full wave rectifier formula
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When measuring the value of an alternating current signal it is often necessary to convert the signal into a direct current signal of equivalent value (known as the RMS, root mean square, value). This process can be quite complex (see root mean square for a detailed mathematical explanation). Most low cost instrumentation and signal converters (for example handheld multimeters of the sort used by maintenance engineers) carry out this conversion by filtering the signal into an average value and applying a correction factor.
The value of the correction factor applied is only correct if the input signal is sinusoidal. The true RMS value is actually proportional to the square-root of the average of the square of the curve, and not to the average of the absolute value of the curve. For any given waveform, the ratio of these two averages will be constant and, as most measurements are carried out on what are (nominally) sine waves, the correction factor assumes this waveform; but any distortion or offsets will lead to errors. Although in most cases this produces adequate results, a correct conversion or the measurement of non sine wave values, requires a more complex and costly converter, known as a True RMS converter.
The RMS value of an alternating current is also known as its heating value, as it is a voltage which is equivalent to the direct current value that would be required to get the same heating effect. For example, if we applied 120VAC RMS to a resistive heating element it would heat up by exactly the same amount as if we had applied 120V DC.
This principle was exploited in early thermal converters. The AC signal would be applied to a small heating element which was twinned with a thermistor which could be used in a DC measuring circuit.
The technique is not particularly precise but it will measure any waveform at any frequency. A big drawback is that it is low impedance, that is the power used to heat the thermistor comes from the circuit being measured. If the circuit being measured can support the heating current, then it is possible to make a post measurement calculation to correct the effect, as the impedance of the heating element is known. If the signal is small then a pre-amplifier is necessary, and the measuring capabilities of the instrument will be limited by this pre-amplifier.
Thermal converters have become quite rare, but as they are inherently simple and cheap they are still used by radio hams and hobbyists, who may remove the thermal element of an old unreliable instrument and incorporate it into a modern design of their own construction.
Analog electronic converters
Analog electronic circuits may use:
- an Analog multiplier in a specific configuration which multiplies the input signal by itself (squares it), averages the result with a capacitor, and then calculates the square root of the value (via a multiplier/squarer circuit in the feedback loop of an operational amplifier, or
- a full-wave precision rectifier circuit to create the absolute value of the input signal, which is fed into a operational amplifier arranged to give an exponential transfer function, then doubled in voltage and fed to an Log amplifier as a means of deriving the square-law transfer function, before time-averaging and calculating the square root of the voltage, similar to above, or
- a Field Effect Transistor may be used to directly create the square-law transfer function, before time-averaging.
Unlike Thermal converters they are subject to bandwidth limitations which makes them unsuitable for most RF work. The circuitry before time averaging is particularly crucial for high frequency performance. The slew rate limitation of the operational amplifier used to create the absolute value (especially at low input signal levels) tends to make the second method the poorest at high frequencies, while the FET method can work close to VHF. Specialist techniques are required to produce sufficiently accurate integrated circuits for complex analog calculations, and very often meters equipped with such circuits offer True RMS conversion as an optional extra with a significant price increase.
Digital RMS converters
If a waveform has been digitialised then the correct RMS value may be calculated directly. Most digital and PC-based oscilloscopes include a function to give the RMS value of a waveform. Obviously the precision and the bandwidth of the conversion is entirely dependent on the analog to digital conversion. In most cases, true RMS measurements are made on repetitive waveforms, and under such conditions digital oscilloscopes (and a few sophisticated sampling multimeters) are able to achieve very high bandwidths as they sample at a fraction of the signal frequency to obtain a stroboscopic effect.
A voltage doubler is an electric circuit with an AC input and a DC output of roughly twice the peak input voltage. They are a variety of voltage multiplier circuit and a voltage doubler is often, but not always, a single stage of a general form of such a circuit. The term is usually applied to circuits consisting of rectifying diodes and capacitors only; other means of doubling voltages are not included.
