Hall effect sensor

A Hall effect sensor is a transducer that varies its output voltage in response to changes in magnetic field. Hall sensors are used for proximity switching, positioning, speed detection, and current sensing applications.
In its simplest form, the sensor operates as an analogue transducer, directly returning a voltage. With a known magnetic field, its distance from the Hall plate can be determined. Using groups of sensors, the relative position of the magnet can be deduced.
Electricity carried through a conductor will produce a magnetic field that varies with current, and a Hall sensor can be used to measure the current without interrupting the circuit. Typically, the sensor is integrated with a wound core or permanent magnet that surrounds the conductor to be measured.
Frequently, a Hall sensor is combined with circuitry that allows the device to act in a digital (on/off) mode, and may be called a switch in this configuration. Commonly seen in industrial applications such as the pictured pneumatic cylinder, they are also used in consumer equipment; for example some computer printers use them to detect missing paper and open covers. When high reliability is required, they are used in keyboards.

Hall sensors are commonly used to time the speed of wheels and shafts, such as for internal combustion engine ignition timing or tachometers. They are used in brushless DC electric motors to detect the position of the permanent magnet. In the pictured wheel carrying two equally spaced magnets, the voltage from the sensor will peak twice for each revolution. This arrangement is commonly used to regulate the speed of disc drives.

Hall probe

A hall probe contains an indium compound crystal mounted on an aluminum backing plate, and encapsulated in the probe head. The plane of the crystal is perpendicular to the probe handle. Connecting leads from the crystal are brought down through the handle to the circuit box.
When the Hall Probe is held so that the magnetic field lines are passing at right angles through the sensor of the probe, the meter gives a reading of the value of magnetic flux density (B). A current is passed through the crystal which, when placed in a magnetic field has a “Hall Effect” voltage developed across it. The Hall Effect is seen when a conductor is passed through a uniform magnetic field. The natural electron drift of the charge carriers causes the magnetic field to apply a Lorentz force (the force exerted on a charged particle in an electromagnetic field) to these charge carriers. The result is what is seen as a charge separation, with a build up of either positive or negative charges on the bottom or on the top of the plate. The crystal measures 5 mm square. The probe handle, being made of a non-ferrous material, has no disturbing effect on the field.
A Hall Probe is sensitive enough to measure the Earth's magnetic field. It must be held so that the Earth's field lines are passing directly through it. It is then rotated quickly so the field lines pass through the sensor in the opposite direction. The change in the flux density reading is double the Earth's magnetic flux density. A hall probe must first be calibrated against a known value of magnetic field strength. For a solenoid the hall probe is placed in the center

Hall Effect Sensor Interface

Hall effect sensor may require analog circuitry to be interfaced to microprocessors. These interfaces may include input diagnostics, fault protection for transient conditions and short/open circuit detection. It may also provide and monitor the current to the hall effect sensor itself. There are precision IC products available to handle these features. For example the Hall Effect Interface IC from Maxim Integrated Products is MAX99

Frequency

Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.

Definitions and units

For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles, or periods, per unit time. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by a Greek letter ν (nu).
In SI units, the unit of frequency is hertz (Hz), named after the German physicist Heinrich Hertz. For example, 1 Hz means that an event repeats once per second.
The period is usually denoted as T, and is the reciprocal of the frequency f:

The SI unit for period is the second.

Measurement

By timing

To calculate the frequency of an event, the number of occurrences of the event within a fixed time interval are counted, and then divided by the length of the time interval.
In experimental work (for example, calculating the frequency of an oscillating pendulum) it is generally more accurate to measure the time taken for a fixed number of occurrences, rather than the number of occurrences within a fixed time. The latter method introduces — if N is the number of counted occurrences — a random error between zero and one count, so on average half a count, causing a biased underestimation of f by ½ f / (N + ½)^{[citation needed]} in its expected value. In the first method, which does not suffer this particular error, frequency is still calculated by dividing the number of occurrences by the time interval; however it is the number of occurrences that is fixed, not the time interval.

By stroboscope effect, or frequency beats

In case when the frequency is so high that counting is difficult or impossible with the available means, another method is used, based on a source (such as a laser, a tuning fork, or a waveform generator) of a known reference frequency f₀, that must be tunable or very close to the measured frequency f. Both the observed frequency and the reference frequency are simultaneously produced, and frequency beats are observed at a much lower frequency Δf, which can be measured by counting. This is sometimes referred to as a stroboscope effect. The unknown frequency is then found from .

Frequency of waves

Frequency has an inverse relationship to the concept of wavelength, simply, frequency is inversely proportional to wavelength λ (lambda). The frequency f is equal to the phase speed v of the wave divided by the wavelength λ of the wave:

In the special case of electromagnetic waves moving through a vacuum, then v = c , where c is the speed of light in a vacuum, and this expression becomes:

When waves from a monochromatic source travel from one medium to another, their frequency remains exactly the same — only their wavelength and speed change.

Examples

Physics of light

Radiant energy is energy which is propagated in the form of electromagnetic waves. Most people think of natural sunlight or electrical light, when considering this form of energy. The type of light which we perceive through our optical sensors (eyes) is classified as white light, and is composed of a range of colors (red, orange, yellow, green, blue, indigo, violet) over a range of wavelengths, or frequencies.
Visible (white) light is only a small fraction of the entire spectrum of electromagnetic radiation. At the short end of that wavelength scale is ultraviolet (UV) light from the sun, which cannot be seen. At the longer end of that spectrum is infrared (IR) light, which is used for night vision and other heat-seeking devices. At even shorter wavelengths than UV are X-rays and Gamma-rays. At longer wavelengths than IR are microwaves, radio waves, electromagnetic waves in megahertz and kHz range, as well as natural waves with frequencies in the millihertz and microhertz range. A 2 millihertz wave has a wavelength approximately equal to the distance from the earth to the sun. A microhertz wave would extend 0.0317 light years. A nanohertz wave would extend 31.6881 light years.

Complete spectrum of electromagnetic radiation with the visible portion highlighted

Electromagnetic radiation is classified according to the frequency (or wavelength) of the light wave. This includes (in order of increasing frequency): natural electromagnetic waves, radio waves, microwaves, terahertz radiation, infrared (IR) radiation, visible light, ultraviolet (UV) radiation, X-rays and gamma rays. Of these, natural electromagnetic waves have the longest wavelengths and gamma rays have the shortest. A small window of frequencies, called the visible spectrum or light, is sensed by the eye of various organisms, with variations of the limits of this narrow spectrum.

Physics of sound

Sound is vibration transmitted through a solid, liquid, or gas; particularly, sound means those vibrations composed of frequencies capable of being detected by ears. For humans, hearing is limited to frequencies between about 20 Hz and 20,000 Hz (20 kHz), with the upper limit generally decreasing with age. Other species have a different range of hearing. For example, some dog breeds can perceive vibrations up to 60,000 Hz.^[1] As a signal perceived by one of the major senses, sound is used by many species for detecting danger, navigation, predation, and communication.
The mechanical vibrations that can be interpreted as sound are able to travel through all forms of matter: gases, liquids, solids, and plasmas. The matter that supports the sound is called the medium. Sound cannot travel through vacuum.

Longitudinal and transverse waves

Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.

Sound is transmitted through gases, plasma, and liquids as longitudinal waves, also called compression waves. Through solids, however, it can be transmitted as both longitudinal and transverse waves. Longitudinal sound waves are waves of alternating pressure deviations from the equilibrium pressure, causing local regions of compression and rarefaction, while transverse waves in solids, are waves of alternating shear stress.
Matter in the medium is periodically displaced by a sound wave, and thus oscillates. The energy carried by the sound wave converts back and forth between the potential energy of the extra compression (in case of longitudinal waves) or lateral displacement strain (in case of transverse waves) of the matter and the kinetic energy of the oscillations of the medium.

Sound wave properties

Sound waves are characterized by the generic properties of waves, which are frequency, wavelength, period, amplitude, intensity, speed, and direction (sometimes speed and direction are combined as a velocity vector, or wavelength and direction are combined as a wave vector).
Transverse waves, also known as shear waves, have an additional property of polarization.
Sound characteristics can depend on the type of sound waves (longitudinal versus transverse) as well as on the physical properties of the transmission medium.
Whenever the pitch of the soundwave is affected by some kind of change, the distance between the sound wave maxima also changes, resulting in a change of frequency. When the loudness of a soundwave changes, so does the amount of compression in airwave that is travelling through it, which in turn can be defined as amplitude.
In music and acoustics, the frequency of the standard pitch A above middle C on a piano is usually defined as 440 Hz, that is, 440 cycles per second ( Listen (help·info)) and known as concert pitch, to which an orchestra tunes.

Other examples

In Europe, Africa, Australia, Southern South America, most of Asia, and Russia, the frequency of the alternating current in household electrical outlets is 50 Hz (close to the tone G), whereas in North America and Northern South America, the frequency of the alternating current is 60 Hz (between the tones B♭ and B — that is, a minor third above the European frequency). The frequency of the 'hum' in an audio recording can show where the recording was made — in countries utilizing the European, or the American grid frequency.

Period versus frequency

As a matter of convenience, longer and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like audio and radio, are usually described by their frequency instead of period. These commonly used conversions are listed below:

Frequency	1 mHz (10-3)	1 Hz (100)	1 kHz (103)	1 MHz (106)	1 GHz (109)	1 THz (1012)
Period (time)	1 ks (103)	1 s (100)	1 ms (10-3)	1 µs (10-6)	1 ns (10-9)	1 ps (10-12)

Other types of frequency

• Angular frequency ω is defined as the rate of change in the orientation angle (during rotation), or in the phase of a sinusoidal waveform (e.g. in oscillations and waves):

.

Angular frequency is measured in radians per second (rad/s).

• Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes.
• Wavenumber is the spatial analogue of angular frequency. In case of more than one spacial dimension, wavenumber is a vector quantity

Resonator

A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonance frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical (including acoustic). Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones.
A cavity resonator, usually used in reference to electromagnetic resonators, is one in which waves exist in a hollow space inside the device. Acoustic cavity resonators, in which sound is produced by air vibrating in a cavity with one opening, are known as Helmholtz resonators.

Explanation

A physical system can have as many resonance frequencies as it has degrees of freedom; each degree of freedom can vibrate as a harmonic oscillator. Systems with one degree of freedom, such as a mass on a spring, pendulums, balance wheels, and LC tuned circuits have one resonance frequency. Systems with two degrees of freedom, such as coupled pendulums and resonant transformers can have two resonance frequencies. As the number of coupled harmonic oscillators grows, the time it takes to transfer energy from one to the next becomes significant. The vibrations in them begin to travel through the coupled harmonic oscillators in waves, from one oscillator to the next.
Resonators can be viewed as being made of millions of coupled moving parts (such as atoms). Therefore they can have millions of resonance frequencies, although only a few may be used in practical resonators. The vibrations inside them travel as waves, at an approximately constant velocity, bouncing back and forth between the sides of the resonator. The oppositely moving waves interfere with each other to create a pattern of standing waves in the resonator. If the distance between the sides is , the length of a round trip is . In order to cause resonance, the phase of a sinusoidal wave after a round trip has to be equal to the initial phase, so the waves will reinforce. So the condition for resonance in a resonator is that the round trip distance, , be equal to an integral number of wavelengths of the wave:

If the velocity of a wave is , the frequency is so the resonance frequencies are:

So the resonance frequencies of resonators, called normal modes, are equally spaced multiples (harmonics), of a lowest frequency called the fundamental frequency. The above analysis assumes the medium inside the resonator is homogeneous, so the waves travel at a constant speed, and that the shape of the resonator is rectilinear. If the resonator is inhomogeneous or has a nonrectilinear shape, like a circular drumhead or a cylindrical microwave cavity, the resonance frequencies may not occur at equally spaced multiples of the fundamental frequency. They are then called overtones instead of harmonics. There may be several such series of resonance frequencies in a single resonator, corresponding to different modes of vibration.

Electromagnetic

A distributed parameter resonator of the distributed network type has capacitance, inductance, and resistance which cannot be isolated into separate lumped capacitors, inductors, or resistors. The time factor of propagation of wave energy in the network is appreciable. Resonators can be of the dielectric type or magnetic type. A hollow conductor that uses resonance to amplify an electromagnetic wave is called a cavity resonator. A single layer coil (or solenoid) that is used as a secondary or tertiary winding in a Tesla Coil or Magnifying Transmitter is also called a resonator.

Cavity resonators

The cavity has interior surfaces which reflect a wave of a specific frequency. When a wave that is resonant with the cavity enters, it bounces back and forth within the cavity, with low loss (see standing wave). As more wave energy enters the cavity, it combines with and reinforces the standing wave, increasing its intensity.

Examples

RF cavities in the linac of the Australian Synchrotron are used to accelerate and bunch beams of electrons; the linac is the tube passing through the middle of the cavity

An illustration of the electric and magnetic field of one of the possible modes in a cavity resonator

The cavity magnetron is a vacuum tube with a filament in the center of an evacuated, lobed, circular cavity resonator. A perpendicular magnetic field is imposed by a permanent magnet. The magnetic field causes the electrons, attracted to the (relatively) positive outer part of the chamber, to spiral outward in a circular path rather than moving directly to this anode. Spaced about the rim of the chamber are cylindrical cavities. The cavities are open along their length and so connect the common cavity space. As electrons sweep past these openings they induce a resonant high frequency radio field in the cavity, which in turn causes the electrons to bunch into groups. A portion of this field is extracted with a short antenna that is connected to a waveguide (a metal tube usually of rectangular cross section). The waveguide directs the extracted RF energy to the load, which may be a cooking chamber in a microwave oven or a high gain antenna in the case of radar.
The klystron, tube waveguide, is a beam tube including at least two apertured cavity resonators. The beam of charged particles passes through the apertures of the resonators, often tunable wave reflection grids, in succession. A collector electrode is provided to intercept the beam after passing through the resonators. The first resonator causes bunching of the particles passing through it. The bunched particles travel in a field-free region where further bunching occurs, then the bunched particles enter the second resonator giving up their energy to excite it into oscillations. It is a particle accelerator that works in conjunction with a specifically tuned cavity by the configuration of the structures. On the beamline of an accelerator system, there are specific sections that are cavity resonators for RF.
The reflex klystron is a klystron utilizing only a single apertured cavity resonator through which the beam of charged particles passes, first in one direction. A repeller electrode is provided to repel (or redirect) the beam after passage through the resonator back through the resonator in the other direction and in proper phase to reinforce the oscillations set up in the resonator.
In a laser, light is amplified in a cavity resonator which is usually composed of two or more mirrors. Thus an optical cavity, also known as a resonator, is a cavity with walls which reflect electromagnetic waves (light). This will allow standing wave modes to exist with little loss outside the cavity.

Mechanical

Mechanical resonators are used in electronic circuits to generate signals of a precise frequency. These are called piezoelectric resonators, the most common of which is the quartz crystal. They are made of a thin plate of quartz with metal plates attached to each side, or in low frequency clock applications a tuning fork shape. The quartz material performs two functions. Its high dimensional stability and low temperature coefficient makes it a good resonator, keeping the resonant frequency constant. Second, the quartz's piezoelectric property converts the mechanical vibrations into an oscillating voltage, which is picked up by the plates on its surface, which are electrically attached to the circuit. These crystal oscillators are used in quartz clocks and watches, to create the clock signal that runs computers, and to stabilize the output signal from radio transmitters. Mechanical resonators can also be used to induce a standing wave in other medium. For example a multiple degree of freedom system can be created by imposing a base excitation on a cantilever beam. In this case the standing wave is imposed on the beam ^[1]. This type of system can be used as a sensor to track changes in frequency or phase of the resonance of the fiber. One application is as a measurement device for dimensional metrology^[2].

Acoustic

The most familiar examples of acoustic resonators are in musical instruments. Every musical instrument has resonators. Some generate the sound directly, such as the wooden bars in a xylophone, the head of a drum, the strings in stringed instruments, and the pipes in an organ. Some modify the sound by enhancing particular frequencies, such as the sound box of a guitar or violin. Organ pipes, the bodies of woodwinds, and the sound boxes of stringed instruments are examples of acoustic cavity resonators.

Automobiles

The exhaust pipes in automobile exhaust systems are designed as acoustic resonators that work with the muffler to reduce noise, by making sound waves "cancel each other out"[1]. The "exhaust note" is an important feature for many vehicle owners, so both the original manufacturers and the after-market suppliers use the resonator to enhance the sound. In 'tuned exhaust' systems designed for performance the resonance of the exhaust pipes is also used to 'pull' the combustion products out of the combustion chamber quicker.

Percussion instruments

In many keyboard percussion instruments, below the centre of each note is a tube, which is an acoustic cavity resonator, referred to simply as the resonator. The length of the tube varies according to the pitch of the note, with higher notes having shorter resonators. The tube is open at the top end and closed at the bottom end, creating a column of air which resonates when the note is struck. This adds depth and volume to the note. In string instruments, the body of the instrument is a resonator.
The tremolo effect of a vibraphone is obtained by a mechanism which opens and shuts the resonators.

Stringed instruments

String instruments such as the bluegrass banjo may also have resonators. Many five-string banjos have removable resonators, to allow the instrument to be used with resonator in bluegrass style, or without in folk music style. The term resonator, used by itself, may also refer to the resonator guitar.
The modern ten-string guitar, invented by Narciso Yepes, adds four string resonators to the traditional classical guitar. By tuning these resonators in a very specific way (C, Bb, Ab, Gb) and making use of their strongest partials (corresponding to the octaves and fifths of the strings' fundamental tones), the bass strings of the guitar now resonate equally with any of the 12 tones of the chromatic octave.