System bandwidth and tracking: For a control system to follow arbitrary input signals accurately, what should be the characteristic of its bandwidth?

Introduction / Context:
Bandwidth in control and communication systems describes the frequency range over which the system can respond effectively. A wider bandwidth indicates faster system response and better tracking of rapid input changes.

Given Data / Assumptions:

• System is linear time-invariant.
• Bandwidth is defined as the frequency at which the gain falls by –3 dB from its low-frequency value.

Concept / Approach:

To follow arbitrary inputs, particularly those containing higher frequency components, the system must have a sufficiently wide bandwidth so that these components are not attenuated.

Step-by-Step Solution:

Verification / Alternative check:

Nyquist and frequency response analysis confirm: system tracking ability correlates with bandwidth. Higher bandwidth → better tracking, at the cost of possible noise sensitivity.

Why Other Options Are Wrong:

• Small or very small bandwidth filters out higher-frequency components, making the system sluggish.
• Neither small nor large is meaningless as bandwidth must be adequate.
• Zero bandwidth would make the system static with no response.

Common Pitfalls:

• Assuming infinite bandwidth is always good; in practice, noise rejection and physical limitations must be balanced.

Final Answer:

Large.