- 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

## 7.12 Driving a Transmission Line

For a high-speed driver launching a signal into a transmission line, the input impedance of the transmission line during the transition time will behave like a resistance that is equivalent to the characteristic impedance of the line. Given this equivalent circuit model, we can build a circuit of the driver and transmission line and calculate the voltage launched into the transmission line. The equivalent circuit is shown in Figure 7-16.

**Figure 7-16** Top: Output gate driving a transmission line. Bottom: Equivalent circuit model showing the voltage source, which is the driver, the output-source impedance of the driver gate itself, and the transmission line modeled as a resistor, which is valid during the round-trip time of flight of the transmission line.

The driver can be modeled as a voltage source element that switches on fast and as a source resistance. The voltage source has a voltage that is specified depending on the transistor technology. For CMOS devices, it ranges from 5 v to 1.5 v, depending on the transistor generation. Older CMOS devices use 5 v, while PCI and some memory buses use 3.3 v. The fastest processors use 2.4 v and lower for their output rails and 1.5 v and lower for their core. These voltages are the supply voltages and are very close to the output voltage when the device is driving an open circuit.

The value of the source resistance also depends on the device technology. It is typically in the 5-Ohm to 60-Ohm range. When the driver suddenly turns on, some current flows through the source impedance to the transmission line, and there is a voltage drop internal to the gate before the signal comes out the pin. This means that the full, open-circuit drive voltage does not appear across the output pins of the driver.

The actual voltage launched into the transmission line can be calculated by modeling this circuit as a resistive-voltage divider. The signal sees a voltage divider composed of the source resistance and the transmission line’s impedance. The magnitude of the voltage initially launched into the line is the ratio of the impedance of the line to the series combination of the line and source resistance. It is given by:

where:

V_{launched} = voltage launched into the transmission line

V_{output} = voltage from the driver when driving an open circuit

R_{source} = output-source impedance of the driver

Z_{0} = characteristic impedance of the transmission line

When the source resistance is high, the voltage launched into the line will be low—usually not a good thing. In Figure 7-17, we plot the percentage of the source voltage that actually gets launched into the transmission line and propagates down it, for a characteristic impedance of 50 Ohms. When the output-source impedance is also 50 Ohms, we see that only half the open-circuit voltage is actually launched into the line. If the output is 3.3 volts, the signal launched into the line is only 1.65 volts. This is probably not enough to reliably trigger a gate that may be connected to the line. However, as the output resistance of the driver decreases, the signal voltage into the line increases.

**Figure 7-17** Amount of voltage launched into a 50-Ohm transmission line as the output source impedance of the driver varies.

We say that in order to “drive a transmission line”—in other words, launch a voltage into the line that is close to the open-circuit source voltage—we need an output impedance of the driver that is very small compared to the characteristic impedance of the line. If the line is 50 Ohms, we need a source impedance less than 10 Ohms, for example.

Output devices that have exceptionally low output impedances, 10 Ohms or less, are often called *line drivers* because they will be able to inject a large percentage of their voltage into the line. Older-technology CMOS devices were not able to drive a line since their output impedances were in the 90-Ohm to 130-Ohm range. Since most interconnects behave like transmission lines, current-generation, high-speed CMOS devices must all be able to drive a line and are designed with low-output impedance gates.