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114-444: Varactors are used as voltage-controlled capacitors . They are commonly used in voltage-controlled oscillators , parametric amplifiers , and frequency multipliers . Voltage-controlled oscillators have many applications such as frequency modulation for FM transmitters and phase-locked loops . Phase-locked loops are used for the frequency synthesizers that tune many radios, television sets , and cellular telephones . The varicap

228-471: A vacuum or an electrical insulator material known as a dielectric . Examples of dielectric media are glass, air, paper, plastic, ceramic, and even a semiconductor depletion region chemically identical to the conductors. From Coulomb's law a charge on one conductor will exert a force on the charge carriers within the other conductor, attracting opposite polarity charge and repelling like polarity charges, thus an opposite polarity charge will be induced on

342-484: A "Low voltage electrolytic capacitor with porous carbon electrodes". He believed that the energy was stored as a charge in the carbon pores used in his capacitor as in the pores of the etched foils of electrolytic capacitors. Because the double layer mechanism was not known by him at the time, he wrote in the patent: "It is not known exactly what is taking place in the component if it is used for energy storage, but it leads to an extremely high capacity." The MOS capacitor

456-454: A bag demonstrates a prior-intent to commit a crime, which in many jurisdictions raises shoplifting from misdemeanor to felony status, because they are considered a "burglary tool." To deter the use of booster bags, some stores have add-on metal detector systems which sense metallic surfaces. Like most systems that rely on transmission of electromagnetic signals through a hostile medium, EAS sensors can be rendered inoperative by jamming . As

570-407: A biasing magnet (to increase signal strength) and to allow deactivation. These strips are not bound together but free to oscillate mechanically. Amorphous metals are used in such systems due to their good magnetoelastic coupling , which implies that they can efficiently convert magnetic energy into mechanical vibrations. The detectors for such tags emit periodic tonal bursts at about 58 kHz,

684-414: A cell phone suffers inside an elevator: The electro-magnetic, or radio waves are effectively blocked, reducing the ability to send or receive information. However, they may miss some tags or be unable to remove or deactivate all of them, especially if concealed or integrated tags are used. As a service to retailers, many manufacturers integrate security tags in the packaging of their products, or even inside

798-458: A cross section of a varactor with the depletion layer formed of a p–n junction. This depletion layer can also be made of a MOS or a Schottky diode . This is important in CMOS and MMIC technology. Generally the use of a varicap diode in a circuit requires connecting it to a tuned circuit , usually in parallel with any existing capacitance or inductance. A DC voltage is applied as reverse bias across

912-480: A dielectric of permittivity ε {\displaystyle \varepsilon } . It is assumed the gap d {\displaystyle d} is much smaller than the dimensions of the plates. This model applies well to many practical capacitors which are constructed of metal sheets separated by a thin layer of insulating dielectric, since manufacturers try to keep the dielectric very uniform in thickness to avoid thin spots which can cause failure of

1026-580: A figure-of-eight. Sensitivity will still be orientation-dependent but detection will be possible at all orientations. A detacher is used to remove re-usable hard tags. The type of detacher used will depend on the type of tag. There are a variety of detachers available, with the majority using powerful magnets. Any store that uses an anti-shoplifting system and has a detacher should take care to keep it secured such that it cannot be removed. Some detachers actually have security tags inside them, to alert store personnel of them being removed from (or being brought into)

1140-700: A finite amount of energy before dielectric breakdown occurs. The capacitor's dielectric material has a dielectric strength U d which sets the capacitor's breakdown voltage at V = V bd = U d d . The maximum energy that the capacitor can store is therefore E = 1 2 C V 2 = 1 2 ε A d ( U d d ) 2 = 1 2 ε A d U d 2 {\displaystyle E={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(U_{d}d\right)^{2}={\frac {1}{2}}\varepsilon AdU_{d}^{2}} The maximum energy

1254-491: A flexible dielectric sheet (like oiled paper) sandwiched between sheets of metal foil, rolled or folded into a small package. Early capacitors were known as condensers , a term that is still occasionally used today, particularly in high power applications, such as automotive systems. The term condensatore was used by Alessandro Volta in 1780 to refer to a device, similar to his electrophorus , he developed to measure electricity, and translated in 1782 as condenser , where

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1368-658: A frequency of 3–400 MHz before adequate transistors had been developed to operate at this higher frequency. This technique is still used to generate much higher frequencies, in the 100 GHz – 1 THz range, where even the fastest GaAs transistors are still inadequate. All semiconductor junction devices exhibit the effect, so they can be used as varicaps, but their characteristics will not be controlled and can vary widely between batches. Popular makeshift varicaps include LEDs, 1N400X series rectifier diodes, Schottky rectifiers and various transistors used with their collector-base junctions reverse biased, particularly

1482-449: A higher-frequency signal or a larger capacitor results in a lower voltage amplitude per current amplitude – an AC "short circuit" or AC coupling . Conversely, for very low frequencies, the reactance is high, so that a capacitor is nearly an open circuit in AC analysis – those frequencies have been "filtered out". Capacitors are different from resistors and inductors in that the impedance

1596-542: A label they will only deactivate the one that is part of their system. If a store does not use an EAS system, they will not deactivate any tags at all. This is often the reason why people trigger an alarm entering a store, which can cause great frustration for both customers and staff. EAS systems can provide a solid deterrent against casual theft. The occasional shoplifter, not being familiar with these systems and their mode of operation, will either get caught by them, or preferably, will be dissuaded from attempting any theft in

