The improved one-BJT current-limiting supply is not much different than the primitive circuit, though its one additional resistor does change the circuit behavior. The improved circuit is shown below.

Analysis quickly proceeds by Thevenizing the base circuit and β-transforming the Thevenin base resistance to the emitter, resulting in the following equivalent circuit.

When the BJT is not saturated, the output current is a maximum of

where *V _{BE} * (

*I*) =

_{O}*V*(sc). Under light load, the BJT saturates and as with the previous circuit,

_{BE}*V*(oc) ≈

_{CB}*V*(oc) and

_{EB}where *V _{EB} * (oc) corresponds to the minimum-current value. In the previous circuit this was

*V*(oc) = 0.50 V at 1.3 μA.

_{EB}Solve for *R _{i} * from the

*V*equation:

_{O}*R _{B }* is found by substituting for

*R*in the

_{i }*I*equation and solving;

_{O}To design, choose *R _{B} * . Its choice is subject to the constraint that

*R*≥ 0 Ω. The subtraction of the

_{E}*R*term in

_{E}*R*results in the maximum

_{B}*R*when

_{B}*R*= 0 Ω. Then for larger

_{E}*R*,

_{E}*R*must be less, and

_{B}Dependence of *I _{O} * on

*β*is minimized when

*δ*

*I*/

_{O}*δ*

*β*is minimum, or whenever*R*>> (_{E}*R*||_{i}*R*)/(_{B}*β*+ 1). This compares with what was found for the primitive one-BJT circuit. For this circuit,*R*makes the inequality easier to satisfy._{i}

**Test Circuit**

To test these equations, a design was carried out and built for *I _{O} * = 20 mA using a 2N2907 BJT selected for a

*β*of 150. The

*V*were calculated using

_{EB}*I*= 5 fA = 5×10

_{S}^{–15}A.

*I*is difficult to obtain directly from the

_{S}*V*(

_{BE}*I*) curves in the parts data because those curves are not exactly exponential. They include the additional linear voltage contribution of series resistance – of

_{C}*r*

_{e}’, the ohmic emitter resistance, and*r*_{b}’, the ohmic base resistance, referred to the emitter. Additional calculation from the curves leads to the conclusion that the total effective ohmic emitter resistance is about 0.5 Ω. If the*V*are calculated from the given_{BE}*I*then the values will be somewhat low, especially for the high-current value. The easiest and most accurate procedure for design is to read the two pairs of numbers off the_{S}*V*curves._{BE}The values used in this design were

The resistor values calculate from the design formulas to be

The circuit was built with these standard +/-5 % parts values but this time a $1000 DMM (a Keithley 2000) was used to go through the 5 % resistor parts bins and select parts within about 0.1 % of these nominal values. Then

*β* dependence is reduced with *R _{E} * six times that of the base-referred resistance, showing the role of

*R*. Also,

_{i}The base divider was disconnected from the base and the measured voltage agreed with the above value in all digits. Then the $30 (DT-182) DMM was used to measure output current by placing it as an ammeter across the output, effectively shorting it. The DMMs were both used to measure voltages, and the following values resulted.

The measured value of *V* was 5.00 V. The measured values of *I _{O} * appear to verify the design equations.

This improved one-BJT current-limited source is not a bad choice for a low-cost, low-parts-count current limiting supply extender. The value of *I _{O} * , unlike the carefully value-selected prototype above, will have a spread of values corresponding to parts tolerances, including BJT

*β*. Many less-demanding applications can be satisfied by it.

By adding one more transistor, some additional improvement can be realized, the topic we consider next.

Hi Dennis,

I was able to almost derive your results, but I have a factor in my results that is different than what you obtained and I wonder if you could take a look. For example, when I try to derive the constraint on R

_{B}, I obtain the following result.R

_{B}≤(β/I_{O})*(V-V_{EB(sc)}/(V-V_{O}-V_{EB(oc}/V))Your result is similar, but I obtain a V instead of V

_{O}-V_{EB(oc)}in my denominator.R

_{B}≤(β/I_{O})*(V-V_{EB(sc)}/(V-V_{O}-V_{EB(oc)}/(V_{O}-V_{EB(oc)}))I was wondering if you could give me any insight on where to look for the problem.

Thanks

Note: Edited to correct an inequality error.

I rechecked my math from the original notebook derivation and you are right that it needs correction. Your result is slightly different that what I ended up with, though closer than my original equation. My result retains the inverted inequality sign (R sub B < =) because if you substitute for R sub i and then solve for R sub B, the R sub E term is subtracted. Consequently, if R sub E > 0 ohms, then R sub B is made smaller so that for R sub E = 0 ohms, R sub B is maximum.

Because the comment editor is not conducive to equation-writing, I have asked the editor to correct the original article. The correction also clarifies how the R sub B equation is derived.

Thanks Dennis.

You are correct about the inequality – I just typed it wrong. I am not used to typing equations using ASCII, and I should have checked my input closer.

Thanks for the interesting article.

Mark

Sorry to bother you again. Could you look at your expression for RE? You have a term, VO-VEB(SC), that my derivation shows should be V. I get all of your other expressions.

great post you have poste here

Mark,

You're right again. My notebook date for the derivation was 23MAR09 – evidently a “bad-algebra day”. Editor Steve Taranovich will be updating the text.

There are a couple of other minor errors and an omission following these formulas. The omission is that the circuit values were solved using V

_{O}= 4.0 V. TheV_{BE}open- and short-circuit values given in the derivation of the parts values are negative for a PNP and should beVinstead._{EB}Thanks again for your feedback. It is always gratifying to see a reader actually work out the math! If you use this circuit, let us know if the measurements agree with the calculated values.

Thanks for mentioning the Vo omission. I was not getting your table results and this explains the discrepancy. I have an application for the circuit and I will be building it in the near future. I will post my results as a comment to this blog post when I complete my work.

I am a big fan of your 4-volume analog design library. Keep writing up your analog work.

Mark Biegert