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A phase locked loop consists of a phase detector, a low-pass filter, and a voltage-controlled oscillator (VCO). The locked output comes out of the VCO and is fed back into the phase detector, which compares the phase with the input signal. The larger the phase difference, the smaller the DC voltage output of the phase detector, but there are also the extraneous original frequencies, harmonics, and sum frequencies. The subsequent low-pass filter strips these off forwarding the more slowly changing DC voltage. If the phase increases the lower voltage will increase the VCO frequency until it catches up with the input signal. If the phase decreases the higher voltage will reduce the VCO frequency until it slows to the input signal.

The advantage of resonance in a circuit is that it permits the circuit to act as straight though wire at resonance. For example this permits the selection of the ideal AC coupling capacitor.

Perpendicular vectors have dot products that are zero due to the cosine(90) being zero.
Parallel vectors have cross products that are zero due to the sin(0) being zero. This means the magnitude of the normal is zero for parallel vectors.

Maxwell’s equations derive from Ampere’s law and Gauss’s law for statics.

The integral forms derive from the Differential forms using Stokes’ Law^[2498] and the Divergence Law.

Ampere’s law for statics is ∇ x H = J. Maxwell added the electric displacement current density J_d = ∂D / ∂t.


The third law of Maxwell’s equations is Gauss’s law.^[2499]

∫_s D • dS = ∫_v q dV

where the vector dS = n*dS is a vector in the outward normal of the surface with magnitude dS.^[2500]

where the vector D is the Displacement Vector = Electric Flux Density = D = ε * E

∫ D cos θ dS = ∫_s D • n dS = ∫_s D • dS

Materials are:

Polarization is in C/m² – Coulombs per square meter, which is a bound surface charge density q_sp.
An increase in temperature for a conductor increases the thermal energy in its lattice structure causing lattice vibration and more collisions for moving electrons, thus a decrease in conductivity.

Semiconductors bridge the gap between Dielectrics and Conductors. In intrinsic (pure) semiconductors the carriers include:

Mobility is (drift velocity)/(unit E field). In semiconductors, drift velocity decreases with increased temperature due to collisions. However, charge density increases with temperature. Hence, with increase in temperature, mobility decreases, while conductivity increases.

The three constitutive properties characterize the electrical property of the material.

The permittivity – ε indicates the storage capacity of a material and is in (Farads/Meter). It indicates how well a material permits an Electric field to pass through. The scale is in an inverse sense such that a vacuum has the smallest permittivity (8.854 * 10^-12) and lets the largest E-field pass. While a higher permittivity, dielectric such as water at 81 would serve as an excellent capacitive material in storing an E-field for release.

The permeability – μ indicates the inductive quality of the material and is in (Henries/Meter). The larger the permeability the material may store a larger magnetic field. In Free Space the permeability is 4π * 10^-7 Henries/Meter.

The conductivity – σ is the inverse ohms per meter and indicates the charge movement quantity capability of the medium 1/(Ω Meters).

The permeability of most dielectric material is the same as free space.

Frequency, permittivity and conductivity that is the loss tangent specify whether a material is a good conductor or a good dielectric:

σ/(ωε) >> 1 Conductor – conduction current density prevails J_c
σ/(ωε) << 1 Dielectric – displacement current density prevails J_d

where σ/(ωε) = tan δ

Hence, the loss tangent tells us the operational behavior of a material at a particular frequency.

The secondary properties describe the dependencies of the constitutive parameters.^[2510] Graphically, convolution of two waves is taking the mirror reflection of the second wave and moving it towards the origin of the first wave, while plotting the area under the curve as a function of time given by the slide of the intersection.

The electrons surrounding the nucleus of an atom also spin around their own axis. Each contributes a ±9 E-24 magnetic moment.^[2513] Only the electrons found in incompletely filled shells contribute to this magnetic moment as the ones in filled shells cancel each other out. The nucleus of an atom also has a spin, but the nuclear spin is much smaller than the electron moment by a factor of E-3.

The propagation constant equals the attenuation constant plus the phase constant:

γ = α + jβ

Phase velocity is:

v_p = ω/β

Beta is the phase constant, phase number, or wave number and is in radians/meter. Also

β = 2π/λ

Beta is the number of waves there are in a meter multiplied by 2π. Hence, Beta is directly proportional to frequency since:

λ = c/f
β = f * 2π/c
β = ω/2π * 2π/c
β = ω / c

where ‘c’ is the speed of light. If we are not in free space than we replace ‘c’ with ‘v_p’ and end up with a form of the equation of phase velocity above.

