Chapter 5: Transmission Line Limitations + Filtering

📚 Chapter 5 — Transmission Line Limitations + Filtering (Asgn05 + Lab05)

🎯 Learning Objectives

By the end of this lesson, students should be able to:

  • Relate pulse width, duty cycle, and baud rate to spectral content.
  • Use Fourier reasoning to identify the first null and determine baud rate.
  • Understand why Baud = 2·fc for a high‑order low‑pass filter.
  • Identify MSI points and interpret eye patterns.
  • Build and test a 3‑pole Sallen‑Key low‑pass filter.

1️⃣ Sampling and Nyquist for Digital Symbols

  • The rate of transmission of electrical symbols… is equal to the Nyquist sampling rate — the data signal must be sampled at a minimum of once per electrical symbol.”

Oversampling must be an integer multiple (2×, 4×, 16×).

2️⃣ Fourier Analysis of Pulses

2.1 First Null = Baud Rate

“The first dropout is the inverse of the pulse width… the first dropout in the spectrum is the Baud Rate.”

Thus: $\mathrm{Baud}=\frac{1}{t_p}$

2.2 Duty Cycle ↔ Number of Spectral Components

“Duty cycle is equal to the inverse of the number of frequency components in a lobe.”

3️⃣Filter Characteristics and Sinc Response

3.1 Sine Cardinal (sinc) Output

High‑order filters produce a sinc‑like response:

“The shape of the output signal is a function of the filter’s characteristics… best modelled using a Sine Cardinal function.”

MSI points occur at zero crossings of the sinc.

3.2 Maximum Baud Rate Through Filter

\[\mathrm{Baud_{\mathnormal{\max }}}=2f_c\]

“The maximum Baud rate through a filtered transmission system will be twice the cutoff frequency.”

4️⃣ Eye Patterns

“Since it looks like a series of open eyes, this is called an Eye Pattern… the middle of each diamond is a point of MSI.”

Students should learn:

  • Wide open eye → good timing margin
  • Narrow eye → intersymbol interference
  • MSI sampling → clean symbol decisions

5️⃣ Lab 05 — Filtering and Spectral Analysis

5.1 Part A — Generate Bipolar Pulse

  • 2 kHz
  • 50 µs pulse width
  • ±5 V
  • FFT to find first null → Baud rate

5.2 Part B — Change Duty Cycle

Observe that:

  • 10% and 90% duty cycles produce identical spectra (symmetry).
  • 25% ↔ 75% also match.

5.3 Part C — Build 3‑Pole Sallen‑Key Filter

Measure:

  • Actual cutoff frequency
  • Pass‑band gain
  • MSI spacing → compute fc

5.4 Part D — Eye Pattern

Feed UART data through the filter and observe:

  • Eye opening
  • MSI points
  • Timing recovery

6️⃣ Assignment 5 Prep Questions

Should be able to compute:

  • Minimum sampling rate for a given baud
  • Oversampling rate
  • First null frequency
  • Duty cycle from spectral components
  • Cutoff frequency from MSI spacing
  • Maximum baud rate through a filter All directly supported by: “The inverse of the time between MSI points is twice the cutoff frequency.” “Baud = 2fc.”