Simulating the Effect of Line Resistance and Capacitance in a Computer

Transcription

1 Simulating the Effect of Line Resistance and Capacitance in a Computer System DR. RAJ L. DESAI Department of Industrial Technology Southeast Missouri State University One University Plaza, MS 4000 Cape Girardeau, MO 63701, USA Abstract: - The resistance of the wiring between the source computer and destination (may be a peripheral or another computer in the case of a network) makes the line imperfect. Wires placed side by side in cables make good capacitors. The line also has some self-inductance but the primary problems are the capacitance and resistance [1]. Students can simulate this by conducting the following experiment. A square wave of 300-Hertz (Hz) will simulate a 300 bits per second (bps) signal, a 1200-Hz square wave will simulate a 1200bps signal, and a 9600-Hz square wave will simulate a 9600 bps signal. Students can be asked to use the relationship between frequency (f) and period (t) of a periodic waveform (f = 1/t) to calculate the correct period for each of the sample frequencies. For 300 Hz, t = 1/f = 1/300 = seconds = 3.33 milliseconds (ms). Now the students can calculate the proper horizontal setting for the oscilloscope to show two complete cycles of the signal at each frequency. This will help the students learn the basics of setting an oscilloscope to display a signal of interest. Two cycles of the waveform can be displayed by using approximately 8 centimeters (cm.) of the screen (the oscilloscope screen is 10 cm. wide). This means that each complete cycle should occupy about 4 cm. of the screen, so the proper horizontal setting can be determined by dividing the period by four and rounding to the nearest available oscilloscope setting. For 300 Hz: 3.33 ms/4 = ms/ div or about 1 ms/div. The students can now monitor the waveform on the oscilloscope and adjust the frequency. When one period occupies exactly 3.33msec, the square wave is set at 300 Hz. Similar procedures are used for the other two speeds. On the circuit board, the students need to connect a 100-picofarad capacitor between the square wave signal generator and ground. This simulates a typical 20-foot cable, which might be used to carry pulses short distances, as between a computer and printer [2]. The resistance, less than half an ohm, of such a cable, is simulated by the contact resistance of the connections just made. Using the oscilloscope, the students should compare the original waveform with the waveform measured across the capacitor. The students need to do this at all the three frequencies and sketch their findings. The students should have seen very little change in the signal as it passed over the simulated cable. Because of their relatively small capacitance and resistance, short cables do not appreciably distort data signals, and thus are widely used to carry signals between equipment located relatively close to one another. Increasing the cable capacitance and resistance (a natural occurrence with increased cable length) also increases the distortion of the received signal. Furthermore students will notice that the effects are not linear. Students will see that distortion increase markedly as the signaling rate is increased. Using a logic probe as a data detector, students will observe that the distortion makes the detector unable to properly detect the received signal. Students will get a good grasp of the effect of imperfect lines and varying signaling speeds on the ability of the signal to be accurately detected at the receiver. Key Words: - Transmission line effects, Line Resistance, Line Capacitance, Bits and Baud, Shannon s Law, Kelvin s Law.

