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A wave signal travelling along an electrical transmission line (usually called incident wave) will be reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impe- dance. This can happen in real life if we join dissimilar transmission lines together. Signals travelling alone the line will be partially reflected at the junction (see illustration below; note that up to this point we have not asked you any question yet). Impedance Discontinuity Forward Current Propagating Voltage Wave Z01 Zo2 Řeturn Current Z01 Zo2 Incident Wave Transmitted Wave Reflected Wave Transmission Line Reflection Suppose a transmission line with characteristic impedance Zo is terminated at one end with an impedance of ZL (recall that impedance is a complex number Z = X+iY where X is the resistance and Y is the reactance), then the reflection coefficient I' is given by the voltage reflection equation ZL – Zo T = ZL + Zo where I', ZL = XL+iYL, and Zo = Xo + iYo are complex numbers. (a) What is the reflection coefficient I when a transmission line with characteristic impedance Zo = 3+2i is terminated by a resistor of S Ohms, where S is the last non-zero digit of your student number? Express your answer in Cartesian form. (NOTE: an ideal resistor has no reactance, which means the terminal impedance ZL is purely real, and equals to the resistance). (b) The argument of the reflection coefficient I' can be interpreted as the phase shift in the reflected signal compared to the incident signal. Determine the argument 0 of the reflection coefficient I', in terms of XL, YL, Xo and Yo (do not use the specific values in question 3.2a, since question 3.2b asks for a general answer). HINT: be careful about the quadrant of I', you may need to adjust your answer depending on the quadrant.

A wave signal travelling along an electrical transmission line (usually called incident wave) will be reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impe- dance. This can happen in real life if we join dissimilar transmission lines together. Signals travelling alone the line will be partially reflected at the junction (see illustration below; note that up to this point we have not asked you any question yet). Impedance Discontinuity Forward Current Propagating Voltage Wave Z01 Zo2 Řeturn Current Z01 Zo2 Incident Wave Transmitted Wave Reflected Wave Transmission Line Reflection Suppose a transmission line with characteristic impedance Zo is terminated at one end with an impedance of ZL (recall that impedance is a complex number Z = X+iY where X is the resistance and Y is the reactance), then the reflection coefficient I' is given by the voltage reflection equation ZL – Zo T = ZL + Zo where I', ZL = XL+iYL, and Zo = Xo + iYo are complex numbers. (a) What is the reflection coefficient I when a transmission line with characteristic impedance Zo = 3+2i is terminated by a resistor of S Ohms, where S is the last non-zero digit of your student number? Express your answer in Cartesian form. (NOTE: an ideal resistor has no reactance, which means the terminal impedance ZL is purely real, and equals to the resistance). (b) The argument of the reflection coefficient I' can be interpreted as the phase shift in the reflected signal compared to the incident signal. Determine the argument 0 of the reflection coefficient I', in terms of XL, YL, Xo and Yo (do not use the specific values in question 3.2a, since question 3.2b asks for a general answer). HINT: be careful about the quadrant of I', you may need to adjust your answer depending on the quadrant.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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A wave signal travelling along an electrical transmission line (usually called incident wave) will be reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impe- dance. This can happen in real life if we join dissimilar transmission lines together. Signals travelling alone the line will be partially reflected at the junction (see illustration below; note that up to this point we have not asked you any question yet). Impedance Discontinuity Forward Current Propagating Voltage Wave Z01 Zo2 Return Current Z01 Zo2 Incident Wave Transmitted Wave Reflected Wave Transmission Line Reflection Suppose a transmission line with characteristic impedance Zo is terminated at one end with an impedance of ZL (recall that impedance is a complex number Z = X +iY where X is the resistance and Y is the reactance), then the reflection coefficient I' is given by the voltage reflection equation ZL – Zo ZL + Zo where I, ZL = XL + iYL, and Zo Xo + iYo are complex numbers. (a) What is the reflection coefficient I when a transmission line with characteristic impedance Zo = 3+2i is terminated by a resistor of S Ohms, where S is the last non-zero digit of your student number? Express your answer in Cartesian form. (NOTE: an ideal resistor has no reactance, which means the terminal impedance ZL is purely real, and equals to the resistance). (b) The argument of the reflection coefficient I' can be interpreted as the phase shift in the reflected signal compared to the incident signal. Determine the argument 0 of the reflection coefficient I', in terms of XL, YL, Xo and Yo (do not use the specific values in question 3.2a, since question 3.2b asks for a general answer). HINT: be careful about the quadrant of I', you may need to adjust your answer depending on the quadrant.
Transcribed Image Text:A wave signal travelling along an electrical transmission line (usually called incident wave) will be reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impe- dance. This can happen in real life if we join dissimilar transmission lines together. Signals travelling alone the line will be partially reflected at the junction (see illustration below; note that up to this point we have not asked you any question yet). Impedance Discontinuity Forward Current Propagating Voltage Wave Z01 Zo2 Return Current Z01 Zo2 Incident Wave Transmitted Wave Reflected Wave Transmission Line Reflection Suppose a transmission line with characteristic impedance Zo is terminated at one end with an impedance of ZL (recall that impedance is a complex number Z = X +iY where X is the resistance and Y is the reactance), then the reflection coefficient I' is given by the voltage reflection equation ZL – Zo ZL + Zo where I, ZL = XL + iYL, and Zo Xo + iYo are complex numbers. (a) What is the reflection coefficient I when a transmission line with characteristic impedance Zo = 3+2i is terminated by a resistor of S Ohms, where S is the last non-zero digit of your student number? Express your answer in Cartesian form. (NOTE: an ideal resistor has no reactance, which means the terminal impedance ZL is purely real, and equals to the resistance). (b) The argument of the reflection coefficient I' can be interpreted as the phase shift in the reflected signal compared to the incident signal. Determine the argument 0 of the reflection coefficient I', in terms of XL, YL, Xo and Yo (do not use the specific values in question 3.2a, since question 3.2b asks for a general answer). HINT: be careful about the quadrant of I', you may need to adjust your answer depending on the quadrant.
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