Concept explainers
Two voltage waves of equal amplitude V0 and radian frequency
(a)
An expression for the net voltage wave which is formed by the superposition of the two voltages.
Answer to Problem 10.5P
The expression for the net voltage wave formed by the superposition of the two voltages is given by
Explanation of Solution
Given information:
The amplitude of two voltage waves is equal to
Calculation:
We write the equation of voltage when propagating in the forward
Hence, the expression is given by
In time domain,
Conclusion:
The expression for the net voltage wave formed by the superposition of the two voltages is given by
(b)
An expression for the net current in the line.
Answer to Problem 10.5P
The expression for the net current in the line is
Explanation of Solution
Given information:
The amplitude of two voltage waves is equal to
Calculation:
Use the previously obtained equation to determine the expression for net current in the line.
We previously obtained
(1) Therefore, the net current in the line is given by
Using the equation (1) for voltage here, we get
In time domain,
Conclusion:
The expression for the net current in the line is
(c)
The expression for the average power in the line.
Answer to Problem 10.5P
The expression for the average power in the line is
Explanation of Solution
Given information:
The amplitude of two voltage waves is equal to
Calculation:
We know of the power flow expression
We use this expressionto determine the expression for the average power in the line.
Power flow is given by,
Where, * represents the complex conjugate and Re represents the real part.
Conclusion:
The expression for the average power in the line is
Want to see more full solutions like this?
Chapter 10 Solutions
Engineering Electromagnetics
- at 20 MHz the characteristic impedance of a transmission line is (20-j2) ohm and the propagation constant is (0.01+j0.2.5) per meter. Find the primary constant?arrow_forwardCOS (2T10 Problem 4. A voltage wave of the form V+ = (2x 10-4V) cos( t-kz is incident from cable 1 with characteristic impedance 201 = 1200 onto a connection to cable 2 with characteristic impedance Z02=1002. Take the speed of the cable wave in each cable to be 2 x 10 m/s. A) Find the amplitudes of the reflected and transmitted voltages. B) Find the incident, reflected, and transmitted powers.arrow_forwardA transmission line of characteristic impedance of Zo=50 ohm with length of A/4 loaded by a load impedance of 150ohm find 1- the load reflection coefficient 2- the standing wave ratio (SWR)arrow_forward
- A transmission line is terminated by a load with admittance Y, = (0.6 + j0.8)/Z,. Find the normalized input impedance at /6 from the load. %3D 3arrow_forwardb. Determine what is the necessary length and characteristic impedance of a cable to be used as a quarter-wave matching transformer so that it can eliminate the standing waves and subsequently provide a matched condition for a 180 O resistive load fed from a 45 0 transmission line. This condition is to exist for a frequency of 95 MHz. Given a velocity factor = 1.0.arrow_forward1. Matching of a transmission line with a characteristic impedance (Zo) and a load impedance (Zn) can be obtained when (a) ZR 0.5Zo (b) ZR=2Zo (c) ZR-Zo (d) ZR-0 2. Standing wave ratio (S) for a short circuit load connected to a transmission line is equal to (a) S=0 (b) S= -1 (c) S= Infinity (d) S=1 3. Any transmission line repeats its impedance, voltage, and current characteristics every . (Where n-0, 1, 2, 3....etc.) (a) nλ/2 (b) nλ/3 (c) ni/5 (d) n2/6arrow_forward
- solve a and b a. Find the line characteristic impedance value so that the standing wave ratio is 1.5 in a lossless transmission line terminated with a resistive load of 100 ohms. b. A radio transmitter is connected to an antenna with an impedance of 80 + 40i by a coaxial cable with a characteristic impedance of 50 ohms. Since this transmitter with an impedance of 50 ohms can transfer 30W of power to a compatible load, how much power will it transfer to this antenna?arrow_forwardFind out the general solution for a transmission line due to transient voltage,where ,e = f(x-at) + F(x+at)arrow_forward1. Matching of a transmission line with a characteristic impedance (Zo) and a load impedance (ZR) can be obtained when (a) ZR=0.5ZO (b) ZR-2Z0 (c) ZR-Zo (d) ZR=0 2. Standing wave ratio (S) for a short circuit load connected to a transmission line is equal to (a) S=0 (b) S=-1 (c) S= Infinity (d) S=1 3. Any transmission line repeats its impedance, voltage, and current characteristics every (Where n-0, 1, 2, 3....etc.) (b) nλ/3 (a) nλ/2 (c) ni/5 (d) nλ/6 4. In smith chart, moving in the clockwise direction means moving a) From load to generator b) From generator to load 5. In Crank diagram, moving in the clockwise direction from the load to the source can be evaluated using the formula a) +j2Bd b)-j3Bx c) -j2Bd d)-j2Bxarrow_forward
- A 219-2 lossless air transmission line is connected to a complex load composed of a 579-Nresistor in series with a 0.01-mH inductor, as shown below. At 4 MHz, determine the voltage standing wave ratio, S. Zo L S = Question 2 A 357-2 lossless air transmission line is connected to a complex load composed of a 740-2 resistor in series with a 0.02-mH inductor, as shown below. At 6 MHz, determine lmaz , the location of the voltage maximum nearest to the load. Zo L Imaz m %3Darrow_forwardAn antenna with a radiation resistance of 48 ohms, a loss resistance of 2 ohms, and a reactance of 50 ohms is connected to a generator with open-circuit voltage of 10 V and internal impedance of 50 ohms via a N4-long transmission line with characteristic impedance of 100 ohms. The power radiated by the antenna is ..... .. 0.1384w 0.1384dB 0.148dB 0.148warrow_forward3. Using Maxwell's equations for uniform harmonic waves to prove that the Poynting vector can be expressed as: WE to.arrow_forward
- Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
- Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,