Subject Name: Microwave and Radar Subject Code: 10EC54 Subject Name: Microwave and Radar-Unit 1 Subject Code: 10EC54 Prepared By: Lakshmi C R, Dharani K G Department: ECE Date: 10.11.14 Subject Name: Microwave and Radar Subject Code: 10EC54 Prepared By: Lakshmi C R Department: ECE Date: 22.8.14 22/8/14

MICROWAVE TRANSMISSION LINES UNIT 1 MICROWAVE TRANSMISSION LINES

Topic Details Transmission Line Introduction Transmission Line Equation and Solution Reflection Coefficient Transmission Coefficient Standing Waves And Standing Wave Ratio Line impedance Line admittance Smith Chart Impedance Matching Using Stubs Microwave Coaxial Connectors 22/8/14

Transmission Line Introduction In an electronic system, the delivery of power requires the connection of two wires between the source and the load. At low frequencies, power is considered to be delivered to the load through the wire. In the microwave frequency region, power is considered to be in electric and magnetic fields that are guided from lace to place by some physical structure. Any physical structure that will guide an electromagnetic wave place to place is called a Transmission Line 22/8/14

Transmission Line Introduction Properties Has two conductors running parallel Can propagate a signal at any frequency Becomes lossy at high frequency Can handle low or moderate amounts of power Does not have signal distortion, unless there is loss May or may not be immune to interference Does not have Ez or Hz components of the fields TEMzi 22/8/14

Types of Transmission Modes 22/8/14

Transmission Line Equation and Solution RDz LDz GDz CDz z v(z+z,t) + - v(z,t) i(z,t) i(z+z,t) 22/8/14

22/8/14

22/8/14

22/8/14

Reflection Coefficient The reflection coefficient is a parameter that describes how much of an electromagnetic wave is reflected by an impedance discontinuity in the transmission medium. It is equal to the ratio of the amplitude of the reflected wave to the incident wave, with each expressed as phasors 22/8/14

Transmission Coefficient Transmission coefficient is defined as the ratio of transmitted voltage to the incident voltage 22/8/14

Standing Waves And Standing Wave Ratio A standing wave is formed by the addition of incident and reflected waves and has nodal points that remain stationary with time. Voltage Standing Wave Ratio: VSWR = Vmax/Vmin Voltage standing wave ratio expressed in decibels is called the Standing Wave Ratio: SWR (dB) = 20log10VSWR The maximum impedance of the line is given by: Zmax = Vmax/Imin The minimum impedance of the line is given by: Zmin = Vmin/Imax or alternatively: Zmin = Zo/VSWR Relationship between VSWR and Reflection Coefficient: VSWR = (1 + |G|)/(1 - |G|) G = (VSWR – 1)/(VSWR + 1) 22/8/14

Smith Chart For complex transmission line problems, the use of the formulae becomes increasingly difficult and inconvenient. An indispensable graphical method of solution is the use of Smith Chart. 22/8/14

The types of problems for which Smith charts are used include the following: Plotting a complex impedance on a Smith chart Finding VSWR for a given load Finding the admittance for a given impedance Finding the input impedance of a transmission line terminated in a short or open. Finding the input impedance at any distance from a load ZL. Locating the first maximum and minimum from any load Matching a transmission line to a load with a single series stub. Matching a transmission line with a single parallel stub Matching a transmission line to a load with two parallel stubs. 22/8/14

Line Impedence and Line Admittance To locate a complex impedance, Z = R+-jX or admittance Y = G +- jB on a Smith chart, normalize the real and imaginary part of the complex impedance. Locating the value of the normalized real term on the horizontal line scale locates the resistance circle. Locating the normalized value of the imaginary term on the outer circle locates the curve of constant reactance. The intersection of the circle and the curve locates the complex impedance on the Smith chart 22/8/14

Impedance Matching Using Single Stubs transmission line used to match another (main) transmission line is called a stub. The length of a stub is chosen to make its admittance be equal –jB. This process of line matching is called single-stub matching. The length of the stub can be made adjustable. Such adjustable-length transmission lines are sometimes called a trombone line. Note that single-stub matching requires two adjustable distances: location of the stub d1 and the length of the stub d2. In some situations, only the stub’s length can be adjusted. In these cases, additional stub(s) may be used. The distances mentioned here are normalized to the wavelength. Therefore, this method allows line matching at particular discrete frequencies. 22/8/14

Microwave Coaxial Connectors For high-frequency operation, the average circumference of a coaxial cable must be limited to about one wavelength in order to reduce multimodal propagation and eliminate erratic reflection coefficients, power losses, and signal distortion 22/8/14