-coloring) solid-state musical instrument power amplifiers offer characteristically similar alternatives to generic tube musical instrument power amplifiers. Yes, differences to generic, "Hi-Fi-er" power amp designs probably were somewhat underlined. But - IMO - this generalisation particularly applies to more distinctly guitar-amp-like designs. By its performance the Quilter power amp design, for example, is essentially more similar to classic vintage Bassman/Marshall power amp than it is to any classic tube power amp favoured by bassists, particularly anything even resembling the SVT. Keep in mind that classic tube power amp designs for bass guitars were - for good reasons - rarely too similar with classic tube power amp designs for electric guitars. But those are what Quilter's designs prominently "model". Not a bad thing at all, on contrary, and certainly more choices for bass guitarists overall, but just something to be aware of and keep in mind. Don't expect a Quilter amp to be a traditional solid-state amp. It's intentionally going to feature characteristics of certain tube power amps, which - however - some people do regard unpreferable in bass amplification.
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Back to the topic, master volume arrangement of Quilter amps is indeed also different to popular master volume arrangements that simply attenuate input signal to power amplifier while retaining a "fixed" output power rating. Such amps basically control perceived loudness simply by "having less to amplify" and their headroom limit remains fixed. The dilemma encountered, and already few decades old, is that if we want to use such power amp as an effect processor that intentionally generates harmonic distortion (and other associated effects) it must be overdriven past producing its rated output power, which is the point where the amp still introduces very low amounts of any harmonic distortion, and effectively that means the rig is often going to be operating at disturbingly and unacceptly loud volume levels.
Reducing output power, or more particularly just the overall "headroom", amount of produced output power where signal is still amplified within the specs quoted by that "@ x % THD" - line, can shift overdrive to take place at lower perceived loudness levels. This is not a new idea by any means. It's basically the key operating principle of schemes like PPIMVs, current starved PIs, pentode/triode switches, user adjustable power supply voltages (e.g. "Power Scaling") and alike: Basically, instead of attenuating the input signal, reduce the rated output power at which harmonic distortion still meets quoted specs. For example: Instead of 1% of THD getting exceeded at 100 watts of output power, make the amp exceed that 1% of THD in the signal already when its producing merely, say, 1 watt of output power. Various different methods to accomplish that goal are legion, and if goal is to simultaneously achieve archetypal "tube power amp-ish" overdrive characteristics not all schemes even manage to capture every nuance of such performance in stunning great detail and realism.
It may sound counter intuitive but Quilter's analog modeling circuit - albeit being entirely solid-state - for example, fairs much more realistic results in replicating performance and behaviour of overdriven push-pull, class-AB biased tube power amp than what any PPIMV or current-starved-PI -based design achieves using real, genuine vacuum tubes. Many dynamic effects overlooked or ignored by inherent nature of such circuit designs have been taken into consideration in Quilter's design and the overall result is therefore much more "realistic" than remotedly close attempts to model real tube power amp / power tube distortion by means of phase inverter distortion, which sounds very similar but lacks all related dynamic effects and nuances that explain great deal of touch sensitivity, feel, and warmth associated to tube amp overdrive. Note that such characteristics, however, may not neccessarily at all correlate with subjective preferences of what is "good tone" or even "tube amp tone", though.
But yeah, Quilter amps call for "new" approach to handle loudness control, an approach again more traditionally favoured by those guitar players: Instead of decreasing overall loudness while retaining a fixed threshold of headroom, reduce that headroom and effectively distortion will appear at lower loudness levels. This is of course just another introduction of the age old dilemma of how to define musically useful concepts like "dynamics"; Is it amp's capability to accurately reproduce high signal transients without distortion, high dynamic range so to speak, or is it increased sensitivity to generate musical effects like harmonic distortion, or perhaps increased amount of "dynamic" characteristics within such effects?
Compression, by definition, limits dynamic range of the signal and signal clipping distortion is form of compression. Then again, there are distinct effects in performance of archetypal push-pull, class-AB tube power amp circuit that are in many ways similar to expanding signal's dynamic range: Signal clipping compresses, but power supply sag can make envelope and amount of that compression very dependent on overall signal dynamics. e.g. Harder sustained overdrive automatically reduces output signal's amplitude, which in turn mimicks more pronounced envelopes of signals that do not have their dynamic range and crest factor reduced by signal compression. Crossover distortion from bias shift during sustained overdrive of power tubes is another dynamically variant effect that affects timbre of amp's distortion, effectively causing the amplifier to introduce and gradually shift between different kinds of patterns of harmonic distortion when ovedriven lightly, overdriven more heavily, and depending on time constants of that sustained overdrive condition. So it can again make the amp react more touch sensitively and "dynamically" to ovedrive even though the overdrive is inherently reducing signal's dynamic range by clipping compression.
Popular trend in bass amplification has been, however, to favour moderately linear, high power amps, with "stiff" power supplies, high headrooms and minimal chances to overdrive even if exposed to signals with HUGE dynamic range. Such performance may even be essential when one employs "slap" techniques to play bass guitar. Low frequency harmonic distortion will also more profoundly than high frequency harmonic distortion introduce the kind of intermodulation distortion that usually doesn't fit too well to generic musical contexts so greater degree of linearity is required than from, say, guitar amp. IOW, amplifying bass signals in decent magnitude of "cleanness" requires more headroom than amplifying mid-range or higher frequencies because relatively lesser amounts of harmonic distortion are tolerable due to effects of IMD involving low frequencies. For example, many intentional "harmonic generation" and "distorting" circuits / effects for bass duties rely on distorting mid-range and higher frequencies only, which gives a bit of "edge" to the tone by enhancing higher order harmonic content. BUT if low frequencies were also distorted in similar magnitude the tone would become unbearable, muddy "farting" because IMD would rise alarmingly high.
While guitar amps, especially when it comes to producing modern high-gain tones, can practically hi-pass filter at @1kHz in order to reduce IMD such technique seldom works in bass amplification. Reproduction of fundamental at full gain may not be neccessary for "strong" bass, but response that extends below mid-range definitely is. So strong, musically-pleasing, "clean" bass calls for greater output power than amplifying more mid-range oriented content.
Additionally, seeming effects of expanding dynamic range with dynamically varying envelope characteristics of the overdrive is also very popularly considered as "squishyness", which can benefit a guitar amp of certain nature, but very rarely bass amp. Perhaps even contrary. Trend of popular features to include in bass amps have for years been built-in signal compressors and limiters (not dynamic range expansion) and "stiff" power supplies to guarantee authoritive, sustained and clean reproduction of bass. High damping factors are also popular preference due to resulting flatter frequency response to all kinds of loads, improved transient response, and tighter control of the cone movement. Solid-state guitar amps have for few decades popularly employed schemes that artifically decrease damping factor and therefore introduce performance more similar to that of tube amps. Implementation is trivial and very cheap, yet implementation of that feature to solid-state bass amplifiers have never enjoyed equal popularity. There must be a reason for that, which probably is very similar to reasons why many bass guitarists also prefer solid-state amplification over tube-based. And it's not just weight, size and cost, though they are admittably part of temptation.
Anyway, what one prefers to employ as bass amplifier is naturally matter of individual and subjective preference. It is just generally interesting to see an intentionally "tube-ish" amplifier being introduced to market crowd that largely has not favoured too "tubey-ish" amplifiers. Whether they have realized that or not.