The Villard circuit consists simply of a capacitor and a diode. While it has the great benefit of simplicity, its output has very poor ripple characteristics. Essentially, the circuit is a diode clamp circuit. The capacitor is charged on the negative half cycles to the peak AC voltage (Vpk). The output is the superposition of the input AC waveform and the steady DC of the capacitor. The effect of the circuit is to shift the DC value of the waveform. The negative peaks of the AC waveform are "clamped" to 0 V (actually −VF, the small forward bias voltage of the diode), so the positive peaks of the output waveform are 2Vpk. The peak-to-peak ripple is an enormous 2Vpk and cannot be smoothed unless the circuit is effectively turned into one of the more sophisticated forms.
The Greinacher voltage doubler is a significant improvement over the Villard circuit for a small cost in increased components. The ripple is much reduced, being nominally zero under open-circuit load conditions, but, when current is being drawn, depends on the resistance of the load and the value of the capacitors used. The circuit works by following a Villard cell stage with what is in essence a peak detector or envelope detector stage. The peak detector cell has the effect of removing most of the ripple while preserving the peak voltage in the output.
This circuit was first invented by Heinrich Greinacher in 1913 (published 1914) in order to provide the 200–300 V he needed for his newly invented ionometer, the 110 V AC supplied by the Zurich power stations of the time being insufficient. He later (1920) extended this idea into a cascade of multipliers. This cascade of Greinacher cells is often inaccurately referred to as a Villard cascade. It is also called a Cockcroft–Walton multiplier after the particle accelerator machine built by John Cockcroft and Ernest Walton, who independently rediscovered the circuit in 1932.
The concept in this topology can be extended to a voltage quadrupler circuit by using two Greinacher cells of opposite polarities driven from the same AC source. The output is taken across the two individual outputs. Note that, like a bridge circuit, it is not possible to simultaneously ground both the input and output of this circuit
The Delon circuit uses a bridge topology for voltage doubling. This form of circuit was, at one time, commonly found in cathode ray tube television sets where it was used to provide an e.h.t. voltage supply. Generating voltages in excess of 5 kV with a transformer has safety issues in terms of domestic equipment and in any case is not economic. However, black and white television sets required an e.h.t. of 10 kV and colour sets even more. Voltage doublers were used to either double the voltage on an e.h.t winding on the mains transformer or were applied to the waveform on the line flyback coils.
The circuit consists of two half-wave peak detectors, functioning in exactly the same way as the peak detector cell in the Greinacher circuit above. Each of the two peak detector cells operates on opposite half-cycles of the incoming waveform. Since their outputs are in series, the output is twice the peak input voltage.
A full-wave version of this circuit has the advantage of lower peak diode currents, improved ripple and better load regulation but requires a centre-tap to the transformer as well as more components.
A power supply is a device that supplies electricalenergy to one or more electric loads. The term is most commonly applied to devices that convert one form of electrical energy to another, though it may also refer to devices that convert another form of energy (e.g., mechanical, chemical, solar) to electrical energy. A regulated power supply is one that controls the output voltage or current to a specific value; the controlled value is held nearly constant despite variations in either load current or the voltage supplied by the power supply's energy source.
Every power supply must obtain the energy it supplies to its load, as well as any energy it consumes while performing that task, from an energy source. Depending on its design, a power supply may obtain energy from:
- Electrical energy transmission systems. Common examples of this include power supplies that convert AC line voltage to DC voltage.
- Energy storage devices such as batteries and fuel cells.
- Electromechanical systems such as generators and alternators.
- Solar power.
A power supply may be implemented as a discrete, stand-alone device or as an integral device that is hardwired to its load. In the latter case, for example, low voltage DC power supplies are commonly integrated with their loads in devices such as computers and household electronics.
Constraints that commonly affect power supplies include:
- The amount of voltage and current they can supply.
- How long they can supply energy without needing some kind of refueling or recharging (applies to power supplies that employ portable energy sources).
- How stable their output voltage or current is under varying load conditions.
- Whether they provide continuous or pulsed energy.
Power supply types
Power supplies for electronic devices can be broadly divided into linear and switching power supplies. The linear supply is usually a relatively simple design, but it becomes increasingly bulky and heavy for high-current equipment due to the need for large mains-frequency transformers and heat-sinked electronic regulation circuitry. Linear voltage regulators produce regulated output voltage by means of an active voltage divider that consumes energy, thus making efficiency low. A switched-mode supply of the same rating as a linear supply will be smaller, is usually more efficient, but will be more complex.
