1745:
1152:
5367:, or ripple current may overheat them. To limit ripple voltage to a specified value the required capacitor size is proportional to the load current and inversely proportional to the supply frequency and the number of output peaks of the rectifier per input cycle. Full-wave rectified output requires a smaller capacitor because it is double the frequency of half-wave rectified output. To reduce ripple to a satisfactory limit with just a single capacitor would often require a capacitor of impractical size. This is because the ripple current rating of a capacitor does not increase linearly with size and there may also be height limitations. For high current applications banks of capacitors are used instead.
3935:
smoothing circuits which reduce the ripple and hence reduce the AC content of the output. Conversion ratio is reduced by losses in transformer windings and power dissipation in the rectifier element itself. This ratio is of little practical significance because a rectifier is almost always followed by a filter to increase DC voltage and reduce ripple. In some three-phase and multi-phase applications the conversion ratio is high enough that smoothing circuitry is unnecessary. In other circuits, like filament heater circuits in vacuum tube electronics where the load is almost entirely resistive, smoothing circuitry may be omitted because resistors dissipate both AC and DC power, so no power is lost.
5821:
1888:
938:
1740:{\displaystyle {\begin{aligned}V_{\mathrm {dc} }={}&V_{\mathrm {av} }={\frac {1}{{\frac {2}{3}}\pi }}\int _{30^{\circ }}^{150^{\circ }}V_{\mathrm {peak} }\sin \varphi \,\mathrm {d} \varphi ={\frac {3V_{\mathrm {peak} }}{2\pi }}\cdot \left(-\cos 150^{\circ }+\cos 30^{\circ }\right)\\={}&{\frac {3V_{\mathrm {peak} }}{2\pi }}\cdot {\Biggl }={\frac {3{\sqrt {3}}\cdot V_{\mathrm {peak} }}{2\pi }}\\\Longrightarrow {}&V_{\mathrm {dc} }=V_{\mathrm {av} }={\frac {3{\sqrt {3}}\cdot {\sqrt {2}}\cdot V_{\mathrm {LN} }}{2\pi }}\\\Longrightarrow {}&V_{\mathrm {av} }={\frac {3{\sqrt {6}}\cdot V_{\mathrm {LN} }}{2\pi }}\approx 1.17V_{\mathrm {LN} }\end{aligned}}}
2462:
5801:
5178:). Half-wave rectification and full-wave rectification using a center-tapped secondary produces a peak voltage loss of one diode drop. Bridge rectification has a loss of two diode drops. This reduces output voltage, and limits the available output voltage if a very low alternating voltage must be rectified. As the diodes do not conduct below this voltage, the circuit only passes current through for a portion of each half-cycle, causing short segments of zero voltage (where instantaneous input voltage is below one or two diode drops) to appear between each "hump".
3774:
3764:
3748:
2036:
1796:
3738:
3847:
5615:
6202:
5270:
1757:
2653:
5424:
as reduce ripple. Filters are often constructed from pairs of series/shunt components called RC (series resistor, shunt capacitor) or LC (series choke, shunt capacitor) sections. Two common filter geometries are known as Pi (capacitor, choke, capacitor) and T (choke, capacitor, choke) filters. Sometimes the series elements are resistors - because resistors are smaller and cheaper - when a lower DC output is desirable or permissible. Another kind of special filter geometry is a
1840:
2457:{\displaystyle {\begin{aligned}V_{\mathrm {dc} }={}&V_{\mathrm {av} }={\frac {1}{{\frac {1}{3}}\pi }}\int _{60^{\circ }}^{120^{\circ }}{\sqrt {3}}\cdot V_{\mathrm {peak} }\cdot \sin \varphi \cdot \mathrm {d} \varphi \\={}&{\frac {3{\sqrt {3}}\cdot V_{\mathrm {peak} }}{\pi }}\cdot \left(-\cos 120^{\circ }+\cos 60^{\circ }\right)\\={}&{\frac {3{\sqrt {3}}\cdot V_{\mathrm {peak} }}{\pi }}\cdot {\Biggl }={\frac {3{\sqrt {3}}\cdot V_{\mathrm {peak} }}{\pi }}\end{aligned}}}
692:
457:
3827:
5673:
680:
3858:, stages of capacitors and diodes are cascaded to amplify a low AC voltage to a high DC voltage. These circuits are capable of producing a DC output voltage potential up to about ten times the peak AC input voltage, in practice limited by current capacity and voltage regulation issues. Diode voltage multipliers, frequently used as a trailing boost stage or primary high voltage (HV) source, are used in HV laser power supplies, powering devices such as
3093:
6127:
5209:
3791:
6258:
5889:
3880:
5291:
2647:
3163:
the phase voltages. However, the differences in the phase voltages result in the six-pulse DC voltage (over the duration of a period). The strict separation of the transformer center from the negative pole (otherwise short-circuit currents will flow) or a possible grounding of the negative pole when powered by an isolating transformer apply correspondingly to the symmetrical operation.
5287:. In its simplest form this can be just a capacitor (functioning as both a smoothing capacitor as well as a reservoir, buffer or bulk capacitor), choke, resistor, Zener diode and resistor, or voltage regulator placed at the output of the rectifier. In practice, most smoothing filters utilize multiple components to efficiently reduce ripple voltage to a level tolerable by the circuit.
5948:
2844:
6172:
6039:
5363:
ripple currents increase IR losses (in the form of heat) in the capacitor, rectifier and transformer windings, and may exceed the ampacity of the components or VA rating of the transformer. Vacuum tube rectifiers specify the maximum capacitance of the input capacitor, and SS diode rectifiers also have current limitations. Capacitors for this application need low
653:
5861:, are suspended above the pool. There may be several auxiliary electrodes to aid in starting and maintaining the arc. When an electric arc is established between the cathode pool and suspended anodes, a stream of electrons flows from the cathode to the anodes through the ionized mercury, but not the other way (in principle, this is a higher-power counterpart to
6265:. The low on-resistance property of a MOSFET reduces ohmic losses compared to the diode rectifier (below 32 A in this case), which exhibits a significant voltage drop even at very low current levels. Paralleling two MOSFETs (pink curve) reduces the losses further, whereas paralleling several diodes won't significantly reduce the forward-voltage drop.
3843:. However, for a given desired ripple, the value of both capacitors must be twice the value of the single one required for a normal bridge rectifier; when the switch is closed each one must filter the output of a half-wave rectifier, and when the switch is open the two capacitors are connected in series with an equivalent value of half one of them.
5484:), then uses a transformer to change the voltage, and finally rectifies power back to DC. A frequency of typically several tens of kilohertz is used, as this requires much smaller inductance than at lower frequencies and obviates the use of heavy, bulky, and expensive iron-cored transformers. Another method of converting DC voltages uses a
868:
5454:
maintain output voltage when source voltage drops. The input filter must prevent the troughs of the ripple dropping below the minimum voltage required by the regulator to produce the required output voltage. The regulator serves both to significantly reduce the ripple and to deal with variations in supply and load characteristics.
917:
5588:, a synchronous rectifier may be used. It consists of a synchronous motor driving a set of heavy-duty electrical contacts. The motor spins in time with the AC frequency and periodically reverses the connections to the load at an instant when the sinusoidal current goes through a zero-crossing. The contacts do not have to
2470:
3862:(CRT) (like those used in CRT based television, radar and sonar displays), photon amplifying devices found in image intensifying and photo multiplier tubes (PMT), and magnetron based radio frequency (RF) devices used in radar transmitters and microwave ovens. Before the introduction of semiconductor electronics,
3088:{\displaystyle {\begin{aligned}{\hat {v}}_{\text{common mode}}={}&V_{\mathrm {peak} }-{\frac {{\sqrt {3}}\cdot V_{\mathrm {peak} }\cdot \sin 60^{\circ }}{2}}\\={}&V_{\mathrm {peak} }\cdot {\Biggl (}1-{\frac {{\sqrt {3}}\cdot \sin 60^{\circ }}{2}}{\Biggl )}=V_{\mathrm {peak} }\cdot 0.25\end{aligned}}}
5492:
597:
5932:
car radios in the 1940s and 1950s. It was a conventional full-wave rectifier tube with two anodes and one cathode, but was unique in that it had no filament (thus the "0" in its type number). The electrodes were shaped such that the reverse breakdown voltage was much higher than the forward breakdown
5916:
device with a tungsten filament cathode and a carbon button anode. It operated similarly to the thermionic vacuum tube diode, but the gas in the tube ionized during forward conduction, giving it a much lower forward voltage drop so it could rectify lower voltages. It was used for battery chargers and
687:
For single-phase AC, if the transformer is center-tapped, then two diodes back-to-back (cathode-to-cathode or anode-to-anode, depending on output polarity required) can form a full-wave rectifier. Twice as many turns are required on the transformer secondary to obtain the same output voltage than for
5445:
shunt with reverse voltage equal to the set voltage. When input voltage rises, the diode dumps current to maintain the set output voltage. This kind of regulator is usually employed only in low voltage, low current circuits because Zener diodes have both voltage and current limitations. It is also
5428:
or tuned choke filter. Unlike the other filter geometries which are low-pass filters, a resonant choke filter is a band-stop filter: it is a parallel combination of choke and capacitor which resonates at the frequency of the ripple voltage, presenting a very high impedance to the ripple. It may be
5414:
In cases where ripple voltage is insignificant, like battery chargers, the input filter may be a single series resistor to adjust the output voltage to that required by the circuit. A resistor reduces both output voltage and ripple voltage proportionately. A disadvantage of a resistor input filter
3934:
is defined as the ratio of DC output power to the input power from the AC supply. Even with ideal rectifiers, the ratio is less than 100% because some of the output power is AC power rather than DC which manifests as ripple superimposed on the DC waveform. The ratio can be improved with the use of
5997:
radio receiver, to provide the high DC plate voltage needed by other vacuum tubes. "Full-wave" versions with two separate plates were popular because they could be used with a center-tapped transformer to make a full-wave rectifier. Vacuum tube rectifiers were made for very high voltages, such as
5507:
radio signals. The signal may be amplified before detection. If not, a very low voltage drop diode or a diode biased with a fixed voltage must be used. When using a rectifier for demodulation the capacitor and load resistance must be carefully matched: too low a capacitance makes the high frequency
5423:
To further reduce ripple, the initial filter element may be followed by additional alternating series and shunt filter components, or by a voltage regulator. Series filter components may be resistors or chokes; shunt elements may be resistors or capacitors. The filter may raise DC voltage as well
5362:
For a given load, sizing of a smoothing capacitor is a tradeoff between reducing ripple voltage and increasing ripple current. The peak current is set by the rate of rise of the supply voltage on the rising edge of the incoming sine-wave, reduced by the resistance of the transformer windings. High
3838:
A variant of this is to use two capacitors in series for the output smoothing on a bridge rectifier then place a switch between the midpoint of those capacitors and one of the AC input terminals. With the switch open, this circuit acts like a normal bridge rectifier. With the switch closed, it acts
3162:
If the circuit is operated asymmetrically (as a simple supply voltage with just one positive pole), both the positive and negative poles (or the isolated reference potential) are pulsating opposite the center (or the ground) of the input voltage analogously to the positive and negative waveforms of
5740:
When two different metals are suspended in an electrolyte solution, direct current flowing one way through the solution sees less resistance than in the other direction. Electrolytic rectifiers most commonly used an aluminum anode and a lead or steel cathode, suspended in a solution of triammonium
5375:
It is also possible to put the rectified waveform into a choke-input filter. The advantage of this circuit is that the current waveform is smoother: current is drawn over the entire cycle, instead of being drawn in pulses at the peaks of AC voltage each half-cycle as in a capacitor input filter.
5325:
is supplied to the load. At the end of the mains quarter cycle, the capacitor is charged to the peak value Vp of the rectifier voltage. Following this, the rectifier input voltage starts to decrease to its minimum value Vmin as it enters the next quarter cycle. This initiates the discharge of the
326:
Depending on the type of alternating current supply and the arrangement of the rectifier circuit, the output voltage may require additional smoothing to produce a uniform steady voltage. Many applications of rectifiers, such as power supplies for radio, television and computer equipment, require a
6898:
The first 25 years of HVDC transmission were sustained by converters having mercury arc valves till the mid-1970s. The next 25 years till the year 2000 were sustained by line-commutated converters using thyristor valves. It is predicted that the next 25 years will be dominated by force-commutated
6186:
diodes are the most widely used rectifiers for lower voltages and powers, and have largely replaced other rectifiers. Due to their substantially lower forward voltage (0.3V versus 0.7V for silicon diodes) germanium diodes have an inherent advantage over silicon diodes in low voltage circuits.
6152:
Typically these rectifiers were made up of stacks of metal plates or washers, held together by a central bolt, with the number of stacks determined by voltage; each cell was rated for about 20 V. An automotive battery charger rectifier might have only one cell: the high-voltage power supply for a
5437:
A more usual alternative to additional filter components, if the DC load requires very low ripple voltage, is to follow the input filter with a voltage regulator. A voltage regulator operates on a different principle than a filter, which is essentially a voltage divider that shunts voltage at the
3802:
Although better than single-phase rectifiers or three-phase half-wave rectifiers, six-pulse rectifier circuits still produce considerable harmonic distortion on both the AC and DC connections. For very high-power rectifiers the twelve-pulse bridge connection is usually used. A twelve-pulse bridge
3424:
The above equations are only valid when no current is drawn from the AC supply or in the theoretical case when the AC supply connections have no inductance. In practice, the supply inductance causes a reduction of DC output voltage with increasing load, typically in the range 10–20% at full load.
6018:
and therefore high voltage drops, causing high power dissipation and low efficiency. They are rarely able to handle currents exceeding 250 mA owing to the limits of plate power dissipation, and cannot be used for low voltage applications, such as battery chargers. Another limitation of the
5565:
These mechanical rectifiers were noisy and had high maintenance requirements, including lubrication and replacement of moving parts due to wear. Opening mechanical contacts under load resulted in electrical arcs and sparks that heated and eroded the contacts. They also were not able to handle AC
5712:
produces a direct current without the need for a commutator. M-G sets are useful for producing DC for railway traction motors, industrial motors and other high-current applications, and were common in many high-power DC uses (for example, carbon-arc lamp projectors for outdoor theaters) before
5453:
circuit. An active regulator employs reactive components to store and discharge energy, so that most or all current supplied by the rectifier is passed to the load. It may also use negative and positive feedback in conjunction with at least one voltage amplifying component like a transistor to
1823:
For low-power applications, double diodes in series, with the anode of the first diode connected to the cathode of the second, are manufactured as a single component for this purpose. Some commercially available double diodes have all four terminals available so the user can configure them for
6148:
were lighter in weight and used less power than comparable vacuum tube rectifiers, they had the disadvantage of finite life expectancy, increasing resistance with age, and were only suitable to use at low frequencies. Both selenium and copper oxide rectifiers have somewhat better tolerance of
3834:
The simple half-wave rectifier can be built in two electrical configurations with the diodes pointing in opposite directions, one version connects the negative terminal of the output direct to the AC supply and the other connects the positive terminal of the output direct to the AC supply. By
2660:
If the three-phase bridge rectifier is operated symmetrically (as positive and negative supply voltage), the center point of the rectifier on the output side (or the so-called isolated reference potential) opposite the center point of the transformer (or the neutral conductor) has a potential
3428:
The effect of supply inductance is to slow down the transfer process (called commutation) from one phase to the next. As result of this is that at each transition between a pair of devices, there is a period of overlap during which three (rather than two) devices in the bridge are conducting
4746:
2673:
of the mains voltage. Powered by a transformer, earthing of the center point of the bridge is possible, provided that the secondary winding of the transformer is electrically isolated from the mains voltage and the star point of the secondary winding is not on earth. In this case, however,
4987:
3705:
5273:
The AC input (yellow) and DC output (green) of a half-wave rectifier with a smoothing capacitor. Note the ripple in the DC signal. The significant gap (about 0.7V) between the peak of the AC input and the peak of the DC output is due to the forward voltage drop of the rectifier
1827:
For higher-power applications, a single discrete device is usually used for each of the six arms of the bridge. For the very highest powers, each arm of the bridge may consist of tens or hundreds of separate devices in parallel (where very high current is needed, for example in
432:
In half-wave rectification of a single-phase supply, either the positive or negative half of the AC wave is passed, while the other half is blocked. Because only one half of the input waveform reaches the output, mean voltage is lower. Half-wave rectification requires a single
5761:
around the same era by suspending many aluminium cones in a tank of triammonium orthophosphate solution. Unlike the rectifier above, only aluminium electrodes were used, and used on A.C., there was no polarization and thus no rectifier action, but the chemistry was similar.
