Fundamentals of Electromagnetics with Engineering Applications
5th Edition
ISBN: 9780471263555
Author: Stuart M. Wentworth
Publisher: John Wiley & Sons
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Chapter 2, Problem 2.46P
To determine
The potential
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Vs(t)
+ v(t)
+ vi(t)
ZR
ZL
Figure 1: Second order RLC circuit
Zc
+
ve(t)
You are requested to design the circuit shown in Figure 1. The circuit is assumed to be operating at its resonant frequency when it is fed by a
sinusoidal voltage source Vs (t) = 2sin(le6t). To help design your circuit you have been given the value of inductive reactance ZL = j1000.
Assume that the amplitude of the current at resonance is Is (t) = 2 mA. Based on this information, answer the following to help design your circuit.
Use cartesian notation for your answers, where required.
For a band-rejection filter, the response drops below this half power point at two locations as visualised in Figure 7, we need to find these
frequencies. Let's call the lower frequency-3dB point as fr and the higher frequency -3dB point fH. We can then find out the bandwidth as
f=fHfL, as illustrated in Figure 7.
0dB
Af
-3 dB
Figure 7. Band reject filter response diagram
Considering your AC simulation frequency response and referring to Figure 7, measure the following from your AC simulation. 1% accuracy:
(a) Upper-3db Frequency (fH) =
Hz
(b) Lower-3db Frequency (fL) =
Hz
(c) Bandwidth (Aƒ) =
Hz
(d) Quality Factor (Q) =
V₁(t)
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ZRI
ZLI
Z12
Zci
Zcz
Figure 4. Notch filter circuit topology
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Consider the second order resonant circuit shown in Figure 4. Impedances ZLIZ C1. ZL2. Z c2 combine together forming a two-stage "band-
reject" filter, so called because it rejects a "band" (aka range) of frequencies. This circuit topology is also commonly referred to as a "band-stop" filter
or "notch" filter.
The output of the DAB receiver block has been approximated via Thevenin's theorem for you as a voltage source Vs (t) and associated series
impedance Z RI
To succeed in our goal, we are going to use an iterative design approach. First we will design the interference rejector, and then repeat the process,
using the output of the interference rejector to check the provided waveform converter works as intended.
Chapter 2 Solutions
Fundamentals of Electromagnetics with Engineering Applications
Ch. 2 - Given P(4, 2, 1) and APQ=2ax+4ay+6az, find the...Ch. 2 - Prob. 2.2PCh. 2 - Prob. 2.3PCh. 2 - Suppose Q1(0.0,-3.0m,0.0)=4.0nC,...Ch. 2 - Prob. 2.5PCh. 2 - Suppose 10.0nC point charges are located on the...Ch. 2 - Four 1.00nC point charges are located at...Ch. 2 - A 20.0nC point charge exists at...Ch. 2 - Prob. 2.9PCh. 2 - Convert the following points from Cartesian to...
Ch. 2 - Prob. 2.11PCh. 2 - Prob. 2.12PCh. 2 - Prob. 2.13PCh. 2 - A 20.0–cm–long section of copper pipe has a...Ch. 2 - A line charge with charge density 2.00nC/m exists...Ch. 2 - You are given two z–directed line charges of...Ch. 2 - Suppose you have a segment of line charge of...Ch. 2 - A segment of line charge L=10.nC/m exists on the...Ch. 2 - In free space, there is a point charge Q=8.0nC at...Ch. 2 - Prob. 2.20PCh. 2 - Sketch the following surfaces and find the total...Ch. 2 - Consider a circular disk in the x–y plane of...Ch. 2 - Suppose a ribbon of charge with density S exists...Ch. 2 - Sketch the following volumes and find the total...Ch. 2 - You have a cylinder of 4.00–in diameter and...Ch. 2 - Consider a rectangular volume with...Ch. 2 - Prob. 2.27PCh. 2 - Prob. 2.28PCh. 2 - Given D=2a+sinazC/m2, find the electric flux...Ch. 2 - Suppose the electric flux density is given by...Ch. 2 - Prob. 2.31PCh. 2 - A cylindrical pipe with a 1.00–cm wall thickness...Ch. 2 - Prob. 2.34PCh. 2 - Prob. 2.35PCh. 2 - A thick–walled spherical shell, with inner...Ch. 2 - Prob. 2.37PCh. 2 - Determine the charge density at the point...Ch. 2 - Given D=3ax+2xyay+8x2y3azC/m2, (a) determine the...Ch. 2 - Suppose D=6cosaC/m2. (a) Determine the charge...Ch. 2 - Suppose D=r2sinar+sincosaC/m2. (a) Determine the...Ch. 2 - Prob. 2.42PCh. 2 - A surface is defined by the function 2x+4y21nz=12....Ch. 2 - For the following potential distributions, use the...Ch. 2 - A 100nC point charge is located at the origin. (a)...Ch. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Prob. 2.48PCh. 2 - Suppose a 6.0–m–diameter ring with charge...Ch. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - The typical length of each piece of jumper wire on...Ch. 2 - A 150–m length of AWG–22 (0.644 mm diameter)...Ch. 2 - Determine an expression for the power dissipated...Ch. 2 - Find the resistance per unit length of a stainless...Ch. 2 - A nickel wire of diameter 5.0 mm is surrounded by...Ch. 2 - Prob. 2.57PCh. 2 - A 20nC point charge at the origin is embedded in...Ch. 2 - Suppose the force is very carefully measured...Ch. 2 - The potential field in a material with r=10.2 is...Ch. 2 - In a mineral oil dielectric, with breakdown...Ch. 2 - Prob. 2.62PCh. 2 - For z0,r1=9.0 and for z0,r2=4.0. If E1 makes a 300...Ch. 2 - Prob. 2.64PCh. 2 - Consider a dielectric–dielectric charge–free...Ch. 2 - A 1.0–cm–diameter conductor is sheathed with a...Ch. 2 - Prob. 2.67PCh. 2 - For a coaxial cable of inner conductor radius a...Ch. 2 - Prob. 2.69PCh. 2 - Prob. 2.70PCh. 2 - A parallel–plate capacitor with a 1.0m2 surface...Ch. 2 - Prob. 2.72PCh. 2 - Prob. 2.73PCh. 2 - Given E=5xyax+3zaZV/m, find the electrostatic...Ch. 2 - Suppose a coaxial capacitor with inner radius 1.0...
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