Simple current source with bjt

Transistors have approximately constant Vbe voltage, so the resistor Re defines what the constant current is that you want at the load, based on Vb that is defined by Zener.

The trick to understanding this design is to understand the behaviour of an emitter-follower:

^{simulate this circuit – Schematic created using CircuitLab}

The "input" here is the potential \$V_B\$, produced by source V1, and the "output" is emitter potential \$V_E\$. As I sweep input V1 from zero to +12V (blue), watch what happens to output \$V_E\$ (orange):

\$V_E\$ is always 0.7V lower than \$V_B\$, hence the name "emitter-follower":

$$ V_E = V_B - 0.7V $$

In other words, we can set whatever potential we like at emitter E, by applying a 0.7V higher potential at base B. We do that with resistor R1 and diode ZD1. Let's say that ZD1 is rated for 5.6V:

^{simulate this circuit}

By doing this we know that:

$$ V_E = V_B - 0.7 = +4.9{\rm V} $$

By Ohm's law we can find emitter current through Re:

$$ I_E = \frac{V_{RE}}{R_E} = \frac{V_E - 0{\rm V}}{R_E} = \frac{4.9{\rm V}}{4.9{\rm k\Omega}} = 1{\rm mA} $$

Since collector current and emitter current are very similar (base current is assumed to be small in comparison), that means that most of this current must be coming from the collector, through whatever's connected up there; an ammeter in this case, showing this to be true.

The circuit you’re looking at is a classic BJT-based constant current source.

R1’s job is to make sure the Zener diode is in its breakdown region, providing a stable reference voltage. When choosing R1, you need to ensure that enough current flows through the Zener so it stays in its stable operating range. You also want to consider the small base current of the BJT, though it’s usually minor compared to the Zener current. Essentially, R1 sets up a reliable reference voltage for the transistor.

Re determines the current through the transistor. The emitter current is almost equal to the collector current, so Re is the component that actually sets your constant current. The voltage across Re minus the base-emitter voltage of the BJT defines this current. One of the advantages of this setup is that the current becomes relatively independent of the load: as long as the voltage across the emitter stays roughly constant, the current will remain stable.

This circuit works as long as your supply voltage is high enough for the Zener to regulate and for the BJT to stay out of saturation. If the supply voltage drops too low, the Zener may not maintain its voltage, or the transistor may enter saturation, and the current will no longer be constant.

\$R_1\$ needs to be sized so that \$I_{\small{Z}}\approx \frac{V_{\small{SRC}}-V_{\small{Z}}}{R_1}\$, where that current is specified in the datasheet for the zener. The load current will be approximately \$I_{\small{LOAD}}\approx\frac{V_{\small{Z}}-700\:\text{mV}}{R_{\small{E}}}\$. You will need to accept the fact that there will only be a compliance voltage for the load of \$\le V_{\small{SRC}}-V_{\small{Z}}\$. And \$I_{\small{LOAD}} \le 10\cdot I_{\small{Z}}\$.