Oh I forgot you mentioned germanium, so .3 instead of .65 for typical Vbe.
For Vb you need to consider the amplitude of the input voltage. Figure out a value to use for maximum input. You want Vb (at DC) low enough that the positive peak of the input is less than Vbe+VR1 or it will clip (of course you may want that if it's a distortion pedal). But you also want Vb high enough that Vce doesn't get too small and clip. That depends on the amount of gain you design and the level of Ve. It's a balancing act. Playing around with this stuff in a simulator is an easy and useful way to start understanding the compromises without smoking components.
Vc (at DC) could be about halfway between the rails, but more accurately it should be about halfway between the negative rail (ground) and a minimum Vc determined by Ve+Vce. There's a minimum Vce that should be maintained if you want to avoid distortion; what that minimum is depends on the transistor.
Ic is about the same as Ie, and you design Ie by choosing Ve and R1. If you use lower value biasing resistors on the base, Ib is negligible compared to the current through the resistors and Vb won't deviate much from a quick voltage divider calculation using R2 and R3. If you use higher value bias resistors Ib will be more significant comparitively and will cause Vb to lower, thus lowering Ve and Ie.
Notice I didn't mention β. With this method you're not choosing Ib and using β to determine Ic, you're choosing Vb which determines Ve and thus Ie (due to R1), which means you can pretty much ignore β.
For Vb you need to consider the amplitude of the input voltage. Figure out a value to use for maximum input. You want Vb (at DC) low enough that the positive peak of the input is less than Vbe+VR1 or it will clip (of course you may want that if it's a distortion pedal). But you also want Vb high enough that Vce doesn't get too small and clip. That depends on the amount of gain you design and the level of Ve. It's a balancing act. Playing around with this stuff in a simulator is an easy and useful way to start understanding the compromises without smoking components.
Vc (at DC) could be about halfway between the rails, but more accurately it should be about halfway between the negative rail (ground) and a minimum Vc determined by Ve+Vce. There's a minimum Vce that should be maintained if you want to avoid distortion; what that minimum is depends on the transistor.
Ic is about the same as Ie, and you design Ie by choosing Ve and R1. If you use lower value biasing resistors on the base, Ib is negligible compared to the current through the resistors and Vb won't deviate much from a quick voltage divider calculation using R2 and R3. If you use higher value bias resistors Ib will be more significant comparitively and will cause Vb to lower, thus lowering Ve and Ie.
Notice I didn't mention β. With this method you're not choosing Ib and using β to determine Ic, you're choosing Vb which determines Ve and thus Ie (due to R1), which means you can pretty much ignore β.
