# For Talk:Negative resistance

One of the reasons I wanted to clarify this is that the fringe pseudoscience "alternative energy" community has fastened on "negative resistance" as a source of "free energy" ("overunity", perpetual motion). [1]. A website by John Bedini gives the impression you can install a "negative resistor" in your garage, and it will power your house for free. There are plenty of sources that "perpetual motion" is impossible, but not that many that make clear that negative resistance is perpetual motion.

# For 5G

## How it works

Like the earlier generation 2G, 3G, and 4G mobile networks, 5G networks are digital cellular networks, in which the service area covered by providers is divided into a mosaic of small geographical areas called cells. Analog signals representing sounds and images are digitized in the phone, converted by an analog to digital converter to a sequence of numbers, and transmitted as a digital signal, a stream of bits. All the 5G wireless devices in a cell communicate by radio waves with a local antenna array and low power automated transceiver (transmitter and receiver) in the cell, over frequency channels assigned by the transceiver from a common pool of frequencies, which are reused in geographically separated cells. The local antennas are connected with the telephone network and the Internet by a high bandwidth optical fiber or wireless backhaul connection. Like existing cellphones, when a user crosses from one cell to another, his mobile device is automatically "handed off" seamlessly to the antenna in the new cell.

Their major advantage is that 5G networks achieve much higher data rates than previous cellular networks, up to 10 Gbps; which is faster than current cable internet, and 100 times faster than the previous cellular technology, 4G LTE.[1][2] Another advantage is lower network latency (faster response time), below 1 millisecond, compared with 30 - 70 ms for 4G.[2] Because of the higher data rates, 5G networks will serve not just cellphones but are also envisioned as a general home and office networking provider, competing with wired internet providers like cable. Previous cellular networks provided low data rate internet access suitable for cellphones, but a cell tower could not economically provide enough bandwidth to serve as a general internet provider for home computers.

5G networks achieve these higher data rates by using higher frequency radio waves, in the millimeter wave band[1] around 28 and 39 GHz while previous cellular networks used frequencies in the microwave band between 700 MHz and 3 GHz. Because of the more plentiful bandwidth at these frequencies, 5G networks will use wider frequency channels to communicate with the wireless device, up to 400 MHz compared with 20 MHz in 4G LTE, which can transmit more data (bits) per second. OFDM (orthogonal frequency division multiplexing) modulation is used, in which multiple carrier waves are transmitted in the frequency channel, so multiple bits of information are being transferred simultaneously, in parallel. A second lower frequency range in the microwave band, below 6 GHz will be used by some providers, but this will not have the high speeds of the new frequencies.

Millimeter waves are absorbed by gases in the atmosphere and have shorter range than microwaves, therefore the cells are limited to smaller size; 5G cells will be the size of a city block, as opposed to the cells in previous cellular networks which could be many miles across. The waves also have trouble passing through building walls, requiring multiple antennas to cover a cell.[1] Millimeter wave antennas are smaller than the large antennas used in previous cellular networks, only a few inches long, so instead of a cell tower 5G cells will be covered by many antennas mounted on telephone poles and buildings.[2] Another technique used for increasing the data rate is massive MIMO (multiple-input multiple-output).[1] Each cell will have multiple antennas communicating with the wireless device, each over a separate frequency channel, received by multiple antennas in the device, thus multiple bitstreams of data will be transmitted simultaneously, in parallel. In a technique called beamforming the base station computer will continuously calculate the best route for radio waves to reach each wireless device, and will organise multiple antennas to work together as phased arrays to create beams of millimeter waves to reach the device.[1][2] The smaller, more numerous cells makes 5G network infrastructure more expensive to build per square kilometer of coverage than previous cellular networks. Deployment is currently limited to cities, where there will be enough users per cell to provide an adequate investment return, and there are doubts about whether this technology will ever reach rural areas.[1]

The new 5G wireless devices also have 4G LTE capability, as the new networks use 4G for initially establishing the connection with the cell, as well as in locations where 5G access is not available.[3]

The high data rate and low latency of 5G are envisioned as opening up new applications in the near future.[3] One is practical virtual reality and augmented reality. Another is fast machine-to-machine interaction in the Internet of Things. For example, computers in vehicles on a road could continuously communicate with each other, and with the road, by 5G.[3] An autonomous vehicle (driverless car) driving down a highway has to extract a huge amount of data about its environment in real time. If nearby vehicles could communicate their locations and intentions, and the roadway could communicate traffic conditions immediately ahead, it would ease the task of driving.

## References

1. Nordrum, Amy (27 January 2017). "Everything you need to know about 5G". IEEE Spectrum magazine. Institute of Electrical and Electronic Engineers. Retrieved 23 January 2019. Unknown parameter |coauthors= ignored (|author= suggested) (help)
2. ^ a b c d Hoffman, Chris (7 January 2019). "What is 5G, and how fast will it be?". How-To Geek website. How-To Geek LLC. Retrieved 23 January 2019.
3. ^ a b c Segan, Sascha (14 December 2018). "What is 5G?". PC Magazine online. Ziff-Davis. Retrieved 23 January 2019.

# For Wireless power

There is no reliable evidence that Tesla ever transmitted significant power beyond his short range demonstrations mentioned above. In the last 100 years equipment similar to Tesla's has been built, but long distance power transmission has not

# For LED lamp

## Electrical characteristics of LEDs

LEDs cannot be connected directly to the AC mains the way an incandescent light can. Low power LED indicator lights are usually powered from a low voltage DC source with a simple series resistor to limit the current. However, higher power LED lamps used for lighting have stricter requirements for the voltage and current through them, and require a solid state driver circuit to provide the power to them. The features of LEDs which make them different from other electric lights are

• LEDs conduct current in only one direction, so they require direct current (DC) to operate continuously, unlike the other lamp types above which operate on alternating current (AC). When powered by AC, the LED will only be on during every other half-cycle of the current, so it will produce less light, and the light will flicker at a 50 or 60 hertz rate, which can be annoying and a health hazard to some people. So LEDs used for lighting are usually powered by DC. Since mains power is AC it must be rectified to DC first.
• LEDs operate at a low voltage, unlike the other lamps above. At their operating current they have a constant voltage drop of a few volts, roughly equal to the band gap of the semiconductor material used. Different color LEDs have different voltage drops; for white LEDs it is around 3.1 - 3.8V. The voltage is approximately constant with changes in current. So the current through the diode determines the power and light output.
• LEDs require a current limiting circuit. An LED chip can be modeled as a constant-voltage load. The current-voltage characteristic (I-V curve) of an LED is exponential; the lamp requires a certain voltage across it to turn on and begin conducting current, but above this the current through it (and light output and power dissipation) increases rapidly with increasing voltage. So LEDs are very sensitive to small changes in voltage. A constant-voltage source cannot control the current adequately, so the chip is usually powered through a feedback current limiting circuit that continually monitors the current and adjusts it to the correct value.
• "Efficiency droop": Low current, low power LED chips are more efficient at light production than high current ones. They also have a longer lifetime. Due to this, typical LED lamps use multiple low power LED chips to give the required light output, rather than a single high power one. They are mounted on a common heat sink to keep them at approximately the same temperature to reduce thermal runaway problems.
• Thermal runaway: The voltage drop across an LED decreases as its temperature rises, by about 2mV per °C. So without current limiting, as the LED gets warmer its voltage decreases, which causes more current to flow through it, which causes additional heat dissipation in the chip, which causes the temperature to rise further, which causes a further voltage decrease, which causes more current, and so on. Under certain conditions this feedback process can continue until the heat destroys the LED chip; this is called "thermal runaway". Current-limiting keeps the current constant, preventing runaway.
• Even with a constant current source, if multiple LED chips are connected in parallel, one chip, the hottest one, will take all the current due to thermal runaway. Therefore multiple LEDs are usually connected in series, so the current through them is the same. If LEDs must be connected in parallel, they require current equalizing devices such as a series resistor or a transistor current mirror in each branch.
• White LEDs typically change color hue somewhat as the current through them changes. Therefore most types of LED lamp cannot be dimmed by reducing the current.