We can breakdown communication into five layers of operation from higher logical layers to lower physical implementations. These are the OSI standard Layers.

Ethernet operates at Layer 2 and its main feature is that it shares the physical network by supporting collision sense and multiple access and collision avoidance (CSMA/CA).

ATM provides protocols from the transport layer down through the physical layer. ATM sends data in cells of 53 bytes in length. Each cell has a 5 byte header and a 48 byte payload. Fixed length cells and simple headers facilitate high speed switching.^[2519] ATM supports virtual channels through its cell header virtual channel identifier (VCI). Packet switches or routers read the VCI and route cells towards the destination. ATM runs over any physical layer achieving speeds of 600 Mps over fiber optics. TCP/IP is operating over 100 Mbps Ethernet and holds a standard position in the PC and LAN arena. IP over ATM operates by a router first processing the IP header and then using the ATM ARP table to process and send the ATM data.

Asynchronous Transfer Mode provides network-assisted congestion control. In essence as a cell of data travels from source to destination, switches along the pathway add information to Resource Management cells denoting on the congestion level. Either the switch or the destination will return the RM cell back to its source. The source in turn will process the RM cell to adjust the maximum rate at which to send data. The source intersperses RM cells amongst Data cells.

Each data cell contains an EFCI (explicit forward, congestion indication) bit. If a switch sets the EFCI bit in a data cell then the destination knows that it must return congestion information to the sender. Consequently, the destination will set the CI (congestion indication) in the subsequent RM cell before returning the cell to the sender.

An RM cell also contains the NI (no increase) bit that a switch may set in a passing RM cell to indicate mild congestion. The switch may set the CI bit on more severe congestion. The destination may return the RM cell intact, or adjust the CI bit itself based on an EFCI from a preceding data cell. Each RM cell also contains a two-byte ER (explicit rate) field. As the RM cells passes from source to destination, the congested switch may only lower ER to the rate of itself. In this manner, the ER field will contain the minimal rate of the entire path when the RM cell is returned to the source.^[2520]

The IP Layer 3 defines Internet communication.

TCP/IP provides end-end congestion control. TCP – Telnet Communication Protocol provides interactive communication. IP – Internet Protocol provides reliable data transfer.

SATCOM – satellite communications applies astronomy, communication theory, and electrical engineering in the development of satellite technology. Uplink frequencies use the higher frequency of the bands while download is of lower frequency. Higher frequency transmission requires more power as the quanta of energy is proportional to frequency. One advantage is that a smaller satellite dish is sufficient to capture a signal at a higher frequency. Newer satellite TV systems transmit at higher frequencies and customers consequently get by with smaller dishes on their roofs.

INTELSAT – International Telecommunications Satellite regulates international satellite location and operation assignments. Individual countries on the other hand operate Domsats – Domestic satellites for services such as voice, data, or video conferencing within a country. Domsats are in geostationary orbit so they have a constant position over a particular country. There is only one geostationary orbit for the world and that is over the equator. Satellites operate at 36,000 km in this functional area.

In contrast to the singular geostationary orbit, there are an infinite number of polar orbits. Weather satellites operate in polar orbits, usually at altitudes of 800 and 900 km. NOAA operates both geostationary operational environment satellites, GOES, and polar operational environment satellites, POES. The polar orbiting satellites are sun synchronous, i.e. crossing the equator at the same local time each day. There are two polar satellites in orbit at a time.

NOAA satellites participate in search and rescue, SAR operation. Russian satellites support this network with Cospas. NOAA satellites operate with Sarsat.^[2521] Originally, SAR operated only with satellites in low earth orbits, LEOs, supporting the system LEOSAR. Recently, NOAA added geostationary satellites to their services, which constitute GEOSAR.

When a vehicle becomes lost, its emergency beacon transmits a signal in the VHF/UHF range at a precise frequency. The velocity of the satellite relative to the beacon enables the satellite to measure the Doppler shift. As a POES satellite nears the latitude of a lost craft’s beacon, the received frequency is higher than the transmitted frequency. As it recedes from the beacon, the received frequency is smaller than the transmitted frequency. In this manner the POES determines the latitude position. On the second pass, the change in the earth’s rotation permits the satellite to determine the effect of rotation on the Doppler shift and to identify a precise longitude position.

