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112-429: A voltage-to-frequency converter ( VFC ) is a special type of VCO designed to be very linear in frequency control over a wide range of input control voltages. VCOs can be generally categorized into two groups based on the type of waveform produced. A voltage-controlled capacitor is one method of making an LC oscillator vary its frequency in response to a control voltage. Any reverse-biased semiconductor diode displays

224-565: A Bode plot . For the RLC circuit's capacitor voltage, the gain of the transfer function H ( iω ) is Note the similarity between the gain here and the amplitude in Equation ( 3 ). Once again, the gain is maximized at the resonant frequency ω r = ω 0 1 − 2 ζ 2 . {\displaystyle \omega _{r}=\omega _{0}{\sqrt {1-2\zeta ^{2}}}.} Here,

336-420: A cathode and a plate . The cathode is either indirectly heated or directly heated . If indirect heating is employed, a heater is included in the envelope. In operation, the cathode is heated to red heat , around 800–1,000 °C (1,470–1,830 °F). A directly heated cathode is made of tungsten wire and is heated by a current passed through it from an external voltage source. An indirectly heated cathode

448-410: A circuit consisting of a resistor with resistance R , an inductor with inductance L , and a capacitor with capacitance C connected in series with current i ( t ) and driven by a voltage source with voltage v in ( t ). The voltage drop around the circuit is Rather than analyzing a candidate solution to this equation like in the mass on a spring example above, this section will analyze

560-420: A steady state solution that is independent of initial conditions and depends only on the driving amplitude F 0 , driving frequency ω , undamped angular frequency ω 0 , and the damping ratio ζ . The transient solution decays in a relatively short amount of time, so to study resonance it is sufficient to consider the steady state solution. It is possible to write the steady-state solution for x ( t ) as

672-505: A circuit is given by its current–voltage characteristic . The shape of the curve is determined by the transport of charge carriers through the so-called depletion layer or depletion region that exists at the p–n junction between differing semiconductors. When a p–n junction is first created, conduction-band (mobile) electrons from the N- doped region diffuse into the P- doped region where there

784-504: A control system, the Laplace transforms of the above signals are useful. Tuning range, tuning gain and phase noise are the important characteristics of a VCO. Generally, low phase noise is preferred in a VCO. Tuning gain and noise present in the control signal affect the phase noise; high noise or high tuning gain imply more phase noise. Other important elements that determine the phase noise are sources of flicker noise (1/ f noise) in

896-571: A crystal resonator and pull its resonant frequency. For low-frequency VCOs, other methods of varying the frequency (such as altering the charging rate of a capacitor by means of a voltage-controlled current source ) are used (see function generator ). The frequency of a ring oscillator is controlled by varying either the supply voltage, the current available to each inverter stage, or the capacitive loading on each stage. VCOs are used in analog applications such as frequency modulation and frequency-shift keying . The functional relationship between

1008-422: A current of electrons flows through the tube from cathode to plate. When the plate voltage is negative with respect to the cathode, no electrons are emitted by the plate, so no current can pass from the plate to the cathode. Point-contact diodes were developed starting in the 1930s, out of the early crystal detector technology, and are now generally used in the 3 to 30 gigahertz range. Point-contact diodes use

1120-404: A definite " knee " around this threshold when viewed on a linear scale, the knee is an illusion that depends on the scale of y-axis representing current. In a semi-log plot (using a logarithmic scale for current and a linear scale for voltage), the diode's exponential curve instead appears more like a straight line. Since a diode's forward-voltage drop varies only a little with the current, and

1232-416: A derivation of the resonant frequency for a driven, damped harmonic oscillator is shown. An RLC circuit is used to illustrate connections between resonance and a system's transfer function, frequency response, poles, and zeroes. Building off the RLC circuit example, these connections for higher-order linear systems with multiple inputs and outputs are generalized. Consider a damped mass on a spring driven by

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1344-477: A function proportional to the driving force with an induced phase change φ , where φ = arctan ⁡ ( 2 ω ω 0 ζ ω 2 − ω 0 2 ) + n π . {\displaystyle \varphi =\arctan \left({\frac {2\omega \omega _{0}\zeta }{\omega ^{2}-\omega _{0}^{2}}}\right)+n\pi .} The phase value

1456-399: A heated cathode and a plate , in which electrons can flow in only one direction, from the cathode to the plate. Among many uses, diodes are found in rectifiers to convert alternating current (AC) power to direct current (DC), demodulation in radio receivers , and can even be used for logic or as temperature sensors . A common variant of a diode is a light-emitting diode , which

1568-442: A long distance, since the frequency will not drift or be affected by noise. Oscillators in this application may have sine or square wave outputs. Where the oscillator drives equipment that may generate radio-frequency interference, adding a varying voltage to its control input, called dithering , can disperse the interference spectrum to make it less objectionable (see spread spectrum clock ). Semiconductor diode A diode

1680-411: A low work function , meaning that they more readily emit electrons than would the uncoated cathode. The plate, not being heated, does not emit electrons; but is able to absorb them. The alternating voltage to be rectified is applied between the cathode and the plate. When the plate voltage is positive with respect to the cathode, the plate electrostatically attracts the electrons from the cathode, so

1792-404: A measure of voltage-dependent capacitance and can be used to change the frequency of an oscillator by varying a control voltage applied to the diode. Special-purpose variable-capacitance varactor diodes are available with well-characterized wide-ranging values of capacitance. A varactor is used to change the capacitance (and hence the frequency) of an LC tank. A varactor can also change loading on