## LED driver circuits

Low power LEDs where efficiency is not an issue are usually driven from a voltage source with a simple series resistor to limit the current. The value of the resistor needed is equal to the difference between the source voltage and the voltage drop across the LED, divided by the rated operating current of the LED. However this circuit is not used for high power lamps, even when operated from a low voltage source, because a certain minimum resistance is required to prevent thermal runaway, and at this resistance a large fraction of the input power is consumed by the resistor, which is dissipated as waste heat.

To achieve high efficiency and prevent thermal runaway, higher power lighting LEDs require a solid state driver circuit between them and the power source. The driver usually consists of these functional blocks:

• Rectifier: If the supply current is AC a rectifier is used to convert it to DC. A full wave semiconductor diode rectifier is used, often a bridge rectifier, followed by a filter consisting of electrolytic capacitors to reduce the ripple. The rectification is usually done at the input voltage, before voltage reduction, because diode rectifiers are less efficient at the lower voltages used by LEDs.
• DC to DC converter: This device converts the DC voltage from the rectifier to the correct voltage to power the series string of LED chips. The voltage needed is just equal to the voltage drop across a single LED chip, multiplied by the number of LEDs. For example, an LED replacement for a standard 60 W incandescent bulb often uses 8 white LEDs in series with a voltage drop of 3V each, for a total voltage of about 24V. For efficiency the voltage reduction is usually done by a switching regulator, which works by switching current rapidly on and off through an inductor or capacitor, using semiconductor switches like transistors. A high switching frequency is used, from 50 kHz to 2 MHz, which reduces the size of the inductors and capacitors needed. If the supply voltage is greater than the voltage drop of the LED string, as it is with mains power, a buck converter circuit is used, which reduces the voltage. If the supply voltage is less than the voltage drop of the LED string, as is often the case with battery power, a boost converter is used, which increases the voltage.
• Current limiter: This is a negative feedback regulator circuit which monitors the current through the LED string, and adjusts the output voltage to keep the current constant. It can be a linear regulator which controls the current using a pass transistor in series with the LEDs. For greater efficiency it can be integrated with the converter and instead control the current by varying the duty cycle of the switching device.

LED lamps are a young technology, and there are many competing system designs. The various types of driver listed below usually differ in where the 3 functional blocks above are located; which ones are in the driver and which are included in the LED lamp module itself:

### Internal vs external

• An internal driver is one that is incorporated in the LED bulb itself, usually in the base. These are used in LED light bulbs and tubes which are drop-in replacements for standard incandescent bulbs and fluorescent tubes in older light fixtures with standard sockets. It is a constant current driver.
• An external driver is one that is located in the light fixture, separate from the LED lamps themselves. Often both the driver and the LEDs can be replaced separately. These are used in light fixtures designed exclusively for LED lamps, such as cove lights, downlights, and tape lights, as well as panels and outdoor-rated lights. One advantage of an external driver is that the driver can be replaced without replacing the LEDs. The drivers in LED lamps often fail before the LEDs, they have a limited lifetime because the heat generated dries out the gel electrolyte in their electrolytic capacitors. Constant-voltage external drivers are used to power multiple LED modules in parallel from one driver, in multicolor LED lights.

### Constant-current driver

This is a driver that performs all three functions above, so it can power a series string of LEDs directly. It takes utility current at 117 VAC (in North America) or 230 VAC (in Europe), rectifies it, converts the voltage to the lower voltage required by the LED string, usually 8, 12 or 24 volts, and outputs a constant DC current of the correct amperage to drive the LEDs, whose voltage may vary over a narrow range to control the current.

### Constant voltage driver

This is a driver which rectifies the current and reduces the voltage, but does not include current limiting. It outputs a constant low DC voltage, usually 12 or 24 volts. It is usually used with constant-voltage LED modules, which have an internal current-limiting device, a series resistor or solid state regulator. It is used to power multiple modules in parallel from a single driver, for multicolor lamps.

### AC driver

This is a driver that just performs the voltage reduction, without rectifying the AC or regulating the current. It is powered by AC utility voltage and outputs a lower AC voltage, usually 12 or 24 volts, and is usually used with lamps that have integral rectifiers and current limiters. This is another name for a no-minimum-load transformer. Ordinary transformers designed for older utility circuits cannot be used with LED lamps, because the current drawn by the LED is so low that the transformer does not operate correctly. So specially-constructed transformers are used which can work with the low LED load.

# For Standing wave

A standing wave is an oscillating wave fixed in space. Unlike a traveling wave in which the points of a given amplitude move with a constant speed, the peak amplitude of the standing wave varies at different points but is constant in time.

# For Inductance

In electromagnetism and electronics, inductance is the property of an electrical conductor by which a change in current through it induces an electromotive force (voltage) in the conductor. It is more accurately called self-inductance. The same property causes a current in one conductor to induce an electromotive force in nearby conductors; this is called mutual inductance.[1]

Inductance is an effect caused by the magnetic field of a current-carrying conductor acting back on the conductor. An electric current through any conductor creates a magnetic field around the conductor. A changing current creates a changing magnetic field. From Faraday's law of induction any change in magnetic flux through a circuit induces an electromotive force (voltage) across the circuit. Inductance is the ratio ${\displaystyle L}$ between this induced voltage ${\displaystyle v}$ and the rate of change of the current ${\displaystyle i(t)}$ in the circuit

${\displaystyle v=L{di(t) \over dt}}$

From Lenz's law, this induced voltage, or "back EMF", will be in a direction so as to oppose the change in current which created it. Thus inductance is a property of a conductor which opposes any change in current through the conductor. An inductor is an electrical component which adds inductance to a circuit. It typically consists of a coil or helix of wire.

The term inductance was coined by Oliver Heaviside in 1886.[2] It is customary to use the symbol ${\displaystyle L}$ for inductance, in honour of the physicist Heinrich Lenz.[3][4] In the SI system, the unit of inductance is the henry (H), which is the amount of inductance which causes a voltage of 1 volt when the current is changing at a rate of one ampere per second. It is named for Joseph Henry, who discovered inductance independently of Faraday.[5]

Electric circuits which are located close together, so the magnetic field created by the current in one passes through the other, are said to be inductively coupled. So a change in current in one circuit will cause the magnetic flux through the other circuit to vary, which will induce a voltage in the other circuit, by Faraday's law. The ratio of the voltage induced in the second circuit to the rate of change of current in the first circuit is called the mutual inductance ${\displaystyle M}$ between the circuits. It is also measured in henries.

