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. *R _{i} * of the previous circuit now becomes

*R*of

_{E2}*Q*2.

The basic idea is that as current through *R _{E1} * increases, the resulting increased voltage drop across

*R*will increase current in

_{E2}*R*and increase

_{B}*V*, thereby limiting

_{B}*I*. This simple 5-component circuit is not trivial to analyze because of the tight interaction of the two BJTs.

_{E1}Analysis is simplified by the observation that the emitter current of *Q* 1 consists of two components: the currents of *R _{E1} * and

*I*. The base current of

_{B2}*Q*1 has both components, and

*I*from

_{B1}*I*is

_{B2}*I*/(

_{B2}*β*+ 1) or

_{1}*I*/

_{C2}*β*x (

_{2}*β*+ 1). This current and

_{1}*I*flow through

_{C2}*R*to contribute to

_{B}*V*and they are proportional, through the

_{B}*β*values. Yet the

*I*component is very small compared with

_{B1}*I*, by a ratio of 1/

_{C2}*β*x (

_{2}*β*+ 1). The total current in

_{1}*R*caused by

_{B}*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 *β _{2} * → ∞. Then

*I*= 0 A. Once we know about this 1/

_{B2}*β*x (

_{2}*β*+ 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.

_{1}**Circuit Analysis**

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 *I _{E1} * , as previously noted, has a

*I*component that can be separated;

_{B2}Grouping the *I _{B2} * terms together,

The last factor of the last term is

To simplify notation, let

Then when the above equation is solved for *V _{B} * ,

where

,

Then *V _{B} * simplifies to

where

G = G1 + G2

This has the form of a feedback equation with additive forward-path gains *G _{1} * and

*G*, and a feedback-path gain of

_{2}*H*= 1. This can be cast in the form of a feedback block diagram as shown below. Two input quantities contribute to

*V*.

_{B}Knowing *V _{B} * , we can now expand the

*I*equation as

_{O}*I*=

_{E1}*I*/

_{O}*α*;

_{1}Then

Using the *I _{B2} * = 0 A approximation, this simplifies to

Also,

**Measured Results for Two-BJT Circuit**

These equations were tested by setting *Q* 1 = 2N2907 with *β _{1} * = 150,

*Q*2 = 2N2907with

*β*large (

_{2}*β*→ ∞ assumption),

_{2}*R*= 20.0 Ω, 1 %,

_{E1}*R*= 1.0 kΩ, 5 %, and

_{E2}*R*= 3.3 kΩ, 5 %. The goal of the design was

_{B}*I*= 60 mA and

_{O}*V*≥ 3.5 V. With BJT

_{O}*I*≈ 5 fA, then

_{S}*V*= 0.50 V at 1.3 μA.

_{EB1}The gain values were calculated as

and *G* = *G _{1} * +

*G*= 4.3709

_{2}The output current then calculates to be

Also,

Iterating *I _{E2} * to obtain both it and

*V*, then

_{BE2}*V*= 0.655 V and

_{BE2}*I*= 0.534 mA. Then

_{E2}and

Two units of the circuit were built and measurements were taken, given in the following table.

For 5 % resistors, the agreement is sufficiently convincing.

**Design Procedure**

The equations from circuit analysis can now be put into a form useful for design, as a procedure.

Given: *I _{O} * (sc) =

*I*;

_{O}*V*(oc) =

_{O}*V*;

_{O}*V*,

*Q*1,

*Q*2 with their

*V*,

_{EB1}*V*at

_{EB2}*I*.

_{O}For Q1, Q2 matched (same type transistor), then

For *V _{EB} * cancellation in

*I*(of the effects of

_{O}*V*and

_{EB1}*V*), then

_{EB2}*V*=

_{EB2}*G*x

_{2}*V*. This is a design optimization constraint leading to

_{EB}and

Then calculate

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 *R _{E1} * to the base side of

*Q*1 and by noting that because the feedback gain,

*H*= 1, that this is equivalent to placing

*R*in parallel with

_{E2}*R*as shown below. This circuit can be reduced to a resistive voltage divider, as shown in the lower diagram.

_{E1}*V _{EB1} * is moved left to join

*V*. Then

*R*is referred to the base of

_{E1}*Q*1.

*Q*2 is assumed to have

*β*→ ∞ so that

_{2}*α*= 1. Then

_{2}*I*=

_{C2}*I*. The voltage across

_{E2}*R*is the same as that across the base-referred

_{E1}*R*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

_{E1}*I*/

_{O}*β*, and

_{1}*I*can be readily calculated from it. The result is identical to the approximated expression derived previously.

_{O}It is perhaps even more evident in this circuit form that for *β _{1} * insensitivity,

*R*<< (

_{E2}*β*+ 1) x

_{1}*R*and that consequently it must be that

_{E1}*G*>>

_{2}*G*, or that

_{1}*G*>>

*G*. Then

_{1}**Closure**

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.

Dennis,

Transistor study has always fascinated me and your analysis has reminded me of how fascinating

and agravatingit can be. man, that's a lot of work for a couple of three pin devices! I think you nailed with the word “seemingly”, because it's never simple once the equations start stacking up.But ironically this last circuit, the most complex of the three, is the only topology that's actually intuitive to me. Anyway, I have a question about your test results and would be design goals.

I'd think that the goal would be to hold the output voltage as close to 5V, in this case, as possible until current limiting kicks in. A “cliff”, so to speak. Instead, with this circuit we see a gradual slide. Would value tweaks get us there or would we need a new topology?

Thanks,

CC

CC,

A “cliff” is exactly the right idea for this circuit, and this third circuit accomplishes it better than the previous two. The second BJT helps to increase the loop gain of the current-limit response. I did not explore this too far in the articles but the equations are there for analyzing voltage fall-off after a given threshold current.

Analog circuit analysis is hard at first but it is a skill that develops over time, and in the long run, is well worth it. Even with powerful circuit simulators, some calculator-level analysis confirms that what is produced from SPICE is the right response. With algebraic equations, it is easier than in SPICE to see what variations in voltages or parts values will do to circuit behavior. This is important for optimal design.

Dennis,

From my recent work on the astable saw-tooth genorator, or whatever it shall be called, I am still in

Breadboard-Dennis'-Two-Transistor-Circuits-Mode,and I decided to go back to this briliant current limitor. I validated your results (woohoo!) and then tweaked both the emmitor resistor values to learn the behavior of the circuit. It turned out to be a good learning experience about this circuits behavior in general, but it also made me doubt its usefulness as a current limiter. In other words, it does operate predictably as a current limitor but that comes at the massive expense of voltage. To stay at or near 5V on the curve you'd better not need much more than 5mA. As such, I'd think of this as more a protection circuit, or a shut-down circuit.Oh boy, there I go with the names again, right? Maybe not. I'm open to the possibility that I am missing this circuits full potential. Perhaps if the pass transistor would be beefier and the Re1 were much smaller it would work well sourcing more current? Are there some other real-world examples out there that you can direct me to? Thanks.

CC,

The purpose of thecircuit is to set a maximum current that can be drawn from the user terminals. That occurs when the terminals are shorted. At less current, the goal of the dsesign is to maintain a terminal voltage as close to the supply as possible, and the saturating pass transistor largely accomplishes this. By varying the resistor values, it is possible to achieve as sharp of a knee in the v-i curve as possible.

The foldback current-limiting circuit is developed in my book

Designing Waveform-Processing Circuits, chapter 1.