47:
6899:
converters . Initially, this new force-commutated era has commenced with
Capacitor Commutated Converters (CCC) eventually to be replaced by self-commutated converters due to the economic availability of high-power switching devices with their superior characteristics.
5989:
in 1884, and a positive voltage on the plate caused a current of electrons through the tube from filament to plate. Since only the filament produced electrons, the tube would only conduct current in one direction, allowing the tube to rectify an alternating current.
4860:
3280:
713:
4431:
4318:
5753:
where the coating is penetrated and the cell is short-circuited. Electrochemical methods are often more fragile than mechanical methods, and can be sensitive to usage variations, which can drastically change or completely disrupt the rectification processes.
5638:, to rectify the low voltage produced by a step-down transformer. Another use was in battery power supplies for portable vacuum tube radios, to provide the high DC voltage for the tubes. These operated as a mechanical version of modern solid state switching
3552:
5282:
voltage component at the source frequency for a half-wave rectifier, and twice the source frequency for a full-wave rectifier. Ripple voltage is usually specified peak-to-peak. Producing steady DC from a rectified AC supply requires a smoothing circuit or
3803:
consists of two six-pulse bridge circuits connected in series, with their AC connections fed from a supply transformer that produces a 30° phase shift between the two bridges. This cancels many of the characteristic harmonics the six-pulse bridges produce.
6829:
3390:
2642:{\displaystyle \Longrightarrow V_{\mathrm {dc} }=V_{\mathrm {av} }={\frac {3{\sqrt {3}}\cdot {\sqrt {2}}\cdot V_{\mathrm {LN} }}{\pi }}\Longrightarrow V_{\mathrm {av} }={\frac {3{\sqrt {6}}\cdot V_{\mathrm {LN} }}{\pi }}\approx 2.34V_{\mathrm {LN} }}
5748:
on the aluminum electrode, formed by first applying a strong current to the cell to build up the coating. The rectification process is temperature-sensitive, and for best efficiency should not operate above 86 °F (30 °C). There is also a
4609:
4138:
3835:
combining both of these with separate output smoothing it is possible to get an output voltage of nearly double the peak AC input voltage. This also provides a tap in the middle, which allows use of such a circuit as a split rail power supply.
397:
Other devices that have control electrodes as well as acting as unidirectional current valves are used where more than simple rectification is required—e.g., where variable output voltage is needed. High-power rectifiers, such as those used in
5468:
The primary application of rectifiers is to derive DC power from an AC supply (AC to DC converter). Rectifiers are used inside the power supplies of virtually all electronic equipment. AC/DC power supplies may be broadly divided into linear
5400:
times the RMS voltage (unloaded) for a capacitor input filter. Offsetting this is superior voltage regulation and higher available current, which reduce peak voltage and ripple current demands on power supply components. Inductors require
4033:
3839:
like a voltage doubling rectifier. In other words, this makes it easy to derive a voltage of roughly 320 V (±15%, approx.) DC from any 120 V or 230 V mains supply in the world, this can then be fed into a relatively simple
5148:
3157:
470:
5040:
1768:
If the AC supply is fed via a transformer with a center tap, a rectifier circuit with improved harmonic performance can be obtained. This rectifier now requires six diodes, one connected to each end of each transformer secondary
1819:
are used, and the circuit again has a pulse number of six. For this reason, it is also commonly referred to as a six-pulse bridge. The B6 circuit can be seen simplified as a series connection of two three-pulse center circuits.
4500:
4210:
2028:
5868:
These devices can be used at power levels of hundreds of kilowatts, and may be built to handle one to six phases of AC current. Mercury-arc rectifiers have been replaced by silicon semiconductor rectifiers and high-power
4617:
897:
rectifier circuits are the norm. As with single-phase rectifiers, three-phase rectifiers can take the form of a half-wave circuit, a full-wave circuit using a center-tapped transformer, or a full-wave bridge circuit.
4868:
3567:
1157:
2677:
The common-mode voltage is formed out of the respective average values of the differences between the positive and negative phase voltages, which form the pulsating DC voltage. The peak value of the delta voltage
1077:
5167:, for silicon devices, of typically 0.7 volts plus an equivalent resistance, in general non-linear)—and at high frequencies, distorts waveforms in other ways. Unlike an ideal rectifier, it dissipates some power.
6303:
Active rectification has many applications. It is frequently used for arrays of photovoltaic panels to avoid reverse current flow that can cause overheating with partial shading while giving minimum power loss.
6104:(lead sulfide), with a light springy wire touching its surface. Its fragility and limited current capability made it unsuitable for power supply applications. It was used widely in radios until the 1920s when
2041:
418:
or multi-phase. Most low power rectifiers for domestic equipment are single-phase, but three-phase rectification is very important for industrial applications and for the transmission of energy as DC (HVDC).
5405:
of iron or other magnetic materials, and add weight and size. Their use in power supplies for electronic equipment has therefore dwindled in favour of semiconductor circuits such as voltage regulators.
932:
on both the AC and DC connections. This type of rectifier is said to have a pulse-number of three, since the output voltage on the DC side contains three distinct pulses per cycle of the grid frequency:
2849:
718:
475:
5298:
The filter capacitor releases its stored energy during the part of the AC cycle when the AC source does not supply any power, that is, when the AC source changes its direction of flow of current.
4757:
863:{\displaystyle {\begin{aligned}V_{\mathrm {dc} }=V_{\mathrm {av} }&={\frac {2\cdot V_{\mathrm {peak} }}{\pi }}\\V_{\mathrm {rms} }&={\frac {V_{\mathrm {peak} }}{\sqrt {2}}}\end{aligned}}}
2744:
3177:
928:
An uncontrolled three-phase, half-wave midpoint circuit requires three diodes, one connected to each phase. This is the simplest type of three-phase rectifier but suffers from relatively high
6243:(IGCT), would be scaled-up in power rating to the point that they would eventually replace simple thyristor-based AC rectification systems for the highest power-transmission DC applications.
4997:
The transformer utilization factor (TUF) of a rectifier circuit is defined as the ratio of the DC power available at the input resistor to the AC rating of the output coil of a transformer.
664:
function. Full-wave rectification converts both polarities of the input waveform to pulsating DC (direct current), and yields a higher average output voltage. Two diodes and a center-tapped
4326:
4221:
904:
are commonly used in place of diodes to create a circuit that can regulate the output voltage. Many devices that provide direct current actually 'generate' three-phase AC. For example, an
5189:
Non-linear loads like rectifiers produce current harmonics of the source frequency on the AC side and voltage harmonics of the source frequency on the DC side, due to switching behavior.
5170:
An aspect of most rectification is a loss from the peak input voltage to the peak output voltage, caused by the built-in voltage drop across the diodes (around 0.7 V for ordinary silicon
3920:), ripple factor, form factor, and peak factor. The two primary measures are DC voltage (or offset) and peak-peak ripple voltage, which are constituent components of the output voltage.
3438:
6877:
6136:
Once common until replaced by more compact and less costly silicon solid-state rectifiers in the 1970s, these units used stacks of oxide-coated metal plates and took advantage of the
5969:, was invented by John Ambrose Fleming in 1904 as a detector for radio waves in radio receivers, and evolved into a general rectifier. It consisted of an evacuated glass bulb with a
6285:. Whereas normal semiconductor diodes have a roughly fixed voltage drop of around 0.5 to 1 volts, active rectifiers behave as resistances, and can have arbitrarily low voltage drop.
5308:
5488:, using rapid switching to change the connections of capacitors; this technique is generally limited to supplies up to a couple of watts, owing to the size of capacitors required.
5181:
Peak loss is very important for low voltage rectifiers (for example, 12 V or less) but is insignificant in high-voltage applications such as HVDC power transmission systems.
3291:
2836:
2798:
979:
1953:
1143:
1923:
1881:
1109:
1011:
4514:
672:
and any AC source (including a transformer without center tap), are needed. Single semiconductor diodes, double diodes with a common cathode or common anode, and four- or six-
4049:
6517:
Mercury-arc current convertors [sic] : an introduction to the theory and practice of vapour-arc discharge devices and to the study of rectification phenomena
6157:
might have dozens of stacked plates. Current density in an air-cooled selenium stack was about 600 mA per square inch of active area (about 90 mA per square centimeter).
5993:
Thermionic diode rectifiers were widely used in power supplies in vacuum tube consumer electronic products, such as phonographs, radios, and televisions, for example the
5398:
6802:
660:
A full-wave rectifier converts the whole of the input waveform to one of constant polarity (positive or negative) at its output. Mathematically, this corresponds to the
3944:
885:
inside a single envelope, achieving full-wave rectification with positive output. The 5U4 and the 80/5Y3 (4 pin)/(octal) were popular examples of this configuration.
5781:
technology in the early 20th century resulted in the invention of various tube-type rectifiers, which largely replaced the noisy, inefficient mechanical rectifiers.
1780:
devices became available, the half-wave circuit, and the full-wave circuit using a center-tapped transformer, were very commonly used in industrial rectifiers using
6343:
A related area of research is to develop smaller rectifiers, because a smaller device has a higher cutoff frequency. Research projects are attempting to develop a
5071:
3806:
The 30-degree phase shift is usually achieved by using a transformer with two sets of secondary windings, one in star (wye) connection and one in delta connection.
311:
power transmission systems. Rectification may serve in roles other than to generate direct current for use as a source of power. As noted, rectifiers can serve as
6239:
As of 2009 it was expected that these high-power silicon "self-commutating switches", in particular IGBTs and a variant thyristor (related to the GTO) called the
5480:
Converting DC power from one voltage to another is much more complicated. One method of DC-to-DC conversion first converts power to AC (using a device called an
3914:
Several ratios are used to quantify the function and performance of rectifiers or their output, including transformer utilization factor (TUF), conversion ratio (
592:{\displaystyle {\begin{aligned}V_{\mathrm {rms} }&={\frac {V_{\mathrm {peak} }}{2}}\\V_{\mathrm {dc} }&={\frac {V_{\mathrm {peak} }}{\pi }}\end{aligned}}}
5425:
5066:
3104:
5376:
The disadvantage is that the voltage output is much lower – the average of an AC half-cycle rather than the peak; this is about 90% of the RMS voltage versus
5003:
5921:, and later semiconductor diodes, supplanted it. These were made up to a few hundred volts and a few amperes rating, and in some sizes strongly resembled an
5477:. In such power supplies, the rectifier will be in series following the transformer and be followed by a smoothing filter and possibly a voltage regulator.
5438:
ripple frequency away from the load. Rather, a regulator increases or decreases current supplied to the load in order to maintain a constant output voltage.
1784:. This was because the three or six AC supply inputs could be fed to a corresponding number of anode electrodes on a single tank, sharing a common cathode.
382:
of
General Electric. With the introduction of semiconductor electronics, vacuum tube rectifiers became obsolete, except for some enthusiasts of vacuum tube
6019:
vacuum tube rectifier is that the heater power supply often requires special arrangements to insulate it from the high voltages of the rectifier circuit.
1787:
With the advent of diodes and thyristors, these circuits have become less popular and the three-phase bridge circuit has become the most common circuit.
3891:
about conversion ratios for at least three-phase half-wave and full-wave rectification, since these rectifiers have their own sections in this article..
6312:
A major area of research is to develop higher frequency rectifiers, that can rectify into terahertz and light frequencies. These devices are used in
4505:
Three-phase rectifiers, especially three-phase full-wave rectifiers, have much greater conversion ratios because the ripple is intrinsically smaller.
4439:
4149:
1958:
4741:{\displaystyle P_{\mathrm {DC} }={\frac {3{\sqrt {3}}\cdot V_{\mathrm {peak} }}{2\pi }}\cdot {\frac {3{\sqrt {3}}\cdot I_{\mathrm {peak} }}{2\pi }}}
4982:{\displaystyle P_{\mathrm {DC} }={\frac {3{\sqrt {3}}\cdot V_{\mathrm {peak} }}{\pi }}\cdot {\frac {3{\sqrt {3}}\cdot I_{\mathrm {peak} }}{\pi }}}
7042:
3700:{\displaystyle V_{\mathrm {dc} }=V_{\mathrm {av} }={\frac {3V_{\mathrm {LLpeak} }}{\pi }}\cdot \cos(\alpha )-6fL_{\mathrm {c} }I_{\mathrm {d} }}
893:
Single-phase rectifiers are commonly used for power supplies for domestic equipment. However, for most industrial and high-power applications,
5845:
A rectifier used in high-voltage direct current (HVDC) power transmission systems and industrial processing between about 1909 to 1975 is a
1016:
378:
stacks were used. The first vacuum tube diodes designed for rectifier application in power supply circuits were introduced in April 1915 by
7003:
5562:
used some form of rotation or resonant vibration driven by electromagnets, which operated a switch or commutator to reverse the current.
232:
5933:
voltage. Once the breakdown voltage was exceeded, the 0Z4 switched to a low-resistance state with a forward voltage drop of about 24 V.
5348:. Transformer internal impedance modifies the reservoir capacitor waveform, changes the peak voltage, and introduces regulation issues.
8080:
5415:
is that it consumes power in the form of waste heat that is not available to the load, so it is employed only in low current circuits.
167:
7916:
5634:, with contacts that reversed the direction of the current on the negative half cycles. They were used in low power devices, such as
5278:
While half-wave and full-wave rectification deliver unidirectional current, neither produces a constant voltage. There is a large AC
5725:
rectifier was a device from the early twentieth century that is no longer used. A home-made version is illustrated in the 1913 book
3171:
The controlled three-phase bridge rectifier uses thyristors in place of diodes. The output voltage is reduced by the factor cos(α):
3866:
powered directly from AC power sometimes used voltage doublers to generate roughly 300 VDC from a 100–120 V power line.
7557:
406:
or other controlled switching solid-state switches, which effectively function as diodes to pass current in only one direction.
5857:, is submerged in a pool of liquid mercury at the bottom of the vessel and one or more high purity graphite electrodes, called
5558:
Before about 1905 when tube-type rectifiers were developed, power conversion devices were purely electro-mechanical in design.
129:
5515:. In such circuits control of the output current is required; this is sometimes achieved by replacing some of the diodes in a
5313:
The above diagram shows the voltage waveforms of the reservoir performance when supplied from a voltage source with near zero
6962:
6935:
6891:
6548:
6498:
6473:
6417:
5642:, with a transformer to step the battery voltage up, and a set of vibrator contacts on the transformer core, operated by its
5441:
A simple passive shunt voltage regulator may consist of a series resistor to drop source voltage to the required level and a
4855:{\displaystyle P_{\mathrm {AC} }=3\cdot {V_{\mathrm {peak} } \over {\sqrt {2}}}\cdot {I_{\mathrm {peak} } \over {\sqrt {2}}}}
2665:. For this reason, these two centers must never be connected to each other, otherwise short-circuit currents would flow. The
6217:
In high-power applications, from 1975 to 2000, most mercury valve arc-rectifiers were replaced by stacks of very high power
3798:
as the switching elements. One six-pulse bridge consists of the even-numbered thyristors, the other is the odd-numbered set.
7474:
6694:
6656:
6240:
3275:{\displaystyle V_{\mathrm {dc} }=V_{\mathrm {av} }={\frac {3{\sqrt {3}}\cdot V_{\mathrm {peak} }}{\pi }}\cdot \cos \alpha }
6014:
equipment. However, compared to modern semiconductor diodes, vacuum tube rectifiers have high internal resistance due to
7255:
7035:
2681:
6236:, have made smaller high voltage DC power transmission systems economical. All of these devices function as rectifiers.
8085:
5769:, an essential component of most rectifier circuit configurations was also developed from the electrolytic rectifier.
5541:
are used to produce alternating current from a DC supply, for example on the
Eurostar Trains to power the three-phase
5317:, such as a mains supply. Both voltages start from zero at time t=0 at the far left of the image, then the capacitor
4426:{\displaystyle P_{\mathrm {DC} }={2\cdot V_{\mathrm {peak} } \over \pi }\cdot {2\cdot I_{\mathrm {peak} } \over \pi }}
4313:{\displaystyle P_{\mathrm {AC} }={V_{\mathrm {peak} } \over {\sqrt {2}}}\cdot {I_{\mathrm {peak} } \over {\sqrt {2}}}}
3429:
simultaneously. The overlap angle is usually referred to by the symbol μ (or u), and may be 20 30° at full load.
