Electronics/Voltage

Electric Field: E
A stationary charge has an electric field surrounding it given by:

$$E A = Q/\epsilon_o$$

A is 4 &pi; r2 the surface area of a sphere Q/&epsilon;o is how much the electric field deforms space

This becomes:

$$E = {Q \over 4 \pi r^2 \epsilon_o}$$

Permittivity: &epsilon

 * Permittivity: (&epsilon) How much energy a material absorbs when subject to an electric field. Similar to stretching a spring, when the electric field is removed, the material gives up the energy it has absorbed.


 * Vacuum Permittivity: The permittivity of the vacuum. &epsilono = 8.85419 10-12 F/m.


 * Relative Permittivity: The permittivity of materials relative to the vacuum. Also known as the Dielectric Constant: &epsilonr. Where &epsilon is the permittivity of the material.


 * $$ \epsilon_{r} = \frac{\epsilon}{\epsilon_{0}} $$


 * Dielectric: Usually an insulator. Acts to decrease the strength of the electric field.


 * Dielectric Strength: The maximum electric field a dieletric can handle before the electric field frees its bound electrons, turning the material into a conductor. The field strength at which breakdown occurs in a given case is dependent on the respective geometries of the dielectric (insulator) and the electrodes with which the electric field is applied, as well as the rate of increase at which the electric field is applied. Voltage is usually less than this number, and breakdown occurs when this number is exceeded.


 * Birefringence: double refraction.


 * Isotropic: behavior does not depend on direction.


 * Anisotropic: behavior depends on direction.

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means "independent of direction". Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.


 * When an electric field is applied, a current flows. The total current flowing in a real medium is in general made of two parts: a conduction current and a displacement one. The displacement current can be thought of as an elastic response which a material has to the applied electric field. As the electric field is increased, the displacement current is stored in the material, and when the electric field is decreased the material releases the displacement current. A perfect dielectric is a material that shows displacement current only, so it stores and returns electrical energy as if it were an ideal 'battery'.

The effect that an electric field has on space. deforms and displaces space and restoring force. &epsilon;o = 8.85419 10-12 F/m.

A dielectric is the material between two charges. It impedes the flow of charge until a certain voltage threshold at which point charge starts flowing, which is called dielectric breakdown and WHICH IS BAD AND DESTROYS THE CAPACITOR. :-)

''When I first learned about capacitors I thought that this was the way capacitors were used. They charge up to a strong enough voltage and then the dielectric breaks down and then they charge up again. I thought this was the basis for timer circuits. We need to be careful to separate dielectric breakdown from things that are supposed to happen in electronic circuits.''

In electromagnetism, permittivity ε is a measure of how much a medium changes to absorb energy when subject to an electric field. It is defined as the ratio D / E where D is the electric displacement by the medium and E is the electric field strength. The displacement D is usually given in units of coulombs per square metre (C/m2), while the electric field E is given as volts per metre (V/m).

In the common case of an isotropic medium, D and E are parallel and ε is a scalar, but in more general anisotropic media this is not the case and ε is a rank-2 tensor (causing birefringence).

Birefringence, or double refraction, is the division of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcite crystals, depending on the polarization of the light. This is explained by assigning two different refractive indices to the material for different polarizations. The birefringence is quantified by:

Δn = ne - no

where no is the refractive index for the ordinary ray and ne is the refractive index for the extraordinary ray.

More generally, an anisotropic dielectric material has a dielectric constant that is a rank-2 tensor (3 by 3 matrix). A birefringent material corresponds to the special cases of a real-symmetric dielectric tensor ε with eigenvalues of, , and along the three orthogonal principle axes of polarization. (Or, sometimes, only two axes are considered, corresponding to a single propagation direction.)

(In principle, birefringence could also arise in magnetic, not dielectric, materials, but substantial variations in magnetic permeability are rare at optical frequencies.)

See also: crystal optics | John Kerr.

The cellophane paper is a cheap birefringent material.

Anisotropic (meaning non-isotropic) is usually used to describe a directionally dependent phenomenon.

