Some additional improvement in circuit performance can be achieved over the improved one-BJT current-limited supply by adding one transistor, Q2, as shown below. Ri of the previous circuit now becomes RE2 of Q2.
The basic idea is that as current through RE1 increases, the resulting increased voltage drop across RE2 will increase current in RB and increase VB, thereby limiting IE1. This simple 5-component circuit is not trivial to analyze because of the tight interaction of the two BJTs.
Analysis is simplified by the observation that the emitter current of Q1 consists of two components: the currents of RE1 and IB2. The base current of Q1 has both components, and IB1 from IB2 is IB2/(β1 + 1) or IC2/β2 x (β1 + 1). This current and IC2 flow through RB to contribute to VB and they are proportional, through the β values. Yet the IB1 component is very small compared with IC2, by a ratio of 1/β2 x (β1 + 1). The total current in RB caused by Q2 is
For a typical β value of 150, the β factor is 44.15 x 10–6 or 44 ppm. Analysis is simplified by making the approximation that this current is negligible, and omitting it. This is equivalent to having β2 → ∞. Then IB2 = 0 A. Once we know about this 1/β2 x (β1 + 1) factor, it is not hard to put it back into the subsequent equations to make them exact, as we shall see. Again, the same design goals hold as for the previous circuits.