1013:
of the input phase voltage (line to neutral voltage, 120 V in North
America, 230 V within Europe at mains operation):
7238:
7134:
6864:
6860:
6623:
6596:
6572:
5701:
5256:
6449:
6433:
5238:
7378:
7105:
6332:, to produce DC electric power. It is thought that arrays of antennas could be a more efficient means of producing
5646:, to repeatedly break the DC battery current to create a pulsing AC to power the transformer. Then a second set of
3547:{\displaystyle V_{\mathrm {dc} }=V_{\mathrm {av} }={\frac {3V_{\mathrm {LLpeak} }}{\pi }}\cdot \cos(\alpha +\mu ).}
5158:
7426:
7225:
5329:
The size of the capacitor C is determined by the amount of ripple r that can be tolerated, where r=(Vp-Vmin)/Vp.
2669:
of the three-phase bridge rectifier in symmetrical operation is thus decoupled from the neutral conductor or the
225:
1851:
The pulsating DC voltage results from the differences of the instantaneous positive and negative phase voltages
7028:
5234:
1925:
of the B6 circuit results from the integral under the graph of a DC voltage pulse with the period duration of
1773:. This circuit has a pulse-number of six, and in effect, can be thought of as a six-phase, half-wave circuit.
284:
and other silicon-based semiconductor switches. Historically, even synchronous electromechanical switches and
3385:{\displaystyle V_{\mathrm {dc} }=V_{\mathrm {av} }={\frac {3V_{\mathrm {LLpeak} }}{\pi }}\cdot \cos \alpha }
264:, since it "straightens" the direction of current. Physically, rectifiers take a number of forms, including
7457:
7209:
6313:
6196:
5865:, which uses the same one-way current transmission properties of the plasma naturally present in a flame).
5820:
5474:
5364:
1887:
937:
450:
281:
51:
7261:
7198:
6324:. Another prospective application for such devices is to directly rectify light waves picked up by tiny
4604:{\displaystyle P_{\mathrm {AC} }=3\cdot {V_{\mathrm {peak} } \over 2}\cdot {I_{\mathrm {peak} } \over 2}}
3098:
The RMS value of the common-mode voltage is calculated from the form factor for triangular oscillations:
2803:
2765:
1833:
946:
438:
415:
399:
308:
5696:
DC from an AC source. In an "M-G set", the shaft of an AC motor is mechanically coupled to that of a DC
5198:
4133:{\displaystyle P_{\mathrm {DC} }={V_{\mathrm {peak} } \over \pi }\cdot {I_{\mathrm {peak} } \over \pi }}
1928:
1118:
445:. Rectifiers yield a unidirectional but pulsating direct current; half-wave rectifiers produce far more
293:
7921:
7468:
6082:
5450:
5230:
3855:
3840:
1896:
1854:
1082:
984:
894:
442:
218:
66:
31:
17:
6824:
7675:
7389:
7232:
7117:
6225:
5873:
circuits in the mid-1970s. The most powerful mercury-arc rectifiers ever built were installed in the
5579:
1777:
386:. For power rectification from very low to very high current, semiconductor diodes of various types (
95:
81:
7684:
7542:
7394:
7250:
6190:
5219:
6985:
6112:
the crystal detector for use at microwave frequencies, developing the first semiconductor diodes.
5737:. A more complex device of this kind was patented by G. W. Carpenter in 1928 (US Patent 1671970).
4028:{\displaystyle P_{\mathrm {AC} }={V_{\mathrm {peak} } \over 2}\cdot {I_{\mathrm {peak} } \over 2}}
7695:
7415:
7214:
6613:
6233:
5538:
5524:
5463:
5379:
5223:
905:
464:
The no-load output DC voltage of an ideal half-wave rectifier for a sinusoidal input voltage is:
6540:
7864:
7431:
7296:
7272:
6344:
6269:
Active rectification is a technique for improving the efficiency of rectification by replacing
5766:
5357:
100:
6952:
6789:
Hawkins
Electrical Guide: Principles of electricity, magnetism, induction, experiments, dynamo
6640:
6586:
5143:{\displaystyle VA=V_{\mathrm {rms} }{\dot {I}}_{\mathrm {rms} }({\text{For secondary coil.}})}
7933:
7885:
7706:
7522:
7437:
7368:
7204:
6686:
6648:
6407:
6293:
6289:
6078:
5705:
5651:
5619:
5481:
5341:
3863:
3432:
With supply inductance taken into account, the output voltage of the rectifier is reduced to
359:
138:
6532:
8007:
7751:
7646:
7420:
7313:
7167:
7128:
7059:
7051:
6365:
6297:
6252:
6221:, silicon devices with two extra layers of semiconductor, in comparison to a simple diode.
5942:
5800:
5697:
5647:
5609:
5559:
5508:
carrier pass to the output, and too high makes the capacitor just charge and stay charged.
5504:
5345:
5337:
5314:
3152:{\displaystyle V_{\text{common mode}}={\frac {{\hat {v}}_{\text{common mode}}}{\sqrt {3}}}}
2666:
1847:
as the switching elements, ignoring supply inductance. The thyristors pulse in order V1–V6.
908:
contains nine diodes, six of which function as a full-wave rectifier for battery charging.
5853:. The device is enclosed in a bulbous glass vessel or large metal tub. One electrode, the
8:
8090:
7727:
7635:
7527:
7363:
7340:
6916:, 1968, Howard W. Sams and Co., no ISBN, Library of Congress Card No. 43-14665 chapter 13
6371:
6054:
5982:
5970:
5956:
5877:
5862:
5745:
5709:
5585:
5279:
929:
446:
344:
320:
285:
250:
6979:
6926:
Arrillaga, Jos; Liu, Yonghe H; Watson, Neville R; Murray, Nicholas J (12 January 2010).
6784:
5523:, effectively diodes whose voltage output can be regulated by switching on and off with
5326:
capacitor through the load while the capacitor holds up the output voltage to the load.
5048:
5035:{\displaystyle {\text{T.U.F}}={\frac {P_{\text{odc}}}{\text{VA rating of transformer}}}}
3893:
Please expand the section to include this information. Further details may exist on the
3773:
3763:
358:
A device that performs the opposite function, that is converting DC to AC, is called an
8032:
7892:
7600:
7567:
7383:
7267:
7245:
6756:
Mansell, A.D.; Shen, J. (1 January 1994). "Pulse converters in traction applications".
6533:
6145:
6130:
5758:
5446:
very inefficient, because it dumps excess current, which is not available to the load.
3815:
3747:
2670:
2662:
1829:
1764:
as the switching elements, with a center-tapped transformer, ignoring supply inductance
273:
110:
105:
3846:
3737:
1795:
8027:
7948:
7839:
7791:
7620:
7547:
7509:
6958:
6931:
6887:
6690:
6652:
6619:
6592:
6568:
6544:
6494:
6469:
6413:
5994:
5922:
5905:
5827:
5790:
5750:
5730:
5622:
battery charger from 1922. It produced 6 A DC at 6 V to charge automobile batteries.
5614:
5284:
3561:
is directly related to the DC current, and the above equation may be re-expressed as
1800:
1781:
402:
power transmission, employ silicon semiconductor devices of various types. These are
352:
336:
269:
181:
90:
74:
54:) and associated mounting hardware. The heavy threaded stud attaches the device to a
3928:
Conversion ratio (also called "rectification ratio", and confusingly, "efficiency")
3420:
is the firing angle of the thyristor (0 if diodes are used to perform rectification)
1839:
7743:
7690:
7517:
7156:
6765:
6718:
6386:
6381:
6348:
6176:
6050:
6043:
6033:
5999:
5901:
5667:
5516:
5500:
5322:
5171:
3859:
638:
460:
Half-wave rectifier, 'U' denotes voltage, 'D' denotes a diode, and 'R' a resistance
371:
332:
312:
206:
7552:
707:
and RMS no-load output voltages of an ideal single-phase full-wave rectifier are:
277:
8020:
7953:
7806:
7537:
7447:
7291:
6883:
6844:
6680:
6515:
6325:
6229:
6121:
6085:
around 1902, it was a significant improvement over earlier detectors such as the
5918:
5913:
5663:
5635:
3821:
1751:
704:
383:
375:
158:
148:
7178:
6201:
6191:
High power: thyristors (SCRs) and newer silicon-based voltage sourced converters
6109:
265:
7995:
7776:
7766:
7532:
7335:
6224:
In medium-power transmission applications, even more complex and sophisticated
6210:
6062:
5874:
5831:
5734:
5643:
5597:
5542:
5321:
follows the rectified AC voltage as it increases, the capacitor is charged and
5269:
5175:
4495:{\displaystyle \eta ={P_{\mathrm {DC} } \over P_{\mathrm {AC} }}\approx 81.0\%}
4205:{\displaystyle \eta ={P_{\mathrm {DC} } \over P_{\mathrm {AC} }}\approx 40.5\%}
3894:
2023:{\displaystyle {\hat {v}}_{\mathrm {DC} }={\sqrt {3}}\cdot V_{\mathrm {peak} }}
661:
391:
387:
304:
254:
186:
176:
153:
120:
6879:
HVDC and FACTS Controllers: Applications of Static
Converters in Power Systems
6565:
Reference Data for
Engineers: Radio, Electronics, Computer, and Communications
6434:"A New Device for Rectifying High Tension Alternating Currents - The Kenotron"
5729:
but it would be suitable for use only at very low voltages because of the low
3777:
Three-phase controlled bridge rectifier at alpha=40° with overlap angle of 20°
3767:
Three-phase controlled bridge rectifier at alpha=20° with overlap angle of 20°
1756:
916:
8074:
8057:
7880:
7796:
7615:
7442:
7410:
6317:
6137:
6094:
6066:
5986:
5966:
5811:
5631:
5534:
5402:
289:
143:
300:(lead sulfide) to serve as a point-contact rectifier or "crystal detector".
7938:
7926:
7814:
7781:
7610:
7595:
7162:
6321:
6278:
6262:
6070:
6015:
5722:
5470:
5164:
673:
669:
379:
303:
Rectifiers have many uses, but are often found serving as components of DC
6769:
2652:
449:
than full-wave rectifiers, and much more filtering is needed to eliminate
7980:
7722:
7671:
7577:
7562:
7345:
7307:
6376:
6333:
6154:
6105:
5959:
5929:
5778:
5627:
5485:
5442:
5333:
2674:(negligible) leakage currents are flowing over the transformer windings.
1812:
874:
665:
7020:
6179:. On the 3 center diodes, a painted band identifies the cathode terminal
5307:
3826:
1824:
single-phase split supply use, half a bridge, or three-phase rectifier.
691:
456:
370:
Before the development of silicon semiconductor rectifiers, vacuum tube
335:). In these applications the output of the rectifier is smoothed by an
8052:
8042:
7975:
7849:
7819:
7786:
7761:
7756:
7733:
7605:
7585:
7463:
7325:
7302:
7188:
7090:
7085:
7080:
6827:, Glenn W. Carpenter, "Liquid Rectifier", issued 1928-06-05
6360:
6337:
6274:
6175:
A variety of silicon diodes of different current ratings. At left is a
6074:
6003:
5835:
5672:
5163:
A real rectifier characteristically drops part of the input voltage (a
2656:
3-phase AC input, half-wave and full-wave rectified DC output waveforms
696:
38:
5491:
1843:
Controlled three-phase full-wave bridge rectifier circuit (B6C) using
1072:{\displaystyle V_{\mathrm {peak} }={\sqrt {2}}\cdot V_{\mathrm {LN} }}
8015:
7859:
7854:
7844:
7771:
7651:
7485:
7480:
7405:
7330:
6282:
6218:
6206:
6126:
5870:
5567:
5537:
systems so that fine control of the traction motors can be achieved.
5520:
3795:
1844:
1761:
921:
901:
679:
403:
340:
6213:
dams. Compare with mercury-arc system from the same dam-site, above.
5654:
rectified the high AC voltage from the transformer secondary to DC.
5208:
3414:
is the peak value of the phase (line to neutral) input voltages, and
1832:) or in series (where very high voltages are needed, for example in
1115:
under the graph of a positive half-wave with the period duration of
8037:
7985:
7965:
7943:
7829:
7824:
7712:
7701:
7630:
7400:
6859:
Pictures of a mercury-arc rectifier in operation can be seen here:
6329:
6141:
6058:
5978:
5880:
HVDC project, with a combined rating of more than 1 GW and 450 kV.
5700:. The DC generator produces multiphase alternating currents in its
5639:
1112:
348:
201:
196:
55:
5708:
on the armature shaft converts into a direct current output; or a
5495:
Output voltage of a full-wave rectifier with controlled thyristors
3790:
3751:
Three-phase bridge rectifier at alpha=0° with overlap angle of 20°
7897:
7834:
7656:
7641:
7495:
7452:
7100:
6183:
6097:
6086:
5854:
5807:
5531:
5512:
5318:
5159:
Diode § Forward threshold voltage for various semiconductors
1770:
981:
of this three-pulse DC voltage are calculated from the RMS value
878:
6539:(4. printing. ed.). New York: Wiley-Interscience. pp.
5449:
A more efficient alternative to a shunt voltage regulator is an
3879:
7970:
7661:
7625:
7590:
7150:
7122:
7095:
7070:
6912:
6257:
6209:
valve stacks used for long-distance transmission of power from
6101:
5888:
297:
191:
5294:
Full-wave diode-bridge rectifier with parallel RC shunt filter
1752:
Three-phase, full-wave circuit using center-tapped transformer
8047:
7958:
7717:
7490:
7283:
7145:
7140:
6270:
6166:
6038:
6011:
5974:
5962:
5909:
5858:
5630:, vibrated by an alternating magnetic field created by an AC
1816:
1804:
882:
434:
316:
5290:
4143:
Thus maximum conversion ratio for a half-wave rectifier is,
1790:
652:
46:
7990:
7373:
7319:
7220:
7173:
7111:
6719:"New equations for capacitance vs ripple in power supplies"
5947:
6954:
Integrated power electronic converters and digital control
6842:
6491:
Power electronics : devices, drivers and applications
3285:
Or, expressed in terms of the line to line input voltage:
3166:
683:
Bridge rectifier: a full-wave rectifier using four diodes.
37:"AC/DC converter" redirects here. Not to be confused with
7001:
6171:
6077:
which produced the sound in the earphones. Invented by
5928:
The 0Z4 was a gas-filled rectifier tube commonly used in
4042:
because no power is delivered on the negative half-cycle)
1760:
Controlled three-phase full-wave rectifier circuit using
920:
Controlled three-phase half-wave rectifier circuit using
6925:
6611:
6089:. One popular type of crystal detector, often called a
5301:
3741:
Three-phase bridge rectifier at alpha=0° without overlap
656:
Full-wave rectifier, with vacuum tube having two anodes.
6928:
Self-Commutating
Converters for High Power Applications
6849:. Vol. 2. American technical society. p. 487.
6228:(VSC) silicon semiconductor rectifier systems, such as
6115:
1807:
that comprise a full-wave three-phase bridge rectifier.
688:
a bridge rectifier, but the power rating is unchanged.
6149:
momentary voltage transients than silicon rectifiers.
5688:, is not strictly a rectifier as it does not actually
5429:
followed by a shunt capacitor to complete the filter.
5917:
similar applications from the 1920s until lower-cost
5744:
The rectification action is due to a thin coating of
5382:
5074:
5051:
5006:
4871:
4760:
4620:
4517:
4442:
4329:
4224:
4152:
4052:
3947:
3570:
3441:
3405:
is the peak value of the line to line input voltages,
3294:
3180:
3107:
2847:
2806:
2768:
2684:
2473:
2039:
1961:
1931:
1899:
1857:
1155:
1121:
1085:
1019:
987:
949:
924:
as the switching elements, ignoring supply inductance
716:
473:
3938:
For a half-wave rectifier the ratio is very modest.
6977:
6679:Smith, Edward H. (2013). "2.3.17. Power supplies".
6464:Lander, Cyril W. (1993). "2. Rectifying Circuits".
5713:high-power semiconductors became widely available.
5418:
2838:minus half of the DC voltage at 60° of the period:
2739:{\displaystyle {\hat {v}}_{\mathrm {common-mode} }}
6823:
6716:
5392:
5142:
5060:
5034:
4981:
4854:
4740:
4603:
4494:
4425:
4312:
4204:
4132:
4027:
3699:
3546:
3384:
3274:
3151:
3087:
2830:
2792:
2738:
2641:
2456:
2022:
1947:
1917:
1875:
1739:
1137:
1103:
1071:
1005:
973:
862:
591:
6913:Reference Data for Radio Engineers, Fifth Edition
3809:
3046:
2998:
2399:
2353:
1486:
1436:
911:
8072:
6744:Reference Data for Radio Engineers Fifth Edition
5973:heated by a separate current, and a metal plate
4992:
253:(AC), which periodically reverses direction, to
6160:
3869:
331:constant DC voltage (as would be produced by a
6746:, 1968, Howard W. Sams pp. 12-14, 12-15, 12-16
6563:Wendy Middleton, Mac E. Van Valkenburg (eds),
6513:
6454:. U. S. patent 1,287,265. Retrieved Nov. 2021.