1710-431: A mandate to improve the shopping experience. These tags are made of a strip of amorphous metal (metglas), which has a very low magnetic saturation value. Except for permanent tags, this strip is also lined with a strip of ferromagnetic material with a moderate coercive field (magnetic "hardness"). Detection is achieved by sensing harmonics and sum or difference signals generated by the non-linear magnetic response of

1824-599: A miniaturized and more reliable low-voltage support capacitor to complement their newly invented transistor . With the development of plastic materials by organic chemists during the Second World War , the capacitor industry began to replace paper with thinner polymer films. One very early development in film capacitors was described in British Patent 587,953 in 1944. Electric double-layer capacitors (now supercapacitors ) were invented in 1957 when H. Becker developed

1938-406: A multitude of other functions requiring large capacitance changes at lower frequencies, generally below 10 MHz. Some designs of electronic security tag readers used in retail outlets require these high capacitance varicaps in their voltage-controlled oscillators. The three leaded devices depicted at the top of the page are generally two common cathode connected varicaps in a single package. In

2052-455: A part of any coherent loss or profit protection system. Disposable tags cost a matter of cents and may have been embedded during manufacture . More sophisticated systems are available, which are more difficult to circumvent. These solutions tend to be product category specific as in the case of high value added electronics and consumables; consequently they are more expensive. Examples are "Safers", transparent secure boxes that completely enclose

2166-408: A piece of metal, such as a large coin on a disposable radio-frequency tag will shield it. Non-disposable tags require stronger magnets or pieces of metal to disable or shield since the strips are inside the casing and thus further away. Most systems can be circumvented by placing the tagged goods in a bag lined with aluminum foil. The booster bag will act as a Faraday cage , shielding the tags from

2280-561: A similar capacitor, which was named the Leyden jar , after the University of Leiden where he worked. He also was impressed by the power of the shock he received, writing, "I would not take a second shock for the kingdom of France." Daniel Gralath was the first to combine several jars in parallel to increase the charge storage capacity. Benjamin Franklin investigated the Leyden jar and came to

2394-423: A small amount (see Non-ideal behavior ). The earliest forms of capacitors were created in the 1740s, when European experimenters discovered that electric charge could be stored in water-filled glass jars that came to be known as Leyden jars . Today, capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In analog filter networks, they smooth

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2508-461: A small magnet. They routinely interfere with CRT displays. Demagnetization-remagnetization units also create intense fields. Acousto-magnetic systems use less power but their signals are pulsed in the 100 Hz range. Radio-frequency systems tend to be the least interfering because of their lower power and operating frequency in the MHz range, making it easy to shield against them. A March 2007 study by

2622-467: A voltage of one volt across the device. Because the conductors (or plates) are close together, the opposite charges on the conductors attract one another due to their electric fields, allowing the capacitor to store more charge for a given voltage than when the conductors are separated, yielding a larger capacitance. In practical devices, charge build-up sometimes affects the capacitor mechanically, causing its capacitance to vary. In this case, capacitance

2736-465: A volume of water in a hand-held glass jar. Von Kleist's hand and the water acted as conductors and the jar as a dielectric (although details of the mechanism were incorrectly identified at the time). Von Kleist found that touching the wire resulted in a powerful spark, much more painful than that obtained from an electrostatic machine. The following year, the Dutch physicist Pieter van Musschenbroek invented

2850-590: Is inversely proportional to the defining characteristic; i.e., capacitance . A capacitor connected to an alternating voltage source has a displacement current to flowing through it. In the case that the voltage source is V 0 cos(ωt), the displacement current can be expressed as: I = C d V d t = − ω C V 0 sin ⁡ ( ω t ) {\displaystyle I=C{\frac {{\text{d}}V}{{\text{d}}t}}=-\omega {C}{V_{0}}\sin(\omega t)} At sin( ωt ) = −1 ,

2964-400: Is a function of dielectric volume, permittivity , and dielectric strength . Changing the plate area and the separation between the plates while maintaining the same volume causes no change of the maximum amount of energy that the capacitor can store, so long as the distance between plates remains much smaller than both the length and width of the plates. In addition, these equations assume that

3078-542: Is a type of system used to prevent shoplifting from retail stores , pilferage of books from libraries , or unwanted removal of properties from office buildings . EAS systems typically consist of two components: EAS antennas and EAS tags or labels. EAS tags are attached to merchandise ; these tags can only be removed or deactivated by employees when the item is properly purchased or checked out. If merchandise bearing an active tag passes by an antenna installed at an entrance/exit, an alarm sounds alerting staff that merchandise

3192-458: Is activated. When the semi-hard magnet is magnetized, the tag is activated. The magnetized strip makes the amorphous strip respond much more strongly to the detectors, because the DC magnetic field given off by the strip offsets the magnetic anisotropy within the amorphous metal. The tag can also be deactivated by demagnetizing the strip, making the response small enough so that it will not be detected by

3306-471: Is added to represent the initial voltage V ( t 0 ). This is the integral form of the capacitor equation: V ( t ) = Q ( t ) C = V ( t 0 ) + 1 C ∫ t 0 t I ( τ ) d τ {\displaystyle V(t)={\frac {Q(t)}{C}}=V(t_{0})+{\frac {1}{C}}\int _{t_{0}}^{t}I(\tau )\,\mathrm {d} \tau } Taking