1904-848: A natural frequency and a damping ratio, ω 0 = 1 L C , {\displaystyle \omega _{0}={\frac {1}{\sqrt {LC}}},} ζ = R 2 C L . {\displaystyle \zeta ={\frac {R}{2}}{\sqrt {\frac {C}{L}}}.} The ratio of the output voltage to the input voltage becomes H ( s ) ≜ V out ( s ) V in ( s ) = ω 0 2 s 2 + 2 ζ ω 0 s + ω 0 2 {\displaystyle H(s)\triangleq {\frac {V_{\text{out}}(s)}{V_{\text{in}}(s)}}={\frac {\omega _{0}^{2}}{s^{2}+2\zeta \omega _{0}s+\omega _{0}^{2}}}} H ( s )

2016-458: A natural frequency depending upon their structure; this frequency is known as a resonant frequency or resonance frequency . When an oscillating force, an external vibration, is applied at a resonant frequency of a dynamic system, object, or particle, the outside vibration will cause the system to oscillate at a higher amplitude (with more force) than when the same force is applied at other, non-resonant frequencies. The resonant frequencies of

2128-415: A particular type of diode in a circuit diagram conveys the general electrical function to the reader. There are alternative symbols for some types of diodes, though the differences are minor. The triangle in the symbols points to the forward direction, i.e. in the direction of conventional current flow. There are a number of common, standard and manufacturer-driven numbering and coding schemes for diodes;

2240-499: A positively charged electroscope, but not a negatively charged electroscope. In 1880, Thomas Edison observed unidirectional current between heated and unheated elements in a bulb, later called Edison effect , and was granted a patent on application of the phenomenon for use in a DC voltmeter . About 20 years later, John Ambrose Fleming (scientific adviser to the Marconi Company and former Edison employee) realized that

2352-452: A process called rectification . As rectifiers, diodes can be used for such tasks as extracting modulation from radio signals in radio receivers . A diode's behavior is often simplified as having a forward threshold voltage or turn-on voltage or cut-in voltage , above which there is significant current and below which there is almost no current, which depends on a diode's composition: This voltage may loosely be referred to simply as

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2464-493: A radio carrier wave, whose amplitude or envelope is proportional to the original audio signal. The diode rectifies the AM radio frequency signal, leaving only the positive peaks of the carrier wave. The audio is then extracted from the rectified carrier wave using a simple filter and fed into an audio amplifier or transducer , which generates sound waves via audio speaker . In microwave and millimeter wave technology, beginning in

2576-438: A region on one side that contains negative charge carriers (electrons), called an n-type semiconductor , and a region on the other side that contains positive charge carriers ( holes ), called a p-type semiconductor . When the n-type and p-type materials are attached together, a momentary flow of electrons occurs from the n to the p side resulting in a third region between the two where no charge carriers are present. This region

2688-475: A sinusoidal, externally applied force. Newton's second law takes the form where m is the mass, x is the displacement of the mass from the equilibrium point, F 0 is the driving amplitude, ω is the driving angular frequency, k is the spring constant, and c is the viscous damping coefficient. This can be rewritten in the form where Many sources also refer to ω 0 as the resonant frequency . However, as shown below, when analyzing oscillations of

2800-472: A small diameter metal wire in contact with a semiconductor crystal, and are of either non-welded contact type or welded contact type. Non-welded contact construction utilizes the Schottky barrier principle. The metal side is the pointed end of a small diameter wire that is in contact with the semiconductor crystal. In the welded contact type, a small P region is formed in the otherwise N-type crystal around

2912-784: A stable single-frequency clock. A digitally controlled oscillator based on a frequency synthesizer may serve as a digital alternative to analog voltage controlled oscillator circuits. VCOs are used in function generators , phase-locked loops including frequency synthesizers used in communication equipment and the production of electronic music , to generate variable tones in synthesizers . Function generators are low-frequency oscillators which feature multiple waveforms, typically sine, square, and triangle waves. Monolithic function generators are voltage-controlled. Analog phase-locked loops typically contain VCOs. High-frequency VCOs are usually used in phase-locked loops for radio receivers. Phase noise

3024-402: A system can be identified when the response to an external vibration creates an amplitude that is a relative maximum within the system. Small periodic forces that are near a resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy . Resonance phenomena occur with all types of vibrations or waves : there

3136-462: A timing signal to synchronize operations in digital circuits. VCXO clock generators are used in many areas such as digital TV, modems, transmitters and computers. Design parameters for a VCXO clock generator are tuning voltage range, center frequency, frequency tuning range and the timing jitter of the output signal. Jitter is a form of phase noise that must be minimised in applications such as radio receivers, transmitters and measuring equipment. When

3248-401: A variety of other minerals as detectors. Semiconductor principles were unknown to the developers of these early rectifiers. During the 1930s understanding of physics advanced and in the mid-1930s researchers at Bell Telephone Laboratories recognized the potential of the crystal detector for application in microwave technology. Researchers at Bell Labs , Western Electric , MIT , Purdue and in

3360-413: A voltage input for fine control. The temperature is selected to be the turnover temperature : the temperature where small changes do not affect the resonance. The control voltage can be used to occasionally adjust the reference frequency to a NIST source. Sophisticated designs may also adjust the control voltage over time to compensate for crystal aging. A clock generator is an oscillator that provides

