The Darlington emitter-follower circuit is a configuration of two bipolar transistors that provides high current gain and low output impedance. It is commonly used in applications where a high current is required with low signal distortion. One such application is in the output stage of a TTL (Transistor-Transistor Logic) gate.

The TTL gate is a widely used digital logic family that operates on the principles of transistor switching. It has a low output impedance and can source or sink current to drive other TTL gates or loads. However, the TTL gate has certain limitations in terms of its output current capability.

The Darlington emitter-follower circuit is used in the output stage of a TTL gate to overcome these limitations and enhance its performance. The main advantage of using the Darlington configuration in this application is to increase the output current capability of the TTL gate.

Explanation of the options:

a) Increase its IOL (Option A): The Darlington emitter-follower circuit provides a significant increase in the output current capability of the TTL gate. This is achieved by the high current gain of the Darlington pair, which is the product of the individual current gains of the two transistors. By increasing the output current (IOL), the TTL gate can drive larger loads or drive multiple gates without signal degradation.

b) Reduce its IOH (Option B): The Darlington emitter-follower circuit does not have a significant impact on the high-level output current (IOH) of the TTL gate. The IOH is determined by the characteristics of the input stage of the TTL gate and is not directly affected by the output stage configuration.

c) Increase its speed of operation (Option C): The Darlington emitter-follower circuit does not directly affect the speed of operation of the TTL gate. The speed of operation is primarily determined by the switching characteristics of the input and output stages of the TTL gate, as well as the propagation delay through the internal logic.

d) Reduce power dissipation (Option D): The Darlington emitter-follower circuit may actually increase the power dissipation of the TTL gate. This is due to the additional transistor in the Darlington configuration, which introduces additional voltage drops and losses. However, the increase in power dissipation is usually negligible compared to the benefits gained in terms of increased output current capability.

In conclusion, the Darlington emitter-follower circuit is used in the output stage of a TTL gate to increase its output current capability (IOL). This allows the TTL gate to drive larger loads or multiple gates without signal degradation.