For example, anisotropic radiation has different intensities in different directions, and an anisotropic field exerts different actions depending on how the test particle is oriented. Magnetic susceptibility or electrical conductivity, for example, can be anisotropic in certain materials, as is the cosmic microwave background radiation. Wood is an anisotropic material as its strength and expansion due to humidity are different in the longitudinal, radial, and tangential directions. See also anisotropic etch, and liquid crystal

This term is also used in the field of computer graphics. For example, an anisotropic surface will change in appearance as it is rotated about its normal, as is the case with velvet. Anisotropic scaling occurs when something is scaled by different amounts in different directions, for example, stretching a 64×64-pixel texture to cover a 12×34-pixel rectangle.

When an electric field is applied, a current flows. The total current flowing in a real medium is in general made of two parts: a conduction current and a displacement one. The displacement current can be thought of as an elastic response which a material has to the applied electric field. As the electric field is increased, the displacement current is stored in the material, and when the electric field is decreased the material releases the displacement current. A perfect dielectric is a material that shows displacement current only, so it stores and returns electrical energy as if it were an ideal 'battery'.

The permittivity ε and magnetic permeability μ of a medium together determine the velocity of electromagnetic radiation through that medium.

In a vacuum, these are given by

where μ0 is the magnetic constant, or permeability of free space, equal to 4π × 10-7 N·A-2, and c is the speed of light, 299,792,458 m/s.

In case of lossy medium (i.e. when the conduction currents are not negligible) the total current density flowing is:

where, σ is the conductivity (responsible for conduction current) of the medium and εd is the relative permittivity (responsible for displacement current).

In this formalism the complex permittivity ε* is defined as:

For realistic materials, both the real and imaginary parts of the permittivity are more complicated functions of frequency ω; since this leads to dispersion of signals containing multiple frequencies, such materials are called dispersive. This frequency dependence reflects the fact that a material's polarization does not respond instantaneously to an applied field—because the response must always be causal (come after the applied field), the dielectric function ε(ω) must have poles only for ω with positive imaginary parts, and ε(ω) therefore satisfies the Kramers-Kronig relations. However, in the narrow frequency ranges that are often studied in practice, the dielectric constants can often be approximated as frequency-independent.

At a given frequency, the imaginary part of ε leads to absorption loss if it is negative (in the above sign convention for frequency) and gain if it is positive. (More generally, one looks at the imaginary parts of the eigenvalues of the anisotropic dielectric tensor.)

See also list of indices of refraction.

The refractive index of a particular material at a particular frequency is the factor by which electromagnetic radiation of that frequency is slowed down (relative to vacuum) when it travels inside the material. For a non-magnetic material, the square of the refractive index is the dielectric constant &epsilon; (sometimes multiplied by &epsilon;0, the permittivity of free space).

The speed of all electromagnetic radiation in vacuum is the same, approximately 3&times;108 meters per second, and is denoted by c. So if v is the phase velocity of radiation of a specific frequency in a specific material, then the refractive index is given by


 * n = c/v.

This number is typically bigger than one: the denser the material, the more the light is slowed down. However, at certain frequencies (e.g. near absorption resonances, and for x-rays), n will actually be smaller than one. This does not contradict the theory of relativity, which holds that no information carrying signal can ever propagate faster than c, because the phase velocity is not the same as the group velocity or the signal velocity.

The phase velocity is defined as the rate at which the crests of the waveform propagate; that is, the rate at which the phase of the waveform is moving. The group velocity is the rate that the envelope of the waveform is propagating; that is, the rate of variation of the amplitude of the waveform. It is the group velocity that (almost always) represents the rate that information (and energy) may be transmitted by the wave, for example the velocity at which a pulse of light travels down an optical fibre.

Sometimes, a "group velocity refractive index", usually called the group index is defined:


 * ng = vg / c ,

where vg is the group velocity. This value should not be confused with n, which is always defined with respect to the phase velocity.