3472-413: A voltage-controlled crystal oscillator can be varied a few tens of parts per million (ppm) over a control voltage range of typically 0 to 3 volts, because the high Q factor of the crystals allows frequency control over only a small range of frequencies. A temperature-compensated VCXO ( TCVCXO ) incorporates components that partially correct the dependence on temperature of the resonant frequency of

Voltage-controlled oscillator - Misplaced Pages Continue

3584-529: A wider selection of clock frequencies is needed the VCXO output can be passed through digital divider circuits to obtain lower frequencies or be fed to a phase-locked loop (PLL). ICs containing both a VCXO (for external crystal) and a PLL are available. A typical application is to provide clock frequencies in a range from 12 kHz to 96 kHz to an audio digital-to-analog converter . A frequency synthesizer generates precise and adjustable frequencies based on

3696-418: Is ω r = ω 0 , {\displaystyle \omega _{r}=\omega _{0},} and the gain is one at this frequency, so the voltage across the resistor resonates at the circuit's natural frequency and at this frequency the amplitude of the voltage across the resistor equals the input voltage's amplitude. Some systems exhibit antiresonance that can be analyzed in

3808-522: Is mechanical resonance , orbital resonance , acoustic resonance , electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR) and resonance of quantum wave functions . Resonant systems can be used to generate vibrations of a specific frequency (e.g., musical instruments ), or pick out specific frequencies from a complex vibration containing many frequencies (e.g., filters). The term resonance (from Latin resonantia , 'echo', from resonare , 'resound') originated from

3920-659: Is a phenomenon that occurs when an object or system is subjected to an external force or vibration that matches its natural frequency . When this happens, the object or system absorbs energy from the external force and starts vibrating with a larger amplitude . Resonance can occur in various systems, such as mechanical, electrical, or acoustic systems, and it is often desirable in certain applications, such as musical instruments or radio receivers. However, resonance can also be detrimental, leading to excessive vibrations or even structural failure in some cases. All systems, including molecular systems and particles, tend to vibrate at

4032-403: Is a "built-in" potential across the depletion zone. If an external voltage is placed across the diode with the same polarity as the built-in potential, the depletion zone continues to act as an insulator, preventing any significant electric current flow (unless electron–hole pairs are actively being created in the junction by, for instance, light; see photodiode ). However, if the polarity of

4144-427: Is a large population of holes (vacant places for electrons) with which the electrons "recombine". When a mobile electron recombines with a hole, both hole and electron vanish, leaving behind an immobile positively charged donor (dopant) on the N side and negatively charged acceptor (dopant) on the P side. The region around the p–n junction becomes depleted of charge carriers and thus behaves as an insulator . However,

4256-491: Is a two- terminal electronic component that conducts current primarily in one direction (asymmetric conductance ). It has low (ideally zero) resistance in one direction and high (ideally infinite) resistance in the other. A semiconductor diode, the most commonly used type today, is a crystalline piece of semiconductor material with a p–n junction connected to two electrical terminals. It has an exponential current–voltage characteristic . Semiconductor diodes were

4368-474: Is also complex, can be written as a gain and phase, H ( i ω ) = G ( ω ) e i Φ ( ω ) . {\displaystyle H(i\omega )=G(\omega )e^{i\Phi (\omega )}.} A sinusoidal input voltage at frequency ω results in an output voltage at the same frequency that has been scaled by G ( ω ) and has a phase shift Φ ( ω ). The gain and phase can be plotted versus frequency on

4480-473: Is approximately proportional to the square of the input voltage, so the response is called square law in this region. Following the end of forwarding conduction in a p–n type diode, a reverse current can flow for a short time. The device does not attain its blocking capability until the mobile charge in the junction is depleted. The effect can be significant when switching large currents very quickly. A certain amount of "reverse recovery time" t r (on

4592-447: Is called the depletion region because there are no charge carriers (neither electrons nor holes) in it. The diode's terminals are attached to the n-type and p-type regions. The boundary between these two regions, called a p–n junction , is where the action of the diode takes place. When a sufficiently higher electrical potential is applied to the P side (the anode ) than to the N side (the cathode ), it allows electrons to flow through

Voltage-controlled oscillator - Misplaced Pages Continue

4704-403: Is heated by infrared radiation from a nearby heater that is formed of Nichrome wire and supplied with current provided by an external voltage source. The operating temperature of the cathode causes it to release electrons into the vacuum, a process called thermionic emission . The cathode is coated with oxides of alkaline earth metals , such as barium and strontium oxides . These have

4816-545: Is more so a function of temperature, this effect can be used as a temperature sensor or as a somewhat imprecise voltage reference . A diode's high resistance to current flowing in the reverse direction suddenly drops to a low resistance when the reverse voltage across the diode reaches a value called the breakdown voltage . This effect is used to regulate voltage ( Zener diodes ) or to protect circuits from high voltage surges ( avalanche diodes ). A semiconductor diode's current–voltage characteristic can be tailored by selecting

4928-459: Is small, the resonant frequency is approximately equal to the natural frequency of the system, which is a frequency of unforced vibrations. Some systems have multiple and distinct resonant frequencies. A familiar example is a playground swing , which acts as a pendulum . Pushing a person in a swing in time with the natural interval of the swing (its resonant frequency) makes the swing go higher and higher (maximum amplitude), while attempts to push

