Constant current source

In the above circuit, the current $I_C$ is a constant independent of $R_L$ provided the transistor if in the active region, as in the active region, $I_C$ is determined by $I_B$. $R_B$ is assumed to be 1K$\Omega$.

$$I_B = \frac{15-0.7}{1\mathrm{K}\Omega}$$

$$= 14.3\times{}10^{-3}\mathrm{ Amps}$$

$$\mathrm{For }\beta=100,$$

$$I_C = 1.43\mathrm{ Amps}$$

$$\mathrm{At saturation,}$$

$$15-R_L\times{1.43} = 0.2$$

$$\mathrm{i.e., for active region, }$$

$$15-R_L\times{1.43} > 0.2$$

$$\therefore R_L < 10.3\Omega$$

Further, we also want the maximum power to be less than a certain value, say, 1 Watt. We have,

$$\mathrm{Power Dissipated} = V_{CE}\times I_C$$

$$\therefore, V_{CE}\times 1.43 \leq 1\mathrm{ Watt}$$

$$\Rightarrow\quad 15-R_L\times 1.43 \leq \frac{1}{1.43}$$

$$\mathrm{or,}R_L \geq 10.0\Omega$$

Therefore, for the circuit to work, we must have,

$$10\Omega\leq R_L<10.3\Omega$$

We would obviously like to increase the range for which this current source works. In the same circuit, if we now take $R_B=10K\Omega$, we get with similar calculations,

$$56\Omega\leq R_L<103\Omega$$

This is a much better situation.