The Perelandra Boost / Overdrive is a recreation of the Xotic BB Preamp, a flexible tone machine that lets you go from a clean volume boost to a nice smooth overdrive with a 2-band EQ to shape the tone.
The BB Preamp is very similar to the Ibanez Tube Screamer, but with an active Baxandall tone control added before the output buffer so that the treble and bass can be independently boosted or cut.
In fact, if you look at the schematic for the BB Preamp, you can see that the original Tube Screamer tone control stage is left intact, but with the tone knob is fixed at 5% rotation (i.e. almost fully to the dark side of the control) by using a 1k and a 19k resistor. The main difference between the BB Preamp and the AC or RC Booster is the presence of this Tube Screamer tone control stage to shape the tone going into the Baxandall EQ.
The BB Preamp was first released in 2002, and Andy Timmons was an early and enthusiastic adopter. Xotic revised the circuit in April 2007 (serial 3643 and higher) to add a second clipping diode in each direction, which has the effect of making it a little more crunchy and transparent and less compressed and gainy.
Since Andy preferred the original circuit, Xotic released the Andy Timmons Signature version of the BB Preamp in 2009, often abbreviated as the AT or BB-AT. The post-2007 circuit was later renamed the “Version 1.5” to avoid confusion with the AT model. (Note that there is nothing that is officially called version 2. The “1.5” is just to indicate that it’s been slightly updated from Version 1, which is the AT circuit.)
Also in 2009, Xotic released the Custom Shop “MB” version of the BB Preamp. Based on the marketing copy and photos of the interior, it’s clear that this model just restores the original Tube Screamer tone control, which due to the addition of dedicated bass & treble controls later in the circuit, mainly impacts the lower and upper mids.
In 2012, Xotic released a second Custom Shop model called the “Comp”. Again, based on marketing copy and photos, this model just puts the clipping diodes on a switch, selecting between AT (one diode in each direction) and 1.5 (two diodes in each direction) as well as a diode-lift mode in the middle.