5040-409: Is the resonant frequency for this system. Again, the resonant frequency does not equal the undamped angular frequency ω 0 of the oscillator. They are proportional, and if the damping ratio goes to zero they are the same, but for non-zero damping they are not the same frequency. As shown in the figure, resonance may also occur at other frequencies near the resonant frequency, including ω 0 , but

5152-468: Is the transfer function between the input voltage and the output voltage. This transfer function has two poles –roots of the polynomial in the transfer function's denominator–at and no zeros–roots of the polynomial in the transfer function's numerator. Moreover, for ζ ≤ 1 , the magnitude of these poles is the natural frequency ω 0 and that for ζ < 1/ 2 {\displaystyle {\sqrt {2}}} , our condition for resonance in

5264-406: Is the most important specification in this application. Audio-frequency VCOs are used in analog music synthesizers. For these, sweep range, linearity, and distortion are often the most important specifications. Audio-frequency VCOs for use in musical contexts were largely superseded in the 1980s by their digital counterparts, digitally controlled oscillators (DCOs), due to their output stability in

5376-417: Is used as electric lighting and status indicators on electronic devices. The most common function of a diode is to allow an electric current to pass in one direction (called the diode's forward direction), while blocking it in the opposite direction (the reverse direction). Its hydraulic analogy is a check valve . This unidirectional behavior can convert alternating current (AC) to direct current (DC),

5488-546: Is useful in microwave and switching circuits. Diodes, both vacuum and semiconductor, can be used as shot-noise generators . Thermionic ( vacuum-tube ) diodes and solid-state (semiconductor) diodes were developed separately, at approximately the same time, in the early 1900s, as radio receiver detectors . Until the 1950s, vacuum diodes were used more frequently in radios because the early point-contact semiconductor diodes were less stable. In addition, most receiving sets had vacuum tubes for amplification that could easily have

5600-412: Is usually taken to be between −180° and 0 so it represents a phase lag for both positive and negative values of the arctan argument. Resonance occurs when, at certain driving frequencies, the steady-state amplitude of x ( t ) is large compared to its amplitude at other driving frequencies. For the mass on a spring, resonance corresponds physically to the mass's oscillations having large displacements from

5712-469: The Shockley diode equation article. In detector and mixer applications, the current can be estimated by a Taylor's series. The odd terms can be omitted because they produce frequency components that are outside the pass band of the mixer or detector. Even terms beyond the second derivative usually need not be included because they are small compared to the second order term. The desired current component

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5824-535: The UK intensively developed point-contact diodes ( crystal rectifiers or crystal diodes ) during World War II for application in radar. After World War II, AT&T used these in its microwave towers that criss-crossed the United States, and many radar sets use them even in the 21st century. In 1946, Sylvania began offering the 1N34 crystal diode. During the early 1950s, junction diodes were developed. In 2022,

5936-651: The diode law (named after the bipolar junction transistor co-inventor William Bradford Shockley ) models the exponential current–voltage (I–V) relationship of diodes in moderate forward or reverse bias. The article Shockley diode equation provides details. At forward voltages less than the saturation voltage, the voltage versus current characteristic curve of most diodes is not a straight line. The current can be approximated by I = I S e V D / ( n V T ) {\displaystyle I=I_{\text{S}}e^{V_{\text{D}}/(nV_{\text{T}})}} as explained in

6048-499: The semiconductor materials and the doping impurities introduced into the materials during manufacture. These techniques are used to create special-purpose diodes that perform many different functions. For example, to electronically tune radio and TV receivers ( varactor diodes ), to generate radio-frequency oscillations ( tunnel diodes , Gunn diodes , IMPATT diodes ), and to produce light ( light-emitting diodes ). Tunnel, Gunn and IMPATT diodes exhibit negative resistance , which

6160-434: The "unilateral conduction" across a contact between a metal and a mineral . Indian scientist Jagadish Chandra Bose was the first to use a crystal for detecting radio waves in 1894. The crystal detector was developed into a practical device for wireless telegraphy by Greenleaf Whittier Pickard , who invented a silicon crystal detector in 1903 and received a patent for it on 20 November 1906. Other experimenters tried

6272-417: The 1930s, researchers improved and miniaturized the crystal detector. Point contact diodes ( crystal diodes ) and Schottky diodes are used in radar, microwave and millimeter wave detectors. Rectifiers are constructed from diodes, where they are used to convert alternating current (AC) electricity into direct current (DC). Automotive alternators are a common example, where the diode, which rectifies

6384-549: The AC into DC, provides better performance than the commutator or earlier, dynamo . Similarly, diodes are also used in Cockcroft–Walton voltage multipliers to convert AC into higher DC voltages. Since most electronic circuits can be damaged when the polarity of their power supply inputs are reversed, a series diode is sometimes used to protect against such situations. This concept is known by multiple naming variations that mean

6496-622: The Edison effect could be used as a radio detector . Fleming patented the first true thermionic diode, the Fleming valve , in Britain on 16 November 1904 (followed by U.S. patent 803,684 in November 1905). Throughout the vacuum tube era, valve diodes were used in almost all electronics such as radios, televisions, sound systems, and instrumentation. They slowly lost market share beginning in

