Fundamentals of Applied Electromagnetics (7th Edition)
7th Edition
ISBN: 9780133356816
Author: Fawwaz T. Ulaby, Umberto Ravaioli
Publisher: PEARSON
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Textbook Question
Chapter 2.6, Problem 11E
A 140 Ω lossless line is terminated in a load impedance
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The voltage waveform on a lossless TL in air is given by:
+ -20e*Bz (V).
The TL has a characteristic impedance of 100 Q and
length 0.5 X.
What is the load reflection coefficient ?
What is the value of the load Z ?
0.35λ long with characteristic impedance Z0= 50 ohmstransmission line is combined with ZL=10+j25 load. in the source andShow the reflection coefficient at the input using the Smith chart.
Zin=?
Γ=?
SWR=?
c) For a transmission line w/characteristic impedance Z0 = 50 W. At some point of the line,
a forward wave has the voltage V+ = 10V and backward wave has the voltage V- = 4V.
i) Currents of the forward wave and backward wave at that point.
ii) Measured voltage and current at that point.
d) A transmission line has the following properties:
Length, L = 3 m. Characteristic impedance Z0 = 50 W. The load impedance ZL = 100 W.
And phase constant b = p/3.
Assume the forward voltage at z = 0 is VA =10ejp/4
At z = 3m, calculate:
i) Forward voltage and forward current.
ii) Backward voltage and backward current.
iii) Measured (total) voltage and current across the load
Chapter 2 Solutions
Fundamentals of Applied Electromagnetics (7th Edition)
Ch. 2.2 - What is a transmission line? When should...Ch. 2.2 - Prob. 2CQCh. 2.2 - What constitutes a TEM transmission line?Ch. 2.2 - Prob. 4CQCh. 2.2 - Prob. 1ECh. 2.2 - Calculate the transmission line parameters at 1...Ch. 2.4 - Verify that Eq. (2.26a) indeed provides a solution...Ch. 2.4 - A two-wire air line has the following line...Ch. 2.6 - The attenuation constant represents ohmic losses....Ch. 2.6 - How is the wavelength of the wave traveling on...
Ch. 2.6 - Prob. 7CQCh. 2.6 - What is a standing-wave pattern? Why is its period...Ch. 2.6 - Prob. 9CQCh. 2.6 - For a lossless transmission line, = 20.7 cm at 1...Ch. 2.6 - A lossless transmission line uses a dielectric...Ch. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 10ECh. 2.6 - A 140 lossless line is terminated in a load...Ch. 2.8 - What is the difference between the characteristic...Ch. 2.8 - What is a quarter-wave transformer? How can it be...Ch. 2.8 - Prob. 12CQCh. 2.8 - Prob. 13CQCh. 2.8 - if the input impedance of a lossless line is...Ch. 2.8 - Prob. 12ECh. 2.8 - A 300 feedline is to be connected to a 3 m long,...Ch. 2.9 - According to Eq. (2.102b), the instantaneous value...Ch. 2.9 - Prob. 16CQCh. 2.9 - What fraction of the incident power is delivered...Ch. 2.9 - Prob. 18CQCh. 2.9 - For a 50 lossless transmission line terminated in...Ch. 2.9 - For the line of Exercise 2-14, what is the...Ch. 2.10 - The outer perimeter of the Smith chart represents...Ch. 2.10 - What is an SWR circle? What quantities are...Ch. 2.10 - What line length corresponds to one complete...Ch. 2.10 - Which points on the SWR circle correspond to...Ch. 2.10 - Prob. 23CQCh. 2.10 - Use the Smith chart to find the values of ...Ch. 2.11 - Prob. 24CQCh. 2.11 - Prob. 25CQCh. 2.12 - What is transient analysis used for?Ch. 2.12 - Prob. 28CQCh. 2.12 - What is the difference between the bounce diagram...Ch. 2 - A transmission line of length l connects a load to...Ch. 2 - Show that the transmission-line model shown in...Ch. 2 - A 1 GHz parallel-plate transmission line consists...Ch. 2 - For the parallel-plate transmission line of...Ch. 2 - In addition to not dissipating power, a lossless...Ch. 2 - For a distortionless line [see Problem 2.13] with...Ch. 2 - Prob. 15PCh. 2 - A transmission line operating at 125 MHz has Z0 =...Ch. 2 - Prob. 17PCh. 2 - Polyethylene with r=2.25 is used as the insulating...Ch. 2 - Prob. 20PCh. 2 - Prob. 21PCh. 2 - Prob. 22PCh. 2 - Prob. 23PCh. 2 - A 50 lossless line terminated in a purely...Ch. 2 - Prob. 26PCh. 2 - Prob. 27PCh. 2 - Prob. 29PCh. 2 - Prob. 30PCh. 2 - Two half-wave dipole antennas, each with an...Ch. 2 - Prob. 34PCh. 2 - For the lossless