Noise performance of radar receiver: A radar receiver has a noise figure of 10 dB at T = 300 K with a bandwidth of 2.5 MHz. What is the minimum detectable input power?

Introduction / Context:
Receiver sensitivity is defined by the minimum input power that can be detected above noise. It depends on thermal noise, bandwidth, and the noise figure (NF) of the receiver. This is a classic problem in communication and radar systems.

Given Data / Assumptions:

• Noise figure NF = 10 dB.
• Equivalent noise temperature T = 300 K.
• Bandwidth B = 2.5 MHz = 2.5 × 10^6 Hz.
• Boltzmann constant k = 1.38 × 10^-23 J/K.

Concept / Approach:

Thermal noise power P_n = k T B. Noise figure F (linear) multiplies this to give effective noise at the receiver input: P_min = F k T B. Convert NF from dB to linear for calculation.

Step-by-Step Solution:

Verification / Alternative check:

Standard radar equation references often approximate sensitivity values in the 10^-15 W range for such bandwidths and noise figures, confirming the result.

Why Other Options Are Wrong:

• 1.38 × 10^-15 W: corresponds to thermal noise without noise figure scaling.
• 7.5 × 10^-15 W or 93.15 × 10^-15 W: incorrect due to misapplication of NF.

Common Pitfalls:

• Forgetting to convert NF from dB to linear before calculation.
• Confusing thermal noise floor with receiver sensitivity (must include NF).

Final Answer:

3.45 × 10^-15 W