BAND-STOP FILTERS

Band-stop filters are also called band-elimination, band-reject, or notch filters; this kind of filter passes all frequencies above and below a particular range set by the component values. This type of filters can be made out of a low-pass and a high-pass filter, just like the band-pass design, except that the two filter sections are connected in parallel with each other instead of in series.

The low-pass filter section is comprised of R1, R2, and C1 in a “T” configuration. The high pass filter section is comprised of C2, C3, and R3 in a “T” configuration as well. Together, this arrangement is commonly known as a “Twin-T” filter, giving sharp response when the component values are chosen in the following ratios:

Component value ratios for the "Twin-T" band-stop filter

R1 = R2 = 2(R3)

C2 = C3 = (0.5) C1

The frequency of maximum rejection (the “notch frequency”) can be calculated as follows:

fnotch =1/4*3.14*R3C3

BAND-PASS FILTERS

In applications such as a particular band, or spread, or frequencies need to be filtered from a wider range of mixed signals. This can be achieved by combining the properties of low-pass and high-pass into a single filter. The result is called a band-pass filter.

The series combination of these two filter circuits is a circuit that will only allow passage of those frequencies that are neither too high nor too low. This type of band-pass filter works by relying on either section to block unwanted frequencies, it can be difficult to design such a filter to allow unhindered passage within the desired frequency range. Both the low pass and high-pass will always block signals to some extent, and their combined effort makes for an attenuated signal at best, even at the peak of the “pass-band” frequency range.

HIGH-PASS FILTERS

A high-pass filter’s task is just the opposite of a low-pass filter it offers easy passage of a high-frequency signal and difficult passage to a low-frequency signal. The capacitor’s impedance increases with decreasing frequency. This high impedance in series tends to block low-frequency signals from getting to load.

The inductance impedance decreases with decreasing frequency. This low impedance in parallel tends to short out low-frequency signals from getting to the load resistor. As a consequence, most of the voltage gets dropped across series resistor R.

LOW-PASS FILTERS:

A low-pass filter is a circuit that offers easy passage to low-frequency signals and difficult passage to high frequency signals. There are two basic kinds of circuits in low pass filters,

The inductive low-pass filter and the capacitive low-pass filter,

The inductance impedance increases with increasing frequency. This high impedance in series tends to block high-frequency signals from getting to the load.

The capacitor’s impedance decreases with increasing frequency. This low impedance in parallel with the load resistance tends to short out high-frequency signals, dropping most of the voltage across series resistor R.

All low-pass filters are rated at a certain cutoff frequency. That is, the frequency above which the output voltage falls below 70.7% of the input voltage. In a simple capacitive/resistive low-pass filter, it is the frequency at which capacitive reactance in ohms equals resistance in ohms. In a simple capacitive low-pass filter (one resistor, one capacitor), the cutoff frequency is given as:

fcutoff =1/2*3.14*RC

FILTER:

There are circuits that are capable of selectively filtering one frequency or range of frequencies out of a mix of different frequencies in a circuit. A circuit designed to perform this frequency selection is called a filter circuit, or simply a filter. A common need for filter circuits is in high-performance stereo systems, where certain ranges of audio frequencies need to be amplified or suppressed for best sound quality and power efficiency. Equalizers and crossover networks are examples of filters, designed to accomplish filtering of certain frequencies.

Filters are of different types;

• Low-pass filters
• High-pass filters
• Band-pass filters
• Band-stop filters
• Resonant filters

REACTIVE POWER , TRUE POWER, APPARENT POWER

The reactive loads such as inductors and capacitors dissipate zero power, the voltage drop and draw current gives the deceptive impression that actually do dissipate power. This is called reactive power, and it is measured in a unit called Volt-Amps-Reactive (VAR), rather than watts. The mathematical symbol for reactive power is (unfortunately) the capital letter Q.

The actual amount of power being used, or dissipated, in a circuit is called true power, and it is measured in watts (symbolized by the capital letter P, as always).

The combination of reactive power and true power is called apparent power, and it is the product of a circuit’s voltage and current, without reference to phase angle. Apparent power is measured in the unit of Volt-Amps(VA) and is symbolized by the capital letter S.

The true power is a function of a circuit’s dissipative elements, usually resistances (R). Reactive power is a function of a circuit’s reactance (X). Apparent power is a function of a circuit’s total impedance (Z).

