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TELECOMMUNICATIONS Dr. Hugh Blanton ENTC 4307/ENTC 5307 Transmission Line Transformations • A lossless transmission line is a cascade of series inductors and parallel capacitors. • Cascading a transmission line to a complex termination has a rotating effect on the Smith Chart. Dr. Blanton - ENTC 4307 - Introduction 3 / 30 • To calculate the input impedance (ZIN) of a lossless transmission line (having characteristic impedance ZTL and electrical length q) cascaded to ZT. 1. Locate the normalized termination (zT) on a Smith Chart that is normalized to Zo = ZT. 2. Draw a concentric circle (constant VSWR) through zT and rotate clockwise on this circle twice the electrical length (2q in degrees) of the line. 3. Mark the end of the rotation of the circle and read the normalized value of zIN. 4. Multiply zIN by Z0 to find ZIN. Dr. Blanton - ENTC 4307 - Introduction 4 / 30 • Textbooks recommend different procedures for transmission line transformations on the Smith Chart: • one for movement towards loads and • another toward sources. • Instead of having two different directions, always rotate clockwise from the starting impedance to find a new impedance along the line. Dr. Blanton - ENTC 4307 - Introduction 5 / 30 • Since the Chart is a reflection coefficient tool, a wave must travel twice (incident and reflected) through the transmission line. • Accordingly, we must rotate through an angle in degrees that is two times the electrical length of the line. Dr. Blanton - ENTC 4307 - Introduction 6 / 30 • Find the input impedance (ZIN) of the circuit shown at f = 1 GHz. Dr. Blanton - ENTC 4307 - Introduction 7 / 30 ZT 30 j15 1. Find zT 0.4 j 0.2 on a Smith Chart ZTL 75 that is normalized to ZTL. 2. Draw a constant VSWR circle through zT rotate 2q=90 clockwise (154 to 64) from zT. 3. Read the normalized input impedance zIN = 1 +j1. 4. Unnormalize, ZIN = zIN Zo =( 1 +j1)75W. 5. Read GIN75=O.45Z64 in the 75~ system 6. 6. NOTE THAT Zin ALWAYS falls on the constant VSWR circle that passes thru Z~ Dr. Blanton - ENTC 4307 - Introduction 8 / 30 Dr. Blanton - ENTC 4307 - Introduction 9 / 30 • At a given frequency, lumped capacitors and inductors may be replaced by their equivalent open circuited or short circuited transmission line stubs. Dr. Blanton - ENTC 4307 - Introduction 10 / 30 • If a transmission line of less than 90 electrical length is open circuited at one side, the other end becomes similar to a capacitor. • This element can be used as an open-circuited parallel stub. Dr. Blanton - ENTC 4307 - Introduction 11 / 30 The input reflection coefficient of an open-circuited line is found on the Smith Chart by starting at an open circuit termination (ZT =) and rotate clockwise twice the electrical length (2 x 45 = 90) Dr. Blanton - ENTC 4307 - Introduction 12 / 30 • If a transmission line of less than 90 electrical length is short circuited at one end, the other side behaves like an inductor. • When used as a parallel branch, it represents a parallel short circuited stub. Dr. Blanton - ENTC 4307 - Introduction 13 / 30 Dr. Blanton - ENTC 4307 - Introduction 14 / 30
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