- 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
7.6 Spatial Extent of the Leading Edge
Every signal has a rise time, RT, usually measured from the 10% to 90% voltage levels. As a signal moves down a transmission line, the leading-edge spreads out on the transmission line and has a spatial extent. If we could freeze time and look at the size of the voltage distribution as it moves out, we would find something like Figure 7-7.
Figure 7-7 Spatial extent of the leading edge of the signal as it propagates down a transmission line.
The length of the rise time, Len, on the transmission line depends on the speed of the signal and the rise time:
where:
Len = spatial extent of the rise time, in inches
RT = rise time of the signal, in nsec
v = speed of the signal, in inches/nsec
For example, if the speed is 6 inches/nsec and the rise time is 1 nsec, the spatial extent of the leading edge is 1 nsec × 6 inches/nsec = 6 inches. As the leading edge moves down the circuit board, it is really a 6-inch section of rising voltage moving down the board. A rise time of 0.1 nsec has a spatial extent of 0.6 inch.