vision electricity: 10/10/09

Saturday, October 10, 2009

Schematic symbols used to denote a bidirectional transient voltage suppression diode.

A transient voltage suppression (TVS) diode is an electronic component used to protect sensitive electronics from voltage spikes induced on connected wires. It is also commonly referred to as a transorb, after the brand name TransZorb registered by General Semiconductor (now part of Vishay). STMicroelectronics sells them under the name Transil. The name Tranzil can also be seen.
The device operates by shunting excess current when the induced voltage exceeds the avalanche breakdown potential. It is a clamping device, suppressing all overvoltages above its breakdown voltage. Like all clamping devices, it automatically resets when the overvoltage goes away, but absorbs much more of the transient energy internally than a similarly rated crowbar device.
A transient voltage suppression diode may be either unidirectional or bidirectional. A unidirectional device operates as a rectifier in the forward direction like any other avalanche diode, but is made and tested to handle very large peak currents. (The popular 1.5KE series allows 1500 W of peak power, for a short time.)
A bidirectional transient voltage suppression diode can be represented by two mutually opposing avalanche diodes in series with one another and connected in parallel with the circuit to be protected. While this representation is schematically accurate, physically the devices are now manufactured as a single component.
A transient voltage suppression diode can respond to over-voltages faster than other common over-voltage protection components such as varistors or gas discharge tubes. The actual clamping occurs in roughly one picosecond, but in a practical circuit the inductance of the wires leading to the device imposes a higher limit. This makes transient voltage suppression diodes useful for protection against very fast and often damaging voltage transients. These fast over-voltage transients are present on all distribution networks and can be caused by either internal or external events, such as lightning or motor arcing.

Characterization

A TVS diode is characterised by:

Leakage current: the amount of current conducted when voltage applied is below the Maximum Reverse Standoff Voltage.
Maximum Reverse Standoff Voltage:: the voltage below which no significant conduction occurs.
Breakdown voltage: the voltage at which some specified and significant conduction occurs.
Clamping voltage: the voltage at which the device will conduct its fully rated current (hundreds to thousands of amperes).
Parasitic capacitance: The nonconducting diode behaves like a capacitor, which can have a deleterious effect on high-speed signals. Lower capacitance is generally preferred.
Parasitic inductance: Because the actual overvoltage switching is so fast, the package inductance is the limiting factor for response speed.
Amount of energy it can absorb: Because the transients are so brief, all of the energy is initially stored internally as heat; a heat sink only affects the time to cool down afterward. Thus, a high-energy TVS must be physically large. If this capacity is too small, the overvoltage will possibly destroy the device and leave the circuit unprotected.

VOLTAGE SPIKE

Voltage spike

In electrical engineering, spikes are fast, short duration electrical transients in voltage (voltage spikes), current (current spike), or transferred energy (energy spikes) in an electrical circuit.
Fast, short duration electrical transients (overvoltages) in the electric potential of a circuit are typically caused by

lightning strikes
power outages
tripped circuit breakers
short circuits
power transitions in other large equipment on the same power line
malfunctions caused by the power company
electromagnetic pulses (EMP) with electromagnetic energy distributed typically up to the 100 kHz and 1 MHz frequency range.
Inductive spikes

In the design of critical infrastructure and military hardware, one concern is of pulses produced by nuclear explosions , whose nuclear electromagnetic pulse (EMP) distribute large energies in frequencies from 1 kHz into the Gigahertz range through the atmosphere.
The effect of a voltage spike is to produce a corresponding increase in current (current spike). However some voltage spikes may be created by current sources. Voltage would increase as necessary so that a constant current will flow. Current from a discharging inductor is one example.
For sensitive electronics, excessive current can flow if this voltage spike exceeds a material's breakdown voltage, or if it causes avalanche breakdown. In semiconductor junctions, excessive electrical current may destroy or severely weaken that device. An avalanche diode, transient voltage suppression diode, transil, varistor, overvoltage crowbar, or a range of other overvoltage protective devices can divert (shunt) this transient current thereby minimizing voltage.
While generally referred to as a voltage spike, the phenomenon in question is actually an energy spike, in that it is measured not in volts but in joules; a transient response defined by a mathematical product of voltage, current, and time.
Voltage spike may be created by a rapid buildup or decay of a magnetic field, which may induce energy into the associated circuit. However voltage spikes can also have more mundane causes such as a fault in a transformer or higher-voltage (primary circuit) power wires falling onto lower-voltage (secondary circuit) power wires as a result of accident or storm damage.
Voltage spikes may be longitudinal (common) mode or metallic (normal or differential) mode. Some equipment damage from surges and spikes can be prevented by use of surge protection equipment. Each type of spike requires selective use of protective equipment. For example a longitudinal mode voltage spike may not even be detected by a protector installed for normal mode transients.

