In the golden age of analog sound every link in the chain introduced warming distortions ...
If you've done any reading about tube amps you've probably noticed that much of the legendary "warmth" is attributed to the differences in the way tubes and transistors respond to overload signals. I believe this is true, as far as it goes, but it doesn't tell the whole story. Let me explain.
In the old analog days EVERY link in the signal chain, from tape to vinyl to tubes to transformers, had one interesting common characteristic: When driven to their limits they didn't just suddenly splat up against a brick wall and clip, first they gracefully compress the signal. For lack of a better term I'm going to refer to these compressing nonlinearites at the fringe of the operating range as squashing, which in the field of Computational Neurodynamics is hip slang for the "S" shaped transfer functions of brain cells. In nerve cells squashing increases dynamic range, just as it does in any signal path; but in neural systems it's even more interesting because without it multi-layer networks of neurons can't do anything that can't be done with a single layer, which isn't much. In a very real way, without squashing we wouldn't have brains at all. But I digress*.
In audio, squashing nonlinearities have other interesting properties as well. In contrast to the strong high order harmonics that result from clipping, the harmonic series produced by squashing falls off rapidly in amplitude at higher frequencies. Another useful thing to know is that when the distorted waveform is asymmetrical, which is to say more squashed on the top or the bottom, the harmonic series will not only be of low order, it will also consist of musically benign even harmonics (octaves and other justly-intoned intervals) while potentially dissonant odd harmonics go away.
One by one these squashing characteristics have been removed. The first improvement was transistors. It's difficult and expensive to make tube circuitry linear, they just really don't want to do it. Individual transistors are no more linear than tubes, but they're cheap so you can afford to use lots of them. One or more can be used in various ways to cancel out the nonlinearities of others without heavy economic or power usage penalties.
Silicon being less expensive than steel, coupling and output transformers were eliminated as higher power transistors and altered circuit topologies evolved to drive speakers directly. Enthusiasts began whispering the heresy that the new super linear Solid State amps didn't sound quite as good somehow as the old Vacuum Tube space heaters.
The next to go was vinyl, replaced by CDs. The murmuring grew louder. Net surfers began to see apocryphal messages reporting vacuum tube DACs that dramatically improved the sound of CDs. Friends confided to friends that they really preferred their "personal use" (wink, nudge) tape copies of CDs to the CDs themselves.
Analog tape has been the final squashing element to be cleansed as the editing and duplicating advantages of DAT and HD recording have made them the medium of choice among serious artists and engineers. Of course there are the renegades who still insist on going to analog tape for source recording even if they wind up in the digital domain for editing. And those that feed their DATs with Vacuum Tube pre's. Sounds better, they say; warmer, fuller.
What's going on here? You want me to stop all this self indulgent mental masturbation and take a position, don't you? OK, I will: When loafing along within their design envelopes, there is no discernible difference between Solid State and Vacuum Tube amplifiers. This has been shown again and again in well designed double blind tests. But, when asked to give just a little more than they were designed for, perfectly straight and linear (Solid State / digital) gives you garbage every time and squashing sometimes hands you magic. Maybe you know people that are this way too?
Can you design a solid state circuit that models squashing? Sure, but this isn't the only difference between Vacuum Tube and Solid State, only the steady-state one. Common tube designs respond to strong transients with dynamic nonlinearities caused by DC level shifts that are missing in op-amp circuitry. These transient nonlinearities must be duplicated too, because they're responsible for "punch". Like I said; it isn't easy. Your model will get pretty hairy by the time you're done, and it still won't have the neat rosy glow of a filament.
Why does this added complexity sound better to many professional ears? There are a lot of ideas: All natural musical instrument add harmonics when played fortissimo and this, more than volume, is how you perceive they're being played loud. Maybe we expect the signal chain to do the same thing. We've all grown up with at least some of these anomalies of sound reinforcement and recording and perhaps we've learned to expect them. It's impossible to record and reproduce anything without some artifacts of the process; if you don't think that a learned preference for an artifact is important start counting the lens flares in "photo realistically" rendered computer graphics. Maybe further evolution will select out those cro-magnon types that like tubes, but maybe even when we're able to jack-in direct to our brains the audio part of the experience will be better if it's been run through glass.
Fig 1 shows a typical triode vacuum tube. Because of the Edison Effect, heat from the filament causes free electrons to boil off of an oxide coating on the cathode. A positive voltage on the plate attracts the electrons and the moving electrons produce a current flow. A negative bias voltage on the grid repels some of the electrons and prevents them from reaching the plate, resulting in less current flow. In this way a changing negative charge on the grid modulates the plate current.
One of the sources of non-linearity in vacuum tubes is "space charge"; electrons that leave the cathode but don't make it to the plate simply accumulate. This cloud of negatively charged electrons has the same effect as a negative voltage applied to the grid - it decreases current flow. This is often referred to as "self-biasing" and it's a non-linear term because increasing negative grid voltages block electrons, which produces more space charge, which is like making the grid even more negative, and so on.
Operating a vacuum tube at low plate voltages is sometimes called "starving" it and doesn't greatly affect the number of electrons that leave the cathode, which is primarily set by filament temperature. But at low plate voltages and currents space charge becomes an even bigger factor, just as many electrons are leaving the cathode but fewer of them are winding up at the plate, and the non-linearity which is present in all tubes is exaggerated.
In PAiA tube preamps the "Starved Tube" circuitry operates at such low voltage and current that it completely self-biases. You can see this by using a high impedance oscilloscope or voltmeter to measure the voltage at the tube grids. You will find that the grid is about a Volt negative relative to ground. All of this negative voltage is the result of electrons boiling off the cathode and clouding up around the grid.
There is more on this topic in the Design Analysis sections of any of the Assembly and Using manuals for PAiA tube preamps. You can download a zipped pdf file of the TubeHead two channel preamp here.