Engineering Electromagnetics
Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 13, Problem 13.7P

Pertinent dimensions for the transmission line shown in Figure 13.2 are b = 3 mm and d= 0.2 mm. The conductors and the dielectric are nonmagnetic. (a) If the characteristic impedance of the line is 15 Ω , find ϵ r' . Assume a low-loss dielectric. (b) Assume copper conductors and operation at 2 × 10 8 rad/s. If RC = GL, determine the loss tangent of the dielectric.

Expert Solution
Check Mark
To determine

(a)

The dielectric constant εr , so that Z0=15Ω.

Answer to Problem 13.7P

The dielectric constant εr , so that Z0=15Ω is εr=2.8.

Explanation of Solution

Given:

The given figure is shown below..

Engineering Electromagnetics, Chapter 13, Problem 13.7P , additional homework tip  1.

   d=0.2mmb=3mmZ0=15Ω.

Calculation:

The characteristic impedance of the transmission line is given as:.

   Z0=με(db)Z0=μεr(db)εr=(37715)2.049εr=2.8.

Conclusion:

Thus, the dielectric constant εr , so that Z0=15Ω is εr=2.8.

Expert Solution
Check Mark
To determine

(b)

The loss tangent of the dielectric, when RC=GL.

Answer to Problem 13.7P

The loss tangent of the dielectric, when RC=GL is 5.85×102 .

Explanation of Solution

Given:

The given figure is shown below:.

Engineering Electromagnetics, Chapter 13, Problem 13.7P , additional homework tip  2.

   d=0.2mmb=3mmZ0=15Ωω=2×108rad/sec.

Calculation:

For copper conductivity is σc=5.8×107S/m and therefore skin depth can be calculated as:.

   δ=2ωμ0σcσc=5.8×107S/m.ω=2×108rad/sec.δ=2(2×108)(4π×107)(5.8×107)δ=1.2×105m.

Thus, resistance can be calculated as:.

   R=2σcδbb=3mm=.003mσc=5.8×107S/mδ=1.2×105mR=2(5.8×107)(1.2×105)(.003)R=0.98Ω/m.

Capacitance can be calculated as:.

   C=εbdC=εrε0bdε0=8.854×1012εr=2.8d=0.2mmb=3mmC=2.8×8.854×1012×30.2C=3.7×1010F/m.

Inductance can be calculated as:.

   L=μ0dbL=4π×107×0.23L=8.4×108H/m.

As,

   RC=GLG=RCLG=0.98×(3.7×1010)8.4×108G=4.4×103S/m.

Conductivity can also be given as:.

   G=σdbdσd=Gdbσd=Gdbd=0.2mmb=3mmG=4.4×103S/mσd=4.4×103×0.23σd=2.9×104S/m.

The loss tangent is given as:.

   l.t=σdωεl.t=2.9×104(2×108)(2.8)(8.854×1012)l.t=5.85×102.

Conclusion:

Thus, the loss tangent of the dielectric, when RC=GL is 5.85×102.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Can you rewrite the solution because it is unclear? AM (+) = 8(1+0.5 cos 1000kt +0.5 ros 2000 thts) = cos 10000 πt. 8 cos wat + 4 cos wit + 4 cos Wat coswet. J4000 t j11000rt $14+) = 45 jqooort +4e + e + e j 12000rt. 12000 kt + e +e +e Le jsoort -; goon t te +e Dcw> = 885(W- 100007) + 8 IS (W-10000) - USB
Can you rewrite the solution because it is unclear? Q2 AM ①(+) = 8 (1+0.5 cos 1000πt +0.5 ros 2000kt) $4+) = 45 = *cos 10000 πt. 8 cos wat + 4 cosat + 4 cos Wat coswet. j1000016 +4e -j10000πt j11000Rt j gooort -j 9000 πt + e +e j sooort te +e J11000 t + e te j 12000rt. -J12000 kt + с = 8th S(W- 100007) + 8 IS (W-10000) <&(w) = USB -5-5 -4-5-4 b) Pc 2² = 64 PSB = 42 + 4 2 Pt Pc+ PSB = y = Pe c) Puss = PLSB = = 32 4² = 8 w 32+ 8 = × 100% = 140 (1)³×2×2 31 = 20% x 2 = 3w 302 USB 4.5 5 5.6 6 ms Ac = 4 mi = 0.5 mz Ac = 4 ५ M2 = =0.5
A. Draw the waveform for the following binary sequence using Bipolar RZ, Bipolar NRZ, and Manchester code. Data sequence= (00110100) B. In a binary PCM system, the output signal-to-quantization ratio is to be hold to a minimum of 50 dB. If the message is a single tone with fm-5 kHz. Determine: 1) The number of required levels, and the corresponding output signal-to-quantizing noise ratio. 2) Minimum required system bandwidth.
Knowledge Booster
Background pattern image
Electrical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Power System Analysis and Design (MindTap Course ...
Electrical Engineering
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:Cengage Learning
How do Electric Transmission Lines Work?; Author: Practical Engineering;https://www.youtube.com/watch?v=qjY31x0m3d8;License: Standard Youtube License