## History

Faraday's experiment showing mutual inductance between coils of wire: The liquid battery (right) provides a current that flows through the small coil (A), creating a magnetic field. When the coils are stationary, no current is induced. But when the small coil is moved in or out of the large coil (B), the magnetic flux through the large coil changes, inducing a current due to their mutual inductance which is detected by the galvanometer (G).

In 1820 Danish physics professor Hans Christian Ørsted discovered the first connection between electricity and magnetism; he found that an electric current created a magnetic field around it. William Sturgeon discovered in 1923 that a wire wound around a piece of iron would produce a much stronger magnetic field, and his invention, the electromagnet, was the first ferromagnetic inductor and encouraged researchers to experiment with coils of wire.

The effect of mutual inductance, electromagnetic induction, was discovered by British scientist Michael Faraday in 1831. The American physicist Joseph Henry discovered it independently in 1832, and the SI unit of inductance, the henry is named in honor of him. In Faraday's experiment, he wrapped two wires around opposite sides of an iron ring, making a transformer. He applied current from a battery through one coil of wire. He expected that, when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. Using a galvanometer, he saw a transient current flow in the second coil of wire, each time the battery was connected or disconnected from the first coil. This current was induced by the change in magnetic flux that occurred when the battery was connected and disconnected. Faraday explored induction in many other experiments. He found that moving a bar magnet into or out of a coil of wire also induced a pulse of current in the wire. From this he formulated the general principle that any change in the magnetic field through a circuit induced a voltage in the circuit, which became known as Faraday's law of induction.

Russian physicist Emil Lenz in 1834 stated a simple rule, Lenz's law, for the direction of the EMF induced in a circuit by a change in flux; the induced voltage was always in a direction which opposed the current change which caused it.[6] In honor of Lenz, the variable ${\displaystyle L}$ is customarily used to represent inductance. The first practical device that made use of inductance, the induction coil, was invented in 1836 by Irish scientist and Catholic priest Nicholas Callan. The improvement of induction coils, the first transformers, over the next 50 years resulted in the discovery of much practical technology for making ferromagnetic inductors and transformers, resulting in the first AC power transformers , designed in 1884 by Hungarian engineers Károly Zipernowsky, Ottó Bláthy and Miksa Déri. In 1845 German physicist Franz Neumann formulated Faraday's law in forms that could be used to calculate the mutual inductance and self-inductance of circuits. The first analysis of a tuned circuit was done in 1853 by British scientist William Thomson (Lord Kelvin) who showed mathematically that the discharge of a Leyden jar through an inductance should be oscillatory, and derived its resonant frequency. Scottish physicist James Clerk Maxwell in 1864 incorporated Faraday's law into a set of equations governing all electromagnetism, which became known as Maxwell's equations.

The word inductance was coined in 1886, by self-taught British mathematician Oliver Heaviside. In the 1860s he calculated the effect of inductance and capacitance in telegraph lines, and found that adding inductors, called loading coils, to the lines could prevent distortion that was slowing signaling speed. Loading coils were installed widely on telegraph and telephone lines and were one of the first large applications of inductors.

One of the largest applications of inductors was in radio. The discovery of electromagnetic waves (radio waves by Heinrich Hertz in 1887 led to the first radio transmitters and receivers in 1894-5. Since inductive reactance, the resistance of an inductor to an alternating current, increases with frequency, inductance was a much more important effect in radio than at lower frequencies. German Karl Ferdinand Braun and Oliver Lodge found around 1897 that resonant circuits consisting of capacitance and inductance enabled a receiver to select the radio signal of a particular transmitter from multiple transmitters operating simultaneously.

## Inductive reactance and phasors

The voltage (${\displaystyle v}$, blue) and current (i, red) waveforms in an ideal inductor to which an alternating current has been applied. The current lags the voltage by 90°

When a sinusoidal alternating current is passing through a linear inductance, the induced back-EMF will also be sinusoidal. If the current through the inductance is ${\displaystyle i(t)=I_{p}\sin(2\pi ft)}$, from (1) above the voltage across it will be

${\displaystyle v(t)=L{di \over dt}=L{d \over dt}[I_{p}\sin(2\pi ft)]=2\pi fLI_{p}\cos(2\pi ft)=2\pi fLI_{p}\sin(2\pi ft-{\pi \over 2})}$

where ${\displaystyle I_{p}}$ is the amplitude (peak value) of the sinusoidal current in amperes, ${\displaystyle f}$ is the frequency of the alternating current in hertz, and ${\displaystyle L}$ is the inductance.
Thus the amplitude (peak value) of the voltage across the inductance will be

${\displaystyle V_{p}=2\pi fLI_{p}}$

Reactance of an inductor is defined analogously to electrical resistance in a resistor, as the ratio of the amplitude of voltage to current

${\displaystyle X_{L}={V_{p} \over I_{p}}=2\pi fL}$

Sometimes the angular frequency ${\displaystyle \omega =2\pi f}$ is used instead. Reactance has units of ohms. It can be seen that inductive reactance increases proportionally with frequency, so an inductor conducts less current for a given applied voltage as the frequency increases. Because the induced voltage is greatest when the current is increasing, the voltage and current waveforms are out of phase; the voltage peaks occur earlier in each cycle than the current peaks. The phase difference between the current and the induced voltage is ${\displaystyle \phi =\pi /2}$ radians or 90 degrees, showing that in an ideal inductor the current lags the voltage by 90°.

In phasor notation used widely in electronics the magnitude and phase angle of the current is represented more compactly by complex numbers. The sinusoidal factor is represented in polar form by ${\displaystyle e^{j\omega t}=\cos \omega t+j\sin \omega t}$, where ${\displaystyle e}$ is the base of natural logarithms, and ${\displaystyle j={\sqrt {-1}}}$ is the imaginary unit. The actual voltage or current is obtained by taking the real part of the complex voltage or current: ${\displaystyle v(t)={\text{Re}}[Ve^{j\omega t}]=V\cos {\omega t}}$ Since all the voltages and currents have the same frequency ${\displaystyle \omega }$ and just differ in phase, in phaser notation this factor ${\displaystyle e^{j\omega t}}$ is omitted.

