The Darlington pair is two BJTs wired so the emitter of the first drives the base of the second, both collectors tied together. The result is a compound transistor with a current gain roughly equal to the product of the individual betas: β_total ≈ β₁ × β₂. Two ordinary transistors with β=100 each give you a compound device with β≈10,000. That's why Darlingtons dominated relay drivers, audio output stages, and solenoid switches for decades before power MOSFETs took over.

The circuit: Q1's collector connects to Q2's collector (the output). Q1's emitter feeds Q2's base directly. Q1's base is the input. Base current entering Q1 gets multiplied by β₁ at Q1's emitter, which then becomes Q2's base current, multiplied again by β₂. Tiny drive currents control large loads — a 100 µA input can switch 1 A of collector current.

Real-world example: The venerable TIP120 (NPN Darlington, TO-220 package) can switch 5 A at 60 V with a spec'd h_FE of 1000. A microcontroller GPIO pushing 5 mA through a base resistor can drive a 12 V automotive relay coil pulling 200 mA with margin to spare — no gate driver, no charge pump, no fuss. This is why every 1980s-era motor controller and every hobbyist "arduino relay board" uses one.

The hidden costs — and there are three big ones:

• Doubled V_BE drop: You need ~1.4 V at the input base to turn the pair on (two junctions in series). Compare to 0.7 V for a single BJT or ~2 V threshold for a logic-level MOSFET.
• High V_CE(sat): When "on," a Darlington drops roughly 0.7 V + V_CE(sat) of Q2, typically 0.9 to 1.5 V. At 3 A, that's 3–4.5 W of heat — brutal compared to a MOSFET's I²R loss on a 20 mΩ R_DS(on) (0.18 W).
• Slow turn-off: Q2's base has no path to discharge stored charge except through Q1's leakage. Most integrated Darlingtons include a base-emitter shunt resistor (typically 5–10 kΩ across each B-E junction) to speed turn-off and improve leakage — check the datasheet schematic; it's always drawn in.

Rule of thumb: Budget 1 V × I_load of dissipation for any Darlington output stage. At 1 A that's 1 W — manageable with a small heatsink. At 5 A it's 5 W and you need serious thermal design. If your load exceeds ~500 mA and efficiency matters, skip the Darlington and use a logic-level MOSFET instead.