3420-480: Is applied across a varicap to deliberately vary the capacitance at signal rate to generate higher harmonics, which are extracted through filtering. If a sine wave current of sufficient amplitude is applied driven through a varicap, the resultant voltage gets "peaked" into a more triangular shape, and odd harmonics are generated. This was one early method used to generate microwave frequencies of moderate power, 1–2 GHz at 1–5 watts, from about 20 watts at

3534-408: Is applied across the terminals of a capacitor, for example when a capacitor is connected across a battery, an electric field develops across the dielectric, causing a net positive charge to collect on one plate and net negative charge to collect on the other plate. No current actually flows through a perfect dielectric . However, there is a flow of charge through the source circuit. If the condition

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3648-408: Is approximately the same width as the plate separation, d {\displaystyle d} , and assuming d {\displaystyle d} is small compared to the plate dimensions, it is small enough to be ignored. Therefore, if a charge of + Q {\displaystyle +Q} is placed on one plate and − Q {\displaystyle -Q} on

3762-447: Is defined as C = Q / V {\displaystyle C=Q/V} . Substituting V {\displaystyle V} above into this equation C = ε A d {\displaystyle C={\frac {\varepsilon A}{d}}} Therefore, in a capacitor the highest capacitance is achieved with a high permittivity dielectric material, large plate area, and small separation between

3876-419: Is defined in terms of incremental changes: C = d Q d V {\displaystyle C={\frac {\mathrm {d} Q}{\mathrm {d} V}}} In the hydraulic analogy , voltage is analogous to water pressure and electrical current through a wire is analogous to water flow through a pipe. A capacitor is like an elastic diaphragm within the pipe. Although water cannot pass through

3990-471: Is easy to perform, it is also easy to detect. A simple firmware upgrade should be adequate for modern DSP-based EAS systems to detect jamming. Nevertheless, the vast majority of EAS systems do not currently detect it. All electronic article surveillance systems emit electromagnetic energy and thus can interfere with electronics. Magneto-harmonic systems need to bring the tags to magnetic saturation and thus create magnetic fields strong enough to be felt through

4104-475: Is equal to the energy density per unit volume in the electric field multiplied by the volume of field between the plates, confirming that the energy in the capacitor is stored in its electric field. The current I ( t ) through any component in an electric circuit is defined as the rate of flow of a charge Q ( t ) passing through it. Actual charges – electrons – cannot pass through the dielectric of an ideal capacitor. Rather, one electron accumulates on

4218-471: Is leaving the store unauthorized. Some stores also have antennas at entrances to restrooms to deter shoppers from taking unpaid-for merchandise into the restroom where they could remove the tags. EAS tags that could be attached to items in stores were invented by Arthur Minasy in 1964. He filed a patent for his "Method and Apparatus for Detecting the Unauthorized Movement of Articles" in 1965 with

4332-462: Is maintained sufficiently long, the current through the source circuit ceases. If a time-varying voltage is applied across the leads of the capacitor, the source experiences an ongoing current due to the charging and discharging cycles of the capacitor. Capacitors are widely used as parts of electrical circuits in many common electrical devices. Unlike a resistor , an ideal capacitor does not dissipate energy, although real-life capacitors do dissipate

4446-491: Is not strictly necessary. Indeed, some shoplifters use clothes lined with aluminum foil. Low-frequency magnetic systems will require more shielding than radio-frequency systems due to their use of near-field magnetic coupling. Magnetic shielding, with steel or mu-metal, would be more effective, but also cumbersome and expensive. The shielding technique is well known amongst shoplifters and store owners. Some countries have specific laws against it. In any case, possession of such

4560-956: Is the time constant of the system. As the capacitor reaches equilibrium with the source voltage, the voltages across the resistor and the current through the entire circuit decay exponentially . In the case of a discharging capacitor, the capacitor's initial voltage ( V Ci ) replaces V 0 . The equations become I ( t ) = V C i R e − t / τ 0 V ( t ) = V C i e − t / τ 0 Q ( t ) = C V C i e − t / τ 0 {\displaystyle {\begin{aligned}I(t)&={\frac {V_{Ci}}{R}}e^{-t/\tau _{0}}\\V(t)&=V_{Ci}\,e^{-t/\tau _{0}}\\Q(t)&=C\,V_{Ci}\,e^{-t/\tau _{0}}\end{aligned}}} Impedance ,

4674-419: Is the imaginary unit and ω is the angular frequency of the sinusoidal signal. The − j phase indicates that the AC voltage V = ZI lags the AC current by 90°: the positive current phase corresponds to increasing voltage as the capacitor charges; zero current corresponds to instantaneous constant voltage, etc. Impedance decreases with increasing capacitance and increasing frequency. This implies that

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4788-400: Is the intellectual property (IP) protection against theft: Security paper with embedded microwires, which is used to detect confidential documents if they are removed from a building. These are similar to magnetic tags in that they are made of two strips: a strip of magnetostrictive , ferromagnetic amorphous metal and a strip of a magnetically semi-hard metallic strip, which is used as

4902-482: Is the capacitance for a single plate and n {\displaystyle n} is the number of interleaved plates. As shown to the figure on the right, the interleaved plates can be seen as parallel plates connected to each other. Every pair of adjacent plates acts as a separate capacitor; the number of pairs is always one less than the number of plates, hence the ( n − 1 ) {\displaystyle (n-1)} multiplier. To increase

