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 T, 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 T, you may need to adjust your answer depending on the quadrant.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Question
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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