WARD LEONARD CONTROL

Ward Leonard Control, also known as the Ward Leonard Drive System, was a widely used DC motor speed control system introduced by Harry Ward Leonard in 1891. In early 1900s, the control system of Ward Leonard was adopted by the U.S. Navy and also used in passenger lift of large mines. It also provided a solution to a moving sidewalk at the Paris Exposition of 1900, where many others had failed to operate properly.^{[citation needed]} Until the 1980s, when the Ward Leonard control system started to be replaced by other systems, primarily thyristor controllers, it was widely used for elevators because it offered smooth speed control and consistent torque. Many Ward Leonard control systems and variations on them remain in use.

Basic concept

A Ward Leonard drive is a high-power amplifier in the multi-kilowatt range, built from rotating electrical machinery. A Ward Leonard drive unit consists of a motor and generator with shafts coupled together. The motor, which turns at a constant speed, may be AC or DC powered. The generator is a DC generator, with field windings and armature windings. The input to the amplifier is applied to the field windings, and the output comes from the armature windings. The amplifier output is usually connected to a second motor, which moves the load, such as an elevator. With this arrangement, small changes in current applied to the input, and thus the generator field, result in large changes in the output, allowing smooth speed control. Armature voltage control only controls the motor speed from zero to motor base speed. If higher motor speeds are needed the motor field current can be lowered,however by doing this the available torque at the motor armature will be reduced.

A more technical description

A Ward Leonard Control system with generator and motor connected directly.

The speed of motor is controlled by varying the voltage fed from the generator, V_gf, which varies the output voltage of the generator. The varied output voltage will change the voltage of the motor, since they are connected directly through the armature. Consequently changing the V_gf will control the speed of the motor. The picture of the right shows the Ward Leonard control system, with the V_gf feeding the generator and V_mf feeding the motor.

Mathematical approach

Among many ways of defining the characteristic of a system, obtaining a transfer characteristic is one of the most commonly used methods. Below are the steps to obtain the transfer function, eq 4.
Before going into the equations, first conventions should be set up, which will follow the convention Datta used. The first subscripts 'g' and 'm' each represents generator and motor. The superscripts 'f', 'r',and 'a', correspond to field, rotor, and armature.
W_i = plant state vertor K = gain t = time constant J = polar moment of inertia D = angular viscous friction G = rotational inductance constant s = laplace operator
eq 1: The generator field equation

V_g^f = R_g^fI_g^f + L_g^fI_g^f

eq 2: The equation of electrical equilibrium in the armature circuit

-G_g^faI_g^fW_g^r + (R_g^a + R_m^a) I^a + (L_g^a + L_m^a) I^a + G_m^faI_m^fW_m^r = 0

eq 3: Motor torque equation

-T_L = J_mW_m^r+D_mW_m^r

With total impedance, L_g^a + L_m^a, neglected, the transfer function can be obtained by solving eq 3 T_L = 0.
eq 4: Transfer function

$\frac{W_m^r(S)}{V_g^f(S)} = \cfrac{K_BK_v/D_m}{(t_g^fs+1)\left[t_ms+\cfrac{K_m}{D_m}\right]}$

with the constants defined as below.

$K_B = \tfrac{G_m^faV_m^f}{R_m^f(R_g^a+R_m^a)}$

$K_v = \tfrac{G_g^faW_g^r}{R_g^f}$

$t_m = \tfrac{J_m}{D_m}$

$t_g^f = \tfrac{L_g^f}{R_g^f}$

$K_m = D_m+K_B^2(R_g^a + R_m^a)$

WATTMETER

The wattmeter is an instrument for measuring the electric power (or the supply rate of electrical energy) in watts of any given circuit

Electrodynamic

Early wattmeter on display at the Historic Archive and Museum of Mining in Pachuca, Mexico.