5016-407: Is the charge stored in the capacitor, V {\displaystyle V} is the voltage across the capacitor, and C {\displaystyle C} is the capacitance. This potential energy will remain in the capacitor until the charge is removed. If charge is allowed to move back from the positive to the negative plate, for example by connecting a circuit with resistance between

5130-800: Is then I (0) = V 0 / R . With this assumption, solving the differential equation yields I ( t ) = V 0 R e − t / τ 0 V ( t ) = V 0 ( 1 − e − t / τ 0 ) Q ( t ) = C V 0 ( 1 − e − t / τ 0 ) {\displaystyle {\begin{aligned}I(t)&={\frac {V_{0}}{R}}e^{-t/\tau _{0}}\\V(t)&=V_{0}\left(1-e^{-t/\tau _{0}}\right)\\Q(t)&=CV_{0}\left(1-e^{-t/\tau _{0}}\right)\end{aligned}}} where τ 0 = RC

5244-538: The condenser microphone . It is a passive electronic component with two terminals . The utility of a capacitor depends on its capacitance . While some capacitance exists between any two electrical conductors in proximity in a circuit , a capacitor is a component designed specifically to add capacitance to some part of the circuit. The physical form and construction of practical capacitors vary widely and many types of capacitor are in common use. Most capacitors contain at least two electrical conductors , often in

5358-460: The 1N5408 , exhibit similar changes in junction capacitance, with the exception that the BA ;102 possesses a specified set of characteristics in relation to junction capacitance (whereas the 1N5408 does not) and the "Q" of the 1N5408 is less. Before the development of the varicap, motor driven variable capacitors or saturable-core reactors were used as electrically controllable reactances in

5472-405: The 2N2222 and BC547 . Reverse biasing the emitter-base junctions of transistors also is quite effective as long as the AC amplitude remains small. Maximum reverse bias voltage is usually between 5 and 7 Volts, before the avalanche process starts conducting. Higher-current devices with greater junction area tend to possess higher capacitance. The Philips BA 102 varicap and a common zener diode,

5586-912: The AC ground node changing bias and operating points of active devices such as varicaps and transistors. These circuit configurations are quite common in television tuners and electronically tuned broadcast AM and FM receivers, as well as other communications equipment and industrial equipment. Early varicap diodes usually required a reverse voltage range of 0–33 V to obtain their full capacitance ranges, which were still quite small, approximately 1–10 pF. These types were – and still are – extensively used in television tuners, whose high carrier frequencies require only small changes in capacitance. In time, varicap diodes were developed which exhibited large capacitance ranges, 100–500 pF, with relatively small changes in reverse bias: 0–5 V or 0–12 V. These newer devices allow electronically tuned AM broadcast receivers to be realized as well as

5700-528: The Food and Department Store environments are dominated by RF technology. One significant problem from source tagging is something called "tag pollution" caused when non-deactivated tags carried around by customers cause unwanted alarms, decreasing the effectiveness and integrity of the EAS system. The problem is that no store has more than one system. Therefore, if a store actually has an anti-shoplifting system to deactivate

5814-518: The LA1851N AM radio chip. Two lower-capacitance dual varactors used in the FM section (which operates at a frequency about one hundred times greater) are highlighted by red arrows. In this case four diodes are used, via a dual package for the tank / bandpass filter and a dual package for the local oscillator. In some applications, such as harmonic multiplication , a large signal amplitude alternating voltage

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5928-460: The VCOs and filters of equipment like World War II German spectrum analyzers . Capacitor In electrical engineering , a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser , a term still encountered in a few compound names, such as

6042-416: The advantage of reducing the AC component of voltage across each device and has symmetrical distortion should the AC component possess enough amplitude to bias the varicaps into forward conduction. When designing tuning circuits with varicaps it is usually good practice to maintain the AC component of voltage across the varicap at a minimal level, usually less than 100 mV peak to peak, to prevent changing

6156-404: The alarm. These tags are permanent and somewhat costly. They are mostly used in clothing stores and have practically been withdrawn from use. Source tagging is the application of EAS security tags at the source, the supplier or manufacturer, instead of at the retail side of the chain. For the retailer, source tagging eliminates the labor expense needed to apply the EAS tags themselves, and reduces

6270-432: The antennas. Although some vendors claim that their acousto-magnetic systems cannot be defeated by bags shielded with aluminum foil, a sufficient amount of shielding (in the order of 30 layers of standard 20 μm foil) will defeat all standard systems. Although the amount of shielding required depends on the system, its sensitivity, and the distance and orientation of the tags relative to its antennas, total enclosure of tags

6384-465: The article to be protected, Spiders that wrap around packaging and Electronic Merchandise Security Systems that allow phones and tablets to be used securely in the store before purchase. All of these require specific detachers or electronic keys at the point-of-sale desk. They have the advantages of being reusable, strong visual deterrents to potential theft. Except for microwave, the detection rate for all these tags depends on their orientation relative to

6498-428: The capacitance is inversely proportional to the square root of applied voltage. For hyperabrupt junction profile capacitance change is more non-linear, but hyperabrupt varicaps have larger capacitance variation and can work with lower voltages. All diodes exhibit this variable junction capacitance, but varactors are manufactured to exploit the effect and increase the capacitance variation. The figure shows an example of

6612-546: The capacitor has a maximum (or peak) current whereby I 0 = ωCV 0 . The ratio of peak voltage to peak current is due to capacitive reactance (denoted X C ). X C = V 0 I 0 = V 0 ω C V 0 = 1 ω C {\displaystyle X_{C}={\frac {V_{0}}{I_{0}}}={\frac {V_{0}}{\omega CV_{0}}}={\frac {1}{\omega C}}} X C approaches zero as ω approaches infinity. If X C approaches 0,