Time functions Complex exponentials Phasors
${\displaystyle i(t)=I_{p}\cos {\omega t}}$

${\displaystyle v(t)=L{d \over dt}[I_{p}\cos {\omega t}]=-\omega LI_{p}\sin {\omega t}}$
${\displaystyle |X|={\Big |}{V_{p} \over I_{p}}{\Big |}={\Big |}{\omega LI_{p} \over I_{p}}{\Big |}=\omega L}$

${\displaystyle i(t)={\text{Re}}\,I_{p}e^{j\omega t}}$

${\displaystyle v(t)={\text{Re}}[L{d \over dt}(I_{p}e^{j\omega t})]={\text{Re}}[j\omega LI_{p}e^{j\omega t}]={\text{Re}}[\omega LI_{p}e^{j\pi /2}e^{j\omega t}]}$
${\displaystyle X={v(t) \over i(t)}={\text{Re}}{v(t) \over i(t)}={\text{Re}}{\omega LI_{p}e^{j\pi /2}e^{j\omega t} \over I_{p}e^{j\omega t}}={\text{Re}}\,[\omega Le^{j\pi /2}]={\text{Re}}\,[\omega L\angle 90^{\circ }]}$

${\displaystyle I(j\omega )=I_{p}}$

${\displaystyle V(j\omega )=j\omega LI_{p}}$
${\displaystyle Z(j\omega )=R+jX(\omega )={V(j\omega ) \over I(j\omega )}={j\omega LI_{p} \over I_{p}}=j\omega L=\omega L\angle 90^{\circ }}$

Thus the complex reactance of an inductor is

${\displaystyle X_{L}(j\omega )=j\omega L}$
1. ^ Sears and Zemansky 1964:743
2. ^ Heaviside, Oliver (1894). Electrical Papers. Macmillan and Company. p. 271.
3. ^ Glenn Elert. "The Physics Hypertextbook: Inductance". Retrieved 2016-07-30.
4. ^ Michael W. Davidson (1995–2008). "Molecular Expressions: Electricity and Magnetism Introduction: Inductance".
5. ^
6. ^ Lenz, E. (1834), "Ueber die Bestimmung der Richtung der durch elektodynamische Vertheilung erregten galvanischen Ströme", Annalen der Physik und Chemie, 107 (31), pp. 483–494. A partial translation of the paper is available in Magie, W. M. (1963), A Source Book in Physics, Harvard: Cambridge MA, pp. 511–513.

# For Reactance

## Capacitive reactance

The relation between voltage and current in an ideal capacitance is

${\displaystyle i(t)=C{dv(t) \over dt}}$

where ${\displaystyle v(t)}$ is the voltage and ${\displaystyle i(t)}$ is the current in amperes as a function of time ${\displaystyle t}$, and ${\displaystyle C}$ is the capacitance in farads. So if a sinusoidal alternating voltage ${\displaystyle i(t)=V_{p}\cos(2\pi ft)}$ is applied to a capacitor, the current into a lead of the capacitor will be

${\displaystyle i(t)=C{d \over dt}[V_{p}\cos(2\pi ft)]=-2\pi fCV_{p}\sin(2\pi ft)=2\pi fCV_{p}\cos(2\pi ft+{\pi \over 2})}$

where ${\displaystyle V_{p}}$ is the amplitude (peak value) of the sinusoidal voltage in volts, ${\displaystyle f}$ is the frequency of the alternating current in hertz.
Thus the amplitude (peak value) ${\displaystyle I_{p}}$ of the current into a plate of the capacitor will be

${\displaystyle I_{p}=2\pi fCV_{p}}$

Reactance is defined as the ratio of the amplitude (peak value) of the alternating voltage to current in a capacitance or inductance, analoguously to how electrical resistance is defined for a resistor. Thus the magnitude of the reactance will be

${\displaystyle X_{C}={V_{p} \over I_{p}}={1 \over 2\pi fC}={1 \over \omega C}}$

where ${\displaystyle \omega =2\pi f}$ is the angular frequency. Like resistance, reactance has units of ohms. It can be seen that the reactance of a capacitor is inversely proportional to the frequency; a fixed capacitance presents less opposition to an alternating voltage as its frequency increases. It can also be seen that the voltage and current waveforms are out of phase; since the current is greatest when the voltage is changing fastest, the current peaks precede the voltage peaks in the waveform. The phase difference between the voltage and current is ${\displaystyle \phi =\pi /2}$ radians or 90 degrees, showing that in a capacitor the current leads the voltage by 90°.

# For Electric field

## The reality of the field

It is sometimes asked whether the electric field is "real"; whether it is an actual condition of space, or whether it is merely a mathematical technique useful for calculating forces on charges. After all, any calculation of forces using the electric field can also be made without the electric field, using Coulomb's law.

• Principle of locality: When a stationary charge is moved from its position, its Coulomb force on other charges of course changes due to the change in position. For example, if a charge ${\displaystyle q_{2}}$ at position ${\displaystyle {\boldsymbol {x_{2}}}}$ is suddenly moved further away from a charge ${\displaystyle q_{1}}$ at position ${\displaystyle {\boldsymbol {x_{1}}}}$, its force ${\displaystyle F_{1}}$ on charge ${\displaystyle q_{1}}$ will drop to some lower value. However it is found experimentally that the force on other charges does not change simultaneously with the movement. There is a delay before the change in force is felt by other charges, which is proportional to their distance from the moved charge. For particle 1 the delay is ${\displaystyle \Delta t=|{\boldsymbol {x_{2}}}-{\boldsymbol {x_{1}}}|/c}$, where ${\displaystyle c}$ is the speed of light. In other words the Coulomb force is not an instantaneous "action at a distance", but propagates through space with the speed of light. After charge 2 moves, during the time ${\displaystyle \Delta t}$ before the force on charge 1 changes, what is it that 'remembers" the old force ${\displaystyle F_{1}}$? There must be some local property of the space at ${\displaystyle {\boldsymbol {x_{1}}}}$ that determines the electric force on particle 1. This is the electric field.
This argument is called the principle of locality. Classical electromagnetism is a local theory; the electric and magnetic fields are needed as the medium through which electric and magnetic forces propagate, to account for the finite time delay between cause and effect. In quantum mechanics this principle is violated in some limited circumstances, when entangled particles are involved, but in most circumstances electric and magnetic forces still travel at the speed of light, requiring electric and magnetic fields as a medium of propagation.
• Energy and momentum of the field: When an electric charge is accelerated it is found to lose energy and momentum. This is because it radiates electromagnetic radiation, consisting of time-varying electric and magnetic fields. If the energy and momentum carried by the electric and magnetic fields are calculated, they are found to equal the energy and momentum lost by the charge. Thus electric and magnetic fields are necessary, otherwise accelerating charges would violate the fundamental principles of conservation of energy and conservation of momentum.
For example, if two charges have been stationary for a length of time, the Coulomb force of charge 1 on charge 2, ${\displaystyle {\boldsymbol {F}}_{2}}$, is equal and opposite to the force of charge 2 on charge 1, ${\displaystyle {\boldsymbol {F}}_{1}}$. This, called Newton's third law, is the result of the law of conservation of momentum. If the two charges are free particles, the momentum imparted to charge 1, ${\displaystyle {\boldsymbol {p}}_{1}}$, during the interval of time ${\displaystyle \Delta t}$ due to the force of charge 2 is ${\displaystyle {\boldsymbol {p}}_{1}={\boldsymbol {F}}_{1}(t)\Delta t}$. Similarly the momentum imparted to charge 2 by charge 1 in the same time is ${\displaystyle {\boldsymbol {p}}_{2}={\boldsymbol {F}}_{2}(t)\Delta t}$. Conservation of momentum requires that ${\displaystyle {\boldsymbol {p}}_{1}+{\boldsymbol {p}}_{2}=0}$ so ${\displaystyle {\boldsymbol {p}}_{2}=-{\boldsymbol {p}}_{1}}$ and therefore ${\displaystyle {\boldsymbol {F}}_{2}=-{\boldsymbol {F}}_{1}}$
However in the above example, when charge 2 is moved away, the force on it by charge 1, ${\displaystyle F'_{2}}$ decreases immediately. But the force on charge 1 ${\displaystyle F'_{1}}$ stays the same until the change in electric field propagates to its location at time ${\displaystyle \Delta t}$, so ${\displaystyle |{\boldsymbol {F}}'_{2}|<|{\boldsymbol {F}}'_{1}|}$, and therefore ${\displaystyle |{\boldsymbol {p}}_{2}|<|{\boldsymbol {p}}_{1}|}$. So during the period ${\displaystyle \Delta t}$ after charge 2 is moved and before the force on charge 1 changes, there is an apparent violation of conservation of momentum. The explanation of this is that the changing electric field (actually a magnetic field accompanies it so it is an electromagnetic field) carries momentum. The momentum of the electromagnetic field ${\displaystyle {\boldsymbol {p}}_{E}}$ must be included for momentum to be conserved: ${\displaystyle \sum {\boldsymbol {p}}={\boldsymbol {p}}_{1}+{\boldsymbol {p}}_{1}+{\boldsymbol {p}}_{E}={\boldsymbol {0}}}$. A similar argument demonstrates that the changing electromagnetic field also carries energy, and in order for energy to be conserved, the energy of the field must be included. Both of these arguments require an electric field to exist to carry the "missing" energy and momentum.