Power Factor

In the equation P =(VmIm/2)cosθ, the factor that has significant control over the delivered power level is the cosθ. No matter how large the voltage or current, if cosθ= 0, the power is zero; if cosθ=1,the power delivered is a maximum.Thus the power factor is defined by,

power factor= cosθ

For situations where the load is a combination of resistive and reactive elements, the power factor will vary between 0 and 1. The more resistive the total impedance, the closer the power factor is to 1; the more reactive the total impedance, the closer the power factor is to 0.

Power factor=True power/ Apparent power

INSULATION

Insulating materials are used in electric devices to keep current from flowing where it is not desired. They are simply materials with a sufficiently high resistance or sufficiently low conductance, also known as dielectric materials. Typically, plastics or ceramics are used.

When an insulator is functional, its resistance is infinite or the conductance will be zero so that current will not flows through it. If the voltage difference between two sides of the insulator becomes too large, its insulating properties may break down due to microscopic changes in the material, where it actually becomes conducting. Generally, the thicker the insulator, the higher the voltage difference it can sustain. However, temperature is important ie, plastic wire insulation may melt if the wire becomes too hot. The insulators often seen on high-voltage equipment consist of strings of ceramic bells, holding the energized wires away from other components . The shape of these bells serves to inhibit the formation of arcs along their surface. The number of bells is roughly proportional to the voltage level, though it also depends on climate.

DERIVATIVES AND INTEGRALS FORMULAE

SYNCHRONOUS GENERATOR:Construction details and types

The synchronous generator converts mechanical energy from the turbine into electrical energy. This type of generator requires a winding carrying direct current (or in small sizes a series of permanent magnets) to establish the magnetic flux. Mostly in all machines this excitation winding (known as the field winding) is carried on the rotor, which for a 50 or 60 Hz output must rotate at the synchronous speed.

The synchronous generator has two parts:

• Stator: Stator carries 3 (3-phase) armature windings, AC, physically displaced from each other by 120 degrees
• Rotor: Rotor carries field windings, connected to an external DC source via slip rings and brushes or to revolving DC source via a special brushless configuration.

There are two types of synchronous generator based on the type of rotor used;

1)Turbogenerators

This family of machines use a cylindrical rotor in which the field winding is housed in axial slots. They are invariably driven by a steam turbine or a gas turbine. At ratings below 60MW a gear box may be used to provide a rotational speed of 3600 (2 pole) or 1800 rev/min(4 pole) to provide power at 60 Hz, or 3000 rev/min (2 pole) or 1500 rev/min (4 pole) to provide power at 50 Hz. Alternatively, and especially at higher power ratings the generator is directly driven by the steam or gas turbine. The rotors will thus have either two or four poles. Smaller machines may use a laminated construction for the rotor while larger machines will use a forged rotor. A feature of these machines is that their length is several times their diameter. Power outputs range from a few megawatts up to about 1500MW. The machine is cooled by circulating air or hydrogen over the active parts or water through the windings. Hydrogen was commonly used for outputs greater than about 50MW; water was, and still is, used for the stator winding with outputs exceeding about 200MW. Air-cooled machines are now available upto almost 200MW.

2) Hydrogenerators

This type of generators uses salient pole type rotor which are driven by water turbines at a speed in the range 50 ±1000 rev/min. The speed depends on the type of turbine, which in turn depends on the head and the flow rate of the water available. At low speeds, the permissible rotor diameter will be several times its active length. Generally, the largest allowable diameter of rotor is used to maximize the machine's inertia which is an important part of governing the water turbine. Outputs up to 800MW have been achieved. A small high-speed unit will have a horizontal shaft, but for reasons of mechanical construction and stability larger machines have vertical shafts.

The synchronous generator is so-named because it functions properly only at synchronous speed that. Synchronous speed can be defined as the speed for which the induced voltage in the armature (stator) windings is synchronized with (has same frequency as) the network voltage.

HVDC

High voltage direct current (HVDC):

High voltage direct current (HVDC) is used to convert energy from AC to DC, to transport the energy as DC, and to convert it back from DC to AC. To meet the ever growing demand for bulk power transmission over long distance, one solution is to build HVDC transmission lines.

This is a simple system with two converters C1 and C2, and one DC line.Based on the polarity of DC lines, HVDC systems are classified as monopolar, bipolar, and homopolar systems. a monopolar system, has only one DC line that normally has negative polarity and uses the ground as the current return path. The monopolar system is mainly implemented to reduce the cost of line construction. Bipolar systems uses two DC lines, one positive and the other negative. All lines have the same polarity in the homopolar connection.

