Characterization of LeftHanded Materials
Massachusetts Institute of Technology
6.635 lecture notes
1
Introduction
1. How are they realized?
2. Why the denomination LeftHanded?
3. What are their properties?
4. Does it really work?
It has already been sho
5.8.1)
Given:
For the 1/2turn ferrite bead whose measured impedance is shown in Fig. 5.33a,
Find:
To determine the equivalent inductance.
Diagram and Data:
Assumption:
Assuming resistor is very small and could be neglected at low frequency.
Analysis:
To
6.2.5:
Given:
The band reject filter is shown in Fig. 6.7(d).
Find:
Determine and equation for the insertion loss of this filter?
Diagram and Data:
Figure 6.7 (d) bandreject
Analysis:
Insertion Loss is given by equation 6.7 on pg. no. 386 from the book.
I
6.2.3)
Given:
The high pass filter is shown in Fig. 6.7(b).
Find:
Determine an equation for the insertion loss of this filter?
Diagram and Data:
Figure 6.7: (b) highpass
Analysis:
Insertion Loss is given by equation 6.7 on page: 386 from the book
ILdB = 1
1.5.1 )
Given:
The voltages in each case.
Find :
Determine the voltage in each case in (dBV) and (dBm).
Diagram:
Non
Assumption: Assuming the load resistor equals to 50 Ohm:
R 50
Analysis and Final answer:
First, we can define a function as follows:
To f
3.1.1:
Given:
The waveforms are shown in Fig. P3.1.1 below in the diagram section.
Find:
To determine the period (T), fundamental frequency (f0) and the average value and hence c0 of
the waveforms?
Diagram and Data:
Assumption:
No need for assumptions in
1.4.2)
Given:
(1) 120 MHz, 18 cm, in air,
(3) 500 MHz, 10 in, in glass epoxy,
(5) The 3 m length of FCC regulations at lower 30 MHz and upper 1 GHz in air,
(7) An automobile (12 ft) at lower frequency of AM band (450 kHz),
Find:
Determine the physical dim
Problem 3.1.5:
Given:
A periodc waveforms is given in the gure 2, below.
Find:
Determin the (one sided) Fourier series expansion in the gure below ?
Diagram
Figure 2: Periodic Waveform problem 3.1.5
Analysis and equa ons:
t1 + T
The expansion coefficients
5.7.1)
Given:
For the toroid of NiZn whose measured impedance is shown in Fig. 5.29b, model the
impedance as an inductor in parallel with a resistance that is in parallel with a parasitic
capacitance of the windings.
Find:
To determine the inductance, res
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Problem 3.2.4:
Given:
A 10MHz clock oscillator transitioning from 0 to 5 V with rise/falltimes of 10 ns and a 50% duty cycle is connected to a gate as shown in Fig.5,
below .
Find:
Determine the value of the capctance such that the 5th harmonic is reduce
Problem 3.2.1:
Given:
A 10MHz clock oscillator transitioning from 0 to 5 V with rise/falltimes of 20 ns and a 50% duty cycle is connected to a gate as shown in Fig.3,
below . A filter is connected as shown.
Find:
Determine the level of the 11th harmonic
3.1.3)
Given:
The waveform in Fig. P3.1.3.
Find:
The (onesided) Fourier series expansion?
Diagram and Data:
Assumptions:
We will assume that:
T 1 s and A 1
Analysis:
The expansion coefficients are:
t1 + T
2
1j n t
T
1
cn x (t) e
dt
T 0
For the periodic
Dispertion relations in LeftHanded Materials
Massachusetts Institute of Technology
6.635 lecture notes
1
Introduction
We know already the following properties of LH media:
1.
r
and r are frequency dispersive.
2.
r
and r are negative over a similar freque
Greens functions for planarly layered media
Massachusetts Institute of Technology
6.635 lecture notes
1
Introduction: Greens functions
The Greens functions is the solution of the wave equation for a point source (dipole). For scalar
problems, the wave equ
Greens functions for planarly layered media (continued)
Massachusetts Institute of Technology
6.635 lecture notes
We shall here continue the treatment of multilayered media Greens functions, starting from
the TE/TM decomposition we have presented in the p
Integral Equations in Electromagnetics
Massachusetts Institute of Technology
6.635 lecture notes
Most integral equations do not have a closed form solution. However, they can often be
discretized and solved on a digital computer.
Proof of the existence of
The Method of Moments in Electromagnetics
Massachusetts Institute of Technology
6.635 lecture notes
1
Introduction
In the previous lecture, we wrote the EFIE for an incident TE plane wave on a PEC surface.
The solution was then obtained by some types of i
Time Domain Method of Moments
Massachusetts Institute of Technology
6.635 lecture notes
1
Introduction
The Method of Moments (MoM) introduced in the previous lecture is widely used for solving
integral equations in the frequency domain. Yet, some attempts
Study of EM waves in Periodic Structures
with addenda: Study of EM waves in Periodic Structures (mathematical details)
Massachusetts Institute of Technology
6.635 lecture notes
1
Introduction
We will study here the distribution of electromagnetic elds in
Study of EM waves in Periodic Structures (mathematical details)
Massachusetts Institute of Technology
6.635 partial lecture notes
1
Introduction: periodic media nomenclature
1. The space domain is dened by a basis,(a1 , a2 , a3 ), where any vector can be
Study of EM waves in Periodic Structures: Photonic Crystals and
Negative refraction
Massachusetts Institute of Technology
6.635 lecture notes
1
Introduction
In the previous class, we have introduced various concepts necessary for the study of EM waves
in
1.1.3)
Given:
Find:
Below dimmensions for each case.
Convert the following dimmensions to those indicated.
Diagram: Non
Analysis and Final Answer:
For each case below:
1) Convert from 30 miles to km:
our answer for this case is:
30 mi = 48.28 km
3) Conver
6.1.1)
Given:
In order to illustrate that the LISN essentially presents 50 V impedances between phase
and ground and between neutral and ground,
Find:

Use PSPICE to plot the frequency response of the impedance looking into one side of
the LISN shown in