The traditional analog wattmeter is an electrodynamic instrument. The device consists of a pair of fixed coils, known as current coils, and a movable coil known as the potential coil.
The current coils connected in series with the circuit, while the potential coil is connected in parallel. Also, on analog wattmeters, the potential coil carries a needle that moves over a scale to indicate the measurement. A current flowing through the current coil generates an electromagnetic field around the coil. The strength of this field is proportional to the line current and in phase with it. The potential coil has, as a general rule, a high-value resistor connected in series with it to reduce the current that flows through it.
The result of this arrangement is that on a dc circuit, the deflection of the needle is proportional to both the current and the voltage, thus conforming to the equation W=VA or P=VI. On an ac circuit the deflection is proportional to the average instantaneous product of voltage and current, thus measuring true power, and possibly (depending on load characteristics) showing a different reading to that obtained by simply multiplying the readings showing on a stand-alone voltmeter and a stand-alone ammeter in the same circuit.
The two circuits of a wattmeter can be damaged by excessive current. The ammeter and voltmeter are both vulnerable to overheating — in case of an overload, their pointers will be driven off scale — but in the wattmeter, either or even both the current and potential circuits can overheat without the pointer approaching the end of the scale! This is because the position of the pointer depends on the power factor, voltage and current. Thus, a circuit with a low power factor will give a low reading on the wattmeter, even when both of its circuits are loaded to the maximum safety limit. Therefore, a wattmeter is rated not only in watts, but also in volts and amperes.

Electrodynamometer

Siemens electrodynamometer, circa 1910. F = Fixed coil, D = Movable coil, S = Spiral spring, T = Torsion head, MM = Mercury cups, I = Index needle.

An early current meter was the electrodynamometer. Used in the early 20th century, the Siemens electrodynamometer, for example, is a form of an electrodynamic ammeter, that has a fixed coil which is surrounded by another coil having its axis at right angles to that of the fixed coil. This second coil is suspended by a number of silk fibres, and to the coil is also attached a spiral spring the other end of which is fastened to a torsion head. If then the torsion head is twisted, the suspended coil experiences a torque and is displaced through and angle equal to that of the torsion head. The current can be passed into and out of the movable coil by permitting the ends of the coil to dip into two mercury cups.
If a current is passed through the fixed coil and movable coil in series with one another, the movable coil tends to displace itself so as to bring the axes of the coils, which are normally at right angles, more into the same direction. This tendency can be resisted by giving a twist to the torsion head and so applying to the movable coil through the spring a restoring torque, which opposes the torque due to the dynamic action of the currents. If then the torsion head is provided with an index needle, and also if the movable coil is provided with an indicating point, it is possible to measure the torsional angle through which the head must be twisted to bring the movable coil back to its zero position. In these circumstances, the torsional angle becomes a measure of the torque and therefore of the product of the strengths of the currents in the two coils, that is to say, of the square of the strength of the current passing through the two coils if they are joined up in series. The instrument can therefore be graduated by passing through it known and measured continuous currents, and it then becomes available for use with either continuous or alternating currents. The instrument can be provided with a curve or table showing the current corresponding to each angular displacement of the torsion head.

Electronic wattmeter

Prodigit Model 2000MU (UK version), shown in use and displaying a reading of 10 Watts being consumed by the appliance.

Electronic wattmeters are used for direct, small power measurements or for power measurements at frequencies beyond the range of electrodynamometer-type instruments.

Digital

A modern digital electronic wattmeter/energy meter samples the voltage and current thousands of times a second. The average of the instantaneous voltage multiplied by the current is the true power. The true power divided by the apparent volt-amperes (VA) is the power factor. A computer circuit uses the sampled values to calculate RMS voltage, RMS current, VA, power (watts), power factor, and kilowatt-hours. The simple models display that information on LCD. More sophisticated models retain the information over an extended period of time, and can transmit it to field equipment or a central location.