Sarsat’s downlink frequency is 1544.5 MHz. to local user terminals, LUTs. The higher frequency alleviated the false alerts caused by interference from the older emergency locator transmitters, ELTs, operating at 121.5 MHz. There are about 600,000 distress beacons on aircraft and small vessels.

Radio signals are vertically polarized while TV signals are horizontally polarized.

Skin depth of microwave frequency radiation is dependent on the conductivity of skin which varies with frequency.

δ_s = sqrt (1/(f *π*μ₀*σ)) where σ is the conductivity of the material. μ₀ is mobility in free space 4πe-7.
For sea water σ = 4 siemens/meter at 10 GHz gives δ_s = 0.002515 meters or ~ 2 mm.
The conductivity of skin varies over frequency so σ ≈ 1:10 siemens/meter from 1:10 GHz.^[2522]
A microwave oven works at 2.45 GHz.

The Reflection coefficient is negative for a short circuit type of fault or positive if the fault is of an open circuit type from the following analysis. Z_L is the load resistance that is 0 for a short circuit or infinity for an open circuit. Z₀ is the intrinsic impedance.

Isolating problems in test engineering is similar to being a detective. These axioms apply:

At night, one can lower the thermostat to a minimum of 55 degrees. For each degree reduction for an eight-hour period, one can save 1% on heating costs.^[2524] For example, for a 5-degree reduction for 16 hours, one can save 10% on the monthly heating bill and even more if the heating rates are progressive. Pipe freezing may occur if the house is set to 50 degrees so there is a 5-degree margin here. “If you're away from home during winter, set the thermostat in your house to no lower than 55 degrees to prevent pipes from freezing during a cold snap while you're away. Open cabinet doors to allow heat to get to uninsulated pipes under sinks and appliances near exterior walls.”^[2525]

“For winter operation, consider setting the thermostat to 55 degrees at night when you sleep and at 68 degrees when you're home. (In colder parts of California, it's not recommended to set the temperature below 50 degrees, because indoor water pipes may freeze.)

For summer operation, set the temperature to 78 degrees when you're home and at 85 degrees or higher when the house is unoccupied. In the summer season, you might need to program your thermostat to cool only for one period of the day, such as the late afternoon and evening hours, when the family returns home.”^[2526]

^[2498] Advanced Engineering Electromagnetics, Balanis, p.5.
^[2499] Advanced Engineering Electromagnetics, Constantine Balanis, p.6
^[2500] Fields and Waves in Communication Engineering, Ramo, p.13
^[2501] AEE, p.59
^[2502] AEE, p.44
^[2503] AEE, Balanis, p.60
^[2504] AEE, Balanis, p.3
^[2505] AEE, p.80
^[2506] AEE, pp.53-54
^[2507] AEE, Balanis, Fig.2-9.p.54.
^[2508] AEE p.45
^[2509] Random House Dictionary
^[2510] AEE, Balanis, pp.7-8
^[2511] AEE, Balanis, p.71
^[2512] Ibid, p.71
^[2513] AEE, Balanis p.56
^[2514] Classical Electromagnetic Radiation 3^rd Edition, Heald and Marion, 1995, p.23
^[2515] Ibid
^[2516] Classical Electromagnetic Radiation 3^rd Edition, Heald and Marion, 1995, p.24
^[2517] AEE, Balanis p.85
^[2518] Advanced Engineering Electromagnetics, Balanis p.58
^[2519] Computer Networking, Kurose and Ross, p 57.
^[2520] Computer Networking A Top-Down Approach Featuring the Internet, James Kurose and Keith Ross.
^[2521] Sarsat refers to locating equipment on the satellite.
^[2522] http://ej.iop.org/links/q47/cAkVjWiQU1Qf9fZG,l18cA/m10603.pdf Changes in the dielectric properties of rat tissue as a function of age at microwave frequencies http://www.telecomlab.gr/2002/oct/rhodes/pap3rs/N%20123%20(p875%20-%20p881).pdf Heat Effect Analysis of Microwave Exposed Skin by Using a Multilayer Human Skin Model
^[2523] When Sherlock tries to determine a frequency for repelling flies and Watson resorts to the fly swatter.
^[2524] http://www.utah.gov/governor/docs/Energy_Conservation_Tips.pdf
^[2525] http://www.statefarm.com/sflocal/sunland/sun_hm.htm
^[2526] http://www.consumerenergycenter.org/homeandwork/homes/inside/heatandcool/thermostats.html

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