At the microscale an electromagnetic wave is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the permittivity. This oscillation of charges itself causes the radiation of an electromagnetic wave that is slightly out-of-phase with the original. The sum of the two waves creates a wave with the same frequency but shorter wavelength than the original, leading to a slowing in the wave's travel.

Sometimes the refractive index is defined as a complex number, with the imaginary part of the number representing the absorption of the material. This is particularly useful when analysing the propagation of electromagnetic waves through metals.

If the refractive indices of two materials are known for a given frequency, then one can compute the angle by which radiation of that frequency will be refracted as it moves from the first into the second material from Snell's law.

The refractive index of a material varies with frequency (except in vacuum, where all frequencies travel at the same speed, c). This effect, known as dispersion, lets a prism divide white light into its constituent spectral colors, explains rainbows, and is the cause of chromatic aberration in lenses.

Some representative refractive indices at different wavelengths:

The refractive index of certain media may be different depending on the polarization and direction of propagation of the light through the medium. This is known as birefringence or anisotropy and is described by the field of crystal optics. In the most general case, the dielectric constant is a rank-2 tensor (a 3 by 3 matrix), which cannot simply be described by refractive indices except for polarizations along principle axes. In magneto-optic (gyro-magnetic) materials, the principle axes are complex (corresponding to elliptical polarizations), and the dielectric tensor is complex-Hermitian (for lossless media); such materials break time-reversal symmetry and are used e.g. to construct optical isolators.

The strong electric field of high intensity light (such as output of a laser) may cause a medium's refractive index to vary as the light passes through it, giving rise to nonlinear optics. If the index varies quadratically with the field (linearly with the intensity), it is called the optical Kerr effect and causes phenomena such as self-focusing and self phase modulation. If the index varies linearly with the field (which is only possible in materials that do not possess inversion symmetry), it is known as the Pockels effect.

See also list of indices of refraction.

In telecommunication, a dielectric waveguide is a waveguide that consists of a dielectric material surrounded by another dielectric material, such as air, glass, or plastic, with a lower refractive index.

An example of a dielectric waveguide is an optical fiber.

A metallic waveguide filled with a dielectric material is not a dielectric waveguide. -->

Voltage: V
The difference between two points in an electric field is the voltage V.

$$V = E \Delta x$$

Voltage is used in accelerators to accelerate charged particles to the speed of light. In Electronics voltage is the potential between two opposing charges given by:

$$ V = {q_1 \over 4 \pi \epsilon_o r_1} + {q_2 \over 4 \pi \epsilon_o r_2} $$

Where &epsilono is the permittivity of the vacuum, q1 and q2 are the values of the two charges (in coulombs), and r1 and r2 are their distances. Note how the Voltage falls off as 1/r.

If the charges were similar it would not make any sense. But if the particles have opposite charges then the voltage connects the charges. Through voltage positive charges go to the negative end, and negative charges go to the positive end.

Voltage causes charged particles to move according to the rules of repulsion and attraction, so electrons move from negative to positive. Two charged particles have a potential between them that relates to their separation distance.

Charged particles separated by a distance have a voltage associated with them. If the particles have a similar charge the voltage is repulsive and does not mean much.

Work: W
PE A charged particle in an electric field at distance r has an electrical potential energy U associated with it.

$$U = Q V$$

KE When a charged particle is place in an electric field at distance r it has a force on it. The direction of force depends on the two charges, but minimizes the PE.

$$F = Q E$$

Acceleration

When a charged particle moves due to the force of an electric field it does work. This work causes the particle to accelerate.

Work W is the change in U, or F applied at a distance.

$$W = \Delta U = F \Delta x$$

Falling downhill is positive work for the electric field and climbing uphill is positive work for the charged particle. Similar charges repel so bringing them together is uphill. Opposite charges attract so moving them apart is uphill.

Current: I
So the voltage on a charged particle causes it to accelerate. This is known as current.

It is sometimes taught that current in electric circuits is composed of electrons, which flow from the negative terminal of the power source to the positive at the speed of light. This is not (completely) true.