5596:a large current to supply the locomotive's DC
5584:To convert alternating into direct current in
288:have been used. Early radio receivers, called
7036:
6632:
6612:Atul P.Godse; U. A. Bakshi (1 January 2008).
6605:
6409:A History of the World Semiconductor Industry
5834:power station, Radisson, Canada converted AC
5548:
5192:
5068:rating of the transformer can be defined as:
2762:of the peak value of the phase input voltage
628:, the peak value of the phase input voltages,
226:
6717:Cartwright, Kenneth; Kaminsky, Edit (2017).
5936:
5332:These circuits are very frequently fed from
3720:is the commutating inductance per phase, and
7004:"Harvesting the sun's energy with antennas"
6836:
6776:
6755:
6726:Latin American Journal of Physics Education
5409:
5237:. Unsourced material may be challenged and
323:is used to detect the presence of a flame.
7043:
7029:
6672:
6645:Electronics for Electricians and Engineers
6273:with actively controlled switches such as
5883:
5757:Similar electrolytic devices were used as
5592:a large current, but they must be able to
5570:above several thousand cycles per second.
5530:Thyristors are used in various classes of
1893:The ideal, no-load average output voltage
645:
427:
422:
233:
219:
7050:
6950:
6578:
6507:
6230:insulated gate bipolar transistors (IGBT)
5838:to DC for transmission to distant cities.
5351:
5257:Learn how and when to remove this message
5199:Ripple (electrical) § Ripple voltage
5152:
1791:Three-phase bridge rectifier uncontrolled
1281:
888:
257:(DC), which flows in only one direction.
6981:Standard polyphase apparatus and systems
6638:
6493:(2nd ed.). Basingstoke: Macmillan.
6488:
6256:
6200:
6170:
6125:
6108:replaced it. In the 1930s, researchers
6037:
5946:
5887:
5671:
5613:
5573:
5511:Rectifiers supply polarized voltage for
5490:
5289:
5268:
3845:
3825:
3789:
3772:
3762:
3746:
3736:
2651:
1838:
1794:
1755:
915:
690:
678:
651:
455:
296:" of fine wire pressing on a crystal of
45:
27:Electrical device that converts AC to DC
6803:"How To Make An Electrolytic Rectifier"
6782:
6530:
6457:
4751:For a three-phase full-wave rectifier,
4508:For a three-phase half-wave rectifier,
3830:Switchable full bridge/voltage doubler.
3167:Three-phase bridge rectifier controlled
2661:difference in the form of a triangular
1955:(from 60° to 120°) with the peak value
676:are manufactured as single components.
14:
8073:
6984:(5th ed.). Van Nostrand. p.
6584:
6489:Williams, B. W. (1992). "Chapter 11".
6463:
6405:
5998:the high voltage power supply for the
5657:
5603:
5184:
4215:Similarly, for a full-wave rectifier,
3785:
249:is an electrical device that converts
7024:
6944:
6869:
6865:Belsize Park deep shelter rectifier 2
6861:Belsize Park deep shelter rectifier 1
6678:
6618:. Technical Publications. p. 8.
6468:(3rd ed.). London: McGraw-Hill.
5432:
5370:
5302:Performance with low impedance source
3864:transformerless vacuum tube receivers
1079:. The average no-load output voltage
453:of the AC frequency from the output.
409:
7475:Three-dimensional integrated circuit
6875:
6682:Mechanical Engineer's Reference Book
6585:Rashid, Muhammad (13 January 2011).
6351:that would function as a rectifier.
6241:integrated gate-commutated thyristor
6116:Selenium and copper oxide rectifiers
5553:
5235:adding citations to reliable sources
5202:
3873:
3794:Twelve pulse bridge rectifier using
374:and copper oxide- or selenium-based
365:
7256:Programmable unijunction transistor
6843:American Technical Society (1920).
6615:Elements of Electronics Engineering
6316:, which has myriad applications in
6307:
6246:
6027:
5985:(the Edison effect), discovered by
3923:
3856:Cockcroft-Walton voltage multiplier
3850:Cockcroft Walton voltage multiplier
2831:{\displaystyle V_{\mathrm {peak} }}
2793:{\displaystyle V_{\mathrm {peak} }}
974:{\displaystyle V_{\mathrm {peak} }}
873:Very common double-diode rectifier
619:– the DC or average output voltage,
347:, or set of capacitors, chokes and
24:
7157:Multi-gate field-effect transistor
7002:Idaho National Laboratory (2007).
6439:pp. 156 - 167. Retrieved Nov. 2021
6261:Voltage drop across a diode and a
5123:
5120:
5117:
5096:
5093:
5090:
4967:
4964:
4961:
4958:
4921:
4918:
4915:
4912:
4881:
4878:
4837:
4834:
4831:
4828:
4802:
4799:
4796:
4793:
4770:
4767:
4721:
4718:
4715:
4712:
4670:
4667:
4664:
4661:
4630:
4627:
4590:
4587:
4584:
4581:
4559:
4556:
4553:
4550:
4527:
4524:
4489:
4475:
4472:
4460:
4457:
4411:
4408:
4405:
4402:
4372:
4369:
4366:
4363:
4339:
4336:
4295:
4292:
4289:
4286:
4260:
4257:
4254:
4251:
4234:
4231:
4199:
4185:
4182:
4170:
4167:
4119:
4116:
4113:
4110:
4088:
4085:
4082:
4079:
4062:
4059:
4014:
4011:
4008:
4005:
3983:
3980:
3977:
3974:
3957:
3954:
3691:
3679:
3634:
3631:
3628:
3625:
3622:
3619:
3598:
3595:
3580:
3577:
3505:
3502:
3499:
3496:
3493:
3490:
3469:
3466:
3451:
3448:
3358:
3355:
3352:
3349:
3346:
3343:
3322:
3319:
3304:
3301:
3248:
3245:
3242:
3239:
3208:
3205:
3190:
3187:
3069:
3066:
3063:
3060:
2987:
2984:
2981:
2978:
2930:
2927:
2924:
2921:
2893:
2890:
2887:
2884:
2822:
2819:
2816:
2813:
2784:
2781:
2778:
2775:
2730:
2727:
2724:
2721:
2715:
2712:
2709:
2706:
2703:
2700:
2633:
2630:
2606:
2603:
2572:
2569:
2548:
2545:
2504:
2501:
2486:
2483:
2438:
2435:
2432:
2429:
2336:
2333:
2330:
2327:
2231:
2228:
2225:
2222:
2182:
2160:
2157:
2154:
2151:
2075:
2072:
2053:
2050:
2014:
2011:
2008:
2005:
1980:
1977:
1948:{\displaystyle {\frac {1}{3}}\pi }
1909:
1906:
1867:
1864:
1727:
1724:
1695:
1692:
1661:
1658:
1624:
1621:
1580:
1577:
1562:
1559:
1525:
1522:
1519:
1516:
1414:
1411:
1408:
1405:
1314:
1311:
1308:
1305:
1283:
1266:
1263:
1260:
1257:
1191:
1188:
1169:
1166:
1138:{\displaystyle {\frac {2}{3}}\pi }
1095:
1092:
1063:
1060:
1035:
1032:
1029:
1026:
997:
994:
965:
962:
959:
956:
843:
840:
837:
834:
813:
810:
807:
785:
782:
779:
776:
748:
745:
730:
727:
574:
571:
568:
565:
544:
541:
520:
517:
514:
511:
490:
487:
484:
25:
8102:
8081:Electric power systems components
7135:Insulated-gate bipolar transistor
6990:synchronous rectifier commutator.
6846:Cyclopedia of applied electricity
6292:-driven switches or motor-driven
5892:Tungar bulbs from 1917, 2 ampere
1918:{\displaystyle V_{\mathrm {av} }}
1876:{\displaystyle V_{\mathrm {LN} }}
1104:{\displaystyle V_{\mathrm {av} }}
1006:{\displaystyle V_{\mathrm {LN} }}
168:Electric power systems components
7379:Heterostructure barrier varactor
7106:Chemical field-effect transistor
6639:Sinclair, Ian Robertson (1987).
6520:. Sir I. Pitman & sons, ltd.
6093:, consists of a crystal of some
5819:
5799:
5419:Higher order and cascade filters
5306:
5207:
4035:(the divisors are 2 rather than
3878:
1886:
936:
319:signals. In gas heating systems
7427:Mixed-signal integrated circuit
6995:
6971:
6957:. CRC Press. pp. 145–146.
6919:
6904:
6853:
6817:
6795:
6749:
6736:
6710:
6531:Kimbark, Edward Wilson (1971).
6368:(point-contact rectifier, 1874)
6300:and synchronous rectification.
5716:
5457:
6557:
6524:
6482:
6442:
6426:
6399:
6234:gate turn-off thyristors (GTO)
6022:
5925:with an additional electrode.
5784:
5772:
5626:These consisted of a resonant
5137:
5129:
3810:Voltage-multiplying rectifiers
3661:
3655:
3538:
3526:
3130:
2859:
2692:
2560:
2474:
1969:
1645:
1546:
912:Three-phase, half-wave circuit
641:(RMS) value of output voltage.
13:
1:
6876:Sood, Vijay K (31 May 2004).
6392:
5499:Rectifiers are also used for
5336:, which may have significant
4993:Transformer utilization ratio
355:to produce a steady voltage.
282:silicon-controlled rectifiers
130:Electric power infrastructure
7458:Silicon controlled rectifier
7320:Organic light-emitting diode
7210:Diffused junction transistor
6978:Maurice Agnus Oudin (1907).
6910:H. P. Westman et al., (ed),
6742:H. P. Westman et al., (ed),
6406:Morris, Peter Robin (1990).
6314:optical heterodyne detection
6197:Silicon controlled rectifier
6161:Silicon and germanium diodes
5475:switched-mode power supplies
3870:Quantification of rectifiers
695:Full-wave rectifier using a
52:silicon controlled rectifier
7:
7262:Static induction transistor
7199:Bipolar junction transistor
7151:MOS field-effect transistor
7123:Fin field-effect transistor
6535:Direct current transmission
6451:Electrical Discharge Device
6354:
5676:A small motor-generator set
5393:{\displaystyle {\sqrt {2}}}
1834:high-voltage direct current
400:high-voltage direct current
309:high-voltage direct current
10:
8107:
7469:Static induction thyristor
6783:Hawkins, Nehemiah (1914).
6685:(expanded 12th ed.).
6588:POWER ELECTRONICS HANDBOOK
6567:, p. 14. 13, Newnes, 2002
6250:
6194:
6164:
6119:
6031:
5940:
5788:
5661:
5607:
5577:
5549:Rectification technologies
5461:
5355:
5196:
5193:Rectifier output smoothing
3841:switched-mode power supply
3819:
3813:
877:contained a single common
414:Rectifier circuits may be
36:
32:Rectifier (disambiguation)
29:
8086:Electric power conversion
8006:
7906:
7873:
7805:
7742:
7670:
7638:(Hexode, Heptode, Octode)
7576:
7508:
7390:Hybrid integrated circuit
7354:
7282:
7233:Light-emitting transistor
7187:
7069:
7058:
6930:. John Wiley & Sons.
6758:Power Engineering Journal
6591:. Elsevier. p. 153.
6226:voltage sourced converter
6110:miniaturized and improved
6010:used for power supply in
5937:Diode vacuum tube (valve)
5580:Synchronous rectification
699:transformer and 2 diodes.
394:, etc.) are widely used.
351:, possibly followed by a
96:Electric power conversion
82:Electric power conversion
7685:Backward-wave oscillator
7395:Light emitting capacitor
7251:Point-contact transistor
7221:Junction Gate FET (JFET)
6647:(illustrated ed.).
6296:have also been used for
6205:Two of three high-power
6061:in some of the earliest
5977:. The filament emitted
5965:, originally called the
5914:gas-filled electron tube
5539:Gate turn-off thyristors
5451:active voltage regulator
5410:Resistor as input filter
5028:VA rating of transformer
1883:, phase-shifted by 30°:
1799:Disassembled automobile
260:The process is known as
7696:Crossed-field amplifier
7215:Field-effect transistor
6514:Hendrik Rissik (1941).
6437:General Electric Review
6144:or copper oxide. While
6069:, to rectify the radio
6053:, the earliest type of
5904:Tungar rectifier was a
5884:Argon gas electron tube
5525:phase-fired controllers
5464:Capacitive power supply
2800:and is calculated with
646:Full-wave rectification
428:Half-wave rectification
423:Single-phase rectifiers
272:, stacks of copper and
7865:Voltage-regulator tube
7432:MOS integrated circuit
7297:Constant-current diode
7273:Unijunction transistor
6345:unimolecular rectifier
6266:
6214:
6180:
6133:
6091:cat's whisker detector
6046:
5952:
5897:
5767:electrolytic capacitor
5677:
5623:
5496:
5394:
5358:Capacitor-input filter
5352:Capacitor input filter
5295:
5275:
5153:Rectifier voltage drop
5144:
5062:
5036:
4983:
4856:
4742:
4605:
4496:
4427:
4314:
4206:
4134:
4029:
3889:is missing information
3851:
3831:
3799:
3778:
3768:
3752:
3742:
3729:is the direct current.
3701:
3548:
3386:
3276:
3153:
3089:
2832:
2794:
2740:
2657:
2643:
2458:
2024:
1949:
1919:
1877:
1848:
1815:bridge rectifier, six
1808:
1765:
1741:
1139:
1105:
1073:
1007:
975:
925:
889:Three-phase rectifiers
864:
700:
684:
668:, or four diodes in a
657:
593:
461:
268:, wet chemical cells,
101:HVDC converter station
59:
7934:Electrolytic detector
7707:Inductive output tube
7523:Low-dropout regulator
7438:Organic semiconductor
7369:Printed circuit board
7205:Darlington transistor
7052:Electronic components
6825:US patent 1671970
6791:. New York: T. Audel.
6732:(1): 1301–01 1301–11.
6687:Butterworth-Heinemann
6649:Industrial Press Inc.
6298:mechanical rectifiers
6260:
6204:
6174:
6129:
6079:Jagadish Chandra Bose
6042:Galena cat's whisker
6041:
5950:
5891:
5847:mercury-arc rectifier
5675:
5617:
5574:Synchronous rectifier
5560:Mechanical rectifiers
5494:
5426:series resonant choke
5395:
5293:
5272:
5174:diodes and 0.3 V for
5145:
5063:
5037:
4984:
4857:
4743:
4606:
4497:
4428:
4315:
4207:
4135:
4030:
3849:
3829:
3793:
3776:
3766:
3750:
3740:
3702:
3549:
3387:
3277:
3154:
3090:
2833:
2795:
2741:
2655:
2644:
2459:
2025:
1950:
1920:
1878:
1842:
1836:power transmission).
1798:
1759:
1742:
1140:
1106:
1074:
1008:
976:
919:
906:automobile alternator
865:
694:
682:
655:
594:
459:
274:selenium oxide plates
139:Electric power system
49:
7752:Beam deflection tube
7421:Metal oxide varistor
7314:Light-emitting diode
7168:Thin-film transistor
7129:Floating-gate MOSFET
6448:Dushman, S. (1915).
6432:Dushman, S. (1915).
6366:Karl Ferdinand Braun
6253:Active rectification
5943:List of vacuum tubes
5692:current, but rather
5610:Mechanical rectifier
5586:electric locomotives
5380:
5231:improve this section
5072:
5049:
5004:
4869:
4758:
4618:
4515:
4440:
4327:
4222:
4150:
4050:
3945:
3568:
3439:
3292:
3178:
3105:
2845:
2804:
2766:
2682:
2471:
2037:
1959:
1929:
1897:
1855:
1811:For an uncontrolled
1153:
1145:(from 30° to 150°):
1119:
1083:
1017:
985:
947:
714:
670:bridge configuration
471:
286:motor-generator sets
278:semiconductor diodes
30:For other uses, see
7728:Traveling-wave tube
7528:Switching regulator
7364:Printed electronics
7341:Step recovery diode
7118:Depletion-load NMOS
6770:10.1049/pe:19940407
6372:Precision rectifier
6146:selenium rectifiers
6055:semiconductor diode
6006:receivers, and the
5983:thermionic emission
5878:Nelson River Bipole
5863:flame rectification
5777:The development of
5759:lightning arresters
5746:aluminium hydroxide
5710:homopolar generator
5682:motor-generator set
5658:Motor-generator set
5604:Vibrating rectifier
5505:amplitude modulated
5185:Harmonic distortion
5134:For secondary coil.
