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Chapter 2 · Watch, then practise

Physical Layer

Relate channel bandwidth and noise to the rate at which information can be communicated. Practice capacity calculations while keeping physical assumptions and units explicit.

3 questions · 3 with related videos. Matches are based on playlist titles; broader background matches are labeled.

What to study

  • Bandwidth in hertz
  • Signal-to-noise ratio
  • Shannon capacity

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Notes

L17: Nyquist Limit Theorem, Shannon's Channel Capacity, Maximum Bit Rate with Example | DCN Lectures

Easy Engineering Classes · 13:34

Supplementary lecture on Shannon capacity, bandwidth and signal-to-noise ratio; use the question’s values for the calculation.

1. Capacity calculation

For an ideal band-limited AWGN channel, B = 3,000 Hz and linear SNR = 15. Find the Shannon capacity.

C = B log₂(1 + SNR) = 3,000 × log₂16 = 12,000 bit/s. This is a theoretical limit under the stated channel model, not a promise that a particular modem or coding scheme reaches it.

L17: Nyquist Limit Theorem, Shannon's Channel Capacity, Maximum Bit Rate with Example | DCN Lectures

Easy Engineering Classes · 13:34

Supplementary lecture on Shannon capacity, bandwidth and signal-to-noise ratio; use the question’s values for the calculation.

2. Decibels to linear ratio

A channel has power SNR = 20 dB and B = 1,000 Hz. What value goes into the capacity formula?

Convert first: SNR = 10^(20/10) = 100. Then C = 1,000 log₂101 ≈ 6,658 bit/s. Substituting the number 20 directly would confuse a logarithmic decibel value with a linear power ratio.

L17: Nyquist Limit Theorem, Shannon's Channel Capacity, Maximum Bit Rate with Example | DCN Lectures

Easy Engineering Classes · 13:34

Supplementary lecture on Shannon capacity, bandwidth and signal-to-noise ratio; use the question’s values for the calculation.

3. Bandwidth and noise tradeoff

Does doubling bandwidth always double capacity?

Only if the linear SNR stays fixed in this model. With fixed signal power and fixed noise spectral density, increasing bandwidth also admits more noise. Recalculate SNR before concluding how much capacity changes.

References