6726-575: The capacitor is initially uncharged while the switch is open, and the switch is closed at t = 0 , it follows from Kirchhoff's voltage law that V 0 = v resistor ( t ) + v capacitor ( t ) = i ( t ) R + 1 C ∫ t 0 t i ( τ ) d τ {\displaystyle V_{0}=v_{\text{resistor}}(t)+v_{\text{capacitor}}(t)=i(t)R+{\frac {1}{C}}\int _{t_{0}}^{t}i(\tau )\,\mathrm {d} \tau } Taking

6840-411: The capacitor is the inductor , which stores energy in a magnetic field rather than an electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing C with the inductance  L . A series circuit containing only a resistor , a capacitor, a switch and a constant DC source of voltage V 0 is known as a charging circuit . If

6954-687: The capacitor resembles a short wire that strongly passes current at high frequencies. X C approaches infinity as ω approaches zero. If X C approaches infinity, the capacitor resembles an open circuit that poorly passes low frequencies. The current of the capacitor may be expressed in the form of cosines to better compare with the voltage of the source: I = − I 0 sin ⁡ ( ω t ) = I 0 cos ⁡ ( ω t + 90 ∘ ) {\displaystyle I=-I_{0}\sin({\omega t})=I_{0}\cos({\omega t}+{90^{\circ }})} In this situation,

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7068-413: The capacitor. Since the separation between the plates is uniform over the plate area, the electric field between the plates E {\displaystyle E} is constant, and directed perpendicularly to the plate surface, except for an area near the edges of the plates where the field decreases because the electric field lines "bulge" out of the sides of the capacitor. This "fringing field" area

7182-438: The charge and voltage on a capacitor, work must be done by an external power source to move charge from the negative to the positive plate against the opposing force of the electric field. If the voltage on the capacitor is V {\displaystyle V} , the work d W {\displaystyle dW} required to move a small increment of charge d q {\displaystyle dq} from

7296-430: The conclusion that the charge was stored on the glass, not in the water as others had assumed. He also adopted the term "battery", (denoting the increase of power with a row of similar units as in a battery of cannon ), subsequently applied to clusters of electrochemical cells . In 1747, Leyden jars were made by coating the inside and outside of jars with metal foil, leaving a space at the mouth to prevent arcing between

7410-420: The consumer AM/FM tuner depicted at the right, a single dual-package varicap diode adjusts both the passband of the tank circuit (the main station selector), and the local oscillator with a single varicap for each. This is done to keep costs down – two dual packages could have been used, one for the tank and one for the oscillator, four diodes in all, and this is what was depicted in the application data for

7524-516: The current is out of phase with the voltage by +π/2 radians or +90 degrees, i.e. the current leads the voltage by 90°. When using the Laplace transform in circuit analysis, the impedance of an ideal capacitor with no initial charge is represented in the s domain by: Z ( s ) = 1 s C {\displaystyle Z(s)={\frac {1}{sC}}} where Electronic security tag Electronic article surveillance (EAS)

7638-402: The derivative and multiplying by C , gives a first-order differential equation : R C d i ( t ) d t + i ( t ) = 0 {\displaystyle RC{\frac {\mathrm {d} i(t)}{\mathrm {d} t}}+i(t)=0} At t = 0 , the voltage across the capacitor is zero and the voltage across the resistor is V 0 . The initial current

7752-429: The derivative of this and multiplying by C yields the derivative form: I ( t ) = d Q ( t ) d t = C d V ( t ) d t {\displaystyle I(t)={\frac {\mathrm {d} Q(t)}{\mathrm {d} t}}=C{\frac {\mathrm {d} V(t)}{\mathrm {d} t}}} for C independent of time, voltage and electric charge. The dual of

7866-426: The detection loops. For a pair of planar loops forming a Helmholtz coil , magnetic field lines will be approximately parallel in their center. Orienting the tag so that no magnetic flux from the coils crosses them will prevent detection, as the tag won't be coupled to the coils. This shortcoming, documented in the first EAS patents, can be solved by using multiple coils or by placing them in another arrangement such as

7980-426: The detectors. AM tags are three dimensional plastic tags, much thicker than electro-magnetic strips and are thus seldom used for books. These tags are essentially an LC tank circuit (L for inductor, C for capacitor) that has a resonance peak anywhere from 1.75 MHz to 9.5 MHz. The standard frequency for retail use is 8.2 MHz. Sensing is achieved by sweeping around the resonant frequency and detecting

8094-415: The device. The amount of reverse bias controls the thickness of the depletion zone and therefore the varactor's junction capacitance. Capacitance change characteristic depends on doping profile. Generally, for abrupt junction profile, the depletion region thickness is proportional to the square root of the applied voltage, and capacitance is inversely proportional to the depletion region thickness. Thus,

8208-480: The diaphragm, it moves as the diaphragm stretches or un-stretches. In a circuit, a capacitor can behave differently at different time instants. However, it is usually easy to think about the short-time limit and long-time limit: The simplest model of a capacitor consists of two thin parallel conductive plates each with an area of A {\displaystyle A} separated by a uniform gap of thickness d {\displaystyle d} filled with