3786:Twelve-pulse bridge
2663:common-mode voltage
2134:
1250:
930:harmonic distortion
439:single-phase supply
321:flame rectification
251:alternating current
8033:Crystal oscillator
7893:Variable capacitor
7568:Switched capacitor
7510:Voltage regulators
7384:Integrated circuit
7268:Tetrode transistor
7246:Pentode transistor
7239:Organic LET (OLET)
7226:Organic FET (OFET)
6951:Ali Emadi (2009).
6805:. Chestofbooks.com
6320:communication and
6267:
6215:
6181:
6134:
6131:Selenium rectifier
6047:
5953:
5951:Vacuum tube diodes
5898:
5704:windings, which a
5678:
5648:rectifier contacts
5624:
5497:
5433:Voltage regulators
5390:
5371:Choke input filter
5338:internal impedance
5296:
5276:
5140:
5061:{\displaystyle VA}
5058:
5032:
4979:
4852:
4738:
4601:
4492:
4423:
4310:
4202:
4130:
4025:
3852:
3832:
3816:Voltage multiplier
3800:
3779:
3769:
3753:
3743:
3697:
3557:The overlap angle
3544:
3382:
3272:
3149:
3085:
3083:
2828:
2790:
2736:
2658:
2639:
2454:
2452:
2106:
2020:
1945:
1915:
1873:
1849:
1830:aluminium smelting
1809:
1803:, showing the six
1782:mercury-arc valves
1766:
1737:
1735:
1222:
1135:
1101:
1069:
1003:
971:
926:
860:
858:
701:
685:
658:
589:
587:
462:
443:three-phase supply
410:Rectifier circuits
270:mercury-arc valves
266:vacuum tube diodes
111:DC-to-DC converter
106:AC-to-AC converter
60:
58:to dissipate heat.
8068:
8067:
8028:Ceramic resonator
7840:Mercury-arc valve
7792:Video camera tube
7744:Cathode-ray tubes
7504:
7503:
7112:Complementary MOS
6964:978-1-4398-0069-0
6937:978-0-470-68212-8
6893:978-1-4020-7890-3
6550:978-0-471-47580-4
6500:978-0-333-57351-8
6475:978-0-07-707714-3
6466:Power electronics
6419:978-0-86341-227-1
5995:All American Five
5923:incandescent lamp
5851:mercury-arc valve
5828:mercury-arc valve
5791:Mercury-arc valve
5751:breakdown voltage
5731:breakdown voltage
5684:, or the similar
5554:Electromechanical
5388:
5267:
5266:
5259:
5135:
5112:
5030:
5029:
5024:
5010:
4977:
4947:
4931:
4901:
4850:
4848:
4815:
4813:
4736:
4701:
4685:
4650:
4599:
4568:
4481:
4421:
4382:
4308:
4306:
4273:
4271:
4191:
4128:
4097:
4023:
3992:
3912:
3911:
3860:cathode ray tubes
3783:
3782:
3757:
3756:
3644:
3515:
3368:
3258:
3228:
3147:
3146:
3139:
3133:
3115:
3042:
3017:
2959:
2910:
2868:
2862:
2695:
2616:
2592:
2558:
2534:
2524:
2448:
2418:
2395:
2377:
2346:
2316:
2241:
2211:
2140:
2104:
2098:
1994:
1972:
1940:
1710:
1681:
1639:
1610:
1600:
1540:
1505:
1482:
1478:
1462:
1458:
1429:
1329:
1220:
1214:
1130:
1111:results from the
1049:
854:
853:
795:
583:
529:
372:thermionic diodes
366:Rectifier devices
353:voltage regulator
339:, which may be a
337:electronic filter
243:
242:
182:Grid-tie inverter
91:Voltage converter
75:Power engineering
16:(Redirected from
8098:
7922:electrical power
7807:Gas-filled tubes
7691:Cavity magnetron
7518:Linear regulator
7067:
7066:
7045:
7038:
7031:
7022:
7021:
7015:
7014:
7012:
7010:
6999:
6993:
6992:
6975:
6969:
6968:
6948:
6942:
6941:
6923:
6917:
6908:
6902:
6901:
6873:
6867:
6857:
6851:
6850:
6840:
6834:
6833:
6832:
6828:
6821:
6815:
6814:
6812:
6810:
6799:
6793:
6792:
6785:"54. Rectifiers"
6780:
6774:
6773:
6753:
6747:
6740:
6734:
6733:
6723:
6714:
6708:
6707:
6705:
6703:
6696:978-1-48310257-3
6689:. p. 2/42.
6676:
6670:
6669:
6667:
6665:
6658:978-0-83111000-0
6636:
6630:
6629:
6609:
6603:
6602:
6582:
6576:
6561:
6555:
6554:
6538:
6528:
6522:
6521:
6511:
6505:
6504:
6486:
6480:
6479:
6461:
6455:
6446:
6440:
6430:
6424:
6423:
6403:
6387:Warsaw rectifier
6382:Vienna rectifier
6349:organic molecule
6308:Current research
6247:Active rectifier
6177:bridge rectifier
6073:and extract the
6057:, was used as a
6051:crystal detector
6044:crystal detector
6034:Crystal detector
6028:Crystal detector
6000:cathode ray tube
5919:metal rectifiers
5902:General Electric
5823:
5803:
5741:orthophosphate.
5733:and the risk of
5727:The Boy Mechanic
5686:rotary converter
5668:Rotary converter
5636:battery chargers
5517:bridge rectifier
5399:
5397:
5396:
5391:
5389:
5384:
5310:
5262:
5255:
5251:
5248:
5242:
5211:
5203:
5149:
5147:
5146:
5141:
5136:
5133:
5128:
5127:
5126:
5114:
5113:
5105:
5101:
5100:
5099:
5067:
5065:
5064:
5059:
5041:
5039:
5038:
5033:
5031:
5027:
5026:
5025:
5022:
5016:
5011:
5008:
4988:
4986:
4985:
4980:
4978:
4973:
4972:
4971:
4970:
4948:
4943:
4937:
4932:
4927:
4926:
4925:
4924:
4902:
4897:
4891:
4886:
4885:
4884:
4861:
4859:
4858:
4853:
4851:
4849:
4844:
4842:
4841:
4840:
4821:
4816:
4814:
4809:
4807:
4806:
4805:
4786:
4775:
4774:
4773:
4747:
4745:
4744:
4739:
4737:
4735:
4727:
4726:
4725:
4724:
4702:
4697:
4691:
4686:
4684:
4676:
4675:
4674:
4673:
4651:
4646:
4640:
4635:
4634:
4633:
4610:
4608:
4607:
4602:
4600:
4595:
4594:
4593:
4574:
4569:
4564:
4563:
4562:
4543:
4532:
4531:
4530:
4501:
4499:
4498:
4493:
4482:
4480:
4479:
4478:
4465:
4464:
4463:
4450:
4432:
4430:
4429:
4424:
4422:
4417:
4416:
4415:
4414:
4388:
4383:
4378:
4377:
4376:
4375:
4349:
4344:
4343:
4342:
4319:
4317:
4316:
4311:
4309:
4307:
4302:
4300:
4299:
4298:
4279:
4274:
4272:
4267:
4265:
4264:
4263:
4244:
4239:
4238:
4237:
4211:
4209:
4208:
4203:
4192:
4190:
4189:
4188:
4175:
4174:
4173:
4160:
4139:
4137:
4136:
4131:
4129:
4124:
4123:
4122:
4103:
4098:
4093:
4092:
4091:
4072:
4067:
4066:
4065:
4041:
4040:
4034:
4032:
4031:
4026:
4024:
4019:
4018:
4017:
3998:
3993:
3988:
3987:
3986:
3967:
3962:
3961:
3960:
3924:Conversion ratio
3907:
3904:
3898:
3882:
3874:
3759:
3758:
3733:
3732:
3706:
3704:
3703:
3698:
3696:
3695:
3694:
3684:
3683:
3682:
3645:
3640:
3639:
3638:
3637:
3608:
3603:
3602:
3601:
3585:
3584:
3583:
3553:
3551:
3550:
3545:
3516:
3511:
3510:
3509:
3508:
3479:
3474:
3473:
3472:
3456:
3455:
3454:
3391:
3389:
3388:
3383:
3369:
3364:
3363:
3362:
3361:
3332:
3327:
3326:
3325:
3309:
3308:
3307:
3281:
3279:
3278:
3273:
3259:
3254:
3253:
3252:
3251:
3229:
3224:
3218:
3213:
3212:
3211:
3195:
3194:
3193:
3158:
3156:
3155:
3150:
3148:
3142:
3141:
3140:
3137:
3135:
3134:
3126:
3122:
3117:
3116:
3113:
3094:
3092:
3091:
3086:
3084:
3074:
3073:
3072:
3050:
3049:
3043:
3038:
3037:
3036:
3018:
3013:
3010:
3002:
3001:
2992:
2991:
2990:
2969:
2960:
2955:
2954:
2953:
2935:
2934:
2933:
2911:
2906:
2903:
2898:
2897:
2896:
2875:
2870:
2869:
2866:
2864:
2863:
2855:
2837:
2835:
2834:
2829:
2827:
2826:
2825:
2799:
2797:
2796:
2791:
2789:
2788:
2787:
2761:
2759:
2758:
2755:
2752:
2745:
2743:
2742:
2737:
2735:
2734:
2733:
2697:
2696:
2688:
2648:
2646:
2645:
2640:
2638:
2637:
2636:
2617:
2612:
2611:
2610:
2609:
2593:
2588:
2582:
2577:
2576:
2575:
2559:
2554:
2553:
2552:
2551:
2535:
2530:
2525:
2520:
2514:
2509:
2508:
2507:
2491:
2490:
2489:
2463:
2461:
2460:
2455:
2453:
2449:
2444:
2443:
2442:
2441:
2419:
2414:
2408:
2403:
2402:
2396:
2388:
2383:
2379:
2378:
2370:
2357:
2356:
2347:
2342:
2341:
2340:
2339:
2317:
2312:
2306:
2302:
2293:
2289:
2288:
2287:
2269:
2268:
2242:
2237:
2236:
2235:
2234:
2212:
2207:
2201:
2197:
2185:
2165:
2164:
2163:
2141:
2136:
2133:
2132:
2131:
2121:
2120:
2119:
2105:
2103:
2099:
2091:
2085:
2080:
2079:
2078:
2063:
2058:
2057:
2056:
2029:
2027:
2026:
2021:
2019:
2018:
2017:
1995:
1990:
1985:
1984:
1983:
1974:
1973:
1965:
1954:
1952:
1951:
1946:
1941:
1933:
1924:
1922:
1921:
1916:
1914:
1913:
1912:
1890:
1882:
1880:
1879:
1874:
1872:
1871:
1870:
1746:
1744:
1743:
1738:
1736:
1732:
1731:
1730:
1711:
1709:
1701:
1700:
1699:
1698:
1682:
1677:
1671:
1666:
1665:
1664:
1649:
1640:
1638:
1630:
1629:
1628:
1627:
1611:
1606:
1601:
1596:
1590:
1585:
1584:
1583:
1567:
1566:
1565:
1550:
1541:
1539:
1531:
1530:
1529:
1528:
1506:
1501:
1495:
1490:
1489:
1483:
1474:
1473:
1468:
1464:
1463:
1454:
1453:
1440:
1439:
1430:
1428:
1420:
1419:
1418:
1417:
1394:
1390:
1381:
1377:
1376:
1375:
1357:
1356:
1330:
1328:
1320:
1319:
1318:
1317:
1294:
1286:
1271:
1270:
1269:
1249:
1248:
1247:
1237:
1236:
1235:
1221:
1219:
1215:
1207:
1201:
1196:
1195:
1194:
1179:
1174:
1173:
1172:
1144:
1142:
1141:
1136:
1131:
1123:
1110:
1108:
1107:
1102:
1100:
1099:
1098:
1078:
1076:
1075:
1070:
1068:
1067:
1066:
1050:
1045:
1040:
1039:
1038:
1012:
1010:
1009:
1004:
1002:
1001:
1000:
980:
978:
977:
972:
970:
969:
968:
943:The peak values
940:
869:
867:
866:
861:
859:
855:
849:
848:
847:
846:
827:
818:
817:
816:
796:
791:
790:
789:
788:
762:
753:
752:
751:
735:
734:
733:
639:root mean square
598:
596:
595:
590:
588:
584:
579:
578:
577:
558:
549:
548:
547:
530:
525:
524:
523:
504:
495:
494:
493:
441:, or three in a
235:
228:
221:
207:Protective relay
62:
61:
21:
8106:
8105:
8101:
8100:
8099:
8097:
8096:
8095:
8071:
8070:
8069:
8064:
8002:
7917:audio and video
7902:
7869:
7801:
7738:
7666:
7647:Photomultiplier
7572:
7500:
7448:Quantum circuit
7356:
7350:
7292:Avalanche diode
7278:
7190:
7183:
7072:
7061:
7054:
7049:
7019:
7018:
7008:
7006:
7000:
6996:
6976:
6972:
6965:
6949:
6945:
6938:
6924:
6920:
6909:
6905:
6894:
6884:Springer-Verlag
6874:
6870:
6858:
6854:
6841:
6837:
6830:
6822:
6818:
6808:
6806:
6801:
6800:
6796:
6781:
6777:
6754:
6750:
6741:
6737:
6721:
6715:
6711:
6701:
6699:
6697:
6677:
6673:
6663:
6661:
6659:
6641:"Rectification"
6637:
6633:
6626:
6610:
6606:
6599:
6583:
6579:
6562:
6558:
6551:
6529:
6525:
6512:
6508:
6501:
6487:
6483:
6476:
6462:
6458:
6447:
6443:
6431:
6427:
6420:
6404:
6400:
6395:
6357:
6310:
6255:
6249:
6199:
6193:
6169:
6163:
6124:
6122:Metal rectifier
6118:
6063:radio receivers
6036:
6030:
6025:
5945:
5939:
5886:
5843:
5842:
5841:
5840:
5839:
5824:
5816:
5815:
5804:
5793:
5787:
5775:
5719:
5670:
5664:Motor-generator
5662:Main articles:
5660:
5612:
5606:
5598:traction motors
5582:
5576:
5556:
5551:
5543:traction motors
5466:
5460:
5435:
5421:
5412:
5383:
5381:
5378:
5377:
5373:
5360:
5354:
5340:in the form of
5304:
5263:
5252:
5246:
5243:
5228:
5212:
5201:
5195:
5187:
5176:Schottky diodes
5155:
5132:
5116:
5115:
5104:
5103:
5102:
5089:
5088:
5084:
5073:
5070:
5069:
5050:
5047:
5046:
5021:
5017:
5015:
5007:
5005:
5002:
5001:
4995:
4957:
4956:
4952:
4942:
4938:
4936:
4911:
4910:
4906:
4896:
4892:
4890:
4877:
4876:
4872:
4870:
4867:
4866:
4843:
4827:
4826:
4822:
4820:
4808:
4792:
4791:
4787:
4785:
4766:
4765:
4761:
4759:
4756:
4755:
4728:
4711:
4710:
4706:
4696:
4692:
4690:
4677:
4660:
4659:
4655:
4645:
4641:
4639:
4626:
4625:
4621:
4619:
4616:
4615:
4580:
4579:
4575:
4573:
4549:
4548:
4544:
4542:
4523:
4522:
4518:
4516:
4513:
4512:
4471:
4470:
4466:
4456:
4455:
4451:
4449:
4441:
4438:
4437:
4401:
4400:
4396:
4389:
4387:
4362:
4361:
4357:
4350:
4348:
4335:
4334:
4330:
4328:
4325:
4324:
4301:
4285:
4284:
4280:
4278:
4266:
4250:
4249:
4245:
4243:
4230:
4229:
4225:
4223:
4220:
4219:
4181:
4180:
4176:
4166:
4165:
4161:
4159:
4151:
4148:
4147:
4109:
4108:
4104:
4102:
4078:
4077:
4073:
4071:
4058:
4057:
4053:
4051:
4048:
4047:
4038:
4036:
4004:
4003:
3999:
3997:
3973:
3972:
3968:
3966:
3953:
3952:
3948:
3946:
3943:
3942:
3933:
3926:
3919:
3908:
3902:
3899:
3892:
3883:
3872:
3824:
3822:Voltage doubler
3818:
3812:
3788:
3728:
3719:
3690:
3689:
3685:
3678:
3677:
3673:
3618:
3617:
3613:
3609:
3607:
3594:
3593:
3589:
3576:
3575:
3571:
3569:
3566:
3565:
3489:
3488:
3484:
3480:
3478:
3465:
3464:
3460:
3447:
3446:
3442:
3440:
3437:
3436:
3413:
3404:
3342:
3341:
3337:
3333:
3331:
3318:
3317:
3313:
3300:
3299:
3295:
3293:
3290:
3289:
3238:
3237:
3233:
3223:
3219:
3217:
3204:
3203:
3199:
3186:
3185:
3181:
3179:
3176:
3175:
3169:
3136:
3125:
3124:
3123:
3121:
3112:
3108:
3106:
3103:
3102:
3082:
3081:
3059:
3058:
3054:
3045:
3044:
3032:
3028:
3012:
3011:
3009:
2997:
2996:
2977:
2976:
2972:
2970:
2968:
2962:
2961:
2949:
2945:
2920:
2919:
2915:
2905:
2904:
2902:
2883:
2882:
2878:
2876:
2874:
2865:
2854:
2853:
2852:
2848:
2846:
2843:
2842:
2812:
2811:
2807:
2805:
2802:
2801:
2774:
2773:
2769:
2767:
2764:
2763:
2756:
2753:
2750:
2749:
2747:
2699:
2698:
2687:
2686:
2685:
2683:
2680:
2679:
2629:
2628:
2624:
2602:
2601:
2597:
2587:
2583:
2581:
2568:
2567:
2563:
2544:
2543:
2539:
2529:
2519:
2515:
2513:
2500:
2499:
2495:
2482:
2481:
2477:
2472:
2469:
2468:
2451:
2450:
2428:
2427:
2423:
2413:
2409:
2407:
2398:
2397:
2387:
2369:
2365:
2361:
2352:
2351:
2326:
2325:
2321:
2311:
2307:
2305:
2303:
2301:
2295:
2294:
2283:
2279:
2264:
2260:
2250:
2246:
2221:
2220:
2216:
2206:
2202:
2200:
2198:
2196:
2190:
2189:
2181:
2150:
2149:
2145:
2135:
2127:
2123:
2122:
2115:
2111:
2110:
2090:
2089:
2084:
2071:
2070:
2066:
2064:
2062:
2049:
2048:
2044:
2040:
2038:
2035:
2034:
2004:
2003:
1999:
1989:
1976:
1975:
1964:
1963:
1962:
1960:
1957:
1956:
1932:
1930:
1927:
1926:
1905:
1904:
1900:
1898:
1895:
1894:
1863:
1862:
1858:
1856:
1853:
1852:
1793:
1754:
1749:
1734:
1733:
1723:
1722:
1718:
1702:
1691:
1690:
1686:
1676:
1672:
1670:
1657:
1656:
1652:
1650:
1648:
1642:
1641:
1631:
1620:
1619:
1615:
1605:
1595:
1591:
1589:
1576:
1575:
1571:
1558:
1557:
1553:
1551:
1549:
1543:
1542:
1532:
1515:
1514:
1510:
1500:
1496:
1494:
1485:
1484:
1472:
1452:
1448:
1444:
1435:
1434:
1421:
1404:
1403:
1399:
1395:
1393:
1391:
1389:
1383:
1382:
1371:
1367:
1352:
1348:
1338:
1334:
1321:
1304:
1303:
1299:
1295:
1293:
1282:
1256:
1255:
1251:
1243:
1239:
1238:
1231:
1227:
1226:
1206:
1205:
1200:
1187:
1186:
1182:
1180:
1178:
1165:
1164:
1160:
1156:
1154:
1151:
1150:
1122:
1120:
1117:
1116:
1091:
1090:
1086:
1084:
1081:
1080:
1059:
1058:
1054:
1044:
1025:
1024:
1020:
1018:
1015:
1014:
993:
992:
988:
986:
983:
982:
955:
954:
950:
948:
945:
944:
914:
891:
857:
856:
833:
832:
828:
826:
819:
806:
805:
801:
798:
797:
775:
774:
770:
763:
761:
754:
744:
743:
739:
726:
725:
721:
717:
715:
712:
711:
648:
636:
627:
618:
611:
586:
585:
564:
563:
559:
557:
550:
540:
539:
535:
532:
531:
510:
509:
505:
503:
496:
483:
482:
478:
474:
472:
469:
468:
430:
425:
412:
392:Schottky diodes
388:junction diodes
384:audio equipment
376:metal rectifier
368:
239:
159:Demand response
149:Electrical grid
42:
35:
28:
23:
22:
15:
12:
11:
5:
8104:
8094:
8093:
8088:
8083:
8066:
8065:
8063:
8062:
8061:
8060:
8055:
8045:
8040:
8035:
8030:
8025:
8024:
8023:
8012:
8010:
8004:
8003:
8001:
8000:
7999:
7998:
7996:Wollaston wire
7988:
7983:
7978:
7973:
7968:
7963:
7962:
7961:
7956:
7946:
7941:
7936:
7931:
7930:
7929:
7924:
7919:
7910:
7908:
7904:
7903:
7901:
7900:
7895:
7890:
7889:
7888:
7877:
7875:
7871:
7870:
7868:
7867:
7862:
7857:
7852:
7847:
7842:
7837:
7832:
7827:
7822:
7817:
7811:
7809:
7803:
7802:
7800:
7799:
7794:
7789:
7784:
7779:
7777:Selectron tube
7774:
7769:
7767:Magic eye tube
7764:
7759:
7754:
7748:
7746:
7740:
7739:
7737:
7736:
7731:
7725:
7720:
7715:
7710:
7704:
7699:
7693:
7688:
7681:
7679:
7668:
7667:
7665:
7664:
7659:
7654:
7649:
7644:
7639:
7633:
7628:
7623:
7618:
7613:
7608:
7603:
7598:
7593:
7588:
7582:
7580:
7574:
7573:
7571:
7570:
7565:
7560:
7555:
7550:
7545:
7540:
7535:
7530:
7525:
7520:
7514:
7512:
7506:
7505:
7502:
7501:
7499:
7498:
7493:
7488:
7483:
7478:
7472:
7466:
7461:
7455:
7450:
7445:
7440:
7435:
7429:
7424:
7418:
7413:
7408:
7403:
7398:
7392:
7387:
7381:
7376:
7371:
7366:
7360:
7358:
7352:
7351:
7349:
7348:
7343:
7338:
7336:Schottky diode
7333:
7328:
7323:
7317:
7311:
7305:
7300:
7294:
7288:
7286:
7280:
7279:
7277:
7276:
7270:
7265:
7259:
7253:
7248:
7243:
7242:
7241:
7230:
7229:
7228:
7223:
7212:
7207:
7202:
7195:
7193:
7185:
7184:
7182:
7181:
7176:
7171:
7165:
7160:
7154:
7148:
7143:
7138:
7132:
7126:
7120:
7115:
7109:
7103:
7098:
7093:
7088:
7083:
7077:
7075:
7064:
7056:
7055:
7048:
7047:
7040:
7033:
7025:
7017:
7016:
6994:
6970:
6963:
6943:
6936:
6918:
6903:
6892:
6868:
6852:
6835:
6816:
6794:
6775:
6748:
6735:
6709:
6695:
6671:
6657:
6631:
6624:
6604:
6597:
6577:
6556:
6549:
6523:
6506:
6499:
6481:
6474:
6456:
6441:
6425:
6418:
6412:. p. 18.
6397:
6396:
6394:
6391:
6390:
6389:
6384:
6379:
6374:
6369:
6363:
6356:
6353:
6309:
6306:
6288:Historically,
6251:Main article:
6248:
6245:
6211:Manitoba Hydro
6195:Main article:
6192:
6189:
6165:Main article:
6162:
6159:
6140:properties of
6120:Main article:
6117:
6114:
6095:semiconducting
6067:crystal radios
6032:Main article:
6029:
6026:
6024:
6021:
5938:
5935:
5908:(ex.:5B24) or
5885:
5882:
5875:Manitoba Hydro
5832:Manitoba Hydro
5825:
5818:
5817:
5814:rectifier tube
5805:
5798:
5797:
5796:
5795:
5794:
5789:Main article:
5786:
5783:
5774:
5771:
5735:electric shock
5718:
5715:
5659:
5656:
5644:magnetic field
5608:Main article:
5605:
5602:
5578:Main article:
5575:
5572:
5555:
5552:
5550:
5547:
5471:power supplies
5459:
5456:
5434:
5431:
5420:
5417:
5411:
5408:
5387:
5372:
5369:
5356:Main article:
5353:
5350:
5303:
5300:
5265:
5264:
5215:
5213:
5206:
5194:
5191:
5186:
5183:
5154:
5151:
5139:
5131:
5125:
5122:
5119:
5111:
5108:
5098:
5095:
5092:
5087:
5083:
5080:
5077:
5057:
5054:
5043:
5042:
5020:
5014:
4994:
4991:
4990:
4989:
4976:
4969:
4966:
4963:
4960:
4955:
4951:
4946:
4941:
4935:
4930:
4923:
4920:
4917:
4914:
4909:
4905:
4900:
4895:
4889:
4883:
4880:
4875:
4863:
4862:
4847:
4839:
4836:
4833:
4830:
4825:
4819:
4812:
4804:
4801:
4798:
4795:
4790:
4784:
4781:
4778:
4772:
4769:
4764:
4749:
4748:
4734:
4731:
4723:
4720:
4717:
4714:
4709:
4705:
4700:
4695:
4689:
4683:
4680:
4672:
4669:
4666:
4663:
4658:
4654:
4649:
4644:
4638:
4632:
4629:
4624:
4612:
4611:
4598:
4592:
4589:
4586:
4583:
4578:
4572:
4567:
4561:
4558:
4555:
4552:
4547:
4541:
4538:
4535:
4529:
4526:
4521:
4503:
4502:
4491:
4488:
4485:
4477:
4474:
4469:
4462:
4459:
4454:
4448:
4445:
4434:
4433:
4420:
4413:
4410:
4407:
4404:
4399:
4395:
4392:
4386:
4381:
4374:
4371:
4368:
4365:
4360:
4356:
4353:
4347:
4341:
4338:
4333:
4321:
4320:
4305:
4297:
4294:
4291:
4288:
4283:
4277:
4270:
4262:
4259:
4256:
4253:
4248:
4242:
4236:
4233:
4228:
4213:
4212:
4201:
4198:
4195:
4187:
4184:
4179:
4172:
4169:
4164:
4158:
4155:
4141:
4140:
4127:
4121:
4118:
4115:
4112:
4107:
4101:
4096:
4090:
4087:
4084:
4081:
4076:
4070:
4064:
4061:
4056:
4044:
4043:
4022:
4016:
4013:
4010:
4007:
4002:
3996:
3991:
3985:
3982:
3979:
3976:
3971:
3965:
3959:
3956:
3951:
3929:
3925:
3922:
3915:
3910:
3909:
3886:
3884:
3877:
3871:
3868:
3814:Main article:
3811:
3808:
3787:
3784:
3781:
3780:
3770:
3755:
3754:
3744:
3731:
3730:
3726:
3721:
3717:
3708:
3707:
3693:
3688:
3681:
3676:
3672:
3669:
3666:
3663:
3660:
3657:
3654:
3651:
3648:
3643:
3636:
3633:
3630:
3627:
3624:
3621:
3616:
3612:
3606:
3600:
3597:
3592:
3588:
3582:
3579:
3574:
3555:
3554:
3543:
3540:
3537:
3534:
3531:
3528:
3525:
3522:
3519:
3514:
3507:
3504:
3501:
3498:
3495:
3492:
3487:
3483:
3477:
3471:
3468:
3463:
3459:
3453:
3450:
3445:
3422:
3421:
3415:
3411:
3406:
3402:
3393:
3392:
3381:
3378:
3375:
3372:
3367:
3360:
3357:
3354:
3351:
3348:
3345:
3340:
3336:
3330:
3324:
3321:
3316:
3312:
3306:
3303:
3298:
3283:
3282:
3271:
3268:
3265:
3262:
3257:
3250:
3247:
3244:
3241:
3236:
3232:
3227:
3222:
3216:
3210:
3207:
3202:
3198:
3192:
3189:
3184:
3168:
3165:
3160:
3159:
3145:
3132:
3129:
3120:
3111:
3096:
3095:
3080:
3077:
3071:
3068:
3065:
3062:
3057:
3053:
3048:
3041:
3035:
3031:
3027:
3024:
3021:
3016:
3008:
3005:
3000:
2995:
2989:
2986:
2983:
2980:
2975:
2971:
2967:
2964:
2963:
2958:
2952:
2948:
2944:
2941:
2938:
2932:
2929:
2926:
2923:
2918:
2914:
2909:
2901:
2895:
2892:
2889:
2886:
2881:
2877:
2873:
2861:
2858:
2851:
2850:
2824:
2821:
2818:
2815:
2810:
2786:
2783:
2780:
2777:
2772:
2732:
2729:
2726:
2723:
2720:
2717:
2714:
2711:
2708:
2705:
2702:
2694:
2691:
2650:
2649:
2635:
2632:
2627:
2623:
2620:
2615:
2608:
2605:
2600:
2596:
2591:
2586:
2580:
2574:
2571:
2566:
2562:
2557:
2550:
2547:
2542:
2538:
2533:
2528:
2523:
2518:
2512:
2506:
2503:
2498:
2494:
2488:
2485:
2480:
2476:
2465:
2464:
2447:
2440:
2437:
2434:
2431:
2426:
2422:
2417:
2412:
2406:
2401:
2394:
2391:
2386:
2382:
2376:
2373:
2368:
2364:
2360:
2355:
2350:
2345:
2338:
2335:
2332:
2329:
2324:
2320:
2315:
2310:
2304:
2300:
2297:
2296:
2292:
2286:
2282:
2278:
2275:
2272:
2267:
2263:
2259:
2256:
2253:
2249:
2245:
2240:
2233:
2230:
2227:
2224:
2219:
2215:
2210:
2205:
2199:
2195:
2192:
2191:
2188:
2184:
2180:
2177:
2174:
2171:
2168:
2162:
2159:
2156:
2153:
2148:
2144:
2139:
2130:
2126:
2118:
2114:
2109:
2102:
2097:
2094:
2088:
2083:
2077:
2074:
2069:
2065:
2061:
2055:
2052:
2047:
2043:
2042:
2016:
2013:
2010:
2007:
2002:
1998:
1993:
1988:
1982:
1979:
1971:
1968:
1944:
1939:
1936:
1911:
1908:
1903:
1869:
1866:
1861:
1792:
1789:
1753:
1750:
1748:
1747:
1729:
1726:
1721:
1717:
1714:
1708:
1705:
1697:
1694:
1689:
1685:
1680:
1675:
1669:
1663:
1660:
1655:
1651:
1647:
1644:
1643:
1637:
1634:
1626:
1623:
1618:
1614:
1609:
1604:
1599:
1594:
1588:
1582:
1579:
1574:
1570:
1564:
1561:
1556:
1552:
1548:
1545:
1544:
1538:
1535:
1527:
1524:
1521:
1518:
1513:
1509:
1504:
1499:
1493:
1488:
1481:
1477:
1471:
1467:
1461:
1457:
1451:
1447:
1443:
1438:
1433:
1427:
1424:
1416:
1413:
1410:
1407:
1402:
1398:
1392:
1388:
1385:
1384:
1380:
1374:
1370:
1366:
1363:
1360:
1355:
1351:
1347:
1344:
1341:
1337:
1333:
1327:
1324:
1316:
1313:
1310:
1307:
1302:
1298:
1292:
1289:
1285:
1280:
1277:
1274:
1268:
1265:
1262:
1259:
1254:
1246:
1242:
1234:
1230:
1225:
1218:
1213:
1210:
1204:
1199:
1193:
1190:
1185:
1181:
1177:
1171:
1168:
1163:
1159:
1158:
1147:
1134:
1129:
1126:
1097:
1094:
1089:
1065:
1062:
1057:
1053:
1048:
1043:
1037:
1034:
1031:
1028:
1023:
999:
996:
991:
967:
964:
961:
958:
953:
913:
910:
890:
887:
871:
870:
852:
845:
842:
839:
836:
831:
825:
822:
820:
815:
812:
809:
804:
800:
799:
794:
787:
784:
781:
778:
773:
769:
766:
760:
757:
755:
750:
747:
742:
738:
732:
729:
724:
720:
719:
662:absolute value
647:
644:
643:
642:
634:
629:
625:
620:
616:
609:
600:
599:
582:
576:
573:
570:
567:
562:
556:
553:
551:
546:
543:
538:
534:
533:
528:
522:
519:
516:
513:
508:
502:
499:
497:
492:
489:
486:
481:
477:
476:
429:
426:
424:
421:
411:
408:
367:
364:
305:power supplies
290:crystal radios
255:direct current
241:
240:
238:
237:
230:
223:
215:
212:
211:
210:
209:
204:
199:
194:
189:
187:Energy storage
184:
179:
177:Ring main unit
171:
170:
164:
163:
162:
161:
156:
154:Interconnector
151:
146:
141:
133:
132:
126:
125:
124:
123:
118:
113:
108:
103:
98:
93:
85:
84:
78:
77:
71:
70:
26:
9:
6:
4:
3:
2:
8103:
8092:
8089:
8087:
8084:
8082:
8079:
8078:
8076:
8059:
8058:mercury relay
8056:
8054:
8051:
8050:
8049:
8046:
8044:
8041:
8039:
8036:
8034:
8031:
8029:
8026:
8022:
8019:
8018:
8017:
8014:
8013:
8011:
8009:
8005:
7997:
7994:
7993:
7992:
7989:
7987:
7984:
7982:
7979:
7977:
7974:
7972:
7969:
7967:
7964:
7960:
7957:
7955:
7952:
7951:
7950:
7947:
7945:
7942:
7940:
7937:
7935:
7932:
7928:
7925:
7923:
7920:
7918:
7915:
7914:
7912:
7911:
7909:
7905:
7899:
7896:
7894:
7891:
7887:
7884:
7883:
7882:
7881:Potentiometer
7879:
7878:
7876:
7872:
7866:
7863:
7861:
7858:
7856:
7853:
7851:
7848:
7846:
7843:
7841:
7838:
7836:
7833:
7831:
7828:
7826:
7823:
7821:
7818:
7816:
7813:
7812:
7810:
7808:
7804:
7798:
7797:Williams tube
7795:
7793:
7790:
7788:
7785:
7783:
7780:
7778:
7775:
7773:
7770:
7768:
7765:
7763:
7760:
7758:
7755:
7753:
7750:
7749:
7747:
7745:
7741:
7735:
7732:
7729:
7726:
7724:
7721:
7719:
7716:
7714:
7711:
7708:
7705:
7703:
7700:
7697:
7694:
7692:
7689:
7686:
7683:
7682:
7680:
7677:
7673:
7669:
7663:
7660:
7658:
7655:
7653:
7650:
7648:
7645:
7643:
7640:
7637:
7634:
7632:
7629:
7627:
7624:
7622:
7619:
7617:
7616:Fleming valve
7614:
7612:
7609:
7607:
7604:
7602:
7599:
7597:
7594:
7592:
7589:
7587:
7584:
7583:
7581:
7579:
7575:
7569:
7566:
7564:
7561:
7559:
7556:
7554:
7551:
7549:
7546:
7544:
7541:
7539:
7536:
7534:
7531:
7529:
7526:
7524:
7521:
7519:
7516:
7515:
7513:
7511:
7507:
7497:
7494:
7492:
7489:
7487:
7484:
7482:
7479:
7476:
7473:
7470:
7467:
7465:
7462:
7459:
7456:
7454:
7451:
7449:
7446:
7444:
7443:Photodetector
7441:
7439:
7436:
7433:
7430:
7428:
7425:
7422:
7419:
7417:
7414:
7412:
7411:Memtransistor
7409:
7407:
7404:
7402:
7399:
7396:
7393:
7391:
7388:
7385:
7382:
7380:
7377:
7375:
7372:
7370:
7367:
7365:
7362:
7361:
7359:
7353:
7347:
7344:
7342:
7339:
7337:
7334:
7332:
7329:
7327:
7324:
7321:
7318:
7315:
7312:
7309:
7306:
7304:
7301:
7298:
7295:
7293:
7290:
7289:
7287:
7285:
7281:
7274:
7271:
7269:
7266:
7263:
7260:
7257:
7254:
7252:
7249:
7247:
7244:
7240:
7237:
7236:
7234:
7231:
7227:
7224:
7222:
7219:
7218:
7216:
7213:
7211:
7208:
7206:
7203:
7200:
7197:
7196:
7194:
7192:
7186:
7180:
7177:
7175:
7172:
7169:
7166:
7164:
7161:
7158:
7155:
7152:
7149:
7147:
7144:
7142:
7139:
7136:
7133:
7130:
7127:
7124:
7121:
7119:
7116:
7113:
7110:
7107:
7104:
7102:
7099:
7097:
7094:
7092:
7089:
7087:
7084:
7082:
7079:
7078:
7076:
7074:
7068:
7065:
7063:
7060:Semiconductor
7057:
7053:
7046:
7041:
7039:
7034:
7032:
7027:
7026:
7023:
7005:
6998:
6991:
6987:
6983:
6982:
6974:
6966:
6960:
6956:
6955:
6947:
6939:
6933:
6929:
6922:
6915:
6914:
6907:
6900:
6895:
6889:
6886:. p. 1.