2 1 Introduction Data communication is a general term used for the movement of data by electrical means. A data communication network is an interconnected group of devices (usually computers) that move data back and forth. Our ability to send and receive data has increased tremendously. The world of business is also being revolutionized by this ability to move information instantly from one place to another. By doing this simulation, students will become familiar with data communication techniques, and equipment, their uses, and their characteristics. Students will also understand how digital circuits are used in data communication. 2 Problem Formulation A communications channel is like a water pipe. The water flowing in the pipe represents information flowing in a communication channel. The capacity of the pipe to carry water depends on the pressure of the water and the diameter of the pipe. Exactly the same is true of a communication channel. Once you buy the pipe the diameter is fixed. So the only way to increase the flow of water through the pipe is to increase the pressure. If you keep increasing the pressure without limit, the pipe breaks. Channels, like pipes come in certain sizes. The size of a communications channel is measured in bandwidth. The speed at which we send information over the channel is measured in bits per second, and is like water pressure. Just as with a pipe, there is a maximum limit to what the channel can carry. 2.1 Shannon s Law In 1948, Claude Shannon proved that the maximum capacity of a communication channel could be calculated with the following equation: (1) C = W log [1 + S / N] 2 Where: C = channel capacity in bits per second W = channel bandwidth in hertz S = signal power N = noise power (white noise). If our typical telephone circuit has a bandwidth of 3100 Hz, and the signal-to-noise ratio is 20 decibels, the channel capacity would be 20,628 bits per second [3]. Generally speaking, the faster we send data over a communication circuit, the more we pay for the transmission equipment. 2.2 Bits and Baud We used bits per second for the rate of transmission of information. If we leaf through catalogs for computer and communications equipment we will notice that communications equipment are described by their baud rate. Bit stands for binary digit, whereas baud refers to the rate of flow. In the binary system, (2) Baud Rate = Bit Rate / Bits per Symbol For example, if the bit rate is 600 bits per second and each symbol has two bits, the baud rate would be: Baud rate = 600/2 = 300 Bits per second more accurately describes data transmission rates. Remember bits per second and baud rate are not the same thing. 2.3 Transmission Line Effects: Resistance, Inductance, and Capacitance The transmission line between the source and destination is not perfect. The wires have resistance. Placed side by side in cables, these wires are used to transmit over long distances and make good capacitors. The

3 line also has some inductance, but the primary problems are its capacitance and resistance. The current through the transmission line follows the following equation: (3) I = V (1 e -t/rc ) / R When the voltage at the input to the line is removed, the line capacitor discharges according to the following relationship: (4) I = V (e -t/rc ) / R If the duration of the voltage pulses applied to the line decreases, or if the pulse amplitude decreases, the current received will also decrease. When this happens it will be more difficult to detect each pulse. The above discussion is actually a simplification of the actual characteristics of a DC transmission line effects of line capacitance, inductance, and capacitance. 2.4 Kelvin s Law The time it takes for the current at the receiver to either rise to a steady state value, or to fall from that value, will affect the speed at which we can signal over the transmission line. This effect was quantified by Lord Kelvin, who demonstrated that the maximum signaling speed of a telegraph line could be calculated by the following equation: (5) S = K / ( L 2 ) R C Where: S = maximum signaling speed K = a constant (depends on line involved) L = length of line C = capacitance per unit length of line R = resistance per unit length of line. Kelvin s law shows that the speed decreases according to the square of the line length. Doubling the length of the transmission line decreases the maximum signaling speed by a factor of four. 3 Problem Solution To reduce distortion we must either change one or more of the things that cause distortion, or counteract the results of these transmission imperfections. Kelvin s Law identifies that the shorter the line, the faster we could send a signal over it. If we could insert a receiver on the line before the signal has been badly distorted, the receiver would accurately copy the message at the desired speed, and transmit it on to the next station. A regenerative repeater detects the signal and uses it to operate another repeater that drives the next segment of the transmission line. Regenerative repeaters are widely used in DC signaling applications. Another method of dealing with line distortion was discovered by Heaviside. He showed that distortion introduced by a DC transmission line could be minimized by satisfying the equation: (6) RC = LG Where: R = resistance per unit length C = capacitance per unit length L = inductance per unit length

4 G = conductance per unit length( shunt resistance between cable conductors). Cable capacitance is usually minimized by spacing the pairs and choosing insulation during its construction, so a common solution is to add inductance until the equation is satisfied. This process is known as loading the cable. One advantage of loading the cable is that it is totally passive. However a loaded cable is more expensive than an unloaded cable. When DC signaling is required over long distances and where regenerative repeaters are impractical, as in a submarine cable, loading significantly improves performance. 4 Conclusion The cable that connects your printer or modem to your personal computer is a transmission line carrying a DC signal. So is the cable that connects the disk drive to the drive controller board. DC signaling is all around us. It is simple, dependable, and inexpensive. Knowing its limitations, we can use it intelligently. References: [1] Stanley, Richard A., Data Communications and Networks, Heathkit Company, Inc., [2] Kersey, Roger M., Personal Computer Operation and Troubleshooting, Prentice Hall, Inc., [3] Cole, Marion, Telecommunications, Prentice Hall, Inc., 1999.

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