8322-401: The dielectric for the first capacitors. Paper capacitors, made by sandwiching a strip of impregnated paper between strips of metal and rolling the result into a cylinder, were commonly used in the late 19th century; their manufacture started in 1876, and they were used from the early 20th century as decoupling capacitors in telephony . Porcelain was used in the first ceramic capacitors . In

8436-448: The diode capacitance too much, which would distort the signal and add harmonics. A third circuit, at top right in diagram, uses two series-connected varicaps and separate DC and AC signal ground connections. The DC ground is shown as a traditional ground symbol, and the AC ground as an open triangle. Separation of grounds is often done to (i) prevent high-frequency radiation from the low-frequency ground node, and (ii) prevent DC currents in

8550-411: The dip. Deactivation for 8.2 MHz label tags is typically achieved using a deactivation pad. In the absence of such a device, labels can be rendered inactive by punching a hole, or by covering the circuit with a metallic label, a "detuner". The deactivation pad functions by partially destroying the capacitor . Though this sounds violent, in reality, both the process and the result are unnoticeable to

8664-500: The early years of Marconi 's wireless transmitting apparatus, porcelain capacitors were used for high voltage and high frequency application in the transmitters . On the receiver side, smaller mica capacitors were used for resonant circuits . Mica capacitors were invented in 1909 by William Dubilier. Prior to World War II, mica was the most common dielectric for capacitors in the United States. Charles Pollak (born Karol Pollak ),

8778-442: The electric field is entirely concentrated in the dielectric between the plates. In reality there are fringing fields outside the dielectric, for example between the sides of the capacitor plates, which increase the effective capacitance of the capacitor. This is sometimes called parasitic capacitance . For some simple capacitor geometries this additional capacitance term can be calculated analytically. It becomes negligibly small when

8892-447: The first place. Informed shoplifters are conscious of how tags can be removed or deactivated. A common method of defeating RF tags is the use of so-called booster bags . These are typically large paper bags that have been lined with multiple layers of aluminium foil to effectively shield the RF label from detection, much like a Faraday cage . A similar situation would be the loss of signal that

9006-476: The foils. The earliest unit of capacitance was the jar , equivalent to about 1.11 nanofarads . Leyden jars or more powerful devices employing flat glass plates alternating with foil conductors were used exclusively up until about 1900, when the invention of wireless ( radio ) created a demand for standard capacitors, and the steady move to higher frequencies required capacitors with lower inductance . More compact construction methods began to be used, such as

9120-418: The form of metallic plates or surfaces separated by a dielectric medium. A conductor may be a foil, thin film, sintered bead of metal, or an electrolyte . The nonconducting dielectric acts to increase the capacitor's charge capacity. Materials commonly used as dielectrics include glass , ceramic , plastic film , paper , mica , air, and oxide layers . When an electric potential difference (a voltage )

9234-405: The inventor of the first electrolytic capacitors , found out that the oxide layer on an aluminum anode remained stable in a neutral or alkaline electrolyte , even when the power was switched off. In 1896 he was granted U.S. Patent No. 672,913 for an "Electric liquid capacitor with aluminum electrodes". Solid electrolyte tantalum capacitors were invented by Bell Laboratories in the early 1950s as

9348-708: The material under a mixture of low-frequency (in the 10 Hz to 1000 Hz range) magnetic fields. When the ferromagnetic material is magnetized, it biases the amorphous metal strip into saturation, where it no longer produces harmonics. Deactivation of these tags is therefore done with magnetization. Activation requires demagnetization. The EM systems can be used by libraries to protect books and media. In shops, unlike AM and RF, EM can be placed on small or round items and products with foil packaging or metal objects, like cosmetics, baby milk cans, medicines, DIY tools, homeware etc. EM systems can also detect objects placed in foil bags or in metal briefcases. A further application

9462-492: The naked eye. The deactivator causes a micro short circuit in the label. This is done by submitting the tag to a strong electromagnetic field at the resonant frequency, which induces voltages exceeding the capacitor's breakdown voltage . In terms of deactivation, radio frequency is the most efficient of the three technologies (RF, EM, AM – there are no microwave labels) given that the reliable "remote" deactivation distance can be up to 30 cm (11.8 in). It also benefits

9576-618: The name referred to the device's ability to store a higher density of electric charge than was possible with an isolated conductor. The term became deprecated because of the ambiguous meaning of steam condenser , with capacitor becoming the recommended term in the UK from 1926, while the change occurred considerably later in the United States. Since the beginning of the study of electricity , non-conductive materials like glass , porcelain , paper and mica have been used as insulators . Decades later, these materials were also well-suited for use as

9690-415: The negative plate for each one that leaves the positive plate, resulting in an electron depletion and consequent positive charge on one electrode that is equal and opposite to the accumulated negative charge on the other. Thus the charge on the electrodes is equal to the integral of the current as well as proportional to the voltage, as discussed above. As with any antiderivative , a constant of integration

9804-911: The negative to the positive plate is d W = V d q {\displaystyle dW=Vdq} . The energy is stored in the increased electric field between the plates. The total energy W {\displaystyle W} stored in a capacitor (expressed in joules ) is equal to the total work done in establishing the electric field from an uncharged state. W = ∫ 0 Q V ( q ) d q = ∫ 0 Q q C d q = 1 2 Q 2 C = 1 2 V Q = 1 2 C V 2 {\displaystyle W=\int _{0}^{Q}V(q)\,\mathrm {d} q=\int _{0}^{Q}{\frac {q}{C}}\,\mathrm {d} q={\frac {1}{2}}{\frac {Q^{2}}{C}}={\frac {1}{2}}VQ={\frac {1}{2}}CV^{2}} where Q {\displaystyle Q}