## Electric field due to a charge distribution

The electric field due to a continuous distribution of charge ${\displaystyle \rho ({\boldsymbol {x}})}$ in space (where ${\displaystyle \rho }$ is the charge density in coulombs per cubic meter) can be calculated by considering the charge ${\displaystyle \rho ({\boldsymbol {x'}})dV}$ in each small volume of space ${\displaystyle dV}$ at point ${\displaystyle {\boldsymbol {x'}}}$ as a point charge, and calculating its electric field ${\displaystyle d{\boldsymbol {E}}({\boldsymbol {x}})}$ at point ${\displaystyle {\boldsymbol {x}}}$

${\displaystyle d{\boldsymbol {E}}({\boldsymbol {x}})={1 \over 4\pi \varepsilon _{0}}{\rho ({\boldsymbol {x}})dV \over ({\boldsymbol {x'-x}})^{2}}{\boldsymbol {{\hat {r}}'}}}$

where ${\displaystyle {\boldsymbol {{\hat {r}}'}}}$ is the unit vector pointing from ${\displaystyle {\boldsymbol {x'}}}$ to ${\displaystyle {\boldsymbol {x}}}$, then adding up the contributions from all the increments of volume by integrating over the volume of the charge distribution ${\displaystyle V}$

${\displaystyle {\boldsymbol {E}}({\boldsymbol {x}})={1 \over 4\pi \varepsilon _{0}}\iiint \limits _{V}\,{\rho ({\boldsymbol {x'}})dV \over ({\boldsymbol {x'-x}})^{2}}{\boldsymbol {{\hat {r}}'}}}$

## Electric field due to moving charges

As mentioned above, if an electric charge moves, the resulting change in the electric field does not appear at all points instantly, but propagates through (empty) space with the speed of light. Therefore if a charge is moving, the instantaneous electric field at a point is not the one due to the current position of the charge, but one created when the charge was at a previous location..

# For Charge density

## Definitions

The volume charge density at a point is equal to the ratio of charge ${\displaystyle \Delta q}$ to volume ${\displaystyle \Delta V=\Delta x\Delta y\Delta z}$, in a small volume centered on point ${\displaystyle {\boldsymbol {x}}}$.[1]

${\displaystyle \rho ({\boldsymbol {x}})=\lim _{\Delta V\to 0}{\Delta q({\boldsymbol {x}}) \over \Delta V}={dq({\boldsymbol {x}}) \over dV}}$

Similarly, if ${\displaystyle \Delta A}$ is a small area of the surface, the surface charge density is defined as

${\displaystyle \sigma ({\boldsymbol {x}})=\lim _{\Delta A\to 0}{\Delta q({\boldsymbol {x}}) \over \Delta A}={dq({\boldsymbol {x}}) \over dA}}$

and if ${\displaystyle \Delta S}$ is a small segment of the line charge distribution, linear charge density is defined as

${\displaystyle \lambda ({\boldsymbol {x}})=\lim _{\Delta S\to 0}{\Delta q({\boldsymbol {x}}) \over \Delta S}={dq({\boldsymbol {x}}) \over dS}}$
1. ^ Purcell, Edward (2011). Electricity and Magnetism, 2nd Ed. Cambridge University Press. pp. 20–21. ISBN 1139503553.

# For Audion

Consider these lead sentences from WP articles:

• "A bicycle... is a human-powered, pedal-driven vehicle" The first crude bicycles did not have petals, but were pushed by the feet on the ground. Bicycles are often ridden by chimpanzees in circuses.
• "A photocopier (also known as a copier or copy machine) is a machine that makes paper copies of documents" Carlson's first machines failed to make copies.
• "A...receiver... receives radio waves and converts the information carried by them to a usable form." Hertz's first "receivers", spark gaps in loop antennas, did not receive or convert "information" but were just sensors that detected pulses of radio waves.
• "A clock is an instrument to measure, keep, and indicate time." This is one of the most inaccurate. A sundial and a wristwatch "measure, keep, and indicate time", but neither are called clocks. The first mechanical clocks in the 12th century did not have faces and did not "indicate" time, but merely chimed the canonical hours, acting as alarms calling the community to prayer. In contrast, an electric clock, alarm clock and mantle clock clearly fit the definition, but in horology are technically not called a "clock" unless they strike the hours; if they cannot chime they are called a "timepiece".
• "A computer is a device that can be instructed to carry out arbitrary sequences of arithmetic or logical operations automatically." At the time digital computers were devised, the word "computer" meant not a device, but an employee that performed arithmetical computations. The earliest 'computers' the analog computer and the differential analyzer cannot be 'instructed' or programmed, but must be physically rebuilt to carry out different operations.

I support all these sentences and wouldn't change them, they are

# For Talk:Magnetic field

First I want to say that ‎Sdc870, Brian Everlasting and yourself have conducted this discussion in a very collegial and collaborative way. I
TStein: But I don't understand your objection to the word "force". Yes, a magnetic field only exerts force on moving charges. But it does exert force on them. Yes, forces on magnetic materials only occur in a non-uniform magnetic field. Torques on dipoles (a type of force) occur in uniform fields. Yes, because the Lorentz force (like a centripetal force) is perpendicular to the velocity, magnetic force does not do work on a particle, so integral ${\displaystyle B\cdot dl=0}$. But it does accelerate it. Beyond these things, what does a magnetic field do? What "influence" does it have? Not much. A time varying magnetic field creates an electric field, but a magnetostatic field's "influence" is limited to exerting forces and torques.
And forces exerted by magnets are likely to be the only effects of a magnetic field that nontechnically-educated readers (the vast majority of readers of this introduction) are acquainted with. "magnetic forces" seems an acceptable way to describe the effects of a magnetic field to general readers, and unlike "influence" actually tells them something.

"A magnetic field is a condition of space surrounding magnetic materials, moving electric charges and electric currents that is responsible for magnetic forces and effects. Since the magnetic influence varies in magnitude and direction at different points, it is described mathematically as a field."

