- 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

## 7.10 Famous Characteristic Impedances

Over the years, various specs have been established for specialized controlled-impedance interconnects. A number of these are listed in Figure 7-11. One of the most common ones is RG58. Virtually all general-purpose coax cables used in the lab, with bayonet type BNC connectors, are made with RG58 cable. This spec defines an inner- and outer-conductor diameter and a dielectric constant. In addition, when the spec is followed, the characteristic impedance is about 52 Ohms. Look on the side of the cable, and you will see “RG58” stamped.

**Figure 7-11** Some famous controlled-impedance interconnects, based on their specified characteristic impedance.

There are other cable specs as well. RG174 is useful to know about. It is a thinner cable than RG58 and is much more flexible. When trying to snake a cable around in tight spaces or when low stress is required, the flexibility of RG174 is useful. It is specified with a characteristic impedance of 50 Ohms.

The coax cable used in cable TV systems is specified at 75 Ohms. This cable will have a lower capacitance per length than a 50-Ohm cable and in general is thicker than a comparable 50-Ohm cable. For example, RG59 is thicker than RG58.

Twisted pairs, typically used in high-speed serial links, small computer system interface (SCSI) applications, and telecommunications applications are made with 18- to 26-gauge wire. With the typical insulation thickness commonly used, the characteristic impedance is about 100 Ohms to 130 Ohms. This is typically a higher impedance than used in circuit boards, but it matches the differential impedance of typical board traces. Differential impedance is introduced in Chapter 11, “Differential Pairs and Differential Impedance.”

There is one characteristic impedance that has special, fundamental significance: free space. As described previously, a signal propagating in a transmission line is really light, the electric and magnetic fields trapped and guided by the signal- and return-path conductors. As a propagating field, it travels at the speed of light in the composite dielectric medium.

Without the conductors to guide the fields, light will propagate in free space as waves. These are waves of electric and magnetic fields. As the wave propagates through space, the electric and magnetic fields will see an impedance. The impedance a wave sees is related to two fundamental constants—the permeability of free space and the permittivity of free space:

The combination of these two constants is the instantaneous impedance a propagating wave will see. We call this the *characteristic impedance of free space*, and it is approximately 377 Ohms. This is a fundamental number. The amount of radiated energy from an antenna is optimized when its impedance matches the 377 Ohms of free space. There is only one characteristic-impedance value that has fundamental significance, and it is 377 Ohms. All other impedances are arbitrary. The characteristic impedance of an interconnect can be almost any value, limited by manufacturability constraints.

But what about 50 Ohms? Why is it so commonly used? What’s so special about 50 Ohms? Its use became popular in the early 1930s, when radio communications and radar systems became important and drove the first requirements for using high-performance transmission lines. The application was to transmit the radio signal from the not-very-efficient generator to the radio antenna with the minimum attenuation.

As we show in Chapter 9, “Lossy Lines, Rise-Time Degradation, and Material Properties,” the attenuation of a coax cable is related to the series resistance of the inner conductor and outer conductor divided by the characteristic impedance. If the outer diameter of the cable is fixed, using the largest-diameter cable possible, there is an optimum inner radius that results in minimum attenuation.

With too large an inner radius, the resistance is lower, but the characteristic impedance is lower as well, and the attenuation is higher. Too small a diameter of the inner conductor, and the resistance and attenuation are both high. When you explore the optimum value of inner radius, you find that the value for the lowest attenuation is also the value that creates 50 Ohms.

The reason 50 Ohms was chosen almost 100 years ago was to minimize the attenuation in coax cables for a fixed outer diameter. It was adopted as a standard to improve radio and radar system efficiency, and it was easily manufactured. Once adopted, the more systems using this value of impedance, the better their compatibility. If all test and measurement systems matched to this standard 50 Ohms, then reflections between instruments were minimized, and signal quality was optimized.

In FR4, a 50-Ohm microstrip can be easily fabricated if the line is twice as wide as the dielectric is thick. A broad range of characteristic impedances around 50 Ohms can also be fabricated, so it is a soft optimum in printed circuit board technology.

In high-speed digital systems, a number of trade-offs determine the optimum characteristic impedance of the entire system. Some of these are illustrated in Figure 7-12. A good starting place is 50 Ohms. Using a higher characteristic impedance with the same pitch means more cross talk; however, higher characteristic impedance connectors or twisted-pair cables will cost less because they are easier to fabricate. Lower characteristic impedance means lower cross talk and lower sensitivity to delay adders caused by connectors, components, and vias, but it also means higher power dissipation when terminated. This is important in high-speed systems.

**Figure 7-12** Trade-offs in various system issues based on changing the characteristic impedance of the interconnects. Deciding on the optimum characteristic impedance, balancing performance and cost, is a difficult process. 50 Ohms is a good compromise in most systems.

Every system will have its own balance for the optimum characteristic impedance. In general, it is a very soft optimum, and the exact value chosen is not critically important as long as the same impedance is used throughout the system. Unless there is a strong driving force otherwise, 50 Ohms is usually used. In the case of Rambus memory, timing was critically important, and a low impedance of 28 Ohms was chosen to minimize the impact from delay adders. Manufacturing such a low impedance requires wide lines. But since the interconnect density in Rambus modules is low, the wider lines have only a small impact.