6608-923: The Laplace domain the voltage across the inductor is V out ( s ) = s L I ( s ) , {\displaystyle V_{\text{out}}(s)=sLI(s),} V out ( s ) = s 2 s 2 + R L s + 1 L C V in ( s ) , {\displaystyle V_{\text{out}}(s)={\frac {s^{2}}{s^{2}+{\frac {R}{L}}s+{\frac {1}{LC}}}}V_{\text{in}}(s),} V out ( s ) = s 2 s 2 + 2 ζ ω 0 s + ω 0 2 V in ( s ) , {\displaystyle V_{\text{out}}(s)={\frac {s^{2}}{s^{2}+2\zeta \omega _{0}s+\omega _{0}^{2}}}V_{\text{in}}(s),} using

6720-486: The advantages of having no off-chip components (expensive) or on-chip inductors (low yields on generic CMOS processes). Commonly used VCO circuits are the Clapp and Colpitts oscillators. The more widely used oscillator of the two is Colpitts and these oscillators are very similar in configuration. A voltage-controlled crystal oscillator ( VCXO ) is used for fine adjustment of the operating frequency. The frequency of

6832-458: The amplitude of the output's steady-state oscillations to the input's oscillations is called the gain, and the gain can be a function of the frequency of the sinusoidal external input. Peaks in the gain at certain frequencies correspond to resonances, where the amplitude of the measured output's oscillations are disproportionately large. Since many linear and nonlinear systems that oscillate are modeled as harmonic oscillators near their equilibria,

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6944-399: The capacitor combined in series. Equation ( 4 ) showed that the sum of the voltages across the three circuit elements sums to the input voltage, so measuring the output voltage as the sum of the inductor and capacitor voltages combined is the same as v in minus the voltage drop across the resistor. The previous example showed that at the natural frequency of the system, the amplitude of

7056-432: The circuit is divided among the three circuit elements, and each element has different dynamics. The capacitor's voltage grows slowly by integrating the current over time and is therefore more sensitive to lower frequencies, whereas the inductor's voltage grows when the current changes rapidly and is therefore more sensitive to higher frequencies. While the circuit as a whole has a natural frequency where it tends to oscillate,

7168-669: The circuit, the output power level, and the loaded Q factor of the resonator. (see Leeson's equation ). The low frequency flicker noise affects the phase noise because the flicker noise is heterodyned to the oscillator output frequency due to the non-linear transfer function of active devices. The effect of flicker noise can be reduced with negative feedback that linearizes the transfer function (for example, emitter degeneration ). VCOs generally have lower Q factor compared to similar fixed-frequency oscillators, and so suffer more jitter . The jitter can be made low enough for many applications (such as driving an ASIC), in which case VCOs enjoy

7280-504: The control voltage and the output frequency for a VCO (especially those used at radio frequency ) may not be linear, but over small ranges, the relationship is approximately linear, and linear control theory can be used. A voltage-to-frequency converter (VFC) is a special type of VCO designed to be very linear over a wide range of input voltages. Modeling for VCOs is often not concerned with the amplitude or shape (sinewave, triangle wave, sawtooth) but rather its instantaneous phase. In effect,

7392-423: The crystal. A smaller range of voltage control then suffices to stabilize the oscillator frequency in applications where temperature varies, such as heat buildup inside a transmitter . Placing the oscillator in a crystal oven at a constant but higher-than-ambient temperature is another way to stabilize oscillator frequency. High stability crystal oscillator references often place the crystal in an oven and use

7504-469: The current and input voltage, respectively, and s is a complex frequency parameter in the Laplace domain. Rearranging terms, I ( s ) = s s 2 L + R s + 1 C V in ( s ) . {\displaystyle I(s)={\frac {s}{s^{2}L+Rs+{\frac {1}{C}}}}V_{\text{in}}(s).} An RLC circuit in series presents several options for where to measure an output voltage. Suppose

7616-414: The damaging voltage spikes that would otherwise occur. (A diode used in such an application is called a flyback diode ). Many integrated circuits also incorporate diodes on the connection pins to prevent external voltages from damaging their sensitive transistors . Specialized diodes are used to protect from over-voltages at higher power (see Diode types above). Resonant frequency Resonance

7728-620: The depletion region from the N-type side to the P-type side. The junction does not allow the flow of electrons in the opposite direction when the potential is applied in reverse, creating, in a sense, an electrical check valve . Another type of junction diode, the Schottky diode , is formed from a metal–semiconductor junction rather than a p–n junction, which reduces capacitance and increases switching speed. A semiconductor diode's behavior in

7840-737: The different dynamics of each circuit element make each element resonate at a slightly different frequency. Suppose that the output voltage of interest is the voltage across the resistor. In the Laplace domain the voltage across the resistor is V out ( s ) = R I ( s ) , {\displaystyle V_{\text{out}}(s)=RI(s),} V out ( s ) = R s L ( s 2 + R L s + 1 L C ) V in ( s ) , {\displaystyle V_{\text{out}}(s)={\frac {Rs}{L\left(s^{2}+{\frac {R}{L}}s+{\frac {1}{LC}}\right)}}V_{\text{in}}(s),} and using

7952-460: The diode but with laser light would be the optical isolator , also known as an optical diode, that allows light to only pass in one direction. It uses a Faraday rotator as the main component. The first use for the diode was the demodulation of amplitude modulated (AM) radio broadcasts. The history of this discovery is treated in depth in the crystal detector article. In summary, an AM signal consists of alternating positive and negative peaks of

