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Seemingly Simple Circuits, User-Proof External Supplies: Circuit 3: The Two-BJT Current-Limited Supply

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.

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 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 ,

where

,

Then VB simplifies to

where

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 ;

Then

Using the IB2 = 0 A approximation, this simplifies to

Also,

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

Also,

Iterating IE2 to obtain both it and VBE2 , then VBE2 = 0.655 V and IE2 = 0.534 mA. Then

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: 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

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 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

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.

4 comments on “Seemingly Simple Circuits, User-Proof External Supplies: Circuit 3: The Two-BJT Current-Limited Supply

  1. CC VanDorne
    March 18, 2016

    Dennis,

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

     

  2. D Feucht
    March 19, 2016

    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.

     

  3. CC VanDorne
    June 21, 2016

    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.

  4. D Feucht
    June 22, 2016

    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.

     

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