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  "slug": "comm-pcm",
  "title": "PCM & ADC — Pulse Code Modulation, Quantization, Companding, ADC Architectures — Communication",
  "category": "communication",
  "category_label": "Communication",
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  "description": "The PCM & ADC workbench covers the end-to-end pulse-code modulation pipeline. Sample a signal at F_s (≥ 2·BW by Nyquist), quantize each sample to one of 2^N levels (uniform, μ-law, or A-law), encode the level as N bits, transmit. At the receiver, decode and reconstruct with ZOH / linear / sinc filter. Compare Flash, SAR, Pipeline, and Σ-Δ ADC architectures side-by-side.",
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    "PCM",
    "ADC",
    "DAC",
    "quantization",
    "compander",
    "mu-law",
    "A-law",
    "SQNR",
    "ENOB",
    "SNDR",
    "flash ADC",
    "SAR ADC",
    "sigma-delta",
    "oversampling",
    "aliasing",
    "GATE ECE",
    "communication"
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    "formulas": [
      "Uniform quantizer: Δ = (V_max − V_min) / 2^N, max error = ±Δ/2",
      "SQNR (full-scale sine, uniform): 6.02·N + 1.76 dB",
      "ENOB = (SNDR − 1.76) / 6.02",
      "μ-law: F(x) = sgn(x)·ln(1 + μ·|x|) / ln(1 + μ), μ = 255",
      "A-law: F(x) = sgn(x)·A·|x| / (1 + ln A) for |x| ≤ 1/A, A = 87.6",
      "Σ-Δ: in-band SQNR = 6.02·N + 1.76 + (2L+1)·10·log₁₀(OSR) dB",
      "Nyquist rate: F_s ≥ 2·BW"
    ],
    "citations": [
      "Oppenheim & Schafer, \"Discrete-Time Signal Processing,\" 3rd ed., 2010, Ch. 4.",
      "Kester, W., \"Data Conversion Handbook,\" Analog Devices, 2005."
    ],
    "faq": [
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        "q": "Why is the SQNR exactly 6.02·N + 1.76 dB?",
        "a": "For a full-scale sine: signal power = A²/2, quantizer noise power = Δ²/12 = A²/(3·2^(2N)). Ratio = 1.5·2^(2N) = 6.02·N + 1.76 dB."
      },
      {
        "q": "When should I use compander (μ-law / A-law) vs uniform?",
        "a": "Compander for speech (most of the time the signal is small, dynamic range matters). Uniform for sinusoidal test signals and instrumentation. The workbench shows the SQNR vs amplitude trade-off."
      }
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  "last_updated": "2026-07-05"
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