[LAU] Tape emulation - is it worth the effort ?

Hello all, The purpose of this post is to gather some opinions on the use of 'tape distortion' plugins. The way an analog magnetic tape recorder distorts the signal is quite complicated. The non-linear response is mainly due to the hysteresis of the magnetisation process, and how this interacts with the HF bias added to the recorded signal. Simplifying things a bit, as the tape moves past the recording head and away from it, it goes through several cycles of an hysteresis loop with decreasing amplitude, and it finally converges to some value more or less proportional to the signal. The bias signal itself does not remain on the tape, or at most at a very low level. The same process but with just a very high level HF bias is used to erase the tape. Simulating this accurately is quite complicated, and very CPU intensive. The sample rate must be at least twice the bias frequency (around 100 kHz for 'pro' equipment) and for each sample you need to evaluate the hysteresis loop up to a hundred times (depending on tape speed) to simulate the convergence. Over the past few months I've written the code to do this, with the aim to present a useful 'tape emulation' plugin at the next LAC. It uses a somewhat simplified form of the Preisach algorithm for the hysteresis. <http://kokkinizita.linuxaudio.org/linuxaudio/downloads/preisach-model.pdf> But the first results are somewhat sobering. Have a look at <http://kokkinizita.linuxaudio.org/linuxaudio/downloads/tapesaturation.png> This shows the tranfer function (recorded magnetic signal as a function of the input) for three values of the HF bias. The blue line is what you get without bias. It result in a very smooth saturation for high level signals, but a low amplitude signal will be severly distorted due to the flat region around zero. As bias level is increased, this effect is reduced and the low level gain increases up to some maximum. This is shown by the orange curve. The recommended way to set the correct bias level is to further increase it until the small signal gain is reduced by a few dB (typically 1 or 2 dB, depending on tape type). This is shown by the green curve. The central part of this is very linear (less than 1% THD). But now the smooth saturation is almost transformed into hard clipping. The sharp bend in the curve occurs when the signal amplitude is higher than the bias amplitude. The only effect that remains in a complete simulation is the result of the EQ applied to the signal to be recorded. Higher frequencies have a 'self erasure' effect (which is nicely reproduced by the simulation) and so need to be amplified. The net result is that they will saturate at a lower input level. How much EQ is required depends mainly on tape speed, higher speeds need less. At the most popular 'pro' speed (381 mm/s) this would be something around 10 dB at 10 kHz. At the higher (762 mm/s) speed typically used for 'master tapes' it's just a few dB. So what does effectively remain of the 'smooth saturation and compression' that is claimed to give tape recording its magical 'warm' character ? Is it just a myth ? I also simulated the green curve directly without going through the complicated full simulation, and honestly, to me that sounds just the same. And unless you really use very high levels (much more than would actually be used) the net effect is marginal. Maybe the hard clipping can be useful when applied to individual tracks (e.g. drums or bass), but then there are much simpler ways to do this than 'tape emulation'. Comments invited !!