9918-416: The other plate (the situation for unevenly charged plates is discussed below), the charge on each plate will be spread evenly in a surface charge layer of constant charge density σ = ± Q / A {\displaystyle \sigma =\pm Q/A} coulombs per square meter, on the inside surface of each plate. From Gauss's law the magnitude of the electric field between

10032-431: The output of power supplies . In resonant circuits they tune radios to particular frequencies . In electric power transmission systems, they stabilize voltage and power flow. The property of energy storage in capacitors was exploited as dynamic memory in early digital computers, and still is in modern DRAM . Natural capacitors have existed since prehistoric times. The most common example of natural capacitance are

10146-455: The patent being granted in 1970. There are several major types of electronic article surveillance systems: Concealed EAS systems have no visible pedestals or hindrance in the store facade. These systems are installed below the floor and dropped from the ceiling and can protect merchandise of retailers from being stolen. There are site conditions and other parameters which enable them to be installed, but often malls insist on concealed system as

10260-668: The plates is E = σ / ε {\displaystyle E=\sigma /\varepsilon } . The voltage(difference) V {\displaystyle V} between the plates is defined as the line integral of the electric field over a line (in the z-direction) from one plate to another V = ∫ 0 d E ( z ) d z = E d = σ ε d = Q d ε A {\displaystyle V=\int _{0}^{d}E(z)\,\mathrm {d} z=Ed={\frac {\sigma }{\varepsilon }}d={\frac {Qd}{\varepsilon A}}} The capacitance

10374-451: The plates, the charge moving under the influence of the electric field will do work on the external circuit. If the gap between the capacitor plates d {\displaystyle d} is constant, as in the parallel plate model above, the electric field between the plates will be uniform (neglecting fringing fields) and will have a constant value E = V / d {\displaystyle E=V/d} . In this case

10488-446: The plates. Since the area A {\displaystyle A} of the plates increases with the square of the linear dimensions and the separation d {\displaystyle d} increases linearly, the capacitance scales with the linear dimension of a capacitor ( C ∝ L {\displaystyle C\varpropto L} ), or as the cube root of the volume. A parallel plate capacitor can only store

10602-565: The point of sale. Deactivation of RF labels is also dependent on the size of the label and the power of the deactivation pad (the larger the label, the greater the field it generates for deactivation to take place. For this reason very small labels can cause issues for consistent deactivation). It is common to find RF deactivation built into barcode flat and vertical scanners at the POS in food retail especially in Europe and Asia where RF EAS technology has been

10716-492: The product itself, though this is rare and not especially desirable either for the retailer or the manufacturer. The practical totality of EAS labels are discarded with the product packaging. This is of particular application in everyday items that consumers might carry on their person to avoid the inconvenience of potentially live reactivated EAS tags when walking in and out of retail stores. Hard tags, typically used for clothing or ink tags, known as benefit denial tags, may reduce

10830-586: The rate of tag manipulation. Also, shoplifters deactivating or detaching tags may be spotted by the shop staff. Shoplifting tools are illegal in many jurisdictions, and can, in any case, serve as evidence against the perpetrators. Hence, informed shoplifters, although they decrease their risk of being caught by the EAS, expose themselves to much greater judicial risks if they get caught with tools, booster bags, or while trying to remove tags, as this shows intent to steal. The possession of shoplifting tools (e.g. lined bags or wire cutters to cut bottle tags) can lead to

10944-499: The ratios of plate width to separation and length to separation are large. For unevenly charged plates: For n {\displaystyle n} number of plates in a capacitor, the total capacitance would be C = ε o A d ( n − 1 ) {\displaystyle C=\varepsilon _{o}{\frac {A}{d}}(n-1)} where C = ε o A / d {\displaystyle C=\varepsilon _{o}A/d}

11058-412: The resistor to increase the source impedance of the control voltage so as not to load the tuned circuit and decrease its Q. Another common configuration uses two back-to-back (anode to anode) varicap diodes. (See lower left circuit in diagram.) The second varicap effectively replaces the blocking capacitor in the first circuit. This reduces the overall capacitance and the capacitance range by half, but has

11172-405: The same as the resonance frequency of the amorphous strips. This causes the strip to vibrate longitudinally by magnetostriction, and it continues to oscillate after the burst is over. The vibration causes a change in magnetization in the amorphous strip, which induces an AC voltage in the receiver antenna. If this signal meets the required parameters (correct frequency, repetition, etc.), the alarm

11286-463: The signals from tags are very low-power (their cross-section is small, and the exits are wide), jamming requires little power. Evidently, shoplifters will not feel the need to follow radio transmission regulations; hence crude, easy-to-build transmitters will be adequate for them. However, due to their high frequency of operation, building a jammer can be difficult for microwave circuits; these systems are therefore less likely to be jammed. Although jamming

11400-471: The standard for nearly a decade. In apparel retail deactivation usually takes the form of flat pads of approx. 30x30 cm. These permanent tags are made of a non-linear element (a diode ) coupled to one microwave and one electrostatic antenna. At the exit, one antenna emits a low-frequency (about 100 kHz) field, and another one emits a microwave field. The tag acts as a mixer re-emitting a combination of signals from both fields. This modulated signal triggers