6885:
6881:
6880:
6872:
6866:
6862:
6856:
6848:
6847:
6839:
6826:
6820:
6804:
6798:
6790:
6786:
6779:
6771:
6767:
6763:
6759:
6752:
6745:
6739:
6731:
6727:
6720:
6713:
6698:
6692:
6688:
6684:
6683:
6675:
6660:
6654:
6651:p. 151.
6650:
6646:
6642:
6635:
6627:
6625:9788184312928
6621:
6617:
6616:
6608:
6600:
6598:9780123820372
6594:
6590:
6589:
6581:
6574:
6573:0-7506-7291-9
6570:
6566:
6560:
6552:
6546:
6542:
6537:
6536:
6527:
6519:
6518:
6510:
6502:
6496:
6492:
6485:
6477:
6471:
6467:
6460:
6453:
6452:
6445:
6438:
6435:
6429:
6421:
6415:
6411:
6410:
6402:
6398:
6388:
6385:
6383:
6380:
6378:
6375:
6373:
6370:
6367:
6364:
6362:
6359:
6358:
6352:
6350:
6346:
6341:
6339:
6335:
6331:
6327:
6323:
6322:atomic clocks
6319:
6318:optical fiber
6315:
6305:
6301:
6299:
6295:
6291:
6286:
6284:
6280:
6279:power MOSFETs
6276:
6272:
6264:
6259:
6254:
6244:
6242:
6237:
6235:
6231:
6227:
6222:
6220:
6212:
6208:
6203:
6198:
6188:
6185:
6178:
6173:
6168:
6158:
6156:
6150:
6147:
6143:
6139:
6138:semiconductor
6132:
6128:
6123:
6113:
6111:
6107:
6103:
6099:
6096:
6092:
6088:
6084:
6083:G. W. Pickard
6080:
6076:
6072:
6068:
6064:
6060:
6056:
6052:
6045:
6040:
6035:
6020:
6017:
6013:
6009:
6005:
6001:
5996:
5991:
5988:
5987:Thomas Edison
5984:
5980:
5976:
5972:
5968:
5967:Fleming valve
5964:
5961:
5958:
5949:
5944:
5934:
5931:
5926:
5924:
5920:
5915:
5911:
5907:
5906:mercury vapor
5903:
5895:
5890:
5881:
5879:
5876:
5872:
5866:
5864:
5860:
5856:
5852:
5848:
5837:
5833:
5829:
5822:
5813:
5812:mercury vapor
5809:
5802:
5792:
5782:
5780:
5770:
5768:
5763:
5760:
5755:
5752:
5747:
5742:
5738:
5736:
5732:
5728:
5724:
5714:
5711:
5707:
5703:
5699:
5695:
5691:
5687:
5683:
5674:
5669:
5665:
5655:
5653:
5649:
5645:
5641:
5637:
5633:
5632:electromagnet
5629:
5621:
5616:
5611:
5601:
5599:
5595:
5591:
5587:
5581:
5571:
5569:
5563:
5561:
5546:
5544:
5540:
5536:
5535:rolling stock
5533:
5528:
5526:
5522:
5518:
5514:
5509:
5506:
5502:
5493:
5489:
5487:
5483:
5478:
5476:
5472:
5465:
5455:
5452:
5447:
5444:
5439:
5430:
5427:
5416:
5407:
5404:
5385:
5368:
5366:
5359:
5349:
5347:
5343:
5339:
5335:
5330:
5327:
5324:
5320:
5316:
5311:
5309:
5299:
5292:
5288:
5286:
5281:
5271:
5261:
5258:
5250:
5240:
5236:
5232:
5226:
5225:
5221:
5216:This section
5214:
5210:
5205:
5204:
5200:
5190:
5182:
5179:
5177:
5173:
5168:
5166:
5161:
5160:
5150:
5109:
5106:
5085:
5081:
5078:
5075:
5055:
5052:
5018:
5012:
5000:
4999:
4998:
4974:
4953:
4949:
4944:
4939:
4933:
4928:
4907:
4903:
4898:
4893:
4887:
4873:
4865:
4864:
4845:
4823:
4817:
4810:
4788:
4782:
4779:
4776:
4762:
4754:
4753:
4752:
4732:
4729:
4707:
4703:
4698:
4693:
4687:
4681:
4678:
4656:
4652:
4647:
4642:
4636:
4622:
4614:
4613:
4596:
4576:
4570:
4565:
4545:
4539:
4536:
4533:
4519:
4511:
4510:
4509:
4506:
4486:
4483:
4467:
4452:
4446:
4443:
4436:
4435:
4418:
4397:
4393:
4390:
4384:
4379:
4358:
4354:
4351:
4345:
4331:
4323:
4322:
4303:
4281:
4275:
4268:
4246:
4240:
4226:
4218:
4217:
4216:
4196:
4193:
4177:
4162:
4156:
4153:
4146:
4145:
4144:
4125:
4105:
4099:
4094:
4074:
4068:
4054:
4046:
4045:
4020:
4000:
3994:
3989:
3969:
3963:
3949:
3941:
3940:
3939:
3936:
3932:
3921:
3918:
3906:
3896:
3890:
3887:This section
3885:
3881:
3876:
3875:
3867:
3865:
3861:
3857:
3848:
3844:
3842:
3836:
3828:
3823:
3817:
3807:
3804:
3797:
3792:
3775:
3771:
3765:
3761:
3760:
3749:
3745:
3739:
3735:
3734:
3725:
3722:
3716:
3713:
3712:
3711:
3686:
3674:
3670:
3667:
3664:
3658:
3652:
3649:
3646:
3641:
3614:
3610:
3604:
3590:
3586:
3572:
3564:
3563:
3562:
3560:
3541:
3535:
3532:
3529:
3523:
3520:
3517:
3512:
3485:
3481:
3475:
3461:
3457:
3443:
3435:
3434:
3433:
3430:
3426:
3419:
3416:
3410:
3407:
3401:
3398:
3397:
3396:
3379:
3376:
3373:
3370:
3365:
3338:
3334:
3328:
3314:
3310:
3296:
3288:
3287:
3286:
3269:
3266:
3263:
3260:
3255:
3234:
3230:
3225:
3220:
3214:
3200:
3196:
3182:
3174:
3173:
3172:
3164:
3143:
3127:
3118:
3109:
3101:
3100:
3099:
3078:
3075:
3055:
3051:
3039:
3033:
3029:
3025:
3022:
3019:
3014:
3006:
3003:
2993:
2973:
2965:
2956:
2950:
2946:
2942:
2939:
2936:
2916:
2912:
2907:
2899:
2879:
2871:
2856:
2841:
2840:
2839:
2808:
2770:
2718:
2689:
2675:
2672:
2668:
2664:
2654:
2625:
2621:
2618:
2613:
2598:
2594:
2589:
2584:
2578:
2564:
2555:
2540:
2536:
2531:
2526:
2521:
2516:
2510:
2496:
2492:
2478:
2467:
2466:
2445:
2424:
2420:
2415:
2410:
2404:
2392:
2389:
2384:
2380:
2374:
2371:
2366:
2362:
2358:
2348:
2343:
2322:
2318:
2313:
2308:
2298:
2290:
2284:
2280:
2276:
2273:
2270:
2265:
2261:
2257:
2254:
2251:
2247:
2243:
2238:
2217:
2213:
2208:
2203:
2193:
2186:
2178:
2175:
2172:
2169:
2166:
2146:
2142:
2137:
2128:
2124:
2116:
2112:
2107:
2100:
2095:
2092:
2086:
2081:
2067:
2059:
2045:
2033:
2032:
2031:
2000:
1996:
1991:
1986:
1966:
1942:
1937:
1934:
1901:
1891:
1889:
1884:
1859:
1846:
1841:
1837:
1835:
1831:
1825:
1821:
1818:
1814:
1806:
1802:
1797:
1788:
1785:
1783:
1779:
1774:
1772:
1763:
1758:
1719:
1715:
1712:
1706:
1703:
1687:
1683:
1678:
1673:
1667:
1653:
1635:
1632:
1616:
1612:
1607:
1602:
1597:
1592:
1586:
1572:
1568:
1554:
1536:
1533:
1511:
1507:
1502:
1497:
1491:
1479:
1475:
1469:
1465:
1459:
1455:
1449:
1445:
1441:
1431:
1425:
1422:
1400:
1396:
1386:
1378:
1372:
1368:
1364:
1361:
1358:
1353:
1349:
1345:
1342:
1339:
1335:
1331:
1325:
1322:
1300:
1296:
1290:
1287:
1278:
1275:
1272:
1252:
1244:
1240:
1232:
1228:
1223:
1216:
1211:
1208:
1202:
1197:
1183:
1175:
1161:
1149:
1148:
1146:
1132:
1127:
1124:
1114:
1087:
1055:
1051:
1046:
1041:
1021:
989:
951:
941:
939:
934:
931:
923:
918:
909:
907:
903:
899:
896:
886:
884:
880:
876:
850:
829:
823:
821:
802:
792:
771:
767:
764:
758:
756:
740:
736:
722:
710:
709:
708:
706:
698:
693:
689:
681:
677:
675:
674:diode bridges
671:
667:
663:
654:
650:
640:
633:
630:
624:
621:
615:
608:
605:
604:
603:
580:
560:
554:
552:
536:
526:
506:
500:
498:
479:
467:
466:
465:
458:
454:
452:
448:
444:
440:
436:
420:
417:
407:
405:
401:
395:
393:
389:
385:
381:
377:
373:
363:
361:
356:
354:
350:
346:
342:
338:
334:
330:
324:
322:
318:
314:
310:
306:
301:
299:
295:
294:cat's whisker
291:
287:
283:
279:
275:
271:
267:
263:
262:rectification
258:
256:
252:
248:
236:
231:
229:
224:
222:
217:
216:
214:
213:
208:
205:
203:
200:
198:
195:
193:
190:
188:
185:
183:
180:
178:
175:
174:
173:
172:
169:
166:
165:
160:
157:
155:
152:
150:
147:
145:
144:Power station
142:
140:
137:
136:
135:
134:
131:
128:
127:
122:
119:
117:
114:
112:
109:
107:
104:
102:
99:
97:
94:
92:
89:
88:
87:
86:
83:
80:
79:
76:
73:
72:
68:
64:
63:
57:
53:
50:A thyristor (
48:
44:
40:
33:
19:
7815:Cold cathode
7782:Storage tube
7672:Vacuum tubes
7621:Neutron tube
7596:Beam tetrode
7578:Vacuum tubes
7163:Power MOSFET
7007:. Retrieved
6997:
6989:
6980:
6973:
6953:
6946:
6927:
6921:
6911:
6906:
6897:
6878:
6871:
6855:
6845:
6838:
6819:
6807:. Retrieved
6797:
6788:
6778:
6761:
6757:
6751:
6743:
6738:
6729:
6725:
6712:
6700:. Retrieved
6681:
6674:
6662:. Retrieved
6644:
6634:
6614:
6607:
6587:
6580:
6564:
6559:
6534:
6526:
6516:
6509:
6490:
6484:
6465:
6459:
6450:
6444:
6436:
6428:
6408:
6401:
6342:
6311:
6302:
6287:
6268:
6238:
6223:
6216:
6182:
6151:
6135:
6106:vacuum tubes
6090:
6071:carrier wave
6048:
6016:space charge
6007:
5992:
5954:
5927:
5899:
5896:and 6 ampere
5893:
5867:
5850:
5846:
5844:
5826:150 kV
5776:
5764:
5756:
5743:
5739:
5726:
5723:electrolytic
5720:
5717:Electrolytic
5693:
5689:
5685:
5681:
5679:
5625:
5593:
5589:
5583:
5564:
5557:
5529:
5510:
5498:
5479:
5467:
5458:Applications
5448:
5440:
5436:
5422:
5413:
5374:
5361:
5334:transformers
5331:
5328:
5312:
5305:
5297:
5277:
5253:
5247:October 2017
5244:
5229:Please help
5217:
5188:
5180:
5172:p–n junction
5169:
5165:voltage drop
5162:
5156:
5044:
4996:
4750:
4507:
4504:
4214:
4142:
3937:
3930:
3927:
3916:
3913:
3903:October 2017
3900:
3888:
3853:
3837:
3833:
3805:
3801:
3723:
3714:
3709:
3558:
3556:
3431:
3427:
3423:
3417:
3408:
3399:
3394:
3284:
3170:
3161:
3097:
2676:
2659:
1892:
1885:
1850:
1826:
1822:
1810:
1786:
1775:
1767:
942:
935:
927:
900:
892:
875:vacuum tubes
872:
702:
686:
659:
649:
631:
622:
613:
606:
601:
463:
431:
416:single-phase
413:
396:
380:Saul Dushman
369:
357:
328:
325:
302:
261:
259:
246:
244:
115:
43:
7981:Transformer
7723:Sutton tube
7563:Charge pump
7416:Memory cell
7346:Zener diode
7308:Laser diode
7191:transistors
7073:transistors
6377:Rectiformer
6347:, a single
6338:solar cells
6334:solar power
6294:commutators
6275:transistors
6155:vacuum tube
6023:Solid state
5960:vacuum tube
5930:vacuum tube
5810:industrial
5785:Mercury-arc
5779:vacuum tube
5773:Plasma type
5765:The modern
5568:frequencies
5486:charge pump
5443:Zener diode
3138:common mode
3114:common mode
2867:common mode
1813:three-phase
1778:solid state
895:three-phase
666:transformer
8091:Rectifiers
8075:Categories
8053:reed relay
8043:Parametron
7976:Thermistor
7954:resettable
7913:Connector
7874:Adjustable
7850:Nixie tube
7820:Crossatron
7787:Trochotron
7762:Iconoscope
7757:Charactron
7734:X-ray tube
7606:Compactron
7586:Acorn tube
7543:Buck–boost
7464:Solaristor
7326:Photodiode
7303:Gunn diode
7299:(CLD, CRD)
7081:Transistor
6764:(4): 183.