8064-411: The diode's forward voltage drop or just voltage drop , since a consequence of the steepness of the exponential is that a diode's voltage drop will not significantly exceed the threshold voltage under normal forward bias operating conditions. Datasheets typically quote a typical or maximum forward voltage (V F ) for a specified current and temperature (e.g. 20 mA and 25  ° C for LEDs), so

8176-427: The displacement x ( t ), the resonant frequency is close to but not the same as ω 0 . In general the resonant frequency is close to but not necessarily the same as the natural frequency. The RLC circuit example in the next section gives examples of different resonant frequencies for the same system. The general solution of Equation ( 2 ) is the sum of a transient solution that depends on initial conditions and

8288-458: The external voltage opposes the built-in potential, recombination can once again proceed, resulting in a substantial electric current through the p–n junction (i.e. substantial numbers of electrons and holes recombine at the junction) that increases exponentially with voltage. A diode's current–voltage characteristic can be approximated by four operating regions. From lower to higher bias voltages, these are: The Shockley ideal diode equation or

8400-400: The face of temperature changes during operation. Since the 1990s, musical software has become the dominant sound-generating method. Voltage-to-frequency converters are voltage-controlled oscillators with a highly linear relation between applied voltage and frequency. They are used to convert a slow analog signal (such as from a temperature transducer) to a signal suitable for transmission over

8512-474: The field of acoustics, particularly the sympathetic resonance observed in musical instruments, e.g., when one string starts to vibrate and produce sound after a different one is struck. Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a simple pendulum). However, there are some losses from cycle to cycle, called damping . When damping

8624-424: The first semiconductor electronic devices . The discovery of asymmetric electrical conduction across the contact between a crystalline mineral and a metal was made by German physicist Ferdinand Braun in 1874. Today, most diodes are made of silicon , but other semiconducting materials such as gallium arsenide and germanium are also used. The obsolete thermionic diode is a vacuum tube with two electrodes ,

8736-450: The first superconducting diode effect without an external magnetic field was realized. At the time of their invention, asymmetrical conduction devices were known as rectifiers . In 1919, the year tetrodes were invented, William Henry Eccles coined the term diode from the Greek roots di (from δί ), meaning 'two', and ode (from οδός ), meaning 'path'. The word diode however

8848-413: The focus is not on the time-domain signal A sin( ωt + θ 0 ) but rather the argument of the sine function (the phase). Consequently, modeling is often done in the phase domain. The instantaneous frequency of a VCO is often modeled as a linear relationship with its instantaneous control voltage. The output phase of the oscillator is the integral of the instantaneous frequency. For analyzing

8960-401: The frequency response of this circuit. Taking the Laplace transform of Equation ( 4 ), s L I ( s ) + R I ( s ) + 1 s C I ( s ) = V in ( s ) , {\displaystyle sLI(s)+RI(s)+{\frac {1}{sC}}I(s)=V_{\text{in}}(s),} where I ( s ) and V in ( s ) are the Laplace transform of

9072-445: The gain in Equation ( 6 ) using the capacitor voltage as the output, this gain has a factor of ω in the numerator and will therefore have a different resonant frequency that maximizes the gain. That frequency is ω r = ω 0 1 − 2 ζ 2 , {\displaystyle \omega _{r}={\frac {\omega _{0}}{\sqrt {1-2\zeta ^{2}}}},} So for

9184-419: The gain, notice that the gain goes to zero at ω = ω 0 , which complements our analysis of the resistor's voltage. This is called antiresonance , which has the opposite effect of resonance. Rather than result in outputs that are disproportionately large at this frequency, this circuit with this choice of output has no response at all at this frequency. The frequency that is filtered out corresponds exactly to

9296-456: The harmonic oscillator example, the poles are closer to the imaginary axis than to the real axis. Evaluating H ( s ) along the imaginary axis s = iω , the transfer function describes the frequency response of this circuit. Equivalently, the frequency response can be analyzed by taking the Fourier transform of Equation ( 4 ) instead of the Laplace transform. The transfer function, which

9408-404: The late 1940s due to selenium rectifier technology and then to semiconductor diodes during the 1960s. Today they are still used in a few high power applications where their ability to withstand transient voltages and their robustness gives them an advantage over semiconductor devices, and in musical instrument and audiophile applications. In 1874, German scientist Karl Ferdinand Braun discovered

9520-927: The mass on a spring example, the resonant frequency remains ω r = ω 0 1 − 2 ζ 2 , {\displaystyle \omega _{r}=\omega _{0}{\sqrt {1-2\zeta ^{2}}},} but the definitions of ω 0 and ζ change based on the physics of the system. For a pendulum of length ℓ and small displacement angle θ , Equation ( 1 ) becomes m ℓ d 2 θ d t 2 = F 0 sin ⁡ ( ω t ) − m g θ − c ℓ d θ d t {\displaystyle m\ell {\frac {\mathrm {d} ^{2}\theta }{\mathrm {d} t^{2}}}=F_{0}\sin(\omega t)-mg\theta -c\ell {\frac {\mathrm {d} \theta }{\mathrm {d} t}}} and therefore Consider

9632-548: The maximum response is at the resonant frequency. Also, ω r is only real and non-zero if ζ < 1 / 2 {\textstyle \zeta <1/{\sqrt {2}}} , so this system can only resonate when the harmonic oscillator is significantly underdamped. For systems with a very small damping ratio and a driving frequency near the resonant frequency, the steady state oscillations can become very large. For other driven, damped harmonic oscillators whose equations of motion do not look exactly like

