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.