Transmission Lines PDF

Transmission Lines Transmission Media and Antenna System (EST 131) Prepared by: Engr. Rochelle M. Sabarillo Balanced Versus Unbalanced Lines A balanced line is one in which neither wire is connected to ground. Instead, the signal on each wire is referenc...

Transmission Lines Transmission Media and Antenna System (EST 131) Prepared by: Engr. Rochelle M. Sabarillo Balanced Versus Unbalanced Lines A balanced line is one in which neither wire is connected to ground. Instead, the signal on each wire is referenced to ground. The same current flows in each wire with respect to ground, although the direction of current in one wire is 180° out of phase with the current in the other wire. In an unbalanced line, one conductor is connected to ground. Examples: Twisted-pair – may be used in a balanced or an unbalanced arrangement Open-wire line – balanced configuration Coaxial – unbalanced lines Department of Electrical Engineering & Technology 2 Balanced Versus Unbalanced Lines Balanced-line wires , like open-wire line, offer significant protection from noise pickup and cross talk. Because of the identical polarities of the signals on balanced lines, any external signal induced into the cable appears on both wires simultaneously but cancels at the receiver. This is called common-mode rejection, and noise reduction can be as great as 60 to 70 dB. Coaxial cable and shielded twisted-pair cable, which are unbalanced lines, provide significant but not complete protection from noise pickup or cross talk from inductive or capacitive coupling due to external signals. Unshielded lines may pick up signals and cross talk and can even radiate energy, resulting in an undesirable loss of signal. It is sometimes necessary or desirable to convert from balanced to unbalanced operation or vice versa. This is done with a device called a Department of Electrical Engineering & Technology 3 balun, from “balanced-unbalanced.” Balanced Versus Unbalanced Lines Department of Electrical Engineering & Technology 4 Transmission Lines Department of Electrical Engineering & Technology 5 Wavelength of Cables A pair of current-carrying conductors is not considered to be a transmission line unless it is at least 0.1 λ long at the signal frequency. The distance represented by a wavelength in a given cable depends on the type of cable. The speed in a cable can be anywhere from 0.5 to 0.95 times the speed of light waves (radio waves) in space, and the signal wavelength in a cable will be proportionally less than the wavelength of that signal in space. Thus, the calculated length of cables is shorter than wavelengths in free space. Sample Problems: 1.For an operating frequency of 450 MHz, what length of a pair of conductors is considered to be a transmission line? 2.Calculate the physical length of the transmission line in Problem 1 a 3⁄8 λ long. Department of Electrical Engineering & Technology 6 Connectors Most transmission lines terminate in some kind of connector, a device that connects the cable to a piece of equipment or to another cable. Coaxial Cable Connectors Coaxial connectors are designed not only to provide a convenient way to attach and disconnect equipment and cables but also to maintain the physical integrity and electrical properties of the cable. The choice of a coaxial connector depends on the type and size of cable, the frequency of operation, and the application. The most common types are the PL-259 or UHF, BNC, F, SMA, and N-type connectors. Department of Electrical Engineering & Technology 7 Coaxial Cable Connectors Department of Electrical Engineering & Technology 8 Characteristic Impedance When the length of a transmission line is longer than several wavelengths at the signal frequency, the two parallel conductors of the transmission line appear as a complex impedance. The wires exhibit considerable series inductance whose reactance is significant at high frequencies. In series with this inductance is the resistance of the wire or braid making up the conductors, which includes inherent ohmic resistance plus any resistance due to skin effect. Furthermore, the parallel conductors form a distributed capacitance with the insulation, which acts as the dielectric. In addition, there is a shunt or leakage resistance or conductance (G) across the cable as the result of imperfections in the insulation between the conductors. The result is that to a high-frequency signal, the transmission line appears as a distributed low-pass filter consisting of series inductors and resistors and shunt capacitors and resistors. This is called a lumped model of a distributed line. Department of Electrical Engineering & Technology 9 Characteristic Impedance An RF generator connected to such a transmission line sees an impedance that is a function of the inductance, resistance, and capacitance in the circuit—the characteristic or surge impedance Z 0. If we assume that the length of the line is infinite, this impedance is resistive. The characteristic impedance is also purely resistive for a finite length of line if a resistive load equal to the characteristic impedance is connected to the end of the line. For an infinitely long transmission line, the characteristic impedance Z0 is given by the formula: where Z0 is in ohms, L is the inductance of the transmission line for a given length, and C is the capacitance for that same length. If the line, load, and generator impedances are made equal, as is the case with matched generator and load resistances, the criterion for maximum power transfer is met. The characteristic impedance of a cable is independent of length. Department of Electrical Engineering & Technology 10 Velocity Factor An important consideration in transmission line applications is that the speed of the signal in the transmission line is slower than the speed of a signal in free space. The velocity of propagation of a signal in a cable is less than the velocity of propagation of light in free space by a fraction called the velocity factor (VF), which is the ratio of the velocity in the transmission line Vp to the velocity in free space Vc: Velocity factors in transmission lines vary from approximately 0.5 to 0.9. The velocity factor of a coaxial cable is typically 0.6 to 0.8. Open-wire line has a VF of about 0.9, and 300-Ohms twin-lead line has a velocity factor of about 0.8. Velocity Factor/Transmission Line Length Calculations: Department of Electrical Engineering & Technology 11 Time Delay Because the velocity of propagation of a transmission line is less than the velocity of propagation in free space, it is logical to assume that any line will slow down or delay any signal applied to it. A signal applied at one end of a line appears some time later at the other end of the line. This is called the time delay or transit time for the line. A transmission line used specifically for the purpose of achieving delay is called a delay line. The amount of delay time is a function of a line’s inductance and capacitance. where td is in seconds and L and C are the inductance and capacitance, respectively, per unit length of line. Time delay introduced by a coaxial cable can also be calculated by using the formula: Period and Phase-Shift Calculations: Department of Electrical Engineering & Technology 12 Department of Electrical Engineering & Technology 13 Transmission Line Specifications Table here summarizes the specifications of several popular types of coaxial cable. Many coaxial cables are designated by an alphanumeric code beginning with the letters RG or a manufacturer’s part number. Department of Electrical Engineering & Technology 14 Coaxial Cable Attenuation Attenuation versus frequency for four coaxial cable types is plotted below. The loss is significant at very high frequencies. However, the larger the cable, the lower the loss. Several things can be done to minimize loss. First, every attempt should be made to find a way to shorten the distance between the transmitter and the antenna. If that is not feasible, it may be possible to use a larger cable. When you are considering the relationship between cable length and attenuation, remember that a transmission line is a low-pass filter whose cutoff frequency depends both on distributed inductance and capacitance along the line and on length. The longer the line, the lower its cutoff frequency. This means that higher-frequency signals beyond the cutoff frequency are rolled off at a rapid rate. Department of Electrical Engineering & Technology 15 Reminder Prepare for oral recitation. Department of Electrical Engineering & Technology 1 6 Thank You for Listening :) Do you have any questions? Email me at [email protected] or you may post a message in our Google Classroom.