9744-412: The metal point during manufacture by momentarily passing a relatively large current through the device. Point contact diodes generally exhibit lower capacitance, higher forward resistance and greater reverse leakage than junction diodes. A p–n junction diode is made of a crystal of semiconductor , usually silicon, but germanium and gallium arsenide are also used. Impurities are added to it to create

9856-434: The object. Light and other short wavelength electromagnetic radiation is produced by resonance on an atomic scale , such as electrons in atoms. Other examples of resonance include: Resonance manifests itself in many linear and nonlinear systems as oscillations around an equilibrium point. When the system is driven by a sinusoidal external input, a measured output of the system may oscillate in response. The ratio of

9968-421: The order of tens of nanoseconds to a few microseconds) may be required to remove the reverse recovery charge Q r from the diode. During this recovery time, the diode can actually conduct in the reverse direction. This might give rise to a large current in the reverse direction for a short time while the diode is reverse biased. The magnitude of such a reverse current is determined by the operating circuit (i.e.,

10080-622: The output voltage of interest is the voltage drop across the capacitor. As shown above, in the Laplace domain this voltage is V out ( s ) = 1 s C I ( s ) {\displaystyle V_{\text{out}}(s)={\frac {1}{sC}}I(s)} or V out = 1 L C ( s 2 + R L s + 1 L C ) V in ( s ) . {\displaystyle V_{\text{out}}={\frac {1}{LC(s^{2}+{\frac {R}{L}}s+{\frac {1}{LC}})}}V_{\text{in}}(s).} Define for this circuit

10192-483: The peak inverse voltage rating for application in high voltage rectifiers), and required a large heat sink (often an extension of the diode's metal substrate ), much larger than the later silicon diode of the same current ratings would require. The vast majority of all diodes are the p–n diodes found in CMOS integrated circuits , which include two diodes per pin and many other internal diodes. The symbol used to represent

10304-413: The resonance corresponds physically to having a relatively large amplitude for the steady state oscillations of the voltage across the capacitor compared to its amplitude at other driving frequencies. The resonant frequency need not always take the form given in the examples above. For the RLC circuit, suppose instead that the output voltage of interest is the voltage across the inductor. As shown above, in

10416-400: The same RLC circuit but with the voltage across the inductor as the output, the resonant frequency is now larger than the natural frequency, though it still tends towards the natural frequency as the damping ratio goes to zero. That the same circuit can have different resonant frequencies for different choices of output is not contradictory. As shown in Equation ( 4 ), the voltage drop across

10528-470: The same definitions for ω 0 and ζ as in the previous example. The transfer function between V in ( s ) and this new V out ( s ) across the inductor is H ( s ) = s 2 s 2 + 2 ζ ω 0 s + ω 0 2 . {\displaystyle H(s)={\frac {s^{2}}{s^{2}+2\zeta \omega _{0}s+\omega _{0}^{2}}}.} This transfer function has

10640-455: The same natural frequency and damping ratio as in the capacitor example the transfer function is H ( s ) = 2 ζ ω 0 s s 2 + 2 ζ ω 0 s + ω 0 2 . {\displaystyle H(s)={\frac {2\zeta \omega _{0}s}{s^{2}+2\zeta \omega _{0}s+\omega _{0}^{2}}}.} This transfer function also has

10752-451: The same natural frequency and damping ratios as the previous examples, the transfer function is H ( s ) = s 2 + ω 0 2 s 2 + 2 ζ ω 0 s + ω 0 2 . {\displaystyle H(s)={\frac {s^{2}+\omega _{0}^{2}}{s^{2}+2\zeta \omega _{0}s+\omega _{0}^{2}}}.} This transfer has

10864-669: The same poles as the previous RLC circuit examples, but it only has one zero in the numerator at s = 0. For this transfer function, its gain is G ( ω ) = 2 ζ ω 0 ω ( 2 ω ω 0 ζ ) 2 + ( ω 0 2 − ω 2 ) 2 . {\displaystyle G(\omega )={\frac {2\zeta \omega _{0}\omega }{\sqrt {\left(2\omega \omega _{0}\zeta \right)^{2}+(\omega _{0}^{2}-\omega ^{2})^{2}}}}.} The resonant frequency that maximizes this gain

10976-671: The same poles as the previous examples but has zeroes at Evaluating the transfer function along the imaginary axis, its gain is G ( ω ) = ω 0 2 − ω 2 ( 2 ω ω 0 ζ ) 2 + ( ω 0 2 − ω 2 ) 2 . {\displaystyle G(\omega )={\frac {\omega _{0}^{2}-\omega ^{2}}{\sqrt {\left(2\omega \omega _{0}\zeta \right)^{2}+(\omega _{0}^{2}-\omega ^{2})^{2}}}}.} Rather than look for resonance, i.e., peaks of

11088-623: The same poles as the transfer function in the previous example, but it also has two zeroes in the numerator at s = 0 . Evaluating H ( s ) along the imaginary axis, its gain becomes G ( ω ) = ω 2 ( 2 ω ω 0 ζ ) 2 + ( ω 0 2 − ω 2 ) 2 . {\displaystyle G(\omega )={\frac {\omega ^{2}}{\sqrt {\left(2\omega \omega _{0}\zeta \right)^{2}+(\omega _{0}^{2}-\omega ^{2})^{2}}}}.} Compared to

