### Some Important Pointers on Antenna Theory

• To create radiation, there must be an acceleration/deceleration of charge (i.e. changing current or AC current/voltage). This also implies that DC won't work on straight conductors as radiators unless the conductor is bent or has discontinuities (presence of centripetal acceleration in charge)
• If pulses of shorter and more compact duration are fed into a radiating element, stronger radiation with more frequency components will occur (I don't know by what magnitude radiation is amplified but it could serve as a possible driver of Microwave-generated hurricanes, though I doubt that the amplification factor could reach that high).
• Radiated fields do not need the continuous presence of electric charge to sustain their existence.
• An omnidirectional radiator is non-directional in one dimension while it is directional in other dimensions. An isotropic radiator is non-directional.
• The regions of antenna radiation can be divided into 3 parts:

-Reactive Near Field Region

Exists at R<0.62*sqrt((D^3)/lambda)

Exists at R<2*(D^2)/lambda

-Far Field (Fraunhofer) Region

Exists at greater distances than above

(D-antenna diameter; lambda-wavelength)

• The power density of radiated EM waves in the far field are mostly real values of the poynting vector. (The poynting vector is a way of expressing the amount of power associated with an EM wave and is expressed as the cross-product of the electric and magnetic field intensities) Also, the imaginary part is usually related to the inductive and capacitive characteristics of the radiated EM wave.
• There is no such thing as an isotropic radiator. It only exists in our imagination.
• The term directive gain has been "deprecated" by the 1983 version of the IEEE Standard Definitions of Terms for Antennas.
• The directivity of an isotropic source is unity.
• The 2 most popular methods in analysis of modern antenna problems are the Integral Equation method and Geometrical Theory of Diffraction.
The Integral Equation method is best used with analyzing electrically small/wire-type antennas. 2 integral equations are formulated in the analysis, the electric field integral equation and the magnetic field integral equation.
(sometimes the 2 methods are combined)
• The total efficiency of an antenna depends on the product of its reflection, conduction, and dielectric efficiencies.
• Right Hand Polarization- clockwise electric field rotation
• Left Hand Polarization- counter-clockwise electric field rotation
• In circular polarization, the magnitudes of the electric and magnetic fields are the same and their phase differences are odd multiples of 90 degrees.
• In elliptical polarization, the magnitudes of the electric and magnetic fields are NOT the same OR their phase differences are not multiples of 90 degrees (whatever the magnitude).
• If the phase differences are multiples of 180 degrees, then the radiated EM wave is linearly polarized.
• The figure of merit for polarization is the polarization efficiency/polarization mismatch/loss factor.
• Right hand polarized antennas cannot receive left hand polarized EM waves and vice versa.
• The free-space loss factor is the loss due to the spherical spreading of the EM energy radiated.
• Friis Transmission Equation relates the transmit and receive powers through the transmitter and receiver efficiencies, reflection coefficients, directivities, polarizations (Note: the dot product becomes zero when the transmitter polarization is vertical and the receiver polarization is horizontal - the dot product of i and j is zero thus the entire equation becomes equated to zero!!) and the free space loss.
• The Radar Range Equation is just like Friis Transmission Equation only with the added echo area factor divided by 4*pi.
• Every object with a temperature above absolute zero radiates energy (Stefan-Boltzmann) and this relationship can be used for antennas (antenna temperature/brightness temperature).
• Analysis - specify the source, require the fields
• Synthesis - specify the fields, find the source
• Infinitesimal wire dipoles are used to represent top-hat loaded (capacitor plate) antennas.
• Slightly rough surface- rms height much smaller than wavelength
• Very rough surface- rms height is much greater than wavelength
• Electrically small loop antennas are poor radiators.
• Superdirective antennas- antennas whose directivities are much larger than the directivity of a reference antenna of the same size

### Calculator Techniques for the Casio FX-991ES and FX-991EX Unraveled

In solving engineering problems, one may not have the luxury of time. Most situations demand immediate results. The price of falling behind schedule is costly and demeaning to one's reputation. Therefore, every bit of precaution must be taken to expedite calculations. The following introduces methods to tackle these problems speedily using a Casio calculator FX-991ES and FX-991EX.

►For algebraic problems where you need to find the exact value of a dependent or independent variable, just use the CALC or [ES] Mode 5 functions or [EX] MENU A functions.

►For definite differentiation and integration problems, simply use the d/dx and integral operators in the COMP mode.

►For models that follow the differential equation: dP/dx=kt and models that follow a geometric function(i.e. A*B^x).

[ES]
-Simply go to Mode 3 (STAT) (5)      e^x
-For geometric functions Mode 3 (STAT) 6 A*B^x
-(Why? Because the solution to the D.E. dP/dx=kt is an exponential function e^x.
When we know the boundary con…

### Common Difficulties and Mishaps in 6.004 Computation Structures (by MITx)

Updated:
May 6, 2018
VLSI Project: The Beta Layout [help needed]Current Tasks: ►Complete 32-bit ALU layout [unpipelined] in a 3-metal-layer C5 process. ►Extend Excel VBA macro to generate code for sequential instructions (machine language to actual electrical signals).
Current Obstacles/Unresolved Decisions:
►Use of complementary CMOS or pass transistor logic (do both? time expensive, will depend on sched.
►Adder selection: Brent-Kung; Kogge Stone; Ladner Fischer (brent takes up most space but seems to be fastest, consider fan-out) [do all? time expensive, will depend on sched.)
►layout requirements and DRC errors