## History

### Use during wireless telegraphy era

#### Crystodyne

I've noticed a few classes of antenna which (AFAIK) are missing from Deep web (except for the batwing antenna): TV and FM broadcasting antennas. These are widely used, but there are many specialized types which are mainly known by broadcast engineers. They consist of specialized dipole, turnstile, and reflective array antennas, with multiple antennas stacked vertically along the supporting mast to increase the gain. My question is, where do you think they should be put? I would like to have a discussion on this with any interested editors, to try to come to a consensus before adding them. Some options:

# Talk:Alnico

• "They [Alnico alloys] are characterized by high remanence and available energy and moderately high coercivity" Laughlin, Warne, Electrical Engr's Reference Book, p.8-14
• "Permanent magnet materials are differentiated from the softer substances more particularly by their high coercivity" Heck, Magnetic Materials, p.238
• "A major breakthrough came in 1931 with the discovery of the ... high coercive field of the...aluminum-nickel-cobalt-iron alloys (Alnico alloys). With these alloys the coercive field was increased by an order of magnitude compared to the old tungsten and chromium steels" Gerber, Wright, Asti, Applied Magnetism, p.335
• "The materials for making permanent magnets...must have high coercivity. So...some alloys like Alnico and Ticonol are preferred for making permanent magnets" Tata, Physics for class XII, p.114
• "[Alnico] exhibited coercivity of over 30kA/m, which was almost double that of the best steel magnets then available. Until the development of the rare earth magnets...alnico was the main hard [high coercivity] magnetic material" Tumanski, Handbook of Magnetic Measurements, p.146
• "These [Alnico] are characterized by high remanence, high available energy and moderately high coercivity" Newne's Electric Power Engineer's Handbook, p.35
• "Hard magnetic materials are usually classified as having coercivities over 10kA/m (125 Oe), but some permanent magnet materials have coercivities two orders of magnitude greater than this. For example...56 kA/m (700 Oe) in Alnico.

# For Talk:Electrical telegraph

A separate issue is the evolution of terminology. During the initial period of invention, inventors try a number of technologies, and a blanket term is used for them. For example from the 1850s the term "wireless telegraphy" covered a variety of experimental systems: ground and water conduction telegraphs, electrostatic induction and electromagnetic induction telegraphs, and heliographs. Typically one technology proves most successful and takes over, and the others are abandoned and become dead ends. Radio waves were discovered and became the most successful method of wireless telegraphy, and by 1920 "wireless telegraphy" had narrowed to mean radiotelegraphy, which is its meaning today. In the late 1940s the word "computer" also included mechanical computers like differential analyzers, electronic analog computers, and even humans with adding machines, as well as digital computers. Today the word has narrowed to mean electronic digital computers.

## Structural design

To ensure that the mast acts as a single conductor, the separate structural sections of the mast are connected electrically by copper jumpers.
Typical 200 foot (61 m) triangular guyed lattice mast of an AM radio station in Mount Vernon, Washington, US
The Blosenbergturm, a freestanding tower antenna in Beromünster, Switzerland

Most mast radiators are built as guyed masts. Steel lattice masts of triangular cross-section are the most common type. Square lattice masts and tubular masts are also sometimes used. To ensure that the tower is a continuous conductor, the tower's structural sections are electrically bonded at the joints by short copper jumpers which are soldered to each side or "fusion" (arc) welds across the mating flanges.

Base fed monopole masts, the most common type, must be insulated from the ground. At its base, the mast is usually mounted on a thick ceramic insulator, which has the compressive strength to support the tower's weight and the dielectric strength to withstand the high voltage applied by the transmitter. The RF power to drive the antenna is supplied by a matching network, usually housed in an antenna tuning hut next to the mast, and the cable supplying the current is simply bolted to the tower. The actual transmitter is usually located in a separate building, which supplies RF power to the antenna tuning hut via a transmission line.

To keep it upright the mast has tensioned guy wires attached, usually in sets of 3 at 120° angles, which are anchored to the ground usually with concrete anchors. The guy lines have strain insulators inserted, usually at the top near the attachment point to the tower, to insulate the conductive cable from the tower, preventing the high voltage on the tower from reaching the ground. At certain lengths the conductive guy cables can act electrically as resonant antennas (parasitic elements), absorbing and reradiating radio waves from the mast, disturbing the radiation pattern of the mast, so frequently additional strain insulators are inserted in the guy cables at carefully calculated points to divide the line into nonresonant lengths.

Mast radiators are also built as free-standing towers. These towers can have a triangular or a square cross section, with each leg supported on an insulator. One of the best-known radiating towers is the Blosenbergturm in Beromünster, Switzerland.

### Fencing

Base-fed mast radiators have a high voltage on the base of the mast, which can deliver a dangerous electric shock to anyone touching it. Electrical codes require such exposed high voltage equipment to be fenced off from the public, so the mast and antenna tuning hut are surrounded by a locked fence. Usually a chain-link fence is used, but sometimes wooden fences are used to prevent currents induced in a metallic fence from distorting the radiation pattern of the antenna. An alternate design is to mount the mast on top of the antenna tuning hut, out of the reach of the public, eliminating the need for a fence.

## Electrical design

Base feed: Radio frequency power is fed to the mast by a wire attached to it, which comes from a matching network inside the "antenna tuning hut" at right. The brown ceramic insulator at the base keeps the mast isolated from the ground. On the left there is an earthing switch and a spark gap for lightning protection.

A single mast radiator is an omnidirectional antenna which radiates equal radio wave power in all horizontal directions. Directional antennas, which radiate more power in specific directions than others, can be constructed using multiple masts fed with radio current at different phases. Mast radiators radiate vertically polarized radio waves.

### Feed system

The transmitter which generates the radio frequency current is often located in a building a short distance away from the mast, so its sensitive electronics will not be affected by the strong radio waves at the base of the mast. The current from the transmitter is delivered to the mast through a feedline, a specialized cable (transmission line) for carrying radio frequency current, such as a coaxial cable. The feedline is connected to an antenna tuning unit at the base of the mast, to match the transmission line to the mast. Depending on power handled this may be located in a waterproof box or a small shed called an antenna tuning hut (helix house). The antenna tuning circuit matches the characteristic impedance of the feedline to the impedance of the antenna, and includes a reactance, usually a loading coil, to tune out the reactance of the antenna, to make it resonant at the operating frequency. Without the antenna tuner the impedance mismatch between the antenna and feedline would cause a condition called standing waves (high SWR), in which some of the radio power is reflected back down the feedline toward the transmitter, resulting in inefficiency and possibly overheating the transmitter. From the antenna tuner a short feedline is bolted to the mast. The helix house may also include a power supply for aircraft warning lights on the tower.