transmission line circuit shown...Ch. 2 - A lossless transmission line is terminated in a...Ch. 2 - The input impedance of a 31 cm long lossless...Ch. 2 - FM broadcast station uses a 300 transmission line...Ch. 2 - A generator with Vg=300 V and Zg = 50 is...Ch. 2 - If the two-antenna configuration shown in Fig....Ch. 2 - For the circuit shown in Fig. P2.44, calculate the...Ch. 2 - The circuit shown in Fig. P2.45 consists of a 100 ...Ch. 2 - An antenna with a load impedance ZL=(75+j25) is...Ch. 2 - Prob. 47PCh. 2 - Use the Smith chart to determine the input...Ch. 2 - Prob. 52PCh. 2 - A lossless 50 transmission line is terminated in...Ch. 2 - A lossless 50 transmission line is terminated in...Ch. 2 - Use the Smith chart to find yL if zL = 1.5 j0.7.Ch. 2 - Prob. 59PCh. 2 - Prob. 62PCh. 2 - Determine Zin of the feed line shown in Fig....Ch. 2 - Prob. 73PCh. 2 - A 25 antenna is connected to a 75 lossless...Ch. 2 - Prob. 75PCh. 2 - Prob. 76PCh. 2 - Prob. 77PCh. 2 - In response to a step voltage, the voltage...Ch. 2 - Suppose the voltage waveform shown in Fig. P2.77...Ch. 2 - For the circuit of Problem 2.80, generate a bounce...Ch. 2 - In response to a step voltage, the voltage...
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- A 502 transmission line is terminated with a 502 resistor on series with a 2 * 10 H inductor. If the frequency of the operation is 60 10° MHz find the reflection coefficient at the load. * Select one: O a. 0.36e56 О .1 O c.0.45e22 O d. 0.6e 37 Oe. 0arrow_forwardThe capacitance per unit length and the characteristic impedance of a lossless transmission line are C and Zo respectively. The velocity of a travelling wave on the transmission line is (a) Z.C (c) Zo C - UN (b) Z.C (d) Zarrow_forwardA single-phase transmission line consisting of two conductors, the radius of each conductor is 0.4 cm, the distance between the conductors is three and half meters and the height above ground is eight 1-The capacitance in uF/km without effect of ground is 2-The capacitance in pF/km with effect of ground isarrow_forward
- In the transmission line below, Z0=50 ohm operating frequency is 100MHz and wave speed is given as v=10^8 m/s. If d=46cm and l=14cm are chosen to avoid any back reflection in the transmission line, the load impedance ZL=?arrow_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_forwardA 702 high-frequency lossless line is used at a frequency where 2 = 80cm with a load of 140+j91 2 a. Calculate the reflection coefficient and the SWR b. Determine the distance to the first voltage minimum from the load c. Determine the distance to the first voltage maximum from the load d. Calculate the impedance at the point where maximum voltages occurarrow_forward
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- A single-phase transmission line consisting of two conductors, the radius of each conductor is 0.4 cm, the distance between the conductors is three and half meters and the height above ground is eight meter. Determine 1)The capacitance in uF/km without effect of ground 2)The capacitance in uF/km with effect of groundarrow_forward10 V In the lossless transmission line system shown, the switch S is closed at t = 0. a. Find the reflection coefficient IJ. b. Find the reflection coefficient TL. c. Find the transmission coefficient t+. d. Complete the following reflection diagram in order to determine the total voltages VA, VB, Vc, and VD. 752 201=7522 T VA= 5 em |V₁ = ? |V₂ = ? Figure P6 70₂= Son T V₂=? 4 [V=0] Vc 15022arrow_forwardA lossless transmission line (TL) has a characteristic impedance of Zo= 250 N, a load impedance of ZR = 125 – j150 N and its operating frequency is fo Smith chart to evaluate the following parameters: 150 MHz. Use 1) The load admittance YR. 2) The reflection coefficient [Kr|ZOR 3) The voltage standing wave ratio (VSWR). Then calculate the maximum and minimum impedance in this TL, (Zmax and Zmin). 4) The distance from load to the nearest maximum (dmax) and minimum voltage positions (dmin) (in meter). 5) Find Zd at a distance away from a load by d= 3.3 2. Then calculate Zd using TL equation.arrow_forward
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