superfluidity

Superfluidity is a phase of matter or description of heat capacity in which unusual effects are observed when liquids, typically of helium-4 or helium-3, overcome friction by surface interaction when at a stage (known as the "lambda point" for helium-4) at which the liquid's viscosity becomes zero. Also known as a major facet in the study of quantum hydrodynamics, it was discovered by Pyotr Kapitsa, John F. Allen, and Don Misener in 1937 and has been described through phenomenological and microscopic theories. In the 1950s Hall and Vinen performed experiments establishing the existence of quantized vortex lines. In the 1960s, Rayfield and Reif established the existence of quantized vortex rings. Packard has observed the intersection of vortex lines with the free surface of the fluid, and Avenel and Varoquaux have studied the Josephson effect in superfluid ⁴He.

Some theories

L. D. Landau's phenomenological and semi-microscopic theory of superfluidity of ⁴He earned him the Nobel Prize in Physics in 1962. Assuming that sound waves are the most important excitations in ⁴He at low temperatures, he showed that ⁴He flowing past a wall would not spontaneously create excitations if the flow velocity was less than the sound velocity. In this model, the sound velocity is the "critical velocity" above which superfluidity is destroyed.
(⁴He has a lower flow velocity than the sound velocity, but this model is useful to illustrate the concept.) Landau also showed that the sound wave and other excitations could equilibrate with one another and flow separately from the rest of the ⁴He called the "condensate".
From the momentum and flow velocity of the excitations he could then define a "normal fluid" density, which is zero at zero temperature and increases with temperature. At the so-called Lambda temperature, where the normal fluid density equals the total density, the ⁴He is no longer superfluid.
To explain the early specific heat data on superfluid ⁴He, Landau posited the existence of a type of excitation he called a "roton", but as better data became available he considered that the "roton" was the same as a high momentum version of sound.
Bijl in the 1940s^[1], and Feynman around 1955 ^[2], developed microscopic theories for the roton, which was shortly observed with inelastic neutron experiments by Palevsky.
Landau thought that vorticity entered superfluid ⁴He by vortex sheets, but such sheets were shown to be unstable.
Lars Onsager and, later independently, Feynman showed that vorticity enters by quantized vortex lines. They also developed the idea of quantum vortex rings.

Background

Although the phenomenologies of the superfluid states of helium-4 and helium-3 are very similar, the microscopic details of the transitions are very different. Helium-4 atoms are bosons, and their superfluidity can be understood in terms of the Bose statistics that they obey. Specifically, the superfluidity of helium-4 can be regarded as a consequence of Bose-Einstein condensation in an interacting system. On the other hand, helium-3 atoms are fermions, and the superfluid transition in this system is described by a generalization of the BCS theory of superconductivity. In it, Cooper pairing takes place between atoms rather than electrons, and the attractive interaction between them is mediated by spin fluctuations rather than phonons. (See fermion condensate.) A unified description of superconductivity and superfluidity is possible in terms of gauge symmetry breaking.
Superfluids, such as supercooled helium-4, exhibit many unusual properties. (See Helium#Helium II state). Superfluid acts as if it were a mixture of a normal component, with all the properties associated with normal fluid, and a superfluid component. The superfluid component has zero viscosity, zero entropy, and infinite thermal conductivity. (It is thus impossible to set up a temperature gradient in a superfluid, much as it is impossible to set up a voltage difference in a superconductor.) Application of heat to a spot in superfluid helium results in a wave of heat conduction at the relatively high velocity of 20 m/s, called second sound.
One of the most spectacular results of these properties is known as the thermomechanical or "fountain effect". If a capillary tube is placed into a bath of superfluid helium and then heated, even by shining a light on it, the superfluid helium will flow up through the tube and out the top as a result of the Clausius-Clapeyron relation. A second unusual effect is that superfluid helium can form a layer, 30 nm thick, up the sides of any container in which it is placed. See Rollin film.
A more fundamental property than the disappearance of viscosity becomes visible if superfluid is placed in a rotating container. Instead of rotating uniformly with the container, the rotating state consists of quantized vortices. That is, when the container is rotated at speed below the first critical velocity (related to the quantum numbers for the element in question) the liquid remains perfectly stationary. Once the first critical velocity (the speed of sound in the superfluid) is reached, the superfluid will very quickly begin spinning at the critical speed. The speed is quantized, that is, a superfluid can not spin at certain "allowed" or critical speed values. In simplified terms, if the container is rotated to a certain allowed speed, the superfluid will rotate very quickly along with the container, otherwise, if the speed is too slow, then the superfluid will not move at all, unlike how a normal fluid like water will rotate along with its container from the start. (compare this to the london moment)