A battery is an alternative to a line-operated power supply; it is independent of the availability of mains electricity, suitable for portable equipment and use in locations without mains power. A battery consists of several electrochemical cells connected in series to provide the voltage desired. Batteries may be primary (able to supply current when constructed, discarded when drained) or secondary (rechargeable; can be charged, used, and recharged many times)
The primary cell first used was the carbon-zinc dry cell. It had a voltage of 1.5 volts; later battery types have been manufactured, when possible, to give the same voltage per cell. Carbon-zinc and related cells are still used, but the alkaline battery delivers more energy per unit weight and is widely used. The most commonly used battery voltages are 1.5 (1 cell) and 9V (6 cells).
DC power supply
An AC powered unregulated power supply usually uses a transformer to convert the voltage from the wall outlet (mains) to a different, nowadays usually lower, voltage. If it is used to produce DC, a rectifier is used to convert alternating voltage to a pulsating direct voltage, followed by a filter, comprising one or more capacitors, resistors, and sometimes inductors, to filter out (smooth) most of the pulsation. A small remaining unwanted alternating voltage component at mains or twice mains power frequency (depending upon whether half- or full-wave rectification is used)—ripple—is unavoidably superimposed on the direct output voltage.
For purposes such as charging batteries the ripple is not a problem, and the simplest unregulated mains-powered DC power supply circuit consists of a transformer driving a single diode in series with a resistor.
Before the introduction of solid-state electronics equipment used valves (vacuum tubes) which required high voltages; power supplies used step-up transformers, rectifiers, and filters to generate one or more direct voltages of some hundreds of volts, and a low alternating voltage for filaments. Only the most advanced equipment used expensive and bulky regulated power supplies.
AC power supply
An AC power supply typically takes the voltage from a wall outlet (mains supply, often 230v in Europe) and lowers it to the desired voltage (eg 9vac). As well as lowering the voltage some filtering may take place. An example use for an AC power supply is powering certain guitar effects pedals (e.g. the Digitech Whammy pedal) although usually these pedals require DC.
Linear regulated power supply
The voltage produced by an unregulated power supply will vary depending on the load and on variations in the AC supply voltage. For critical electronics applications a
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Answers:The Full wave bridge rectifier is suitable for high voltage applications. The size of the transformer is small for the same dc power output as obtained from full wave rectifier.
Answers:It will tend to clip off the tops of the sine wave causing a lot of distortion. This s a non linear load, and cannot be classified into leading or lagging pF, and cannot be corrected by adding a cap or inductor to the line. Wikipedia. A particularly important class of non-linear loads is the millions of personal computers that typically incorporate switched-mode power supplies (SMPS) with rated output power ranging from a few watts to more than 1 kW. Historically, these very-low-cost power supplies incorporated a simple full-wave rectifier that conducted only when the mains instantaneous voltage exceeded the voltage on the input capacitors. This leads to very high ratios of peak-to-average input current, which also lead to a low distortion power factor and potentially serious phase and neutral loading concerns. A typical switched-mode power supply first makes a DC bus, using a bridge rectifier or similar circuit. The output voltage is then derived from this DC bus. The problem with this is that the rectifier is a non-linear device, so the input current is highly non-linear. That means that the input current has energy at harmonics of the frequency of the voltage. This presents a particular problem for the power companies, because they cannot compensate for the harmonic current by adding simple capacitors or inductors, as they could for the reactive power drawn by a linear load. Many jurisdictions are beginning to legally require power factor correction for all power supplies above a certain power level. Regulatory agencies such as the EU have set harmonic limits as a method of improving power factor. Declining component cost has hastened implementation of two different methods. To comply with current EU standard EN61000-3-2, all switched-mode power supplies with output power more than 75 W must include passive PFC, at least. 80 PLUS power supply certification requires a power factor of 0.9 or more. .
Answers:The raw DC without a smoothing capacitor is a chopped up sinewave. Take the raw DC and put the SCR in series. Put a potential divider on the DC and feed that into the SCR gate. The SCR will then only conduct for part of the cycle.
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