6393:References
6361:AC adapter
6283:power BJTs
6277:, usually
6219:thyristors
6100:, usually
6075:modulation
6004:television
5957:thermionic
5941:See also:
5912:(ex.:328)
5836:hydropower
5706:commutator
5521:thyristors
5462:See also:
5342:resistance
5197:See also:
5157:See also:
3820:See also:
3796:thyristors
1845:thyristors
1801:alternator
1762:thyristors
922:thyristors
902:Thyristors
697:center tap
404:thyristors
292:, used a "
39:AC adapter
18:Rectifiers
8016:Capacitor
7860:Trigatron
7855:Thyratron
7845:Neon lamp
7772:Monoscope
7652:Phototube
7636:Pentagrid
7601:Barretter
7486:Trancitor
7481:Thyristor
7406:Memristor
7331:PIN diode
7108:(ChemFET)
7009:3 October
6330:nantennas
6328:, called
6207:thyristor
6065:, called
5979:electrons
5871:thyristor
5698:generator
5694:generates
5640:inverters
5501:detection
5346:reactance
5315:impedance
5218:does not
5110:˙
4975:π
4950:⋅
4934:⋅
4929:π
4904:⋅
4818:⋅
4783:⋅
4733:π
4704:⋅
4688:⋅
4682:π
4653:⋅
4571:⋅
4540:⋅
4490:%
4484:≈
4444:η
4419:π
4394:⋅
4385:⋅
4380:π
4355:⋅
4276:⋅
4200:%
4194:≈
4154:η
4126:π
4100:⋅
4095:π
3995:⋅
3895:talk page
3665:−
3659:α
3653:
3647:⋅
3642:π
3536:μ
3530:α
3524:
3518:⋅
3513:π
3380:α
3377:
3371:⋅
3366:π
3270:α
3267:
3261:⋅
3256:π
3231:⋅
3131:^
3076:⋅
3034:∘
3026:
3020:⋅
3007:−
2994:⋅
2951:∘
2943:
2937:⋅
2913:⋅
2900:−
2860:^
2719:−
2693:^
2619:≈
2614:π
2595:⋅
2561:⟹
2556:π
2537:⋅
2527:⋅
2475:⟹
2446:π
2421:⋅
2367:−
2359:−
2349:⋅
2344:π
2319:⋅
2285:∘
2277:
2266:∘
2258:
2252:−
2244:⋅
2239:π
2214:⋅
2187:φ
2179:⋅
2176:φ
2173:
2167:⋅
2143:⋅
2129:∘
2117:∘
2108:∫
2101:π
1997:⋅
1970:^
1943:π
1713:≈
1707:π
1684:⋅
1646:⟹
1636:π
1613:⋅
1603:⋅
1547:⟹
1537:π
1508:⋅
1450:−
1442:−
1432:⋅
1426:π
1373:∘
1365:
1354:∘
1346:
1340:−
1332:⋅
1326:π
1288:φ
1279:φ
1276:
1245:∘
1233:∘
1224:∫
1217:π
1133:π
1052:⋅
793:π
768:⋅
581:π
451:harmonics
349:resistors
341:capacitor
313:detectors
247:rectifier
116:Rectifier
8038:Inductor
8008:Reactive
7986:Varistor
7966:Resistor
7944:Antifuse
7830:Ignitron
7825:Dekatron
7713:Klystron
7702:Gyrotron
7631:Nuvistor
7548:Split-pi
7434:(MOS IC)
7401:Memistor
7159:(MuGFET)
7153:(MOSFET)
7125:(FinFET)
6809:15 March
6355:See also
6326:antennas
6290:vibrator
6142:selenium
6059:detector
6008:kenotron
5971:filament
5702:armature
5652:vibrator
5620:vibrator
5482:inverter
2746:amounts
1113:integral
881:and two
360:inverter
202:Recloser
197:Bus duct
121:Inverter
67:a series
65:Part of
56:heatsink
7939:Ferrite
7907:Passive
7898:Varicap
7886:digital
7835:Krytron
7657:Tetrode
7642:Pentode
7496:Varicap
7477:(3D IC)
7453:RF CMOS
7357:devices
7131:(FGMOS)
7062:devices
6702:23 June
6664:23 June
6184:Silicon
6098:mineral
6087:coherer
5855:cathode
5808:3-phase
5690:rectify
5650:on the
5532:railway
5513:welding
5344:and/or
5323:current
5319:voltage
5239:removed
5224:sources
4037:√
3710:where:
3395:where:
2760:
2748:
1776:Before
1771:winding
879:cathode
705:average
602:where:
333:battery
7971:Switch
7662:Triode
7626:Nonode
7591:Audion
7471:(SITh)
7355:Other
7322:(OLED)
7284:Diodes
7235:(LET)
7217:(FET)
7189:Other
7137:(IGBT)
7114:(CMOS)
7101:BioFET
7096:BiCMOS
6961:
6934:
6890:
6831:
6693:
6655:
6622:
6595:
6571:
6547:
6497:
6472:
6416:
6271:diodes
6263:MOSFET
6102:galena
5894:(left)
5859:anodes
5806:Early
5590:switch
5285:filter
5280:ripple
5274:diode.
3403:LLpeak
2667:ground
1817:diodes
1805:diodes
883:anodes
637:, the
447:ripple
329:steady
298:galena
192:Busbar
8048:Relay
8021:types
7959:eFUSE
7730:(TWT)
7718:Maser
7709:(IOT)
7698:(CFA)
7687:(BWO)
7611:Diode
7558:SEPIC
7538:Boost
7491:TRIAC
7460:(SCR)
7423:(MOV)
7397:(LEC)
7316:(LED)
7275:(UJT)
7264:(SIT)
7258:(PUT)
7201:(BJT)
7170:(TFT)
7146:LDMOS
7141:ISFET
6722:(PDF)
6336:than
6167:Diode
6012:X-ray
5975:anode
5963:diode
5910:argon
5594:carry
5519:with
5403:cores
5009:T.U.F
3854:In a
2671:earth
437:in a
435:diode
345:choke
317:radio
7991:Wire
7949:Fuse
7533:Buck
7386:(IC)
7374:DIAC
7310:(LD)
7179:UMOS
7174:VMOS
7091:PMOS
7086:NMOS
7071:MOS
7011:2008
6959:ISBN
6932:ISBN
6888:ISBN
6811:2012
6704:2022
6691:ISBN
6666:2022
6653:ISBN
6620:ISBN
6593:ISBN
6569:ISBN
6545:ISBN
6495:ISBN
6470:ISBN
6414:ISBN
6232:and
6081:and
6049:The
5955:The
5900:The
5721:The
5666:and
5628:reed
5473:and
5222:any
5220:cite
5045:The
4487:81.0
4197:40.5
3412:peak
3079:0.25
2622:2.34
1716:1.17
703:The
626:peak
307:and
7553:Ćuk
6986:236
6766:doi
6541:508
6281:or
6002:of
5981:by
5849:or
5830:at
5503:of
5365:ESR
5233:by
5023:odc
3650:cos
3521:cos
3374:cos
3264:cos
3023:sin
2940:sin
2274:cos
2262:120
2255:cos
2170:sin
2125:120
1362:cos
1350:150
1343:cos
1273:sin
1241:150
635:rms
315:of
8077::
7927:RF
7676:RF
6988:.
6896:.
6882:.
6863:,
6787:.
6760:.
6730:11
6728:.
6724:.
6643:.
6543:.
6340:.
5680:A
5618:A
5600:.
5545:.
5527:.
3030:60
2947:60
2281:60
2113:60
2030::
1369:30
1229:30
617:av
612:,
610:dc
390:,
362:.
343:,
280:,
276:,
245:A
69:on
7678:)
7674:(
7044:e
7037:t
7030:v
7013:.
6967:.
6940:.
6813:.
6772:.
6768::
6762:8
6706:.
6668:.
6628:.
6601:.
6575:.
6553:.
6503:.
6478:.
6422:.
5386:2
5260:)
5254:(
5249:)
5245:(
5241:.
5227:.
5138:)
5130:(
5124:s
5121:m
5118:r
5107:I
5097:s
5094:m
5091:r
5086:V
5082:=
5079:A
5076:V
5056:A
5053:V
5019:P
5013:=
4968:k
4965:a
4962:e
4959:p
4954:I
4945:3
4940:3
4922:k
4919:a
4916:e
4913:p
4908:V
4899:3
4894:3
4888:=
4882:C
4879:D
4874:P
4846:2
4838:k
4835:a
4832:e
4829:p
4824:I
4811:2
4803:k
4800:a
4797:e
4794:p
4789:V
4780:3
4777:=
4771:C
4768:A
4763:P
4730:2
4722:k
4719:a
4716:e
4713:p
4708:I
4699:3
4694:3
4679:2
4671:k
4668:a
4665:e
4662:p
4657:V
4648:3
4643:3
4637:=
4631:C
4628:D
4623:P
4597:2
4591:k
4588:a
4585:e
4582:p
4577:I
4566:2
4560:k
4557:a
4554:e
4551:p
4546:V
4537:3
4534:=
4528:C
4525:A
4520:P
4476:C
4473:A
4468:P
4461:C
4458:D
4453:P
4447:=
4412:k
4409:a
4406:e
4403:p
4398:I
4391:2
4373:k
4370:a
4367:e
4364:p
4359:V
4352:2
4346:=
4340:C
4337:D
4332:P
4304:2
4296:k
4293:a
4290:e
4287:p
4282:I
4269:2
4261:k
4258:a
4255:e
4252:p
4247:V
4241:=
4235:C
4232:A
4227:P
4186:C
4183:A
4178:P
4171:C
4168:D
4163:P
4157:=
4120:k
4117:a
4114:e
4111:p
4106:I
4089:k
4086:a
4083:e
4080:p
4075:V
4069:=
4063:C
4060:D
4055:P
4039:2
4021:2
4015:k
4012:a
4009:e
4006:p
4001:I
3990:2
3984:k
3981:a
3978:e
3975:p
3970:V
3964:=
3958:C
3955:A
3950:P
3931:η
3917:η
3905:)
3901:(
3897:.
3727:d
3724:I
3718:c
3715:L
3692:d
3687:I
3680:c
3675:L
3671:f
3668:6
3662:)
3656:(
3635:k
3632:a
3629:e
3626:p
3623:L
3620:L
3615:V
3611:3
3605:=
3599:v
3596:a
3591:V
3587:=
3581:c
3578:d
3573:V
3559:μ
3542:.
3539:)
3533:+
3527:(
3506:k
3503:a
3500:e
3497:p
3494:L
3491:L
3486:V
3482:3
3476:=
3470:v
3467:a
3462:V
3458:=
3452:c
3449:d
3444:V
3418:α
3409:V
3400:V
3359:k
3356:a
3353:e
3350:p
3347:L
3344:L
3339:V
3335:3
3329:=
3323:v
3320:a
3315:V
3311:=
3305:c
3302:d
3297:V
3249:k
3246:a
3243:e
3240:p
3235:V
3226:3
3221:3
3215:=
3209:v
3206:a
3201:V
3197:=
3191:c
3188:d
3183:V
3144:3
3128:v
3119:=
3110:V
3070:k
3067:a
3064:e
3061:p
3056:V
3052:=
3047:)
3040:2
3015:3
3004:1
2999:(
2988:k
2985:a
2982:e
2979:p
2974:V
2966:=
2957:2
2931:k
2928:a
2925:e
2922:p
2917:V
2908:3
2894:k
2891:a
2888:e
2885:p
2880:V
2872:=
2857:v
2823:k
2820:a
2817:e
2814:p
2809:V
2785:k
2782:a
2779:e
2776:p
2771:V
2757:4
2754:/
2751:1
2731:e
2728:d
2725:o
2722:m
2716:n
2713:o
2710:m
2707:m
2704:o
2701:c
2690:v
2634:N
2631:L
2626:V
2607:N
2604:L
2599:V
2590:6
2585:3
2579:=
2573:v
2570:a
2565:V
2549:N
2546:L
2541:V
2532:2
2522:3
2517:3
2511:=
2505:v
2502:a
2497:V
2493:=
2487:c
2484:d
2479:V
2439:k
2436:a
2433:e
2430:p
2425:V
2416:3
2411:3
2405:=
2400:]
2393:2
2390:1
2385:+
2381:)
2375:2
2372:1
2363:(
2354:[
2337:k
2334:a
2331:e
2328:p
2323:V
2314:3
2309:3
2299:=
2291:)
2271:+
2248:(
2232:k
2229:a
2226:e
2223:p
2218:V
2209:3
2204:3
2194:=
2183:d
2161:k
2158:a
2155:e
2152:p
2147:V
2138:3
2096:3
2093:1
2087:1
2082:=
2076:v
2073:a
2068:V
2060:=
2054:c
2051:d
2046:V
2015:k
2012:a
2009:e
2006:p
2001:V
1992:3
1987:=
1981:C
1978:D
1967:v
1938:3
1935:1
1910:v
1907:a
1902:V
1868:N
1865:L
1860:V
1728:N
1725:L
1720:V
1704:2
1696:N
1693:L
1688:V
1679:6
1674:3
1668:=
1662:v
1659:a
1654:V
1633:2
1625:N
1622:L
1617:V
1608:2
1598:3
1593:3
1587:=
1581:v
1578:a
1573:V
1569:=
1563:c
1560:d
1555:V
1534:2
1526:k
1523:a
1520:e
1517:p
1512:V
1503:3
1498:3
1492:=
1487:]
1480:2
1476:3
1470:+
1466:)
1460:2
1456:3
1446:(
1437:[
1423:2
1415:k
1412:a
1409:e
1406:p
1401:V
1397:3
1387:=
1379:)
1359:+
1336:(
1323:2
1315:k
1312:a
1309:e
1306:p
1301:V
1297:3
1291:=
1284:d
1267:k
1264:a
1261:e
1258:p
1253:V
1212:3
1209:2
1203:1
1198:=
1192:v
1189:a
1184:V
1176:=
1170:c
1167:d
1162:V
1128:3
1125:2
1096:v
1093:a
1088:V
1064:N
1061:L
1056:V
1047:2
1042:=
1036:k
1033:a
1030:e
1027:p
1022:V
998:N
995:L
990:V
966:k
963:a
960:e
957:p
952:V
851:2
844:k
841:a
838:e
835:p
830:V
824:=
814:s
811:m
808:r
803:V
786:k
783:a
780:e
777:p
772:V
765:2
759:=
749:v
746:a
741:V
737:=
731:c
728:d
723:V
632:V
623:V
614:V
607:V
575:k
572:a
569:e
566:p
561:V
555:=
545:c
542:d
537:V
527:2
521:k
518:a
515:e
512:p
507:V
501:=
491:s
488:m
485:r
480:V
234:e
227:t
220:v
41:.
34:.
20:)
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