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© 2008 The McGraw-Hill Companies 1 Principles of Electronic Communication Systems Third Edition Louis E. Frenzel, Jr.
© 2008 The McGraw-Hill Companies 2 Chapter 13 Transmission Lines
© 2008 The McGraw-Hill Companies 3 Topics Covered in Chapter 13 13-1: Transmission-Line Basics 13-2: Standing Waves 13-3: Transmission Lines as Circuit Elements 13-4: The Smith Chart
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Transmission lines in communication carry telephone signals, computer data in LANs, TV signals in cable TV systems, and signals from a transmitter to an antenna or from an antenna to a receiver. Their electrical characteristics are critical and must be matched to the equipment for successful communication to take place. Transmission lines are also circuits.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics The two primary requirements of a transmission line are: 1. The line should introduce minimum attenuation to the signal. 2. The line should not radiate any of the signal as radio energy.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Types of Transmission Lines Parallel-wire line is made of two parallel conductors separated by a space of ½ inch to several inches. A variation of parallel line is the 300-Ω twin-lead. Spacing between the wires is maintained by a continuous plastic insulator.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Types of Transmission Lines The most widely used type of transmission line is the coaxial cable. It consists of a solid center conductor surrounded by a dielectric material, usually a plastic insulator such as Teflon. A second conducting shield made of fine wires covers the insulator, and an outer plastic sheath insulates the braid. Coaxial cable comes in sizes from ¼ inch to several inches in diameter.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Types of Transmission Lines Twisted-pair cable uses two insulated solid copper wires covered with insulation and loosely twisted together. Two types of twisted-pair cable are Unshielded twisted-pair (UTP) cable Shielded twisted-pair (STP) cable
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Figure 13-1: Common types of transmission lines. (a) Open-wire line. (b) Open-wire line called twin lead. (c) Coaxial cable (d) Twisted-pair cable.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Balanced Versus Unbalanced Lines Transmission lines can be balanced or unbalanced. A balanced line is one in which neither wire is connected to ground. The signal on each wire is referenced to ground. In an unbalanced line, one conductor is connected to ground. Open-wire line has a balanced configuration.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Balanced Versus Unbalanced Lines Balanced-line wires offer significant protection from noise pickup and cross talk. Coaxial cables are unbalanced lines. Coaxial cable and shielded twisted-pair provide significant but not complete protection from noise or cross talk. Unshielded lines may pick up signals and cross talk and can even radiate energy, resulting in an undesirable loss of signal. A device called a balun is used to convert from balanced to unbalanced lines and vice versa.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Figure 13-2: (a) Balanced line. (b) Unbalanced line.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Wavelength of Cables The electrical length of conductors is typically short compared to 1 wavelength of the frequency they carry. 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.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics 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. Connectors are a common failure point in many applications.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Connectors: Coaxial Cable Connectors Coaxial cables 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 most common types are the PL-259 or UHF, BNC, F, SMA, and N-type connectors. The PL-259, also referred to as a UHF connector, can be used up to low UHF frequencies (less than 500 MHz.)
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Figure 13-3: UHF connectors. (a) PL-259 male connector. (b) Internal construction and connections for the PL-259. (c) SO-239 female chassis connector.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Connectors: Coaxial Cable Connectors BNC connectors are widely used on 0.25 inch coaxial cables for attaching test equipment. In BNC connectors the center conductor of the cable is soldered or crimped to a male pin and the shield braid is attached the body of the connector. The least expensive coaxial connector is the F-type, which is used for TV sets, VCRs, DVD players, and cable TV. The RCA phonograph connector is used primarily in audio equipment. The best performing coaxial connector is the N-type, which is used mainly on large coaxial cable at higher frequencies.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Figure 13-4: BNC connectors. (a) Male. (b) Female. (c) Barrel connector. (d) T connector.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Figure 13-6: The F connector used on TV sets, VCRs, and cable TV boxes.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Figure 13-7: RCA phonograph connectors are sometimes used for RF connectors up to VHF.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Figure 13-8: N-type coaxial connector.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Characteristic Impedance When the length of transmission line is longer than several wavelengths at the signal frequency, the two parallel conductors of the transmission line appear as a complex impedance. An RF generator connected to a considerable length of 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 ).
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Velocity Factor 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). VF = V p /V c
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Time Delay Because the velocity of propagation of a transmission line is less than the velocity of propagation in free space, 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. A transmission line used specifically for the purpose of achieving delay is called a delay line.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Figure 13-11: The effect of the time delay of a transmission line on signals. (a) Sine wave delay causes a lagging phase shift. (b) Pulse delay.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Transmission-Line Specifications Many coaxial cables are designated by an alphanumeric code beginning with the letters RG or a manufacturer’s part number. Primary specifications are characteristic impedance and attenuation. Other important specifications are maximum breakdown voltage rating, capacitance per foot, velocity factor, and outside diameter in inches. The attenuation is the amount of power lost per 100 ft of cable expressed in decibels at 100 MHz.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Transmission-Line Specifications Attenuation is directly proportional to cable length and increases with frequency. A transmission line is a low-pass filter whose cutoff frequency depends on distributed inductance and capacitance along the line and on length. It is important to use larger, low-loss cables for longer runs despite cost and handling inconvenience. A gain antenna can be used to offset cable loss.
© 2008 The McGraw-Hill Companies : Transmission-Line Basics Figure 13-14: Attenuation versus length for RG-58A/U coaxial cable. Note that both scales on the graph are logarithmic.
© 2008 The McGraw-Hill Companies : Standing Waves When a signal is applied to a transmission line, it appears at the other end of the line some time later because of the propagation delay. If the load on the line is an antenna, the signal is converted into electromagnetic energy and radiated into space. If the load at the end of the line is an open or a short circuit or has an impedance other than the characteristic impedance of the line, the signal is not fully absorbed by the load.