There are three ways of feeding a mast radiator:

• Series excited (base feed): the mast is supported on an insulator, and is fed at the bottom; one side of the feedline from the helix house is connected to the bottom of the mast and the other to a ground system under the mast. This is the most common feed type, used in most AM radio station masts.
• Shunt excited: the bottom of the mast is grounded, and one side of the feedline is connected to the mast part way up, and the other to the ground. (This is a similar approach, on a larger scale, to the 'gamma match' popular among amateur radio operators for VHF and UHF amateur radio antennas). This avoids the need to insulate the mast from the ground, and eliminates electric shock hazard of high voltages on the base of the mast
• Sectional: the mast is divided into two sections with an insulator between to make a vertical dipole antenna, and fed across the insulator. This collinear arrangement enhances low-angle (ground wave) radiation and reduces high-angle (sky wave) radiation. This increases the distance to the mush zone where the ground wave and sky wave are at similar strength at night. This type of antenna is known as an anti-fading aerial. Practical sectionals with 120 over 120 degrees, 180 over 120 degrees and 180 over 180 degrees are presently in operation with good results.

### Mast height

Vertical radiation patterns of ideal monopole antennas over a perfect ground. The distance of the line from the origin at a given elevation angle is proportional to the power density radiated at that angle. For a given power input, the power radiated in horizontal directions increases with height from the quarter-wave monopole (0.25λ, blue) through the half-wave monopole (0.5λ, green) to a maximum at a length of 0.625λ (red)
Guy lines have egg-shaped strain insulators in them, to prevent the high voltage on the mast from reaching the ground

The ideal height of a mast radiator depends on transmission frequency ${\displaystyle f}$, the geographical distribution of the listening audience, and terrain. An unsectionalized mast radiator is a monopole antenna, and its vertical radiation pattern, the amount of power it radiates at different elevation angles, is determined by its height ${\displaystyle h}$ compared to the wavelength ${\displaystyle \lambda =c/f}$ of the radio waves, equal to the speed of light ${\displaystyle c}$ divided by the frequency ${\displaystyle f}$. The height of the mast is usually specified in fractions of the wavelength, or sometimes in "electrical degrees"

${\displaystyle G=360^{\circ }{h \over \lambda }}$

The radio frequency current flows up the mast and reflects from the top. The current distribution on the mast, which determines the radiation pattern, is approximately a sinusoidal standing wave with a node at the top and a maxima one quarter wavelength down

${\displaystyle i(y)=I_{\text{max}}\sin(G-y)}$

where ${\displaystyle i(y)}$ is the current at a height of ${\displaystyle y}$ electrical degrees above the ground, and ${\displaystyle I_{\text{max}}}$ is the maximum current. At heights of slightly less than a multiple of a quarter wavelength, ${\displaystyle {1 \over 4}\lambda ,{1 \over 2}\lambda ,{3 \over 4}\lambda ...}$ (${\displaystyle \theta }$ = 90°, 180°, 270°...) the mast is resonant; at these heights the antenna presents a pure resistance to the feedline, simplifying impedance matching the feedline to the antenna. At other lengths the antenna has capacitive reactance or inductive reactance. However masts of these lengths can be fed efficiently by cancelling the reactance of the antenna by a matching network in the helix house.

At the frequencies at which mast radiator antennas are used, in the medium wave and longwave bands, radio stations cover their listening areas using ground waves; the radio waves travel from the transmitter to the receiver just above the Earth's surface, following the contour of the terrain. Therefore the goal of most mast designs is to radiate a maximum amount of power in horizontal directions.[1] An ideal monopole antenna radiates maximum power in horizontal directions at a height of 225 electrical degrees, about 5/8 or 0.625 of a wavelength (this is an approximation; the exact maximum occurs at ${\displaystyle 2/\pi }$ = .637${\displaystyle \lambda }$[2][3]) As shown in the diagram, at heights below a half wavelength (180 electrical degrees) the radiation pattern of the antenna has a single lobe with a maximum in horizontal directions. At heights above a half wavelength the pattern has a second lobe directed into the sky at an angle of about 60°. The reason horizontal radiation is maximum at 0.625${\displaystyle \lambda }$ is that at slightly above a half wavelength, the small second lobe alters the shape of the main lobe, compressing a maximum amount of the radiated power in horizontal directions.[2] Heights above 0.625${\displaystyle \lambda }$ are not generally used because above this the power radiated in horizontal directions decreases rapidly due to increasing power wasted into the sky in the second lobe.

For medium wave AM broadcast band masts 0.625${\displaystyle \lambda }$ would be a height of 117–341 meters (384–1,119 ft), and taller for longwave masts. The high construction costs of such tall masts mean frequently shorter masts are used.

The above gives the radiation pattern of a perfectly conducting mast over perfectly conducting ground. The actual strength of the received signal at any point on the ground is determined by two factors, the power radiated by the antenna in that direction and the path attenuation between the transmitting antenna and the receiver, which depends on ground conductivity.[4] The design process of an actual radio mast usually involves doing a survey of soil conductivity, then using an antenna simulation computer program to calculate a map of signal strength produced by actual masts over the actual terrain. This is compared with the population distribution to find the best design.[4]

A second design goal that affects height is to reduce multipath fading in the reception area. Some of the radio energy radiated at an angle into the sky is reflected by layers of charged particles in the ionosphere and returns to Earth in the reception area. This is called the skywave. At certain distances from the antenna these radio waves are out of phase with the ground waves, and the two radio waves interfere destructively and partly or completely cancel each other, reducing the signal strength. This is called fading. At night when ionospheric reflection is strongest, this results in an annular region of low signal strength around the antenna in which reception may be inadequate, sometimes called a "zone of silence" or mush zone. However multipath fading only becomes significant if the signal strength of the skywave is within about 50% (3dB) of the ground wave. By reducing the height of a monopole slightly the power radiated in the second lobe can be reduced enough to eliminate multipath fading, with only a small reduction in horizontal gain.[2] The optimum height is around 190 electrical degrees or 0.53${\displaystyle \lambda }$, so this is another common height.[2]

### Electrically short masts

The lower limit to the frequency at which mast radiators can be used is in the low frequency band, due to the increasing inefficiency of masts shorter than a quarter wavelength.

As frequency decreases the wavelength increases, requiring a taller antenna to make a given fraction of a wavelength. Construction costs and land area required increase with height, putting a practical limit on mast height. Masts over 1,000 feet (300 m) are prohibitively expensive; the tallest masts in the world are around 2,000 feet (610 m). Another constraint in some areas is height restrictions on structures; near airports aviation authorities may limit the maximum height of masts, requiring a mast be used that is electrically "short".

Antennas with elements significantly shorter than one-quarter of the wavelength (0.25${\displaystyle \lambda }$, 90 electrical degrees) are called electrically short antennas. Electrically short antennas cannot be driven efficiently due to their low radiation resistance.[2] Below one quarter wavelength the radiation resistance of the antenna, the electrical resistance which represents power radiated as radio waves, decreases with the square of mast height. Other electrical resistances in the antenna system, the ohmic resistance of the mast and the buried ground system, are in series with the radiation resistance, and the transmitter power divides proportionally between them. As the radiation resistance decreases more of the transmitter power is dissipated as heat in these resistances, reducing the efficiency of the antenna. Masts shorter than 0.17${\displaystyle \lambda }$ (60 electrical degrees) are seldom used. At this height the radiation resistance is about 10 ohms, so the typical resistance of a buried ground system, 2 ohms, is about 20% of the radiation resistance, so below this height over 20% of the transmitter power is wasted in the ground system. At an electrical length of 0.07${\displaystyle \lambda }$ (25 electrical degrees) the radiation resistance of a monopole mast drops below 2 ohms, so more than half of the transmitter power is dissipated in the ground system.

