Newbie problem with transistor switching

Question

First post, so I hope that I adhere well to all the rules.

I couldn't find any other posts that could help me, so here's my problem:

I am trying to build a simple transistor switch with a 3906 PNP transistor. The end-goal of this project is to design a circuit that illuminates one of 5 different LED's to indicate the charge of a Li-Ion battery cell.

I'm starting with the Red LED which should illuminate at ~3.3V but it illuminates at ~4.8V.

My 3906 datasheet says that the minimum base current is 50 nA, so I assembled the circuit below to generate 50 nA @ 1.6V on the base when the input reaches 3.3V. I assume the issue is that I'm biasing it badly. (I am trying to get my head around transistor theory and failing, me thinks).

Please forgive me for this terrible MS paint schematic done with a laptop mousepad.

Answer 1

This answer only uses BJTs, because you explicitly mentioned studying transistor theory. An easier solution would be to use a comparator and a voltage reference.

Original schematic

I'll repeat your schematic to make it easier to read:

I cannot reproduce the 4.8V switch on. Simulating on circuitlab shows a ~1.6V switch on (current through LED > 0.5mA).

Even if we fix the base biasing (to put \$V_{BE}\$ to ~0.6V), the switch on characteristic is quite soft.

^{simulate this circuit – Schematic created using CircuitLab}

Second stage

By adding another stage, the switch characteristic is improved:

^{simulate this circuit}