Transmission Lines 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.
Topics Covered in Chapter 13 Transmission-Line Basics Standing Waves Transmission Lines as Circuit Elements The Smith Chart
Transmission-Line Basics The two primary requirements of a transmission line are: The line should introduce minimum attenuation to the signal The line should not radiate any of the signal as radio energy
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 where the spacing between the wires is maintained by a continuous plastic insulator. The most widely used type of transmission line is the coaxial cable, which consists of a solid center conductor surrounded by a dielectric material, usually a plastic insulator such as Teflon. Coaxial cable comes in sizes from ¼ inch to several inches in diameter.
Open Wire 300-Ω Twin Lead
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. Twisted-pair lines may be balanced or unbalanced.
Balanced Versus Unbalanced Lines (Continued) Balanced-line wires offer significant protection from noise pickup and cross talk. Coaxial cable and 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.
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. Wavelength is the length or distance of one cycle of an AC wave or the distance that an AC wave travels in the time required for one cycle of the signal. The distance represented by a wavelength in a given cable depends on the type of 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.)
Connectors (Continued) 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, and cable TV. The RCA phonograph connector is a coaxial connector which 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.
The F Connector
RCA Phonograph Connector
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 circuitthe characteristic or surge impedance (Z 0 ).
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. Velocity factors in transmission lines vary from approximately 0.5 to 0.9. The velocity factor of a coaxial cable is typically in the 0.6 to 0.8 range.
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.
Transmission-Line Specifications Many coaxial cables are designated by an alphanumeric code beginning with the letters RG or a manufacturers 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.
Transmission-Line Specifications (Continued) 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.
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 or has an impedance other than the characteristic impedance of the line, the signal is not fully absorbed by the load.
Standing Waves (Continued) 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.
By Definition… 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 and the 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 called reflected power. The magnitude of the standing waves on a transmission line is determined by the ratio of the maximum current to the minimum current along the line.
Transmission Line Terminated in Its Characteristic Impedance
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.
Resonant Circuits and Reactive Components Shorted and open quarter wavelengths act like LC tuned or resonant circuits at the reference frequency. If the line length is more or less than one-quarter wavelength, the transmission line looks like a capacitor or inductor at the reference frequency.
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.
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 this is equivalent to an unbalanced line. The characteristic impedance of microstrip is dependent on its physical characteristics.
Stripline 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. Characteristic impedance is dependent on its physical characteristics.
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.
The Smith Chart (Continued) Computations with complex numbers are long and time- consuming. Many calculations involve trigonometric relationships and although no individual calculation is difficult, the sheer volume of the calculations can lead to error. The Smith Chart published in 1939, 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.