Electric fields travel at the speed of light - a constant 299,792,458 meters per second regardless of wavelength. However, this fact is only true for the ideal case where the waves are traveling through vacuum away from any other charge sources. In non-ideal situations, where an electric field is traveling through another medium, the speed of the field is slowed. But how slow?
In order to understand how different mediums effect an electric field's velocity, we first need to understand why the speed of light travels at the velocity it does in that idealized case. The first part of this multi-part series is going to discuss the general form of the wave equation followed by a derivation of the speed of light in vacuum.
Since i have found a position with Carnegie Mellon, i now have the time to reflect on my job search and more to the point, the interviews. While most of the time was spent discussing the experience listed on my resume, the question i remember hearing the most was if i could explain what the Hall effect is. Now, i have designed circuits leveraging Hall effect sensors in the past - in motor controllers as angular position sensors, in magnetic switches, and in scroll wheels as linear position sensors, but i never took the time to dig in and understand how the sensors worked. For all i cared it could have been voodoo, black magic, or a combination of the two - one way or another the sensor is able to tell me where it is in relation to a nearby magnetic field. That only gets you so far, so i guess it's time to demystify these little ICs.
What is the Hall effect:
The Hall effect, named after the scientist who first detected it Edwin Hall, is the opposing force a flow of charge carriers (current) induces to cancel out a Lorentz force acting upon it. This opposing forces is equal in magnitude and opposite in sign to the Lorentz force in order for the steady state net force on the carries to be zero, satisfying Newtons 3rd law. This answer requires a basic understanding of the fundamental laws of classical electromagnetic fields - Maxwell's equations, and the Lorentz force where Maxwell's equations describe how moving charge carriers induce EM fields and the Lorentz force is how EM fields effect moving charge carriers.
How to leverage the Hall effect:
One generally uses Hall effect sensors to sense the position of a magnet, or the magnitude of a current. There are 3 main types of position sensors - binary, linear and radial. For each, it is assumed that there is a magnetic field (generally generated by a magnet) that is a part of the component you want to sense the position of, in a location where it will pass over the sensor's active area.
- For a binary sensor, it will switch logic states when the active area is in proximity of a north or south pole (axially magnetized).
- For a linear sensor, it will give you an analog or multiple bit digital output corresponding to the distance the active area is away from a north or south pole.
- For a radial sensor, it will give you an analog or multiple bit digital output corresponding to the angle at which the north/south pole is to the active area. Radial sensors require a diametrically magnetized magnet persistently centered on the sensors active area.
- For current sensing, the Hall sensor's active area is placed perpendicularly to the currents induced magnetic field and will output an analog or multiple bit digital signal corresponding to the current's magnitude.
How do Hall effect sensors work:
Internal to the IC, there is a rectangular plate that a small current travels through in the y-direction, with voltage sensing circuitry connected across the plate in the x-direction. While there is no external magnetic field and therefore no Lorentz force, the current travels linearly through the plate and no voltage difference can be sensed at the sides of the plate. However, in the presence of a magnetic field perpendicular to the current flow (through the large surface of the plate in the z-direction), an electric field is formed called the Hall field which when integrated across the length of the plate gives you the a voltage differential called the Hall voltage.
This post is going to discuss two pitfalls that i encountered while using MODTRAN via the PLEXUS GUI. First is the conversion between Wavenumber to Wavelength, the second is using PLEXUS to perform night time lunar models.
The atmosphere, through its six layers, contains various particles and gases which attenuate impinging solar radiation. The particles which contribute the most to this attenuation are water (H2O) in the troposphere (0-11Km), carbon dioxide (CO2) also in the troposphere, and ozone (O3) in the stratosphere (11-50Km). While there is relatively little solar absorption through the visible bands (380nm - 750nm), there are strong absorption bands in the UVC and LWIR attributed to ozone, while H2O and CO2 absorb intermittently throughout the rest of the solar spectrum. A Transmittance vs. Wavelength graph for two generic scenarios can be seen below. Note: For larger absorption bands, the contributing particles are shown; the full Raytheon infrared wall chart can be found below under references. MODTRAN (MODerate spectral resolution atmospheric TRANSmittance algorithm and computer model) is an atmospheric spectral radiance modeling code developed by the Air Force Research Lab, Space Vehicles Directorate. This code has been combined with several others (MODTRAN4 V2R1, SAMM 1.1, SAMM 1.82, FASCODE3 with HITRAN2K, SHARC Atmosphere Generator (SAG) V1 & V2, and Celestial Background Scene Descriptor (CBSD) V5) into a single software suite called PLEXUS (Phillips Laboratory EXpert-assisted User Software) which provides the user with an easier to use GUI for these atmospheric codes. The most recent version as of the publishing of this post is Release 3 Version 3A. More information on PLEXUS as well as its constituent codes can be found on the AFRL software information page.