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 prop
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
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 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 gi
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 a
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?
Di
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
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
A
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
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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 valu
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
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:
t
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 di
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 p
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
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
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 sur
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
integra
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 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 den
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 v
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:
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 th