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BASIC ELECTRICAL ENGINEERING FORMULAS R- electrical resistance in ohms, L- inductance in henrys, C- capacitance in farads, f - frequency in hertz, t-. Formula. Handbook including. Engineering. Formulae,. Mathematics,. Statistics and. Computer Algebra nvrehs.info - pdf. This Formula Book consists of well-illustra formulae and It includes all the subjects of Electrical Engi jects of Electrical Engineering, Instrumentation.

Main article: Analogue filter The oldest forms of electronic filters are passive analog linear filters, constructed using only resistors and capacitors or resistors and inductors. These are known as RC and RL single- pole filters respectively. However, these simple filters have very limited uses. Multipole LC filters provide greater control of response form, bandwidth and transition bands. The first of these filters was the constant k filter , invented by George Campbell in Campbell's filter was a ladder network based on transmission line theory. Together with improved filters by Otto Zobel and others, these filters are known as image parameter filters. A major step forward was taken by Wilhelm Cauer who founded the field of network synthesis around the time of World War II. Cauer's theory allowed filters to be constructed that precisely followed some prescribed frequency function.

A major step forward was taken by Wilhelm Cauer who founded the field of network synthesis around the time of World War II. Cauer's theory allowed filters to be constructed that precisely followed some prescribed frequency function. Classification by technology[ edit ] Passive filters[ edit ] Passive implementations of linear filters are based on combinations of resistors R , inductors L and capacitors C.

Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do the reverse. A filter in which the signal passes through an inductor , or in which a capacitor provides a path to ground, presents less attenuation to low-frequency signals than high-frequency signals and is therefore a low-pass filter. If the signal passes through a capacitor, or has a path to ground through an inductor, then the filter presents less attenuation to high-frequency signals than low-frequency signals and therefore is a high-pass filter.

Resistors on their own have no frequency-selective properties, but are added to inductors and capacitors to determine the time-constants of the circuit, and therefore the frequencies to which it responds. The inductors and capacitors are the reactive elements of the filter. The number of elements determines the order of the filter.

In this context, an LC tuned circuit being used in a band-pass or band-stop filter is considered a single element even though it consists of two components. At high frequencies above about megahertz , sometimes the inductors consist of single loops or strips of sheet metal, and the capacitors consist of adjacent strips of metal.

These inductive or capacitive pieces of metal are called stubs. Single element types[ edit ] A low-pass electronic filter realised by an RC circuit The simplest passive filters, RC and RL filters, include only one reactive element, except hybrid LC filter which is characterized by inductance and capacitance integrated in one element.

The components can be chosen symmetric or not, depending on the required frequency characteristics. The high-pass T filter in the illustration, has a very low impedance at high frequencies, and a very high impedance at low frequencies.

That means that it can be inserted in a transmission line, resulting in the high frequencies being passed and low frequencies being reflected.

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 converts the AC mains to a DC bus by means of a bridge rectifier or a 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. The filter consists of capacitors or inductors, and makes a non-linear device look more like a linear load. An example of passive PFC is a valley-fill circuit.

A disadvantage of passive PFC is that it requires larger inductors or capacitors than an equivalent power active PFC circuit.

Active power factor correction can be single-stage or multi-stage.

In the case of a switched-mode power supply, a boost converter is inserted between the bridge rectifier and the main input capacitors.

The boost converter attempts to maintain a constant DC bus voltage on its output while drawing a current that is always in phase with and at the same frequency as the line voltage.

Another switched-mode converter inside the power supply produces the desired output voltage from the DC bus. This approach requires additional semiconductor switches and control electronics, but permits cheaper and smaller passive components.

It is frequently used in practice. For a three-phase SMPS, the Vienna rectifier configuration may be used to substantially improve the power factor. That feature is particularly welcome in power supplies for laptops. Dynamic PFC[ edit ] Dynamic power factor correction DPFC , sometimes referred to as "real-time power factor correction," is used for electrical stabilization in cases of rapid load changes e.

DPFC is useful when standard power factor correction would cause over or under correction.

Importance in distribution systems[ edit ] 75 MVAr capacitor bank in a kV substation Power factors below 1. This increases generation and transmission costs. For example, if the load power factor were as low as 0. Line current in the circuit would also be 1. Alternatively, all components of the system such as generators, conductors, transformers, and switchgear would be increased in size and cost to carry the extra current.

When the power factor is close to unity, for the same KVA rating of the transformer more load can be connected.

Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission.