Electrical impedance

Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied. The term complex impedance may be used interchangeably.

Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of a sinusoidal voltage between its terminals to the complex representation of the current flowing through it.[1] In general, it depends upon the frequency of the sinusoidal voltage.

Impedance extends the concept of resistance to AC circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude. When a circuit is driven with direct current (DC), there is no distinction between impedance and resistance; the latter can be thought of as impedance with zero phase angle.

The notion of impedance is useful for performing AC analysis of electrical networks, because it allows relating sinusoidal voltages and currents by a simple linear law. In multiple port networks, the two-terminal definition of impedance is inadequate, but the complex voltages at the ports and the currents flowing through them are still linearly related by the impedance matrix.[2]

Impedance is a complex number, with the same units as resistance, for which the SI unit is the ohm (Ω). Its symbol is usually Z, and it may be represented by writing its magnitude and phase in the form |Z|∠θ. However, cartesian complex number representation is often more powerful for circuit analysis purposes.

The reciprocal of impedance is admittance, whose SI unit is the siemens, formerly called mho.

Instruments used to measure the electrical impedance are called impedance analyzers.

Introduction

The term impedance was coined by Oliver Heaviside in July 1886.[3][4] Arthur Kennelly was the first to represent impedance with complex numbers in 1893.[5]

In addition to resistance as seen in DC circuits, impedance in AC circuits includes the effects of the induction of voltages in conductors by the magnetic fields (inductance), and the electrostatic storage of charge induced by voltages between conductors (capacitance). The impedance caused by these two effects is collectively referred to as reactance and forms the imaginary part of complex impedance whereas resistance forms the real part.

Impedance is defined as the frequency domain ratio of the voltage to the current.[6] In other words, it is the voltage–current ratio for a single complex exponential at a particular frequency ω.

For a sinusoidal current or voltage input, the polar form of the complex impedance relates the amplitude and phase of the voltage and current. In particular:

  • The magnitude of the complex impedance is the ratio of the voltage amplitude to the current amplitude;
  • the phase of the complex impedance is the phase shift by which the current lags the voltage.

Complex impedance

Complex Impedance
A graphical representation of the complex impedance plane

The impedance of a two-terminal circuit element is represented as a complex quantity . The polar form conveniently captures both magnitude and phase characteristics as

where the magnitude represents the ratio of the voltage difference amplitude to the current amplitude, while the argument (commonly given the symbol ) gives the phase difference between voltage and current. is the imaginary unit, and is used instead of in this context to avoid confusion with the symbol for electric current.

In Cartesian form, impedance is defined as

where the real part of impedance is the resistance and the imaginary part is the reactance .

Where it is needed to add or subtract impedances, the cartesian form is more convenient; but when quantities are multiplied or divided, the calculation becomes simpler if the polar form is used. A circuit calculation, such as finding the total impedance of two impedances in parallel, may require conversion between forms several times during the calculation. Conversion between the forms follows the normal conversion rules of complex numbers.

Complex voltage and current

Impedance symbol comparison
Generalized impedances in a circuit can be drawn with the same symbol as a resistor (US ANSI or DIN Euro) or with a labeled box.

To simplify calculations, sinusoidal voltage and current waves are commonly represented as complex-valued functions of time denoted as and .[7][8]

The impedance of a bipolar circuit is defined as the ratio of these quantities:

Hence, denoting , we have

The magnitude equation is the familiar Ohm's law applied to the voltage and current amplitudes, while the second equation defines the phase relationship.

Validity of complex representation

This representation using complex exponentials may be justified by noting that (by Euler's formula):

The real-valued sinusoidal function representing either voltage or current may be broken into two complex-valued functions. By the principle of superposition, we may analyse the behaviour of the sinusoid on the left-hand side by analysing the behaviour of the two complex terms on the right-hand side. Given the symmetry, we only need to perform the analysis for one right-hand term. The results are identical for the other. At the end of any calculation, we may return to real-valued sinusoids by further noting that

Ohm's law

General AC circuit
An AC supply applying a voltage , across a load , driving a current .

The meaning of electrical impedance can be understood by substituting it into Ohm's law.[9][10] Assuming a two-terminal circuit element with impedance is driven by a sinusoidal voltage or current as above, there holds

The magnitude of the impedance acts just like resistance, giving the drop in voltage amplitude across an impedance for a given current . The phase factor tells us that the current lags the voltage by a phase of (i.e., in the time domain, the current signal is shifted later with respect to the voltage signal).

Just as impedance extends Ohm's law to cover AC circuits, other results from DC circuit analysis, such as voltage division, current division, Thévenin's theorem and Norton's theorem, can also be extended to AC circuits by replacing resistance with impedance.

Phasors

A phasor is represented by a constant complex number, usually expressed in exponential form, representing the complex amplitude (magnitude and phase) of a sinusoidal function of time. Phasors are used by electrical engineers to simplify computations involving sinusoids, where they can often reduce a differential equation problem to an algebraic one.

The impedance of a circuit element can be defined as the ratio of the phasor voltage across the element to the phasor current through the element, as determined by the relative amplitudes and phases of the voltage and current. This is identical to the definition from Ohm's law given above, recognising that the factors of cancel.

Device examples

Resistor

VI phase
The phase angles in the equations for the impedance of capacitors and inductors indicate that the voltage across a capacitor lags the current through it by a phase of , while the voltage across an inductor leads the current through it by . The identical voltage and current amplitudes indicate that the magnitude of the impedance is equal to one.

The impedance of an ideal resistor is purely real and is called resistive impedance:

In this case, the voltage and current waveforms are proportional and in phase.

Inductor and capacitor

Ideal inductors and capacitors have a purely imaginary reactive impedance:

the impedance of inductors increases as frequency increases;

the impedance of capacitors decreases as frequency increases;

In both cases, for an applied sinusoidal voltage, the resulting current is also sinusoidal, but in quadrature, 90 degrees out of phase with the voltage. However, the phases have opposite signs: in an inductor, the current is lagging; in a capacitor the current is leading.

Note the following identities for the imaginary unit and its reciprocal:

Thus the inductor and capacitor impedance equations can be rewritten in polar form:

The magnitude gives the change in voltage amplitude for a given current amplitude through the impedance, while the exponential factors give the phase relationship.

Deriving the device-specific impedances

What follows below is a derivation of impedance for each of the three basic circuit elements: the resistor, the capacitor, and the inductor. Although the idea can be extended to define the relationship between the voltage and current of any arbitrary signal, these derivations assume sinusoidal signals. In fact, this applies to any arbitrary periodic signals, because these can be approximated as a sum of sinusoids through Fourier analysis.

Resistor

For a resistor, there is the relation

which is Ohm's law.

Considering the voltage signal to be

it follows that

This says that the ratio of AC voltage amplitude to alternating current (AC) amplitude across a resistor is , and that the AC voltage leads the current across a resistor by 0 degrees.

This result is commonly expressed as

Capacitor

For a capacitor, there is the relation:

Considering the voltage signal to be

it follows that

and thus, as previously,

Conversely, if the current through the circuit is assumed to be sinusoidal, its complex representation being

then integrating the differential equation

leads to

The Const term represents a fixed potential bias superimposed to the AC sinusoidal potential, that plays no role in AC analysis. For this purpose, this term can be assumed to be 0, hence again the impedance

Inductor

For the inductor, we have the relation (from Faraday's law):

This time, considering the current signal to be:

it follows that:

This result is commonly expressed in polar form as

or, using Euler's formula, as

As in the case of capacitors, it is also possible to derive this formula directly from the complex representations of the voltages and currents, or by assuming a sinusoidal voltage between the two poles of the inductor. In this later case, integrating the differential equation above leads to a Const term for the current, that represents a fixed DC bias flowing through the inductor. This is set to zero because AC analysis using frequency domain impedance considers one frequency at a time and DC represents a separate frequency of zero hertz in this context.

Generalised s-plane impedance

Impedance defined in terms of can strictly be applied only to circuits that are driven with a steady-state AC signal. The concept of impedance can be extended to a circuit energised with any arbitrary signal by using complex frequency instead of . Complex frequency is given the symbol s and is, in general, a complex number. Signals are expressed in terms of complex frequency by taking the Laplace transform of the time domain expression of the signal. The impedance of the basic circuit elements in this more general notation is as follows:

Element Impedance expression
Resistor
Inductor
Capacitor

For a DC circuit, this simplifies to s = 0. For a steady-state sinusoidal AC signal s = .

Resistance vs reactance

Resistance and reactance together determine the magnitude and phase of the impedance through the following relations:

In many applications, the relative phase of the voltage and current is not critical so only the magnitude of the impedance is significant.

Resistance

Resistance is the real part of impedance; a device with a purely resistive impedance exhibits no phase shift between the voltage and current.

Reactance

Reactance is the imaginary part of the impedance; a component with a finite reactance induces a phase shift between the voltage across it and the current through it.

A purely reactive component is distinguished by the sinusoidal voltage across the component being in quadrature with the sinusoidal current through the component. This implies that the component alternately absorbs energy from the circuit and then returns energy to the circuit. A pure reactance does not dissipate any power.

Capacitive reactance

A capacitor has a purely reactive impedance that is inversely proportional to the signal frequency. A capacitor consists of two conductors separated by an insulator, also known as a dielectric.

The minus sign indicates that the imaginary part of the impedance is negative.

At low frequencies, a capacitor approaches an open circuit so no current flows through it.

A DC voltage applied across a capacitor causes charge to accumulate on one side; the electric field due to the accumulated charge is the source of the opposition to the current. When the potential associated with the charge exactly balances the applied voltage, the current goes to zero.

Driven by an AC supply, a capacitor accumulates only a limited charge before the potential difference changes sign and the charge dissipates. The higher the frequency, the less charge accumulates and the smaller the opposition to the current.

Inductive reactance

Inductive reactance is proportional to the signal frequency and the inductance .

An inductor consists of a coiled conductor. Faraday's law of electromagnetic induction gives the back emf (voltage opposing current) due to a rate-of-change of magnetic flux density through a current loop.

For an inductor consisting of a coil with loops this gives:

The back-emf is the source of the opposition to current flow. A constant direct current has a zero rate-of-change, and sees an inductor as a short-circuit (it is typically made from a material with a low resistivity). An alternating current has a time-averaged rate-of-change that is proportional to frequency, this causes the increase in inductive reactance with frequency.

Total reactance

The total reactance is given by

(note that is negative)

so that the total impedance is

Combining impedances

The total impedance of many simple networks of components can be calculated using the rules for combining impedances in series and parallel. The rules are identical to those for combining resistances, except that the numbers in general are complex numbers. The general case, however, requires equivalent impedance transforms in addition to series and parallel.

Series combination

For components connected in series, the current through each circuit element is the same; the total impedance is the sum of the component impedances.

Impedances in series

Impedances in series

Or explicitly in real and imaginary terms:

Parallel combination

For components connected in parallel, the voltage across each circuit element is the same; the ratio of currents through any two elements is the inverse ratio of their impedances.

Impedances in parallel
Impedances in parallel

Hence the inverse total impedance is the sum of the inverses of the component impedances:

or, when n = 2:

The equivalent impedance can be calculated in terms of the equivalent series resistance and reactance .[11]

Measurement

The measurement of the impedance of devices and transmission lines is a practical problem in radio technology and other fields. Measurements of impedance may be carried out at one frequency, or the variation of device impedance over a range of frequencies may be of interest. The impedance may be measured or displayed directly in ohms, or other values related to impedance may be displayed; for example, in a radio antenna, the standing wave ratio or reflection coefficient may be more useful than the impedance alone. The measurement of impedance requires the measurement of the magnitude of voltage and current, and the phase difference between them. Impedance is often measured by "bridge" methods, similar to the direct-current Wheatstone bridge; a calibrated reference impedance is adjusted to balance off the effect of the impedance of the device under test. Impedance measurement in power electronic devices may require simultaneous measurement and provision of power to the operating device.

The impedance of a device can be calculated by complex division of the voltage and current. The impedance of the device can be calculated by applying a sinusoidal voltage to the device in series with a resistor, and measuring the voltage across the resistor and across the device. Performing this measurement by sweeping the frequencies of the applied signal provides the impedance phase and magnitude.[12]

The use of an impulse response may be used in combination with the fast Fourier transform (FFT) to rapidly measure the electrical impedance of various electrical devices.[12]

The LCR meter (Inductance (L), Capacitance (C), and Resistance (R)) is a device commonly used to measure the inductance, resistance and capacitance of a component; from these values, the impedance at any frequency can be calculated.

Example

Consider an LC tank circuit. The complex impedance of the circuit is

It is immediately seen that the value of is minimal (actually equal to 0 in this case) whenever

Therefore, the fundamental resonance angular frequency is

Variable impedance

In general, neither impedance nor admittance can vary with time, since they are defined for complex exponentials in which -∞ < t < +∞. If the complex exponential voltage to current ratio changes over time or amplitude, the circuit element cannot be described using the frequency domain. However, many components and systems (e.g., varicaps that are used in radio tuners) may exhibit non-linear or time-varying voltage to current ratios that seem to be linear time-invariant (LTI) for small signals and over small observation windows, so they can be roughly described as-if they had a time-varying impedance. This description is an approximation: Over large signal swings or wide observation windows, the voltage to current relationship will not be LTI and cannot be described by impedance.

See also

References

  1. ^ Callegaro, p. 2
  2. ^ Callegaro, Sec. 1.6
  3. ^ Science, p. 18, 1888
  4. ^ Oliver Heaviside, The Electrician, p. 212, 23 July 1886, reprinted as Electrical Papers, Volume II, p 64, AMS Bookstore, ISBN 0-8218-3465-7
  5. ^ Kennelly, Arthur. Impedance (AIEE, 1893)
  6. ^ Alexander, Charles; Sadiku, Matthew (2006). Fundamentals of Electric Circuits (3, revised ed.). McGraw-Hill. pp. 387–389. ISBN 978-0-07-330115-0
  7. ^ Complex impedance, Hyperphysics
  8. ^ Horowitz, Paul; Hill, Winfield (1989). "1". The Art of Electronics. Cambridge University Press. pp. 31–32. ISBN 978-0-521-37095-0.
  9. ^ AC Ohm's law, Hyperphysics
  10. ^ Horowitz, Paul; Hill, Winfield (1989). "1". The Art of Electronics. Cambridge University Press. pp. 32–33. ISBN 978-0-521-37095-0.
  11. ^ Parallel Impedance Expressions, Hyperphysics
  12. ^ a b George Lewis Jr.; George K. Lewis Sr. & William Olbricht (August 2008). "Cost-effective broad-band electrical impedance spectroscopy measurement circuit and signal analysis for piezo-materials and ultrasound transducers". Measurement Science and Technology. 19 (10): 105102. Bibcode:2008MeScT..19j5102L. doi:10.1088/0957-0233/19/10/105102. PMC 2600501. PMID 19081773. Retrieved 2008-09-15.

External links

Bioelectrical impedance analysis

Bioelectrical impedance analysis (BIA) is a commonly used method for estimating body composition, and in particular body fat. Since the advent of the first commercially available devices in the mid-1980s the method has become popular owing to its ease of use and portability of the equipment. It is familiar in the consumer market as a simple instrument for estimating body fat. BIA actually determines the electrical impedance, or opposition to the flow of an electric current through body tissues which can then be used to estimate total body water (TBW), which can be used to estimate fat-free body mass and, by difference with body weight, body fat.

Brian H. Brown

Brian H. Brown is a medical physicist specialising in medical electronics. He is especially well known for his pioneering work with David C. Barber on electrical impedance tomography (EIT). He is also noted for his work on the recording and understanding of the electrical activity of the gut, the analysis of nerve action potentials, the use of electromyography to investigate and identify carriers of muscular dystropy and the development of aids for the profoundly deaf.

He has contributed to about 270 scientific publications, patents and books and is currently Professor Emeritus at the University of Sheffield.

Brown graduated in Physics from the University of London in 1962 and subsequently completed his PhD

in neurophysiology from the University of Sheffield. After graduation, he worked as a Development Engineer with Pye Ltd. in Cambridge and subsequently as a

Heath Physicist at Berkeley Nuclear Power Station. Later he was employed for a year as a UN Expert in Medical Electronics in Hyderabad, India. He subsequently was appointed to a chair in Medical Physics in Sheffield. He took partial-retirement in 2002

from his post as Chairman of the Department of Medical

Physics and Clinical Engineering at Sheffield Teaching

Hospitals and the University of Sheffield.

Brown has won numerous awards and prizes in recognition of his work including the Herman P. Schwan Award for Pioneering Research into Electrical Impedance Tomography

Electrical Impedance and Diffuse Optical Tomography Reconstruction Software

EIDORS is an open-source software tool box written mainly in MATLAB/GNU Octave designed primarily for image reconstruction from electrical impedance tomography(EIT) data, in a biomedical, industrial or geophysical setting. The name was originally an acronym for Electrical Impedance Tomography and Diffuse Optical Reconstruction Software. While the name reflects the original intention to cover image reconstruction of data from the mathematically similar near infra red diffuse optical imaging, to date there has been little development in that area.

The project was launched in 1999 with a Matlab code for 2D EIT reconstruction which had its origin in the PhD thesis of Marko Vauhkonen and the work of his supervisor Jari Kaipio at the University of Kuopio. While Kuopio also developed a three dimensional EIT code this was not released as open-source. Instead the three dimensional version of EIDORS was developed from work done at UMIST (now University of Manchester) by Nick Polydorides and William Lionheart.

Electrical characteristics of dynamic loudspeakers

The chief electrical characteristic of a dynamic loudspeaker's driver is its electrical impedance as a function of frequency. It can be visualized by plotting it as a graph, called the impedance curve.

Electrical impedance myography

Electrical impedance myography, or EIM, is a non-invasive technique for the assessment of muscle health that is based on the measurement of the electrical impedance characteristics of individual muscles or groups of muscles. The technique has been used for the purpose of evaluating neuromuscular diseases both for their diagnosis and for their ongoing assessment of progression or with therapeutic intervention. Muscle composition and microscopic structure change with disease, and EIM measures alterations in impedance that occur as a result of disease pathology. EIM has been specifically recognized for its potential as an ALS biomarker (also known as a biological correlate or surrogate endpoint) by Prize4Life, a 501(c)(3) nonprofit organization dedicated to accelerating the discovery of treatments and cures for ALS. The $1M ALS Biomarker Challenge focused on identifying a biomarker precise and reliable enough to cut Phase II drug trials in half. The prize was awarded to Dr. Seward Rutkove, chief, Division of Neuromuscular Disease, in the Department of Neurology at Beth Israel Deaconess Medical Center and Professor of Neurology at Harvard Medical School, for his work in developing the technique of EIM and its specific application to ALS. It is hoped that EIM as a biomarker will result in the more rapid and efficient identification of new treatments for ALS. EIM has shown sensitivity to disease status in a variety of neuromuscular conditions, including radiculopathy, inflammatory myopathy, Duchenne muscular dystrophy, and spinal muscular atrophy.In addition to the assessment of neuromuscular disease, EIM also has the prospect of serving as a convenient and sensitive measure of muscle condition. Work in aging populations and individuals with orthopedic injuries indicates that EIM is very sensitive to muscle atrophy and disuse and is conversely likely sensitive to muscle conditioning and hypertrophy. Work on mouse and rats models, including a study of mice on board the final Space Shuttle mission (STS-135), has helped to confirm this potential value.

Electrical impedance tomography

Electrical impedance tomography (EIT) is a noninvasive type of medical imaging in which the electrical conductivity, permittivity, and impedance of a part of the body is inferred from surface electrode measurements and used to form a tomographic image of that part. Electrical conductivity varies considerably among various biological tissues (absolute EIT) or the movement of fluids and gases within tissues (difference EIT). The majority of EIT systems apply small alternating currents at a single frequency, however, some EIT systems use multiple frequencies to better differentiate between normal and suspected abnormal tissue within the same organ (multifrequency-EIT or electrical impedance spectroscopy).

Typically, conducting surface electrodes are attached to the skin around the body part being examined. Small alternating currents will be applied to some or all of the electrodes, the resulting equi-potentials being recorded from the other electrodes (figures 1 and 2). This process will then be repeated for numerous different electrode configurations and finally result in a two-dimensional tomogram according to the image reconstruction algorithms incorporated.Since free ion content determines tissue and fluid conductivity, muscle and blood will conduct the applied currents better than fat, bone or lung tissue. This property can be used to reconstruct static images by morphological or absolute EIT (a-EIT). However, in contrast to linear x-rays used in Computed Tomography, electric currents travel three dimensionally along the path of least resistivity. This means, that a part of the electric current leaves the transverse plane and results in an impedance transfer. This and other factors are the reason why image reconstruction in absolute EIT is so hard, since there is usually more than just one solution for image reconstruction of a three-dimensional area projected onto a two-dimensional plane.

Mathematically, the problem of recovering conductivity from surface measurements of current and potential is a non-linear inverse problem and is severely ill-posed. The mathematical formulation of the problem is due to Alberto Calderón, and in the mathematical literature of inverse problems it is often referred to as "Calderón's inverse problem" or the "Calderón problem". There is extensive mathematical research on the problem of uniqueness of solution and numerical algorithms for this problem.Compared to the tissue conductivities of most other soft tissues within the human thorax, lung tissue conductivity is approximately five-fold lower, resulting in high absolute contrast. This characteristic may partially explain the amount of research conducted in EIT lung imaging. Furthermore, lung conductivity fluctuates intensely during the breath cycle which accounts for the immense interest of the research community to use EIT as a bedside method to visualize inhomogeneity of lung ventilation in mechanically ventilated patients. EIT measurements between two or more physiological states, e.g. between inspiration and expiration, are therefore referred to as time difference EIT (td-EIT).

Time difference EIT (td-EIT) has one major advantage over absolute EIT (a-EIT): inaccuracies resulting from interindividual anatomy, insufficient skin contact of surface electrodes or impedance transfer can be dismissed because most artifacts will eliminate themselves due to simple image subtraction in f-EIT. This is most likely the reason why, as of today, the greatest progress of EIT research has been achieved with difference EIT.Further EIT applications proposed include detection/location of cancer in skin, breast, or cervix, localization of epileptic foci, imaging of brain activity. as well as a diagnostic tool for impaired gastric emptying. Attempts to detect or localize tissue pathology within normal tissue usually rely on multifrequency EIT (MF-EIT), also termed Electrical Impedance Spectroscopy (EIS) and are based on differences in conductance patterns at varying frequencies.

The invention of EIT as a medical imaging technique is usually attributed to John G. Webster and a publication in 1978, although the first practical realization of a medical EIT system was detailed in 1984 due to the work of David C. Barber and Brian H. Brown. Together, Brown and Barber published the first Electrical Impedance Tomogram in 1983, visualizing the cross section of a human forearm by absolute EIT. Even though there has been substantial progress in the meantime, most a-EIT applications are still considered experimental. However, two commercial f-EIT devices for monitoring lung function in intensive care patients have been introduced just recently.

A technique similar to EIT is used in geophysics and industrial process monitoring – electrical resistivity tomography. In analogy to EIT, surface electrodes are being placed on the earth, within bore holes, or within a vessel or pipe in order to locate resistivity anomalies or monitor mixtures of conductive fluids. Setup and reconstruction techniques are comparable to EIT. In geophysics, the idea dates from the 1930s.

Electrical measurements

Electrical measurements are the methods, devices and calculations used to measure electrical quantities. Measurement of electrical quantities may be done to measure electrical parameters of a system. Using transducers, physical properties such as temperature, pressure, flow, force, and many others can be converted into electrical signals, which can then be conveniently measured and recorded. High-precision laboratory measurements of electrical quantities are used in experiments to determine fundamental physical properties such as the charge of the electron or the speed of light, and in the definition of the units for electrical measurements, with precision in some cases on the order of a few parts per million. Less precise measurements are required every day in industrial practice. Electrical measurements are a branch of the science of metrology.

Measurable independent and semi-independent electrical quantities comprise:

Voltage

Electric current

Electrical resistance and electrical conductance

Electrical reactance and susceptance

Magnetic flux

Electrical charge by the means of electrometer

Partial discharge measurement

Magnetic field by the means of Hall sensor

Electric field

Electrical power by the means of electricity meter

S-matrix by the means of network analyzer (electrical)

Electrical power spectrum by the means of spectrum analyzerMeasurable dependent electrical quantities comprise:

Inductance

Capacitance

Electrical impedance defined as vector sum of electrical resistance and electrical reactance

Electrical admittance, the reciprocal of electrical impedance

Phase between current and voltage and related power factor

Electrical spectral density

Electrical phase noise

Electrical amplitude noise

Transconductance

Transimpedance

Electrical power gain

Voltage gain

Current gain

Frequency

Propagation delay

Electrical resistivity tomography

Electrical resistivity tomography (ERT) or electrical resistivity imaging (ERI) is a geophysical technique for imaging sub-surface structures from electrical resistivity measurements made at the surface, or by electrodes in one or more boreholes. If the electrodes are suspended in the boreholes, deeper sections can be investigated. It is closely related to the medical imaging technique electrical impedance tomography (EIT), and mathematically is the same inverse problem. In contrast to medical EIT, however, ERT is essentially a direct current method. A related geophysical method, induced polarization (or spectral induced polarization), measures the transient response and aims to determine the subsurface chargeability properties.

Electroglottograph

The electroglottograph, or EGG, (also referred to as a laryngograph) is a device used for the noninvasive measurement of the degree of contact between the vibrating vocal folds during voice production. Though it is difficult to verify the assumption precisely, the aspect of contact being measured by a typical EGG unit is considered to be the vocal fold contact area (VFCA). To measure VFCA, an electrodes are applied on the surface of the neck so that the EGG records variations in the transverse electrical impedance of the larynx and nearby tissues by means of a small A/C electric current (in megaHertz). This electrical impedance will vary slightly with the area of contact between the moist vocal folds during the setment of the glottal vibratory cycle in which the folds are in contact. However, because the percentage variation in the neck impedance caused by vocal fold contact can be extremely small and varies considerably between subjects, no absolute measure of contact area is obtained, only the pattern of variation for a given subject.

Early commercial available EGG units were compared quite thoroughly by Baken. However, using modern low noise electronics, EGG noise levels can be brought down enough so that the noise is approximately 40 dB (a factor of 100) less than a typical EGG signal from an adult voice.

In addition, by using multiple channels simultaneously, the technique can be made easier to use and more reliable by giving the user an indication of the correct positioning of the electrodes, and providing a quantitative measure of vertical movements of the larynx during voice production.Electroglottograph signals have also been used in stroboscope synchronization, voice fundamental frequency tracking, tracking vocal fold abductory movements and the study of the singing voice.Electroglottographic wavegrams are a new technique for displaying and analyzing EGG signals. This technique provides an intuitive means for quickly assessing vocal fold contact phenomena and their variation over time.

Focused impedance measurement

Focused Impedance Measurement (FIM) is a recent technique for quantifying the electrical resistance in tissues of the human body with improved zone localization compared to conventional methods. This method was proposed and developed by Department of Biomedical Physics and Technology of University of Dhaka under the supervision of Prof. Khondkar Siddique-e-Rabbani; who first introduced the idea. FIM can be considered a bridge between Four Electrode Impedance Measurement (FEIM) and Electrical impedance Tomography (EIT), and provides a middle ground in terms of simplicity and accuracy.

Many biological parameters and processes can be detected and monitored through their effects on bioimpedance. Bioimpedance measurement can be performed with a few simple instruments and non-invasively.

Measurement of electrical impedance to obtain physiological or diagnostic information has been of interest to researchers for many years. However, the human body is geometrically and conductively uneven, with variation between individuals and phases of normal body activity, and bioimpedance results from many factors, including ion concentrations, cell geometry, extra-cellular fluids, intra-cellular fluids, and organ geometry. This makes accurate analysis of results from a small number of electrodes difficult and unreliable. Identifying zones with specific impedances can provide greater certainty regarding the factors behind the impedance.

Conventional Four Electrode or Tetra-polar Impedance Measurement (TPIM) is simple, but the zone of sensitivity is not well defined and may include organs other that those of interest, making interpretation difficult and unreliable. On the other hand, Electrical impedance tomography (EIT) offers reasonable resolution, but is complex and require many electrodes. By placing two FEIM systems perpendicular to each other over a common zone at the center and combining the results, it is possible to obtain enhanced sensitivity over this central zone. This is the basis of FIM, which may be useful for impedance measurements of large organs like stomach, heart, and lungs. Being much simpler in comparison to EIT, multifrequency systems can be simply built for FIM.

FIM may be useful in other fields where impedance measurements are performed, like geology.

Frequency domain sensor

Frequency domain (FD) sensor is an instrument developed for measuring soil moisture content. The instrument has an oscillating circuit, the sensing part of the sensor is embedded in the soil, and the operating frequency will depend on the value of soil's dielectric constant.

There are two types of sensors:

Capacitance probe, or fringe capacitance sensor. Capacitance probes use capacitance to measure the dielectric permittivity of the soil. The volume of water in the total volume of soil most heavily influences the dielectric permittivity of the soil because the dielectric constant of water (80) is much greater than the other constituents of the soil (mineral soil: 4, organic matter: 4, air: 1). Thus, when the amount of water changes in the soil, the probe will measure a change in capacitance (from the change in dielectric permittivity) that can be directly correlated with a change in water content. Circuitry inside some commercial probes change the capacitance measurement into a proportional millivolt output. Other configuration are like the neutron probe where an access tube made of PVC is installed in the soil. The probe consists of sensing head at fixed depth. The sensing head consists of an oscillator circuit, the frequency is determined by an annular electrode, fringe-effect capacitor, and the dielectric constant of the soil.

Electrical impedance sensor, which consists of soil probes and using electrical impedance measurement. The most common configuration is based on the standing wave principle (Gaskin & Miller, 1996). The device comprises a 100 MHz sinusoidal oscillator, a fixed impedance coaxial transmission line, and probe wires which is buried in the soil. The oscillator signal is propagated along the transmission line into the soil probe, and if the probe's impedance differs from that of the transmission line, a proportion of the incident signal is reflected back along the line towards the signal source.Compared to time domain reflectometer (TDR), FD sensors are cheaper to build and have a faster response time. However, because of the complex electrical field around the probe, the sensor needs to be calibrated for different soil types. Some commercial sensors have been able to remove the soil type sensitivity by using a high frequency.

Horn analyzer

A horn analyzer is an test instrument dedicated to determine the resonance and anti-resonance frequencies of ultrasonic parts such as transducers, converters, horns/sonotrodes and acoustic stacks, which are used for ultrasonic welding, cutting, cleaning, medical and industrial applications. In addition, digital horn analyzers are able to determine the electrical impedance of piezoelectric materials, the Butterworth-Van Dyke (BVD)equivalent circuit and the mechanical quality fator (Qm).

Impedance

Impedance is the complex-valued generalization of resistance. It may refer to:

Acoustic impedance, a constant related to the propagation of sound waves in an acoustic medium

Electrical impedance, the ratio of the voltage phasor to the electric current phasor, a measure of the opposition to time-varying electric current in an electric circuit

High impedance, when only a small amount of current is allowed through

Characteristic impedance of a transmission line

Impedance (accelerator physics), a characterization of the self interaction of a charged particle beam

Nominal impedance, approximate designed impedance

Impedance matching, the adjustment of input impedance and output impedance

Mechanical impedance, a measure of opposition to motion of a structure subjected to a force

Wave impedance, a constant related to electromagnetic wave propagation in a medium

Impedance of free space, a universal constant and the simplest case of a wave impedance

Impedance analogy

The impedance analogy is a method of representing a mechanical system by an analogous electrical system. The advantage of doing this is that there is a large body of theory and analysis techniques concerning complex electrical systems, especially in the field of filters. By converting to an electrical representation, these tools in the electrical domain can be directly applied to a mechanical system without modification. A further advantage occurs in electromechanical systems: Converting the mechanical part of such a system into the electrical domain allows the entire system to be analysed as a unified whole.

The mathematical behaviour of the simulated electrical system is identical to the mathematical behaviour of the represented mechanical system. Each element in the electrical domain has a corresponding element in the mechanical domain with an analogous constitutive equation. Every law of circuit analysis, such as Kirchhoff's laws, that apply in the electrical domain also applies to the mechanical impedance analogy.

The impedance analogy is one of the two main mechanical-electrical analogies used for representing mechanical systems in the electrical domain, the other being the mobility analogy. The roles of voltage and current are reversed in these two methods, and the electrical representations produced are the dual circuits of each other. The impedance analogy preserves the analogy between electrical impedance and mechanical impedance whereas the mobility analogy does not. On the other hand, the mobility analogy preserves the topology of the mechanical system when transferred to the electrical domain whereas the impedance analogy does not.

Inverter (disambiguation)

A power inverter is a device that converts direct current to alternating current.

Inverter may also refer to

Inverter (logic gate) or NOT gate, a device that performs a logical operation

Inverter air conditioner, a type of air conditioner that uses a power inverter to vary the speed of the compressor motor to continuously regulate temperature

Impedance inverter, a device that produces the mathematical inverse of an electrical impedance—see Quarter-wave impedance transformer

Phase angle

In the context of phasors, phase angle refers to the angular component of the complex number representation of the function. The notation   for a vector with magnitude (or amplitude) A and phase angle θ, is called angle notation.

This notation is frequently used to represent an electrical impedance. In this case, the phase angle is the phase difference between the voltage applied to the impedance and the current driven through it.

In the context of periodic phenomena, such as a wave, phase angle is synonymous with phase.

Short circuit

A short circuit (sometimes abbreviated to short or s/c) is an electrical circuit that allows a current to travel along an unintended path with no or a very low electrical impedance. This results in an excessive amount of current flowing into the circuit.

The electrical opposite of a short circuit is an "open circuit", which is an infinite resistance between two nodes. It is common to misuse "short circuit" to describe any electrical malfunction, regardless of the actual problem.

Wave impedance

The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields (the transverse components being those at right angles to the direction of propagation). For a transverse-electric-magnetic (TEM) plane wave traveling through a homogeneous medium, the wave impedance is everywhere equal to the intrinsic impedance of the medium. In particular, for a plane wave travelling through empty space, the wave impedance is equal to the impedance of free space. The symbol Z is used to represent it and it is expressed in units of ohms. The symbol η (eta) may be used instead of Z for wave impedance to avoid confusion with electrical impedance.

The wave impedance is given by

where is the electric field and is the magnetic field, in phasor representation. The impedance is, in general, a complex number.

In terms of the parameters of an electromagnetic wave and the medium it travels through, the wave impedance is given by

where μ is the magnetic permeability, ε is the (real) electric permittivity and σ is the electrical conductivity of the material the wave is travelling through (corresponding to the imaginary component of the permittivity multiplied by omega). In the equation, i is the imaginary unit, and ω is the angular frequency of the wave. Just as for electrical impedance, the impedance is a function of frequency. In the case of an ideal dielectric (where the conductivity is zero), the equation reduces to the real number


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