WAVEGUIDE

A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguide for each type of wave. Waveguides differ in their geometry which can confine energy in one dimension such as in slab waveguides or two dimensions as in fiber or channel waveguides.
Electromagnetic waveguides Waveguides can be constructed to carry waves over a wide portion of the electromagnetic spectrum, but are especially useful in the microwave and optical frequency ranges. Depending on the frequency, they can be constructed from either conductive or dielectric materials. Waveguides are used for transferring both power and communication signals
Optical waveguides
Waveguides used at optical frequencies are typically dielectric waveguides, structures in which a dielectric material with high permittivity, and thus high index of refraction, is surrounded by a material with lower permittivity. The structure guides optical waves by total internal reflection. The most common optical waveguide is optical fiber
Other types of optical waveguide are also used, including photonic-crystal fiber, which guides waves by any of several distinct mechanisms. Guides in the form of a hollow tube with a highly reflective inner surface have also been used as light pipes for illumination applications. The inner surfaces may be polished metal, or may be covered with a multilayer film that guides light by Bragg reflection (this is a special case of a photonic-crystal fiber). One can also use small prisms around the pipe which reflect light via total internal reflection such confinement is necessarily imperfect, however, since total internal reflection can never truly guide light within a lower-index core (in the prism case, some light leaks out at the prism corners).

Acoustic waveguides

An acoustic waveguide is a physical structure for guiding sound waves. A duct for sound propagation also behaves like a transmission line. The duct contains some medium, such as air, that supports sound propagation.

WIENER FILTER

In signal processing, the Wiener filter is a filter proposed by Norbert Wiener during the 1940s and published in 1949. Its purpose is to reduce the amount of noise present in a signal by comparison with an estimation of the desired noiseless signal. The discrete-time equivalent of Wiener's work was derived independently by Kolmogorov and published in 1941. Hence the theory is often called the Wiener-Kolmogorov filtering theory

Description

The goal of the Wiener filter is to filter out noise that has corrupted a signal. It is based on a statistical approach.
Typical filters are designed for a desired frequency response. However, the design of the Wiener filter takes a different approach. One is assumed to have knowledge of the spectral properties of the original signal and the noise, and one seeks the LTI filter whose output would come as close to the original signal as possible. Wiener filters are characterized by the following:

Assumption: signal and (additive) noise are stationary linear stochastic processes with known spectral characteristics or known autocorrelation and cross-correlation
Requirement: the filter must be physically realizable, i.e. causal (this requirement can be dropped, resulting in a non-causal solution)
Performance criterion: minimum mean-square error (MMSE)

This filter is frequently used in the process of deconvolution; for this application, see Wiener deconvolution.

Model/problem setup

The input to the Wiener filter is assumed to be a signal,

s (t)

, corrupted by additive noise,

n (t)

. The output, $\hat{s}(t)$ , is calculated by means of a filter,

g (t)

, using the following convolution:

$\hat{s}(t) = g(t) * (s(t) + n(t))$

where

$s (t)$ is the original signal (to be estimated)
$n (t)$ is the noise
$\hat{s}(t)$ is the estimated signal (which we hope will equal $s (t)$ )
$g (t)$ is the Wiener filter's impulse response

The error is defined as

$e(t) = s(t + \alpha) - \hat{s}(t)$

where

$α$ is the delay of the wiener filter (since it is causal)

In other words, the error is the difference between the estimated signal and a the true signal shifted by

α

. Clearly the squared error is

$e^2(t) = s^2(t + \alpha) - 2s(t + \alpha)\hat{s}(t) + \hat{s}^2(t)$

where

$s (t + α)$ is the desired output of the filter
$e (t)$ is the error

Depending on the value of α the problem name can be changed:

If $α > 0$ then the problem is that of prediction (error is reduced when $\hat{s}(t)$ is similar to a later value of s)
If $α = 0$ then the problem is that of filtering (error is reduced when $\hat{s}(t)$ is similar to $s (t)$ )
If $α < 0$ then the problem is that of smoothing (error is reduced when $\hat{s}(t)$ is similar to an earlier value of s)

Writing $\hat{s}(t)$ as a convolution integral: $\hat{s}(t) = \int_{-\infty}^{\infty}{g(\tau)\left[s(t - \tau) + n(t - \tau)\right]\,d\tau}$ .
Taking the expected value of the squared error results in