 * 1) Electricity is carried by charged particles.
 * This can mean any small particles that carry charge and are free to move. In metals, electrons are free to move and the metal nuclei are not.  In salt water, however, electrons, negative ions, and positive ions are free to move, and do, when a voltage is applied (batteries and electrolytic capacitors are examples of electrical components that carry charge as ions).  In your own nerve cells, electricity is carried by moving ions, such as potassium and sodium.  In semiconductors, electricity is carried by electrons, but is often much more easily understood as movement of "holes"; the absence of an electron.  In some static electricity experiments, electricity can be carried by charged dust or small pieces of paper.
 * 1) Electrons drift through conductors.
 * 2) * When you flip the light switch, the light comes on almost instantly. This does not mean that the electrons themselves move that quickly.  In fact, they usually move much much slower.  A typical speed for electron drift in a DC electronic circuit is slower than molasses.  The electrons themselves are moving very quickly, but not in one direction.  They are constantly moving randomly from atom to atom, and only have a very gradual drift, or shift in average position over time.  The speed electrons drift actually depends on voltage, resistance of the conductor, shape of the conductor, material the conductor is made of, temperature, and other factors.
 * 3) * What is actually traveling quickly is electromagnetic waves; the pushing of electrons by their neighbors. This is similar to the way a wave in water works.  When you drop a stone in a pond, a wave spreads out from where the stone hit the surface.  But does the water itself move?  Not really.  The water molecules at the surface are just moving back and forth, and their cumulative effect is the wave that you see, which travels in one direction.  This is similar to the travel of an AC wave down a transmission line.  (we could make a better analogy to waves of car traffic or waves of people in line for a ride at the fair)  An interesting analogy would be moving a hand through air.  The hand is the wave and the air is the random electron movement.
 * 4) Electromagnetic waves only travel at the speed of light in a vacuum.
 * 5) * What is usually meant when someone says "the speed of light" is actually "the speed of light in a vacuum", as light itself slows down while traveling through materials. A typical speed for a signal traveling down common coaxial cable is 2/3 the speed of light (in a vacuum).  (This is about 200,000,000 m/s.)  The wave traveling down the cable is actually the same thing as light, just at a different frequency.  The waves traveling through your nerves as you read this are traveling at about 120 m/s.

As you increase voltage you increase the electric field and the speed at which charged particles travel. This is why increasing voltage directly increases current. Reversing the voltage reverses the current.

Sometimes you have voltage but no current. This is used in analog and digital circuits to control switches.

So, negative particles drift from negative to positive voltage, and positive particles drift in the opposite direction from positive to negative voltage. The particles drift at different speeds in different materials. speed of "holes" based on bandgap. Given the presence of holes we tend to ignore the particles and focus on the current flow. Current is measured by the amount of charge flow per unit time and represents the speed of the electromagnetics waves. In talking about current we will mainly talk about electrons flowing, as they are the predominant charge carriers in metal and many circuit components.

Current = flow of charge (usually electrons

Current is the change in charge over time.

$$I={dQ \over dt}$$

Accumulation of current is charge. Talk about cells and capacitors.

$$Q=\int I dt$$

Resistance: R
Resistance opposes the flow of electrons. In the absence of resistance current shorts and flows unhindered like that of a power surge. Resistance combined with voltage set limits on the current that is allowed to flow through electronics. This is necessary otherwise the parts would melt (extreme electromigration). As resistance increases the flow of charge slows to a trickle until current stops flowing. Given the sheer number of electrons flowing this does not happen until resistance is effectively infinite.

Without resistance this is effectively a short meaning the electrons flow unhindered. The current is limited by the voltage. Resistance stops the flow of current. A short circuit has no resistance. As resistance increases to infinity the current stops flowing and becomes an open circuit.

$$I = {V \over R}$$

This is known as Ohm's law. Which says that Current I is equal to Voltage V divided by Resistance R. Or that voltage creates current and resistance limits the flow of current. In a circuit resistance does not change much, so most of the behavior of a circuit depends on the voltage which controls the current.

Current through a conductor versus an insulator like air.