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An input signal with a certain characteristic is digitized using an N-bit ADC with a fixed input range. The SQNR is 32 dB when N is 7. What should the minimum value of N be if you want an SQNR of at least 46 dB

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ajeigbeibraheem

Answer:

10

Explanation:

From the information given:

The input for a fixed voltage range for SQNR when N = 7 is 32 dB

Required: To find the minimum value of N such that SQNR ≥ 46 dB

For an ADC:

SQNR = 6.02(N) + 1.76 dB

Comparing both SQNR such that SQNR₁ = 32 dB and SQNR₂ = 46 dB

Taking the ratio:

[tex]\dfrac{32 - 1.76}{46-1.76}= \dfrac{7}{N_{minimum}}[/tex]

[tex]\dfrac{30.24}{44.24}= \dfrac{7}{N_{minimum}}[/tex]

[tex]N_{minimum} \times 30.24 = 44.24 \times 7[/tex]

[tex]N_{minimum} = \dfrac{44.24 \times 7}{30.24}[/tex]

[tex]N_{minimum} = 10.24[/tex]

[tex]N_{minimum} \simeq 10[/tex]

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