$E(e^2) = R_s(0) - 2\int_{-\infty}^{\infty}{g(\tau)R_{x\,s}(\tau + \alpha)\,d\tau} + \int_{-\infty}^{\infty}{\int_{-\infty}^{\infty}{g(\tau)g(\theta)R_x(\tau - \theta)\,d\tau}\,d\theta}$

where

$x (t) = s (t) + n (t)$ is the observed signal
$\,\!R_s$ is the autocorrelation function of $s (t)$
$\,\!R_x$ is the autocorrelation function of $x (t)$
$R_{x\,s}$ is the cross-correlation function of $x (t)$ and $s (t)$

If the signal

s (t)

and the noise

n (t)

are uncorrelated (i.e., the cross-correlation $\,R_{sn}\,$ is zero) then note the following

$R_{x\,s} = R_s$
$\,\!R_x = R_s + R_n$

For most applications, the assumption of uncorrelated signal and noise is reasonable because the source of the noise (e.g. sensor noise or quantization noise) do not depend upon the signal itself.
The goal is to then minimize

E (e 2)

by finding the optimal

g (t)

Wiener filter solutions

The Wiener filter problem has solutions for three possible cases: one where a non-causal filter is acceptable (requiring an infinite amount of both past and future data), the case where a causal filter is desired (using an infinite amount of past data), and the FIR case where a finite amount of past data is used. The first case is simple to solve but is not suited for real-time applications. Wiener's main accomplishment was solving the case where the causality requirement is in effect, and in an appendix of Wiener's book Levinson gave the FIR solution.

Noncausal solution

$G(s) = \frac{S_{x,s}(s)e^{\alpha s}}{S_x(s)}$

Provided that

g (t)

is optimal then the MMSE equation reduces to

$E(e^2) = R_s(0) - \int_{-\infty}^{\infty}{g(\tau)R_{x,s}(\tau + \alpha)\,d\tau}$

And the solution,

g (t)

is the inverse two-sided Laplace transform of

G (s)

Causal solution

$G(s) = \frac{H(s)}{S_x^{+}(s)}$

Where

$H (s)$ consists of the causal part of $\frac{S_{x,s}(s)e^{\alpha s}}{S_x^{-}(s)}$ (that is, that part of this fraction having a positive time solution under the inverse Laplace transform)
$S_x^{+}(s)$ is the causal component of $S x (s)$ (i.e. the inverse Laplace transform of $S_x^{+}(s)$ is non-zero only for $t\ge 0$ )
$S_x^{-}(s)$ is the anti-causal component of $S x (s)$ (i.e. the inverse Laplace transform of $S_x^{-}(s)$ is non-zero only for negative t)

This general formula is complicated and deserves a more detailed explanation. To write down the solution

G (s)

in a specific case, one should follow these steps (see ):
1. Start with the spectrum

S x (s)

in rational form and factor it into causal and anti-causal components:

$S_x(s) = S_x^{+}(s) S_x^{-}(s)$

where

S +

contains all the zeros and poles in the left hand plane (LHP) and

S -

contains the zeroes and poles in the RHP. This is called the Wiener–Hopf factorization.
2. Divide

S x, s (s) e α s

by ${S_x^{-}(s)}$ and write out the result as a partial fraction expansion.
3. Select only those terms in this expansion having poles in the LHP. Call these terms

H (s)

.
4. Divide

H (s)

by $S_x^{+}(s)$ . The result is the desired filter transfer function

G (s)

FIR Wiener filter for discrete series

Block diagram view of the FIR Wiener filter for discrete series. An input signal w[n] is convolved with the Wiener filter g[n] and the result is compared to a reference signal s[n] to obtain the filtering error e[n].

