darlington pair

Here is everything you need to know about the Darlington pair, compiled directly from your course materials and optimized for your exam preparation.

1. What is a Darlington Pair?

The Darlington pair (invented by Sidney Darlington in 1953) is a compound solid-state structure consisting of two bipolar junction transistors (BJTs) connected together to act as a single “Super Beta” transistor. Manufacturers often package this pair as a single composite transistor unit with only three external leads (Base, Collector, and Emitter).

2. Circuit Construction

The connection is made so that the current amplified by the first transistor is further amplified by the second transistor.

• The Connection: The emitter of the first transistor ($Q_1$) connects directly to the base of the second transistor ($Q_2$).
• Shared Terminal: Both transistors share the exact same collector terminal.
• Configuration: The setup effectively functions as two cascaded Common-Collector (emitter-follower) stages.

3. Key Characteristics & Advantages

• Massive Current Gain: The most significant feature of the Darlington connection is that its overall current gain (${\beta }_D$ or $A_i$) is the product of the current gains of the two individual transistors (${\beta }_D={\beta }_1{\beta }_2$). Commercially available integrated Darlington pairs can have a short-circuit current gain ($h_{fe}$) as high as 30,000.
• High Input Impedance: It provides an incredibly high input impedance compared to a single-stage emitter follower.
• Space Saving: Because the two transistors share the same collector, the Darlington pair occupies less physical space on a circuit than two individual discrete transistors.
• Output Characteristics: It maintains a low output impedance and provides a voltage gain that is slightly less than 1 (which is characteristic of emitter-followers).

4. Disadvantages

The primary disadvantage of the Darlington pair is its high base-to-emitter voltage drop ($V_{BE}$).

• Because the two base-emitter junctions are in series, the overall base-to-emitter voltage is the sum of both drops: $V_{BE}=V_{BE1}+V_{BE2}$.
• If both are silicon transistors, the total drop is $0.7\text{V}+0.7\text{V}=1.4\text{V}$.
• If $Q_1$ is silicon and $Q_2$ is germanium, the drop is $0.7\text{V}+0.3\text{V}=1.0\text{V}$.

5. Mathematical Proof of Current Gain

You can prove the massive current gain using either general transistor formulas or $h$-parameters:

• General Beta Proof: The input current to the system is $I_{B1}$, and the final output current is $I_{E2}$. For the second transistor, the emitter current is $I_{E2}={\beta }_2{I}_{B2}$ (assuming $\beta \gg 1$). Because the emitter of $Q_1$ feeds directly into the base of $Q_2$, we know that $I_{B2}=I_{E1}$. Since $I_{E1}={\beta }_1{I}_{B1}$, we can substitute this into the first equation to get $I_{E2}={\beta }_2({\beta }_1{I}_{B1})$. Therefore, the total current gain $A_i=\frac{I_{E2}}{I_{B1}}={\beta }_1{\beta }_2$.
• $h$-parameter Proof: When analyzing the pair as cascaded Common-Collector stages using simplified hybrid parameters (assuming $h_{oe}{R}_e\le 0.1$ and $h_{fe}{R}_e\gg h_{ie}$), the overall current gain $A_i$ simplifies precisely to $h_{fe1}{h}_{fe2}$.

6. Practical Application: Touch Sensor

A common practical use of the Darlington pair is in touch sensor circuits. If a person touches a sensor wire connected to the base of $Q_1$, a microscopically small current flows through their finger into the circuit. Because of the Darlington pair’s “Super Beta” amplification (${\beta }_1\times {\beta }_2$), this tiny current is amplified enough to easily light up an LED connected to the circuit.

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PYQ Analysis & Questions on Darlington Pair

Based on the past year questions from ECE 1209, the examiners treat the Darlington pair as one of the most important multistage circuits.

The Pattern Shift: There has been a distinct shift in how the professor asks about this topic.

• Pre-2019: The exams rigorously tested your ability to mathematically derive the current gain using the $h$-parameter model.
• Post-2019: The exams have shifted away from the heavy mathematical derivations and now strictly ask you to explain the physical working principle and draw the circuit diagram.

Exact Past Year Questions to Practice:

Type 1: The Modern Conceptual Question (Highly Repeated)

• “Briefly explain the working principle of Darlington pair circuit using necessary diagram.” (Asked in 2024, 2023, 2019)

Type 2: The Classic Derivation Question (Less frequent now, but important for safety)

• “What is Darlington pair circuit? Derive the expression for current gain ($A_i$) of Darlington pair using h-parameters and comments on the obtained expression.” (Asked in 2018, 2017, 2015) (Note: When the prompt asks for “comments on the obtained expression,” you simply need to state that the derived formula proves the composite transistor pair acts as a single unit whose total current gain is essentially the product of the individual current gains).