The amp that I have in mind is an 18Watt. ...
Please note that it has two possible pre-amps. The one I am planning using is the “LitellB” option. A friend of mine has built an amp using both. He told me that he never uses the other one. I have heard a recording of the “LitellB” option he has made of this and it sounds great.
I want to have two channels. A “clean” channel without overdrive/distortion and a “dirty” channel, with overdrive/distortion. The “dirty” option is easy, because I will build it according to the drawing.
The clean channel is where I get stuck and is in need of some help. I was thinking to by-pass the phase invertor to get a clean channel. ...
You can't dispense with the phase inverter because it is necessary to create a push-pull signal to drive the output tubes properly.
Looking at your schematic, I believe you already have a clean channel available. The Lite IIB preamp has two input jacks, labeled Single and Parallel. The Parallel input places both halves of that 12AX7 in parallel, which will increase the gain over using a single half of the 12AX7 by around 30%. When you use the Single input, you use only one triode and have somewhat reduced gain.
Further, you can't get fewer gain stages than the one triode obtained by using the Single input. So that is your clean channel benchmark. The Parallel input will increase gain some. Gain will be increased even more if you plug into the Superlite TMB input, as the pair of triodes are now cascaded, rather than being in parallel. Placing gain stages in parallel adds their individual gains, while placing them in cascade multiplies the individual stage gains.
For what it's worth, the Superlite TMB preamp is more akin to the topology of a tweed Deluxe, albeit with the tone circuit changed (to one with more flexibility but also more signal loss) and moved to a different point in the circuit.
If I were you, I'd build the entire amp as shown in your schematic. That would yield 3 channels of "Clean, More and Even More". All of these channels will play cleanly if you set the volume low enough (and the VVR high enough).
What you'd think you'll like and what you actually end up liking may be different things, and without experience and a certain knowledge of what will give you what you seek, having more option seems like a good idea.
Or, stick with the Lite IIB, as is. I bet the 18watt forum has more detail on layouts, build specifics, etc.
