__________ number of 3-dB couplers are needed for a 64 × 64 bi-directional star coupler. 

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  1. 128 
  2. 648 
  3. 192 
  4. 4096

Answer (Detailed Solution Below)

Option 3 : 192 
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Concept:

In optical communication, a star coupler is used to distribute optical signals among multiple ports. For an \( N \times N \) **bi-directional star coupler**, the number of **3-dB couplers** needed is given by the formula:

\( \frac{N}{2} \times \log_2 N \)

Given:

N = 64

Calculation:

\( \log_2 64 = 6 \)

\( \text{Number of 3-dB couplers} = \frac{64}{2} \times 6 = 32 \times 6 = 192 \)

Correct Answer: 3) 192

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