11200-520: The same thing: reverse voltage protection, reverse polarity protection, and reverse battery protection. Diodes are frequently used to conduct damaging high voltages away from sensitive electronic devices. They are usually reverse-biased (non-conducting) under normal circumstances. When the voltage rises above the normal range, the diodes become forward-biased (conducting). For example, diodes are used in ( stepper motor and H-bridge ) motor controller and relay circuits to de-energize coils rapidly without

11312-410: The same way as resonance. For antiresonance, the amplitude of the response of the system at certain frequencies is disproportionately small rather than being disproportionately large. In the RLC circuit example, this phenomenon can be observed by analyzing both the inductor and the capacitor combined. Suppose that the output voltage of interest in the RLC circuit is the voltage across the inductor and

11424-429: The series resistance) and the diode is said to be in the storage-phase. In certain real-world cases it is important to consider the losses that are incurred by this non-ideal diode effect. However, when the slew rate of the current is not so severe (e.g. Line frequency) the effect can be safely ignored. For most applications, the effect is also negligible for Schottky diodes . The reverse current ceases abruptly when

11536-413: The spring's equilibrium position at certain driving frequencies. Looking at the amplitude of x ( t ) as a function of the driving frequency ω , the amplitude is maximal at the driving frequency ω r = ω 0 1 − 2 ζ 2 . {\displaystyle \omega _{r}=\omega _{0}{\sqrt {1-2\zeta ^{2}}}.} ω r

11648-507: The stored charge is depleted; this abrupt stop is exploited in step recovery diodes for the generation of extremely short pulses. Normal (p–n) diodes, which operate as described above, are usually made of doped silicon or germanium . Before the development of silicon power rectifier diodes, cuprous oxide and later selenium was used. Their low efficiency required a much higher forward voltage to be applied (typically 1.4 to 1.7 V per "cell", with multiple cells stacked so as to increase

11760-453: The swing at a faster or slower tempo produce smaller arcs. This is because the energy the swing absorbs is maximized when the pushes match the swing's natural oscillations. Resonance occurs widely in nature, and is exploited in many devices. It is the mechanism by which virtually all sinusoidal waves and vibrations are generated. For example, when hard objects like metal , glass , or wood are struck, there are brief resonant vibrations in

11872-463: The thermionic diodes included in the tube (for example the 12SQ7 double diode triode ), and vacuum-tube rectifiers and gas-filled rectifiers were capable of handling some high-voltage/high-current rectification tasks better than the semiconductor diodes (such as selenium rectifiers ) that were available at that time. In 1873, Frederick Guthrie observed that a grounded, white-hot metal ball brought in close proximity to an electroscope would discharge

11984-837: The two most common being the EIA / JEDEC standard and the European Pro Electron standard: The standardized 1N-series numbering EIA370 system was introduced in the US by EIA/JEDEC (Joint Electron Device Engineering Council) about 1960. Most diodes have a 1-prefix designation (e.g., 1N4003). Among the most popular in this series were: 1N34A/1N270 (germanium signal), 1N914/ 1N4148 (silicon signal), 1N400x (silicon 1A power rectifier), and 1N580x (silicon 3A power rectifier). The JIS semiconductor designation system has all semiconductor diode designations starting with "1S". The European Pro Electron coding system for active components

12096-496: The user has a guarantee about when a certain amount of current will kick in. At higher currents, the forward voltage drop of the diode increases. For instance, a drop of 1 V to 1.5 V is typical at full rated current for silicon power diodes. (See also: Rectifier § Rectifier voltage drop ) However, a semiconductor diode's exponential current–voltage characteristic is really more gradual than this simple on–off action. Although an exponential function may appear to have

12208-835: The voltage drop across the resistor equals the amplitude of v in , and therefore the voltage across the inductor and capacitor combined has zero amplitude. We can show this with the transfer function. The sum of the inductor and capacitor voltages is V out ( s ) = ( s L + 1 s C ) I ( s ) , {\displaystyle V_{\text{out}}(s)=(sL+{\frac {1}{sC}})I(s),} V out ( s ) = s 2 + 1 L C s 2 + R L s + 1 L C V in ( s ) . {\displaystyle V_{\text{out}}(s)={\frac {s^{2}+{\frac {1}{LC}}}{s^{2}+{\frac {R}{L}}s+{\frac {1}{LC}}}}V_{\text{in}}(s).} Using

12320-587: The width of the depletion region (called the depletion width ) cannot grow without limit. For each electron–hole pair recombination made, a positively charged dopant ion is left behind in the N-doped region, and a negatively charged dopant ion is created in the P-doped region. As recombination proceeds and more ions are created, an increasing electric field develops through the depletion zone that acts to slow and then finally stop recombination. At this point, there

12432-419: Was already in use, as were triode , tetrode , pentode , hexode , as terms of multiplex telegraphy . Although all diodes rectify , "rectifier" usually applies to diodes used for power supply , to differentiate them from diodes intended for small signal circuits. A thermionic diode is a thermionic-valve device consisting of a sealed, evacuated glass or metal envelope containing two electrodes :

12544-502: Was introduced in 1966 and comprises two letters followed by the part code. The first letter represents the semiconductor material used for the component (A = germanium and B = silicon) and the second letter represents the general function of the part (for diodes, A = low-power/signal, B = variable capacitance, X = multiplier, Y = rectifier and Z = voltage reference); for example: Other common numbering/coding systems (generally manufacturer-driven) include: In optics, an equivalent device for

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