Properties

The normal phase of non-zero entropy and superfluid phase of zero entropy coexist. This gives a strange phenomenon of two-fluid model.
A consequence of is that when the two-fluid pass through a capillary, effectively only the superfluid can flow through due to its zero viscosity along the way. This gives a strange situation where we have mass transfer without heat transfer (since there is no entropy transfer)!

Applications

Recently in the field of chemistry, superfluid helium-4 has been successfully used in spectroscopic techniques as a quantum solvent. Referred to as Superfluid Helium Droplet Spectroscopy (SHeDS), it is of great interest in studies of gas molecules, as a single molecule solvated in a superfluid medium allows a molecule to have effective rotational freedom, allowing it to behave exactly as it would in the "gas" phase.
Superfluids are also used in high-precision devices such as gyroscopes, which allow the measurement of some theoretically predicted gravitational effects (for an example see the Gravity Probe B article).
In 1999, one type of superfluid has been used to trap light and slow its speed greatly. In an experiment performed by Lene Hau, light was passed through a Bose-Einstein condensed gas of sodium (analogous to a superfluid) and found to be slowed to 17 m/s (61.2 km/h) from its normal speed of 299,792,458 metres per second in vacuum.^[3] This does not change the absolute value of c, nor is it completely new: any medium other than vacuum, such as water or glass, also slows down the propagation of light to c/n where n is the material's refractive index. The very slow speed of light and high refractive index observed in this particular experiment, moreover, is not a general property of all superfluids.
The Infrared Astronomical Satellite IRAS, launched in January 1983 to gather infrared data was cooled by 720 litres of superfluid helium, maintaining a temperature of 1.6 K (-271.4 ­°C).

switch

In electronics, a switch is an electrical component that can break an electrical circuit, interrupting the current or diverting it from one conductor to another.^[1][2] The most familiar form of switch is a manually operated electromechanical device with one or more sets of electrical contacts. Each set of contacts can be in one of two states: either 'closed' meaning the contacts are touching and electricity can flow between them, or 'open', meaning the contacts are separated and nonconducting.
A switch may be directly manipulated by a human as a control signal to a system, such as a computer keyboard button, or to control power flow in a circuit, such as a light switch. Automatically-operated switches can be used to control the motions of machines, for example, to indicate that a garage door has reached its full open position or that a machine tool is in a position to accept another workpiece. Switches may be operated by process variables such as pressure, temperature, flow, current, voltage, and force, acting as sensors in a process and used to automatically control a system. For example, a thermostat is an automatically-operated switch used to control a heating process. A switch that is operated by another electrical circuit is called a relay. Large switches may be remotely operated by a motor drive mechanism. Some switches are used to isolate electric power from a system, providing a visible point of isolation that can be pad-locked if necessary to prevent accidental operation of a machine during maintenance, or to prevent electric shock.

Three pushbutton switches (Tactile Switches). Major scale is inches.

s

Contacts

A toggle switch in the "on" position.