A second problem with electrically short masts is that the capacitive reactance of the mast is high, requiring a large loading coil in the antenna tuner to tune it out and make the mast resonant. The high reactance vs the low resistance give the antenna a high Q factor; the antenna and coil act as a high Q tuned circuit, reducing the usable bandwidth of the antenna.

Capacitive "top hat" on mast of AM radio tower in Hamersley, Australia

In circumstances in which electrically short masts must be used, a capacitive topload (top hat) is sometimes added at the top of the mast to increase the radiation resistance.[5] This is a round screen of horizontal wires extending radially from the top of the antenna. It acts as a capacitor plate, increasing the antenna current, which increases the radiated power and radiation resistance, "electrically lengthening" the antenna. Another way to construct a capacity hat is to use sections of the top guy wire set, by inserting the strain insulators in the guy line a short distance from the mast. Capacity hats are structurally limited to the equivalent of 15-30 degrees of added electrical height.

At lower frequencies mast radiators are replaced by more elaborate capacitively toploaded antennas such as the T antenna or umbrella antenna which can have higher efficiency.

### Grounding system

Monopole mast radiators require a grounding (Earthing) system under the antenna to carry the return current. One side of the feedline from the helix house is attached to the mast, and the other side to the ground system. To keep the resistance low the ground system consists of a network of cables buried in the earth. Since for an omnidirectional antenna the Earth currents travel radially toward the ground point from all directions, the grounding system usually consists of a radial pattern of buried cables extending outward from the base of the mast in all directions, connected together to the ground lead at a terminal next to the base. The ground system acts as a conductive mirror for radio waves. A standard widely-used ground system acceptable to the US Federal Communications Commission (FCC) is 120 radial ground wires extending out one quarter of a wavelength (.25${\displaystyle \lambda }$, 90 electrical degrees) from the mast. No. 10 gauge soft-drawn copper wire is typically used, buried 4 to 10 inches deep. For MF broadcast band masts this requires a circular land area extending from the mast 47–136 meters (154–446 ft). This is usually planted with grass, which is kept mowed short as tall grass can increase power loss in certain circumstances.

For masts near a half wavelength high (180 electrical degrees) the mast has a voltage maximum (current node) near its base, which results in strong electric fields in the earth above the ground wires near the mast where the displacement current enters the ground. This can cause significant dielectric power losses in the earth. To reduce this loss these antennas often use an elevated conductive ground screen around the mast, connected to the buried ground wires, to shield the ground from the electric field. Another solution is to increase the number of ground wires near the mast and bury them very shallowly in a surface layer of asphalt pavement, which has low dielectric losses.

## Ancillary equipment

Antenna masts are high enough that they can be a hazard to aircraft, particularly since the narrow mast is hard for a pilot to see from far away. Masts are required by aviation authorities to be painted in alternating strips of international orange and white paint, and have aircraft warning lights along their length, to make them more visible to aircraft. Regulations require flashing lights at the top, and at several points along the length of the tower. Because the tower is at a high RF voltage, where it attaches to the mast the cable carrying power to the lights must be isolated

At its base the mast also usually has a lightning arrester consisting of a spark gap, so that current from lightning strikes to the mast will be conducted to ground and will not damage the transmitter. Also at the base is a grounding switch, which is used to connect the mast to the ground system during maintenance operations to ensure that there is no chance that high voltage will be on the mast when personnel are working on it.

## References

1. ^ Laport, Edmund A. (1952). Radio Antenna Engineering. McGraw-Hill Book Co. pp. 77–80.
2. Williams, Edmund, Ed. (2007). National Association of Broadcasters Engineering Handbook, 10th Ed. Taylor and Francis. pp. 715–716. ISBN 9780240807515.
3. ^ Schmitt, Ron (2002). Electromagnetics Explained: A Handbook for Wireless RF, EMC, and High-Speed Electronics. Newnes. p. 244. ISBN 9780750674034.
4. ^ a b Williams, Ed., Edmund (2007). National Association of Broadcasters Engineering Handbook, 10th Ed. Taylor and Francis. p. 713. ISBN 9780240807515.
5. ^ Williams, Ed., Edmund (2007). National Association of Broadcasters Engineering Handbook, 10th Ed. Taylor and Francis. p. 717. ISBN 9780240807515.

# For Gridiron pendulum

## Condition for compensation

The length of the rods needed for temperature compensation can be calculated from the coefficients of thermal expansion (CTE) of the two metals used. Consider a zinc-steel pendulum which has two iron rods and one zinc rod. The total length ${\displaystyle L}$ of the pendulum from pivot to bob equals the length of the two iron rods ${\displaystyle L_{\text{I1}}}$ and ${\displaystyle L_{\text{I2}}}$ minus the length of the zinc rod ${\displaystyle L_{\text{Z}}}$

${\displaystyle L=L_{\text{I1}}+L_{\text{I2}}-L_{\text{Z}}}$

The change in length ${\displaystyle \Delta L}$ of the pendulum due to a change in temperature ${\displaystyle \Delta T}$ is equal to the thermal expansion of the two iron rods ${\displaystyle \Delta L_{\text{I1}}}$, ${\displaystyle \Delta L_{\text{I2}}}$ minus the thermal expansion of the zinc rod ${\displaystyle \Delta L_{\text{Z}}}$, since the zinc rod lifts the bob up. For the pendulum to stay the same length this must be equal to zero

${\displaystyle \Delta L=\Delta L_{\text{I1}}+\Delta L_{\text{I2}}-\Delta L_{\text{Z}}=0}$

The coefficient of thermal expansion ${\displaystyle \alpha }$ is the fractional change in length of the metal with a temperature change of one degree. So the thermal expansion of each rod is equal to the coefficient of thermal expansion of the metal times the length of the rod times the change in temperature. If ${\displaystyle \alpha _{\text{I}}}$ is the CTE of iron and ${\displaystyle \alpha _{\text{Z}}}$ is the CTE of zinc

${\displaystyle \Delta L_{\text{I1}}=\alpha _{\text{I}}L_{\text{I1}}\Delta T}$
${\displaystyle \Delta L_{\text{I2}}=\alpha _{\text{I}}L_{\text{I2}}\Delta T}$
${\displaystyle \Delta L_{Z}=\alpha _{\text{Z}}L_{\text{Z}}\Delta T}$

Substituting into (1)

${\displaystyle \Delta L=\alpha _{\text{I}}L_{\text{I1}}\Delta T+\alpha _{\text{I}}L_{\text{I2}}\Delta T-\alpha _{\text{Z}}L_{\text{Z}}\Delta T=0}$

Simplifying, for temperature compensation the length of the rods must satisfy

${\displaystyle {L_{\text{I1}}+L_{\text{I2}} \over L_{\text{Z}}}={\alpha _{\text{Z}} \over \alpha _{\text{I}}}}$

That is, the ratio of the total length of the two iron rods to the length of the zinc rod must equal the inverse ratio of the temperature coefficients. The total length of the pendulum must be

${\displaystyle L_{\text{I1}}+L_{\text{I2}}-L_{\text{Z}}=g{\bigg (}{T \over 2\pi }{\bigg )}^{2}}$