The HVDC converter bridge is a three-phase converter bridge circuits as shown in Fig;

Each converter bridge has six branches of valves. The DC terminals of a converter connect to DC lines and the AC terminals to AC lines. The converter transformer is a conventional transformer with on-load tap changers. The turns-ratio of the converter transformer can then vary to manage the converter operation. The ‘‘DC side’’ of the converter transformer is usually delta or Y connected with ungrounded neutral, so that the DC line can have an independent voltage reference relative to the AC network. Harmonic voltages and currents arise during converter operation. The inductance reduces the harmonic voltages and currents on the DC lines, to prevent commutation failure of inverters, to maintain continuous current under light loading, and to curtail short-circuit current in converters during faults.

TRANSMISSION AND DISTRIBUTION

Structure of electric power system:

The modern power system is a complex interconnected network.A power system can be subdivided into four major parts:

1.Generation

2.Transmission and Subtransmission

3.Distribution

4.Loads

The basic components of a power system can be shown as figure below;

DIRECT CURRENT (DC) AND ALTERNATING CURRENT (AC)

DIRECT CURRENT (DC):

Direct current is the electricity flowing in a constant direction, and/or possessing a voltage with constant polarity. It can be expressed in terms of just two variables: polarity (or direction), and magnitude. It is the current that always flows in the same direction, and that does not change in intensity with time. DC is the kind of electricity made by a battery , or the kind of charge generated by rubbing certain types of materials against each other. Batteries and other sources of direct current (dc) produce a constant voltage. This can be represented by a straight, horizontal line on a graph of voltage versus time.

ALTERNATING CURRENT (AC):

In alternating current, the polarity reverses again and again at regular intervals. The magnitude usually changes because of this constant reversal of polarity, although there are certain cases where the magnitude doesn't change even though the polarity does. The rate of change of polarity makes ac so much different from dc. The length of time between one repetition of the pattern, or one cycle, and the next is called the period of the wave. frequency is the cycles per second and is denoted by f, which is the reciprocal of the period. That is, f = 1/T and T = 1/f .unit of frequency is hertz (Hz)

Alternating current (AC) waves are of different types; Such as sine wave, square wave,sawtooth waves,complex and irregular waveforms etc.

CONDUCTOR,INSULATOR AND SEMICONDUCTOR

CONDUCTORS

In some materials, electrons move easily from atom to atom. A conductor is a substance in which the electrons are mobile and that can conduct electricity.The term conductor is applied to any material that will support a generous flow of charge when a voltage source of limited magnitude is applied across its terminals.The best conductor at room temperature is pure elemental silver. Copper, aluminum, iron, steel etc are examples for conductors. In most electrical circuits and systems, copper or aluminum wire is used. Silver is impractical because of its high cost.

INSULATORS:

Some substances prevent electrical currents from flowing through it, those substance are known as insulators. An insulator is a material that offers a very low level of conductivity under pressure from an applied voltage source.Most gases are good electrical insulators. Glass, dry wood, paper, and plastics are other examples. Pure water is a good electrical insulator.

SEMICONDUCTORS:

In a semiconductor, electrons flow, but not as well as they do in a conductor. That is semi conductors are partial conductor of electricity. A semiconductor, therefore, is a material that has a conductivity level somewhere between the extremes of an insulator and a conductor. Semiconductors carry electrons almost as well as good electrical conductors like copper or aluminum; others are almost as bad as insulating materials.

ELECTRICITY :BASICS

GENERAL PHYSICS PRINCIPLES BEHIND THE ELECTRICITY:

Scientists revealed 92 different kinds of fundamental substances in nature called elements. Each element is made up of tiny particles known as its atom. Atoms of different elements are always different.

The atom consists of proton , neutron and the electron. The main part of an atom is the nucleus that consists of proton and the neutron. The number of protons in an element’s nucleus gives, the atomic number, The atomic weight of an element is approximately equal to the sum of the number of protons and the number of neutrons in the nucleus. Electrons are the particles having opposite electric charge from the protons are Surrounding the nucleus of an atom .Electrons can move rather easily from one atom to another in some materials. In other substances, it is difficult to get electrons to move. But in any case, it is far easier to move electrons than it is to move protons. Electricity almost always results, in some way, from the motion of electrons in a material.

Different elements join together to share electrons which the results in a chemical compound.There are about thousands of different chemical compounds that occur in nature.When atoms of elements join together to form a compound, the resulting particles are molecules.All matter, whether it is solid, liquid, or gas, is made of molecules.In a solid, the molecules are interlocked in a sort of rigid pattern, although they vibrate continuously . In a liquid, molecules are loosely packed and these molecules slide around. In a gas, molecules are whizzing all over the place, bumping into each other.