# Seemingly Simple Circuits, User-Proof External Supplies: Circuit 1, the Primitive One-BJT Current Limiter

Ordinary power supply design includes current limiting as a protection feature. In product design, this is usually sufficient in that the engineer decides the loads on the supply by design. However, in some applications a supply must be brought outside the box where it enters the realm of the user. Examples include sensor bridge and solid-state relay (SSR) supplies for data acquisition systems and USB power of computer peripherals. There are multiple commercial products for protected USB supplies but these are not always optimal for non-USB applications.

This three-part article presents three simple circuits that can drive a current-limited supply port intended for use by a potentially terminal-shorting user. The goal is a circuit that has a maximum short-circuit current by design so that this amount of current can be budgeted in the design of its internal source supply. These circuits also use less than half a dozen parts and are low in cost.

Primitive One-BJT Circuit

The first circuit is primitive but provides a conceptual place to start. It is shown below. Following the general scheme used in low-dropout linear regulators, this circuit uses a PNP BJT to pass current to the output. One transistor and two resistors is simple, but the behavior is limited. The maximum, short-circuit output current is calculated by applying the β transform to the base resistance, RB , placing it in the emitter as RB /(β + 1) along with RE . Then at most, For a 2N2907, VBE ≈ 0.78 V at an IO design maximum of 60 mA, and a typical β = 150. Using an internal 5 V supply, V = 5 V. We have two resistor values to choose and one constraint equation, allowing us to apply another constraint. The output voltage is affected by choice of both resistors. The larger RB is made, the higher the voltage. Ideally, VO = V , but to power SSRs, at least 3 V is needed. Then assuming VEB VCB when the BJT is in saturation. The output voltage, VO , for light loads in saturation is assuming ideal voltage saturation of the BJT so that VCE = 0 V. In practice, VCE can typically be from 10 to 50 mV. More precisely, collector open-circuit voltage with IC = 0 A is The thermal voltage, VT ≈ 26 mV at 300 K (tropical room temperature) and the reverse α , or αR , is that of the BJT operated with emitter and collector exchanged from their normal or forward configuration. Collector and emitter junctions are not symmetrical for any well-designed transistor and the minority carrier doping level of the emitter is much higher than collector (for high emitter injection efficiency and high collector-base voltage breakdown). Reversing the BJT results in low αR values. A random selection of 2N2907s from the parts drawer, plugged into the “hFE ” function on a low-cost DMM, resulted in values of 2, 4, 8, and 13. Choosing a low value as αR = 2, then a low αR = 2/3  0.67, a value well below one. Then VCE at zero collector current is about 10.5 mV.

If we choose a very light load of 1.3 μ A as a zero-scale value – about what a low-cost DMM will draw when measuring VO – then at 1.3 μ A, VBE = 0.50 V. (IS ≈ 5 fA for a 2N2907.) However, under light load the BJT is in saturation and β is much less than the non-saturated value and is determined by circuit constraints. Therefore, only the minimum value of RB is of concern. As load demand for current increases, current is diverted from base to collector until the transistor comes out of saturation and has its normal β = βF . When VO has decreased to VB , VCE = 0 V and the BJT is out of saturation. Then load current must be near the maximum. For 60 mA, VBE = 0.78 V and IB for minimum β = 100 is 600 A. Consequently RB < 4.16 kΩ.

With VBE (IO ) at 0.78 V, to make the voltage at which the BJT unsaturates as high as possible, then all the resistance should be in RB and none in RE . The problem with this is that now (referring to the IO formula) IO is most β -dependent. With a wide range of β values among manufactured parts (of 100 to 300 for a 2N2907), it would be best to make RB as small as the voltage constraint will allow and maximize RE ; The conflicting criteria between maximizing VO and  independence make the circuit rather unappealing. However, for a wide tolerance on IO and VO , it suffices with three parts. The basic design equations could be refined for a specified tolerance range for β , but instead we will move along to the next, slightly improved circuit having one additional resistor.

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