In the simplest case, a switch has two pieces of metal called contacts that touch to make a circuit, and separate to break the circuit. The contact material is chosen for its resistance to corrosion, because most metals form insulating oxides that would prevent the switch from working. Contact materials are also chosen on the basis of electrical conductivity, hardness (resistance to abrasive wear), mechanical strength, low cost and low toxicity^[3].
Sometimes the contacts are plated with noble metals. They may be designed to wipe against each other to clean off any contamination. Nonmetallic conductors, such as conductive plastic, are sometimes used.

Actuator

The moving part that applies the operating force to the contacts is called the actuator, and may be a toggle or dolly, a rocker, a push-button or any type of mechanical linkage (see photo).

Arcs and quenching

When the wattage being switched is sufficiently large, the electron flow across opening switch contacts is sufficient to ionize the air molecules across the tiny gap between the contacts as the switch is opened, forming a gas plasma, also known as an electric arc. The plasma is of low resistance and is able to sustain power flow, even with the separation distance between the switch contacts steadily increasing. The plasma is also very hot and is capable of eroding the metal surfaces of the switch contacts.
Where the voltage is sufficiently high, an arc can also form as the switch is closed and the contacts approach. If the voltage potential is sufficient to exceed the breakdown voltage of the air separating the contacts, an arc forms which is sustained until the switch closes completely and the switch surfaces make contact.
In either case, the standard method for minimizing arc formation and preventing contact damage is to use a fast-moving switch mechanism, typically using a spring-operated tipping-point mechanism to assure quick motion of switch contacts, regardless of the speed at which the switch control is operated by the user. Movement of the switch control lever applies tension to a spring until a tipping point is reached, and the contacts suddenly snap open or closed as the spring tension is released.
As the power being switched increases, other methods are used to minimize or prevent arc formation. A plasma is hot and will rise due to convection air currents. The arc can be quenched with a series of nonconductive blades spanning the distance between switch contacts, and as the arc rises its length increases as it forms ridges rising into the spaces between the blades, until the arc is too long to stay sustained and is extinguished. A puffer may be used to blow a sudden high velocity burst of gas across the switch contacts, which rapidly extends the length of the arc to extinguish it quickly.
Extremely large switches in excess of 100,000 watts capacity often place the switch contacts in something other than air to increase the resistance against arc formation, such as enclosing the switch contacts in a vacuum, or immersing the switch contacts in mineral oil.

Contact arrangements

Triple Pole Single Throw (TPST or 3PST) knife switch used to short the windings of a 3 phase wind turbine for braking purposes. Here the switch is shown in the open position.

A pair of contacts is said to be "closed" when current can flow one to the other. When the contacts are separated by an insulating air gap, an air space, they are said to be 'open', and no current can flow at typical voltages.
Switches are classified according to the arrangement of their contacts in electronics. Electricians installing building wiring use different nomenclature, such as "one-way", "two-way", "three-way" and "four-way" switches, which have different meanings in North American and British cultural regions as described in the table below.
Some contacts are normally open (Abbreviated "n.o." or "no") until closed by operation of the switch, while others are normally closed ("n.c. or "nc") and opened by the switch action.
A switch with both types of contact is called a changeover switch. These may be "make-before-break" which momentarily connect both circuits, or may be "break-before-make" which interrupts one circuit before closing the other.
The terms pole and throw are also used to describe switch contact variations. A pole is a set of contacts and terminals that are connected to a single circuit. A throw is one of two or more positions that the switch can adopt. A single-throw switch has one position that closes contacts, a double-throw switch has two position, and so on.
These terms give rise to abbreviations for the types of switch which are used in the electronics industry such as "single-pole, single-throw" (SPST) (the simplest type, "on or off") or "single-pole, double-throw" (SPDT), connecting either of two terminals to the common terminal. In electrical power wiring (i.e. House and building wiring by electricians) names generally involving the suffixed word "-way" are used; however, these terms differ between British and American English and the terms two way and three way are used in both with different meanings.

