- 7.1 Forget the Word Ground
- 7.2 The Signal
- 7.3 Uniform Transmission Lines
- 7.4 The Speed of Electrons in Copper
- 7.5 The Speed of a Signal in a Transmission Line
- 7.6 Spatial Extent of the Leading Edge
- 7.7 “Be the Signal”
- 7.8 The Instantaneous Impedance of a Transmission Line
- 7.9 Characteristic Impedance and Controlled Impedance
- 7.10 Famous Characteristic Impedances
- 7.11 The Impedance of a Transmission Line
- 7.12 Driving a Transmission Line
- 7.13 Return Paths
- 7.14 When Return Paths Switch Reference Planes
- 7.15 A First-Order Model of a Transmission Line
- 7.16 Calculating Characteristic Impedance with Approximations
- 7.17 Calculating the Characteristic Impedance with a 2D Field Solver
- 7.18 An n-Section Lumped-Circuit Model
- 7.19 Frequency Variation of the Characteristic Impedance
- 7.20 The Bottom Line
- End-of-Chapter Review Questions
7.20 The Bottom Line
A transmission line is a fundamentally new ideal-circuit element that accurately describes all the electrical properties of a uniform cross-sectional interconnect.
Forget the word ground. Think return path.
Signals propagate down a transmission line at the speed of light in the material surrounding the conductors. This primarily depends on the dielectric constant of the insulation.
The characteristic impedance of a transmission line describes the instantaneous impedance a signal would see as it propagates down the line. It is independent of the length of the line.
The characteristic impedance of a line primarily depends inversely on the capacitance per length and the speed of the signal.
The input impedance looking into the front end of a transmission line changes with time. It is initially the characteristic impedance of the line during the round-trip time of flight, but it can end up being anything, depending on the termination, the length of the line, and how long we measure the impedance.
A controlled-impedance board has all its traces fabricated with the same characteristic impedance. This is essential for good signal integrity.
A signal propagates through a transmission line as a current loop with the current going down the signal path and looping back through the return path. Anything that disturbs the return path will increase the impedance of the return path and create a ground-bounce voltage noise.
A real transmission line can be approximated with an n-section LC lumped-circuit model. The higher the bandwidth required, the more LC sections required. But it will always be an approximation with limited bandwidth.
For good accuracy, there should be at least 3.5 LC sections along the spatial extent of the leading edge.
An ideal transmission-line model is always a good starting model for a real interconnect, independent of the rise time and interconnect length. An ideal transmission-line model will always have the highest potential bandwidth of any model.