© 2008 The McGraw-Hill Companies : Standing Waves When a line is not terminated properly, some of the energy is reflected and moves back up the line, toward the generator. This reflected voltage adds to the forward or incident generator voltage and forms a composite voltage that is distributed along the line. The pattern of voltage and its related current constitute what is called a standing wave. Standing waves are not desirable.
© 2008 The McGraw-Hill Companies : Standing Waves Figure 13-15: How a pulse propagates along a transmission line.
© 2008 The McGraw-Hill Companies : Standing Waves Matched Lines A matched transmission line is one terminated in a load that has a resistive impedance equal to the characteristic impedance of the line. Alternating voltage (or current) at any point on a matched line is a constant value. A correctly terminated transmission line is said to be flat. The power sent down the line toward the load is called forward or incident power. Power not absorbed by the load is reflected power.
© 2008 The McGraw-Hill Companies : Standing Waves Figure 13-16: A transmission line must be terminated in its characteristic impedance for proper operation.
© 2008 The McGraw-Hill Companies : Standing Waves Calculating the Standing Wave Ratio The magnitude of the standing waves on a transmission line is determined by the ratio of the maximum current to the minimum current, or the ratio of the maximum voltage to the minimum voltage, along the line. These ratios are referred to as the standing wave ratio (SWR). SWR = I max I min = V max V min
© 2008 The McGraw-Hill Companies : Transmission Lines as Circuit Elements The standing wave conditions resulting from open- and short-circuited loads must usually be avoided when working with transmission lines. With quarter- and half-wavelength transmissions, these open- and short-circuited loads can be used as resonant or reactive circuits.
© 2008 The McGraw-Hill Companies : Transmission Lines as Circuit Elements Resonant Circuits and Reactive Components Shorted and open quarter wavelengths act like LC tuned or resonant circuits at the reference frequency. With a shorted line, if the line length is less than one- quarter wavelength at the operating frequency, the shorted line looks like an inductor to the generator. If the shorted line is between one-quarter and one-half wavelength, it looks like a capacitor to the generator. These conditions repeat with multiple one-quarter or one-half wavelengths of shorted line.
© 2008 The McGraw-Hill Companies : Transmission Lines as Circuit Elements Resonant Circuits and Reactive Components With an open line, a one-quarter wavelength line looks like a series resonant circuit to the generator, and a one-half wavelength line looks like a parallel resonant circuit, just the opposite of a shorted line. If the line is less than one-quarter wavelength, the generator sees a capacitance. If the line is between one-quarter and one-half wavelength, the generator sees an inductance. These characteristics repeat for lines that are some multiple of one-quarter or one-half wavelengths.
© 2008 The McGraw-Hill Companies : Transmission Lines as Circuit Elements Figure 13-25: Summary of impedance and reactance variations of shorted and open lines for lengths up to one wavelength.
© 2008 The McGraw-Hill Companies : Transmission Lines as Circuit Elements Stripline and Microstrip Special transmission lines constructed with copper patterns on a printed circuit board (PCB), called microstrip or stripline, can be used as tuned circuits, filters, phase shifters, reactive components, and impedance-matching circuits at high frequencies.
© 2008 The McGraw-Hill Companies : Transmission Lines as Circuit Elements Stripline and Microstrip Microstrip is a flat conductor separated by an insulating dielectric from a large conducting ground plane. The microstrip is usually a quarter or half wavelength long. The ground plane is the circuit common and is equivalent to an unbalanced line. The characteristic impedance of microstrip is dependent on its physical characteristics.
© 2008 The McGraw-Hill Companies : Transmission Lines as Circuit Elements Figure 13-26: Microstrip. (a) Unbalanced. (b) Balanced.
© 2008 The McGraw-Hill Companies : Transmission Lines as Circuit Elements Stripline and Microstrip Stripline is a flat conductor sandwiched between two ground planes. It is more difficult to make than microstrip; however, it does not radiate as microstrip does. The length is one-quarter or one-half wavelength at the desired operating frequency. Shorted lines are more commonly used than open lines.
© 2008 The McGraw-Hill Companies : Transmission Lines as Circuit Elements Figure 13-28: Stripline.
© 2008 The McGraw-Hill Companies : The Smith Chart The mathematics required to design and analyze transmission lines is complex, whether the line is a physical cable connecting a transceiver to an antenna or is being used as a filter or impedance-matching network. This is because the impedances involved are complex ones, involving both resistive and reactive elements. The impedances are in the familiar rectangular form, R + jX.
© 2008 The McGraw-Hill Companies : The Smith Chart The Smith Chart is a sophisticated graph that permits visual solutions to transmission line calculations. Despite the availability of the computing options today, this format provides a more or less standardized way of viewing and solving transmission-line and related problems.
© 2008 The McGraw-Hill Companies : The Smith Chart The horizontal axis is the pure resistance or zero- reactance line. The point at the far left end of the line represents zero resistance, and the point at the far right represents infinite resistance. The resistance circles are centered on and pass through this pure resistance line. The circles are all tangent to one another at the infinite resistance point, and the centers of all the circles fall on the resistance line.
© 2008 The McGraw-Hill Companies : The Smith Chart Any point on the outer circle represents a resistance of 0 Ω. The R = 1 circle passes through the exact center of the resistance line and is known as the prime center. Values of pure resistance and the characteristic impedance of transmission line are plotted on this line. The linear scales printed at the bottom of Smith charts are used to find the SWR, dB loss, and reflection coefficient.
© 2008 The McGraw-Hill Companies : The Smith Chart Figure 13-30: The Smith chart.
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