Some additional improvement in circuit performance can be achieved over the improved one-BJT current-limited supply by adding one transistor, Q 2, as shown below. Ri of the previous circuit now becomes RE2 of Q 2.
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 Q 1 consists of two components: the currents of RE1 and IB2 . The base current of Q 1 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 Q 2 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.
Once we have a prospective circuit, we must first analyze it before we can best determine how to optimize its design. Hence, a few circuit equations are in order, beginning with the variable that is the functional result of the circuit, the output current;
The base voltage of Q 1 is somewhat more involved;
Now IE1 , as previously noted, has a IB2 component that can be separated;
Grouping the IB2 terms together,
The last factor of the last term is
To simplify notation, let
Then when the above equation is solved for VB ,
Then VB simplifies to
G = G1 + G2
This has the form of a feedback equation with additive forward-path gains G1 and G2 , and a feedback-path gain of H = 1. This can be cast in the form of a feedback block diagram as shown below. Two input quantities contribute to VB .
Knowing VB , we can now expand the IO equation as IE1 = IO /α1 ;
Using the IB2 = 0 A approximation, this simplifies to
Measured Results for Two-BJT Circuit
These equations were tested by setting Q 1 = 2N2907 with β1 = 150, Q 2 = 2N2907with β2 large (β2 → ∞ assumption), RE1 = 20.0 Ω, 1 %, RE2 = 1.0 kΩ, 5 %, and RB = 3.3 kΩ, 5 %. The goal of the design was IO = 60 mA and VO ≥ 3.5 V. With BJT IS ≈ 5 fA, then VEB1 = 0.50 V at 1.3 μA.
The gain values were calculated as
and G = G1 + G2 = 4.3709
The output current then calculates to be
Iterating IE2 to obtain both it and VBE2 , then VBE2 = 0.655 V and IE2 = 0.534 mA. Then
Two units of the circuit were built and measurements were taken, given in the following table.
For 5 % resistors, the agreement is sufficiently convincing.
The equations from circuit analysis can now be put into a form useful for design, as a procedure.
Given: IO (sc) = IO ; VO (oc) = VO ; V , Q 1, Q 2 with their VEB1 , VEB2 at IO .
For Q1, Q2 matched (same type transistor), then
For VEB cancellation in IO (of the effects of VEB1 and VEB2 ), then VEB2 = G2 x VEB . This is a design optimization constraint leading to
from which the final resistor value is
Non-Feedback Equivalent Circuit
A simpler equivalent circuit can be derived that does not involve feedback by using the β transform to refer RE1 to the base side of Q 1 and by noting that because the feedback gain, H = 1, that this is equivalent to placing RE2 in parallel with RE1 as shown below. This circuit can be reduced to a resistive voltage divider, as shown in the lower diagram.
VEB1 is moved left to join V . Then RE1 is referred to the base of Q 1. Q 2 is assumed to have β2 → ∞ so that α2 = 1. Then IC2 = IE2 . The voltage across RE1 is the same as that across the base-referred RE1 and the two resistances are in parallel, connecting to the base on the right side. Some Thevenizing produces the equivalent circuit of the lower diagram. Because this is a base circuit, the current is IO /β1 , and IO can be readily calculated from it. The result is identical to the approximated expression derived previously.
It is perhaps even more evident in this circuit form that for β1 insensitivity, RE2 << (β1 + 1) x RE1 and that consequently it must be that G2 >> G1 , or that G >> G1 . Then
Three variations of simple current-limiting circuits have been presented. These circuits can find use wherever a maximum current must be specified while also maintaining a minimum output voltage up to near the current-limit value. How near was not derived but some idea is given in the measurements for the two-BJT circuit. While not trivial to analyze (except perhaps the first), these circuits have less than a half dozen parts and less than a dozen cents US in cost in small quantity. The design procedures have been given, and for the two-BJT circuit, two equivalent-circuit interpretations. Hopefully, you should be able to apply any of them in your designs where appropriate.