In order to derive the coefficients of the Wiener filter, we consider a signal w[n] being fed to a Wiener filter of order N and with coefficients

{a i}

, $i=0,\ldots, N$ . The output of the filter is denoted x[n] which is given by the expression

$x[n] = \sum_{i=0}^N a_i w[n-i]$

The residual error is denoted e[n] and is defined as e[n] = x[n] − s[n] (See the corresponding block diagram). The Wiener filter is designed so as to minimize the mean square error (MMSE criteria) which can be stated concisely as follows:

$a_i = \arg \min ~E\{e^2[n]\}$

where $E\{\cdot\}$ denote the expectation operator. In the general case, the coefficients

a i

may be complex and may be derived for the case where w[n] and s[n] are complex as well. For simplicity, we will only consider the case where all these quantities are real. The mean square error may be rewritten as:

$\begin{array}{rcl} E\{e^2[n]\} &=& E\{(x[n]-s[n])^2\} \\ &=& E\{x^2[n]\} + E\{s^2[n]\} - 2E\{x[n]s[n]\}\\ &=& E\{\big( \sum_{i=0}^N a_i w[n-i] \big)^2\} + E\{s^2[n]\} -2 E\{ \sum_{i=0}^N a_i w[n-i]s[n]\} \end{array}$

To find the vector $[a_0,\ldots,a_N]$ which minimizes the expression above, let us now calculate its derivative w.r.t

a i

$\begin{array}{rcl} \frac{\partial}{\partial a_i} E\{e^2[n]\} &=& 2E\{ \big( \sum_{j=0}^N a_j w[n-j] \big) w[n-i] \} - 2E\{s[n]w[n-i]\} \quad i=0, \ldots ,N \\ &=& 2 \sum_{j=0}^N E\{w[n-j]w[n-i]\} a_j - 2 E\{ w[n-i]s[n] \} \end{array}$

If we suppose that w[n] and s[n] are each stationary and jointly stationary, we can introduce the following sequences $R_w[m] ~\textit{ and }~ R_{ws}[m]$ known respectively as the autocorrelation of w[n] and the cross-correlation between w[n] and s[n] defined as follows

$\begin{align} R_w[m] =& E\{w[n]w[n+m]\} \\ R_{ws}[m] =& E\{w[n]s[n+m]\} \end{align}$

The derivative of the MSE may therefore be rewritten as (notice that

R w s [ - i] = R s w [i]

)

$\frac{\partial}{\partial a_i} E\{e^2[n]\} = 2 \sum_{j=0}^{N} R_w[j-i] a_j - 2 R_{sw}[i] \quad i=0, \ldots ,N$

Letting the derivative be equal to zero, we obtain

$\sum_{j=0}^N R_w[j-i] a_j = R_{sw}[i] \quad i=0, \ldots ,N$

which can be rewritten in matrix form

$\underbrace{ \begin{bmatrix} R_w[0] & R_w[1] & \cdots & R_w[N] \\ R_w[1] & R_w[0] & \cdots & R_w[N-1] \\ \vdots & \vdots & \ddots & \vdots \\ R_w[N] & R_w[N-1] & \cdots & R_w[0] \end{bmatrix} }_{T} \underbrace{ \begin{bmatrix} a_0 \\ a_1 \\ \vdots \\ a_N \end{bmatrix} }_{A} = \underbrace{ \begin{bmatrix} R_{sw}[0] \\R_{sw}[1] \\ \vdots \\ R_{sw}[N] \end{bmatrix} }_{V}$

T * A = V

These equations are known as the Wiener-Hopf equations. The matrix T appearing in the equation is a symmetric Toeplitz matrix. These matrices are known to be positive definite and therefore non-singular yielding a unique solution to the determination of the Wiener filter coefficient vector A:

A = T - 1 V

. Furthermore, there exists an efficient algorithm to solve such Wiener-Hopf equations known as the Levinson-Durbin algorithm so an explicit inversion of T is not required.
The FIR Wiener filter is related to the Least mean squares filter, but minimizing its error criterion does not rely on cross-correlations or auto-correlations. Its solution converges to the Wiener filter solution.

vision electricity

Saturday, October 10, 2009

Characterization

VOLTAGE SPIKE

WARD LEONARD CONTROL

Basic concept

A more technical description

Mathematical approach

WATTMETER

Electrodynamic

Electrodynamometer

Electronic wattmeter

Digital

WAVEGUIDE

Acoustic waveguides

WIENER FILTER

Description

Model/problem setup

Wiener filter solutions

Noncausal solution

Causal solution

FIR Wiener filter for discrete series

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