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*_{BE}(sc). Under light load, the BJT saturates and as with the previous circuit, *V*_{CB}(oc)
≈
*V*_{EB}(oc) and

where *V*_{EB}(oc) corresponds to the minimum-current value. In the previous circuit this was *V*_{EB}(oc) = 0.50 V at 1.3 μA.

Solve for *R*_{i} from the *V*_{O} equation:

*R*_{B} is found by substituting for *R*_{i} in the *I*_{O} equation and solving;

To design, choose *R*_{B}. Its choice is subject to the constraint that *R*_{E} ≥ 0 Ω. The subtraction of the *R*_{E} term in *R*_{B} results in the maximum *R*_{B} when *R*_{E} = 0 Ω. Then for larger *R*_{E}, *R*_{B} must be less, and

Dependence of *I*_{O} on *β* is minimized when *δ**I*_{O}/*δβ* 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*_{i} makes the inequality easier to satisfy.

**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*_{EB} were calculated using *I*_{S} = 5 fA = 5x10^{–15} A. *I*_{S} is difficult to obtain directly from the *V*_{BE} (*I*_{C}) curves in the parts data because those curves are not exactly exponential. They include the additional linear voltage contribution of series resistance - of *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*_{BE} are calculated from the given *I*_{S} 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 *V*_{BE} curves.

*
*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*_{i}. Also,

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.