Electronics specification and abbreviation	Expansion of abbreviation	British mains wiring name	American electrical wiring name	Description	Symbol	IEC 60617
SPST	Single pole, single throw	One-way	Two-way	A simple on-off switch: The two terminals are either connected together or not connected to anything. An example is a light switch.
SPDT	Single pole, double throw	Two-way	Three-way	A simple changeover switch: C (COM, Common) is connected to L1 or to L2.
SPCO SPTT, c.o.	Single pole changeover or Single pole, centre off or Single Pole, Triple Throw			Similar to SPDT. Some suppliers use SPCO/SPTT for switches with a stable off position in the centre and SPDT for those without.[citation needed]
DPST	Double pole, single throw	Double pole	Double pole	Equivalent to two SPST switches controlled by a single mechanism
DPDT	Double pole, double throw			Equivalent to two SPDT switches controlled by a single mechanism: A is connected to B and D to E, or A is connected to C and D to F.
DPCO	Double pole changeover or Double pole, centre off			Equivalent to DPDT. Some suppliers use DPCO for switches with a stable off position in the centre and DPDT for those without.
		Intermediate switch	Four-way switch	DPDT switch internally wired for polarity-reversal applications: only four rather than six wires are brought outside the switch housing; with the above, B is connected to F and C to E; hence A is connected to B and D to C, or A is connected to C and D to B.

Switches with larger numbers of poles or throws can be described by replacing the "S" or "D" with a number or in some cases the letter "T" (for "triple"). In the rest of this article the terms SPST, SPDT and intermediate will be used to avoid the ambiguity in the use of the word "way".

Biased switches

A biased switch is one containing a spring that returns the actuator to a certain position. The "on-off" notation can be modified by placing parentheses around all positions other than the resting position. For example, an (on)-off-(on) switch can be switched on by moving the actuator in either direction away from the centre, but returns to the central off position when the actuator is released.
The momentary push-button switch is a type of biased switch. The most common type is a "push-to-make" (or normally-open or NO) switch, which makes contact when the button is pressed and breaks when the button is released. Each key of a computer keyboard, for example, is a normally-open "push-to-make" switch. A "push-to-break" (or normally-closed or NC) switch, on the other hand, breaks contact when the button is pressed and makes contact when it is released. An example of a push-to-break switch is a button used to release a door held open by an electromagnet.

Special types

Switches can be designed to respond to any type of mechanical stimulus: for example, vibration (the trembler switch), tilt, air pressure, fluid level (the float switch), the turning of a key (key switch), linear or rotary movement (the limit switch or microswitch), or presence of a magnetic field (the reed switch).

Mercury tilt switch

The mercury switch consists of a drop of mercury inside a glass bulb with 2 contacts. The two contacts pass through the glass, and are connected by the mercury when the bulb is tilted to make the mercury roll on to them.
This type of switch performs much better than the ball tilt switch, as the liquid metal connection is unaffected by dirt, debris and oxidation, it wets the contacts ensuring a very low resistance bounce-free connection, and movement and vibration do not produce a poor contact. These types can be used for precision works.
It can also be used where arcing is dangerous (such as in the presence of explosive vapour) as the entire unit is sealed.

Knife switch

Knife switches consist of a flat metal blade, hinged at one end, with an insulating handle for operation, and a fixed contact. When the switch is closed, current flows through the hinged pivot and blade and through the fixed contact. Such switches are usually not enclosed. The parts may be mounted on an insulating base with terminals for wiring, or may be directly bolted to an insulated switch board in a large assembly. Since the electrical contacts are exposed, the switch is used only where people cannot accidentally come in contact with the switch.
The knife and contacts are typically formed of copper, steel, or brass, depending on the application. Fixed contacts may be backed up with a spring. Several parallel blades can be operated at the same time by one handle.
Knife switches are made in many sizes from miniature switches to large devices used to carry thousands of amperes. In electrical transmission and distribution, gang-operated switches are used in circuits up to the highest voltages.
The disadvantages of the knife switch are the slow opening speed and the proximity of the operator to exposed live parts. Metal-enclosed safety disconnect switches are used for isolation of circuits in industrial power distribution. Sometimes spring-loaded auxiliary blades are fitted which momentarily carry the full current during opening, then quickly part to rapidly extinguish the arc.

