Darlington Pair

Part of The Transistor

Two cascaded transistors acting as a single super-transistor with very high current gain.

Why This Matters

The Darlington pair, named after Sidney Darlington who patented it in 1953, connects two transistors so that the emitter of the first feeds directly into the base of the second. The combined current gain is the product of the two individual gains: hFE_total ≈ hFE1 × hFE2. With two transistors each having hFE = 100, the pair has an effective gain of 10,000.

This extreme current gain solves a specific class of problem: driving high-current loads from very low-current control signals. A photoresistor producing only microamps of current can control a relay coil drawing 100 mA. A logic gate that can source only 1 mA can drive a solenoid requiring 500 mA. A millivolt signal from a thermocouple can operate a heavy motor starter. Without the Darlington pair, each of these requires intermediate amplification stages.

For a rebuilding civilization, the Darlington pair enables direct interfacing between sensors and actuators that would otherwise require multiple stages and careful impedance matching. It is a practical building block for motor drivers, relay interfaces, power switches, and touch-sensitive circuits.

Configuration and Operation

Circuit: Q1 (the input transistor) has its emitter directly connected to Q2’s base. Q2’s emitter is the output emitter. Both collectors are connected together (or Q1’s collector connects to Q2’s collector).

Effective parameters:

• hFE_total ≈ hFE1 × hFE2 (for rough calculations; exact: hFE_total = hFE1×hFE2 + hFE1 + hFE2)
• VBE_total = VBE1 + VBE2 ≈ 1.4V (silicon) — two junctions in series
• VCEsat_total = VBE2 + VCEsat1 ≈ 0.7 + 0.2 = 0.9V (worse than a single transistor’s ~0.2V)
• r_π_total ≈ hFE1 × r_π2 — very high input resistance

The compound transistor behaves as a single transistor with extremely high gain but some performance degradations compared to a single transistor.

Switching in Darlington: To turn on, apply VBE1 (0.7V) and provide base current IB1. Q1 amplifies to emitter current IE1 = (hFE1+1) × IB1, which becomes Q2’s base current. Q2 amplifies further. Total collector current: IC ≈ hFE1 × hFE2 × IB1.

Turn-off problem: When base drive is removed, stored charge in both transistors must be swept out before the pair turns off. This is slower than a single transistor. Adding a resistor between base and emitter of Q2 (and optionally Q1) provides a discharge path for stored charge, improving turn-off speed. Typical values: 1-10 kΩ.

Design Example: Relay Driver

Drive a 12V relay coil (resistance 150Ω, current 80 mA) from a 5V microcontroller output (sourcing 1 mA maximum).

Without Darlington: A single transistor with hFE_min = 50 needs IB = 80 mA / 50 = 1.6 mA — but the microcontroller can only source 1 mA. Need intermediate stage.

With Darlington: effective hFE = 50 × 50 = 2500 (conservative). IB needed = 80 mA / 2500 = 32 µA. Well within 1 mA sourcing capability.

Circuit:

• Input: 5V logic signal through 10 kΩ base resistor to Q1 base.
• Q1 base current: (5 - 1.4) / 10,000 = 360 µA. (1.4V is 2× VBE for Darlington pair)
• Collector current: 360 µA × 2500 = 900 mA (limited by relay coil to 80 mA)
• Relay coil: between 12V supply and Q2 collector
• Flyback diode: across relay coil (cathode to 12V, anode to collector) — protects against inductive spike when relay turns off

Verification: With relay on, VCEsat ≈ 0.9V for Darlington (worse than single transistor’s 0.2V). Voltage across relay coil: 12 - 0.9 = 11.1V. Current: 11.1V / 150Ω = 74 mA — relay pulls in (typically requires 50-80% of rated current to activate).

Touch Switch Application

The Darlington pair’s ultra-high input impedance makes it ideal for touch-sensitive circuits:

The human body at 50-100 kΩ impedance provides base current when touching a sensor electrode. With hFE_total = 10,000 and 1 µA of touch-induced base current, collector current = 10 mA — enough to operate an LED or small relay.

Circuit: antenna pad connected to Q1 base through 1 MΩ resistor. Body capacitance and resistance from antenna to the base inject enough AC current (from power line interference or radio signals coupled to the body) to forward-bias Q1 under certain conditions. More reliably: connect antenna to +5V through 1 MΩ, providing small forward base current. When touched, additional current path through the body to ground (via power line ground coupling) increases total base current, toggling the output state.

This is the simplest version of a touch or proximity switch, achievable without integrated circuits, using only the two-transistor Darlington principle.

NPN-PNP Complementary Darlington

Connecting one NPN and one PNP transistor in Darlington configuration:

• Q1: NPN, input base
• Q2: PNP, emitter to Q1’s emitter, base to Q1’s collector
• Output current flows into Q2’s emitter (which is the combined pair’s emitter terminal)

This complementary variant can be driven by either polarity signal and provides output current sinking (NPN output). Used in complementary output stages where you need a PNP Darlington with better characteristics than a straight PNP-PNP combination (PNP transistors typically have lower hFE than NPN in germanium).

Integrated Darlington Arrays

For driving multiple loads (8 relay channels, 8 motor channels), a Darlington array integrates 8 Darlington pairs plus flyback diodes in a single package. The ULN2803 (8-channel) is the standard device. Each channel handles 500 mA collector current, 50V, with input compatible with 5V logic.

Before such integrated circuits exist in a rebuilding context, build the equivalent from discrete transistors. A 4-channel discrete Darlington array on a small circuit board, with appropriate heatsinking, serves the same purpose. Document the layout and performance so it can be replicated for different projects.

For high-current applications (1-10A, motor control), pair a small Darlington driver transistor (TIP120 equivalent) with a large power transistor. The Darlington drive stage requires only µA of input current while the output stage handles amperes.