**Darlington Pair Transistor – Circuit Diagram and its Workings:**

A very popular connection of two BJTs for operation as one “superbeta” transistor is the Darlington connection. In practice, the two transistors are put inside a single package and three terminals E, B and C are brought out, as depicted in Fig. 19.52. The main feature of the Darlington Pair Transistor connection is that the composite transistor acts as a single unit that has a high current gain (product of the current gains of the individual transistors) and high input impedance. The current gain provided by the Darlington connection is of the order of a few thousand.

**Analysis:**

Let β_{1} and β_{2} be the dc values of transistors Q_{1} and Q_{2} respectively. Then by definition.

Collector current of transistor Q_{1},

and Emitter current of transistor Q_{1},

Base current of transistor Q_{2},

So collector current of transistor Q_{2},

Now collector current,

Effective β of Darlington Pair Transistor connection

From above Eq. (19.94) it is obvious that the effective β of the Darlington connection is product plus the sum of the βs of the individual transistors. It is usually true that β_{1}β_{2} >> (β_{1} + β_{2}) so

Darlington Pair Transistor are often fabricated on a single chip to achieve matched transistors Q_{1} and Q_{2} characteristics. For β_{1} = β_{2} = β, we have the effective β of the Darlington connection

It is assumed that the dc and small signal values of β are approximately equal.

**Determination of Small-Signal Input Resistance From B to E, r _{in}_{(DP)}, and The Emitter Resistance r′_{e(DP)}, of The Composite Transistor**

We know that

AC resistance looking into the base of transistor Q_{2},

Now

Since I_{E2} = β_{2}I_{B2} = β_{2}I_{E1}, we have

Substituting I_{E1} = I_{E2}/β_{2 }in Eq. (19.99) we have

The total effective resistance looking into the base of transistor Q_{1}, (across the composite B-E terminals), i.e. the effective small-signal input resistance of the Darlington connection,

Substituting r′_{e1} = β_{2}r′_{e2} from Eq. (19.100) we have

Since β_{DP} ≈ β_{1}β_{2}, the effective emitter resistance