Intermediate switch A DPDT switch has six connections, but since polarity reversal is a very common usage of DPDT switches, some variations of the DPDT switch are internally wired specifically for polarity reversal. These crossover switches only have four terminals rather than six. Two of the terminals are inputs and two are outputs. When connected to a battery or other DC source, the 4-way switch selects from either normal or reversed polarity. Intermediate switches are also an important part of multiway switching systems with more than two switches (see next section).

Light switches

In building wiring, light switches are installed at convenient locations to control lighting and occasionally other circuits. By use of multiple-pole switches, control of a lamp can be obtained from two or more places, such as the ends of a corridor or stairwell.

Power switching

When a switch is designed to switch significant power, the transitional state of the switch as well as the ability to stand continuous operating currents must be considered. When a switch is in the on state its resistance is near zero and very little power is dropped in the contacts; when a switch is in the off state its resistance is extremely high and even less power is dropped in the contacts. However when the switch is flicked the resistance must pass through a state where briefly a quarter (or worse if the load is not purely resistive) of the load's rated power is dropped in the switch.
For this reason, most power switches (most light switches and almost all larger switches) have spring mechanisms in them to make sure the transition between on and off is as short as possible regardless of the speed at which the user moves the rocker.
Power switches usually come in two types. A momentary on-off switch (such as on a laser pointer) usually takes the form of a button and only closes the circuit when the button is depressed. A regular on-off switch (such as on a flashlight) has a constant on-off feature. Dual-action switches incorporate both of these features.

A diagram of a dual-action switch system

Inductive loads

When a strongly inductive load such as an electric motor is switched off, the current cannot drop instantaneously to zero; a spark will jump across the opening contacts. Switches for inductive loads must be rated to handle these cases. The spark will cause electromagnetic interference if not suppressed; a snubber network of a resistor and capacitor in series will quell the spark.

Contact bounce

Contact bounce (also called chatter) is a common problem with mechanical switches and relays. Switch and relay contacts are usually made of springy metals that are forced into contact by an actuator. When the contacts strike together, their momentum and elasticity act together to cause bounce. The result is a rapidly pulsed electrical current instead of a clean transition from zero to full current. The effect is usually unimportant in power circuits, but causes problems in some analogue and logic circuits that respond fast enough to misinterpret the on-off pulses as a data stream^[4].
Sequential digital logic circuits are particularly vulnerable to contact bounce. The voltage waveform produced by switch bounce usually violates the amplitude and timing specifications of the logic circuit. The result is that the circuit may fail, due to problems such as metastability, race conditions, runt pulses and glitches.
The effects of contact bounce can be eliminated by use of mercury-wetted contacts, but these are now infrequently used because of the hazard of mercury release. Contact circuits can be filtered to reduce or eliminate multiple pulses. In digital systems, multiple samples of the contact state can be taken or a time delay can be implemented so that the contact bounce has settled before the contact input is used to control anything.

Electronic switches

Since the advent of digital logic in the 1950s, the term has spread to a variety of digital active devices such as transistors and logic gates whose function is to change their output state between two logic levels or connect different signal lines, and even computers, network switches, whose function is to provide connections between different ports in a computer network.^[5] The term 'switched' is also applied to telecommunications networks, and signifies a network that is circuit switched, providing dedicated circuits for communication between end nodes, such as the public switched telephone network. The common feature of all these usages is they refer to devices that control a binary state: they are either on or off, closed or open, connected or not connected.

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

Vgf = RgfIgf + LgfIgf

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

-GgfaIgfWgr + (Rga + Rma) Ia + (Lga + Lma) Ia + GmfaImfWmr = 0

eq 3: Motor torque equation

-TL = JmWmr+DmWmr

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

with the constants defined as below.

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.