PART III Preamplifiers, Mixers, and Interconnects L c R c R s C cs S S L s FIGURE 7.7 Lumped-circuit model of electrically short coaxial cable. would be zero external field, and zero net inductance, if the two conductors could occupy the same space. The cancellation of round trip inductance due to magnetic coupling varies with cable construc- tion, with typical values of 50% for zip cord, 70% for a twisted pair, and 100% for coaxial construction. At very high frequencies, a cable exhibits very different characteristics than it does at, say, 60 Hz power frequencies. This is caused by the finite speed, called propagation velocity , at which electrical energy travels in wires. It is about 70% of the speed of light for typical cables, making wavelengths in cable correspondingly shorter. A cable is called electrically short when its physical length is under 10% of a wavelength at the highest frequency of interest. Wavelength at 60 Hz for typical cable is about 2200 miles (mi), making any power cable less than 220 mi long electrically short. Likewise, the wavelength at 20 kHz for typical cable is about 34,500 ft, making any audio cable less than about 3500 ft long elec- trically short. Essentially identical instantaneous voltage and current exists at all points on an electric- ally short cable and its signal coupling behavior can be represented by lumped resistance, capacitance, and magnetically coupled inductance as shown in Figure 7.7 . Its equivalent circuit can then be ana- lyzed by normal network theory. When a cable is longer than 10% of a wavelength, signals must be considered to propagate as electro- magnetic waves and the cable can properly be called a transmission line. This includes typical cables longer than 7 ft for 10 MHz video, 8 inch for 100 MHz FM radio, and 0.8 inch for 1000 MHz CATV sig- nals. Significantly different instantaneous voltages exist along the length of a transmission line. For all practical purposes, its electrical equivalent is a distributed circuit consisting of a large number of small inductors and resistors in series and capacitors in parallel. If an electrical impulse were applied to one end of an infinitely long cable, it would appear to have a purely resistive impedance. This characteristic impedance of the cable is a result of its inductance and capacitance per unit length, which is determined by its physical construction. Theoretically, the electrical impulse or wave would ripple down the infi- nite length of the cable forever. But actual transmission lines always have a far end. If the far end is left open or shorted, none of the wave's energy can be absorbed and it will reflect back toward the source. However, if the far end of the line is terminated with a resistor of the same value as the line's character- istic impedance, the wave energy will be completely absorbed. To the wave, the termination appears to be simply more cable. A properly terminated transmission line is often said to be matched. Generally, impedances of both the driving source and the receiving load are matched to the characteristic imped- ance of the line. In a mismatched line, the interaction between outgoing and reflected waves causes a phenomenon called standing waves. A measurement called standing-wave ratio (SWR) indicates mis- match, with an SWR of 1.00 meaning a perfect match. 222 ELECTRONICS OF INTERFACES Balanced and unbalanced interfaces An interface is a signal transport subsystem consisting of three components: a driver (one device's out- put), a line (interconnecting cable), and a receiver (another device's input). These components are connected to form a complete circuit for signal current, which requires a line having two signal con- ductors. The impedances of the signal conductors, usually with respect to ground, are what determine whether an interface is balanced or unbalanced. A concise definition of a balanced circuit is: A balanced circuit is a two-conductor circuit in which both conductors and all circuits connected to them have the same impedance with respect to ground and to all other conductors. The purpose of balancing is to make the noise pickup equal in both conductors, in which case it will be a common-mode signal that can be made to cancel out in the load (Ott, 1988, p. 118.)