Operational Amplifier - BJTs Multiple Scaled Current Sources

In this circuit multiple scaled current sources are created using an operational amplifier and BJTs. The main/reference branch consisting Q1 simply scales the reference voltage, which is derived from a resistive voltage divider, by 1 A / 1000 V. The second branch consisting Q2 scales the reference current by 5. The third branch scales the reference current by 1/2. Transistor Q3 which is in the third branch will have the smallest current among the three. This circuit demonstrates that scaling down can be done when needed but whenever possible it might be advantageous to assign the smallest current to the main/reference branch because less approximation and error is committed in that branch. For transistor Q1: Ve1 = Ie1 · Re1 With collector current approximately equal to emitter current, Ve1 ≈ Ic1 · Re1 Ic1 ≈ Ve1 / Re1. The collector current of transistor Q1 is intended to scale the reference voltage by 1 A / 1000 V, Ic1 ≈ (1 A / 1000 V) · Ve1. So Re1 = 1 kΩ For transistor Q2: Vbe1 + Ve1 = Vbe2 + Ve2 Ve2 = Vbe1 - Vbe2 + Ve1 If the difference between the base-to-emitter voltage drops is negligible, Ve2 ≈ Ve1 Ie2 · Re2 ≈ Ie1 · Re1. With collector currents approximately equal to emitter currents, Ic2 · Re2 ≈ Ic1 · Re1 Re2 ≈ Ic1 · Re1 / Ic2. For a current ratio (Ic2 / Ic1) of 5, Re2 ≈ Re1 / 5 Re2 ≈ 1 kΩ / 5 Re2 ≈ 200 Ω. For transistor Q3: Re3 ≈ Ic1 · Re1 / Ic3. For a current ratio (Ic3 / Ic1) of ½, Re3 ≈ 2 · Re1 Re3 ≈ 2 · 1 kΩ Re3 ≈ 2 kΩ.