11514-449: The static charges accumulated between clouds in the sky and the surface of the Earth, where the air between them serves as the dielectric. This results in bolts of lightning when the breakdown voltage of the air is exceeded. In October 1745, Ewald Georg von Kleist of Pomerania , Germany, found that charge could be stored by connecting a high-voltage electrostatic generator by a wire to

11628-441: The store. With increasing prevalence, stores have metal detectors at the entrance that can warn against the presence of booster bags or detachers. Deactivation of magnetic tags is achieved by straightforward magnetization using a strong magnet. Magneto-acoustic tags require demagnetization. However, sticking a powerful magnet on them will bias disposable magnetic tags and prevent resonance in magneto-acoustic tags. Similarly, sticking

11742-623: The stored energy can be calculated from the electric field strength W = 1 2 C V 2 = 1 2 ε A d ( E d ) 2 = 1 2 ε A d E 2 = 1 2 ε E 2 ( volume of electric field ) {\displaystyle W={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(Ed\right)^{2}={\frac {1}{2}}\varepsilon AdE^{2}={\frac {1}{2}}\varepsilon E^{2}({\text{volume of electric field}})} The last formula above

11856-605: The surface of the other conductor. The conductors thus hold equal and opposite charges on their facing surfaces, and the dielectric develops an electric field. An ideal capacitor is characterized by a constant capacitance C , in farads in the SI system of units, defined as the ratio of the positive or negative charge Q on each conductor to the voltage V between them: C = Q V {\displaystyle C={\frac {Q}{V}}} A capacitance of one farad (F) means that one coulomb of charge on each conductor causes

11970-402: The suspect being arrested for suspicion of theft or "Going equipped for stealing, etc." within the UK judicial system. In summary, while even the least expensive EAS systems will catch most occasional shoplifters, a broader range of measures are still required for an effective response that can protect profits without impeding sales. Tags can be equipped with a built-in alarm which sounds when

12084-447: The tag detects tampering or unauthorized removal from the store. The tag not only triggers the store's electronic article surveillance system, but also sounds an alarm attached to the merchandise. The local alarm continues to sound for several minutes after leaving the store, attracting attention to the shopper carrying the merchandise. A single EAS detector, suitable for a small shop, is accessible to all retail stores, and should form

12198-410: The time between receipt of merchandise and when the merchandise is ready for sale. For the supplier, the main benefit is the preservation of the retail packaging aesthetics by easing the application of security tags within product packaging. Source tagging allows the EAS tags to be concealed and more difficult to remove. The high-speed application of EAS labels, suited for commercial packaging processes,

12312-410: The upper left circuit in the accompanying diagram. Since no significant DC current flows in the varicap, the value of the resistor connecting its cathode back to the DC control voltage resistor can be somewhere in the range of 22 kΩ to 150 kΩ and the blocking capacitor somewhere in the range of 5–100 nF. Sometimes, with very high-Q tuned circuits, an inductor is placed in series with

12426-669: The user in terms of running costs, since the RF de-activator only activates to send a pulse when a circuit is present. Both EM and AM deactivation units are on all the time and consume considerably more electricity. The reliability of "remote" deactivation (i.e. non-contact or non-proximity deactivation) capability makes for a fast and efficient throughput at the checkout. Efficiency is an important factor when choosing an overall EAS solution given that time lost attempting to deactivate labels can be an important drag of cashier productivity as well as customer satisfaction if unwanted alarms are caused by tags that have not been effectively deactivated at

12540-410: The varicap to alter its capacitance. The DC bias voltage must be blocked from entering the tuned circuit. This can be accomplished by placing a DC blocking capacitor with a capacitance about 100 times greater than the maximum capacitance of the varicap diode in series with it and by applying DC from a high impedance source to the node between the varicap cathode and the blocking capacitor as shown in

12654-951: The vector sum of reactance and resistance , describes the phase difference and the ratio of amplitudes between sinusoidally varying voltage and sinusoidally varying current at a given frequency. Fourier analysis allows any signal to be constructed from a spectrum of frequencies, whence the circuit's reaction to the various frequencies may be found. The reactance and impedance of a capacitor are respectively X = − 1 ω C = − 1 2 π f C Z = 1 j ω C = − j ω C = − j 2 π f C {\displaystyle {\begin{aligned}X&=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}\\Z&={\frac {1}{j\omega C}}=-{\frac {j}{\omega C}}=-{\frac {j}{2\pi fC}}\end{aligned}}} where j

12768-667: Was developed by the Pacific Semiconductor subsidiary of the Ramo Wooldridge Corporation who received a patent for the device in June 1961. The device name was also trademarked as the "Varicap" by TRW Semiconductors , the successor to Pacific Semiconductors, in October 1967. This helps explain the different names for the device as it came into use. Varactors are operated in a reverse-biased state, so no DC current flows through

12882-404: Was later widely adopted as a storage capacitor in memory chips , and as the basic building block of the charge-coupled device (CCD) in image sensor technology. In 1966, Dr. Robert Dennard invented modern DRAM architecture, combining a single MOS transistor per capacitor. A capacitor consists of two conductors separated by a non-conductive region. The non-conductive region can either be

12996-461: Was perfected via modifications to standard pressure-sensitive label applicators. Today, consumer goods are source tagged at high speeds with the EAS labels incorporated into the packaging or the product itself. The most common source tags are AM strips and 8.2 MHz radio frequency labels. Most manufacturers use both when source tagging in the USA. In Europe there is little demand for AM tagging given that

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