Author: Sumit Bapu

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Uncategorized

BJT Small Signal Analysis

BJT AC Modelling

  • In amplifier output sinusoidal signal is greater than the input sinusoidal signal, or the output ac power is greater than the input ac power.
  • The question then arises as to how the ac power output can be greater than the input ac power.
  • Conservation of energy dictates that over time the total power output, Po , of a system cannot be greater than its power input, Pi , and that the efficiency defined by h = Po>Pi cannot be greater than 1.
  • But here output ac Power is due to both input ac power & dc biasing both.
    enter image description here
  • The control mechanism is such that the application of a relatively small signal to the control mechanism can result in a substantial oscillation in the output circuit.
  • The superposition theorem is applicable for the analysis and design of the dc and ac components of a BJT network, permitting the separation of the analysis of the dc and ac responses of the system.
  • one can make a complete dc analysis of a system before considering the ac response and once the dc analysis is complete, the ac response can be determined using a completely ac analysis.

BJT TRANSISTOR MODELING

  • A model is a combination of circuit elements, properly chosen, that best approximates the actual behavior of a semiconductor device under specific operating conditions.
  • Once the ac equivalent circuit is determined, the schematic symbol for the device can be replaced by this equivalent circuit and the basic methods of circuit analysis applied to determine the desired quantities of the network.
  • Hybrid equivalent network was employed the most frequently.
  • Specification sheets included the parameters in their listing, and analysis was simply a matter of inserting the equivalent circuit with the listed values.
  • The drawback to using this equivalent circuit, however, is that it is defined for a set of operating conditions that might not match the actual operating conditions.
  • the use of the re model became the more desirable approach because an important parameter of the equivalent circuit was determined by the actual operating conditions.
  • To understand the effect that the ac equivalent circuit will have on the analysis to follow, consider the circuit of Fig
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  • Because we are interested only in the ac response of the circuit, all the dc supplies can be replaced by a zero-potential equivalent (short circuit) because they determine only the dc (quiescent level) of the output voltage and not the magnitude of the swing of the ac output. This is
    clearly demonstrated by Fig.
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  • The coupling capacitors C1 and C2 and bypass capacitor C3 were chosen to have a very small reactance at the frequency of application.
  • Therefore, they, too, may for all practical purposes be replaced by a low-resistance path or a short circuit.
  • This will result in the shorting out of the dc biasing resistor RE .
  • By defining Zi, Zo, Ii, and Io, establishing a common ground and rearranging the elements the equivalent circuit is shown below.
    enter image description here

therefore, the ac equivalent of a transistor network is obtained by:

  1. Setting all dc sources to zero and replacing them by a short-circuit equivalent
  2. Replacing all capacitors by a short-circuit equivalent
  3. Removing all elements bypassed by the short-circuit equivalents introduced by steps 1 and 2
  4. Redrawing the network in a more convenient and logical form

THE re TRANSISTOR MODEL

Common Emitter Configuration

  • The equivalent circuit for the common-emitter configuration will be constructed using the device characteristics and a number of approximations.
  • Starting with the input side, we find the applied voltage Vi is equal to the voltage Vbe with the input current being the base current Ib.
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  • Because the current through the forward-biased junction of the transistor is IE , the characteristics for the input side appear simply as that of a forward-biased diode.
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  • For the equivalent circuit, therefore, the input side is simply a single diode with a current Ie.
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  • If we redraw the collector characteristics to have a constant β(another approximation) and the entire characteristics at the output section can be replaced by a controlled current source whose magnitude is β times of the base current as shown in Fig.
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  • The equivalent model can be difficult to work with due to the direct connection between input and output networks.
  • It can be improved by first replacing the diode by its equivalent resistance as determined by the level of IE.
  • The diode resistance is determined by rD = 26 mV/ID.
  • Using the subscript e because the determining current is the emitter current will result in re=26mV/IE.
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  • The result is that the impedance seen looking into the base of the network is a resistor equal to β times the value of re , as shown in Fig.
  • The collector output current is still linked to the input current by β as shown in the same figure.
  • Improved BJT equivalent circuit is given below.
enter image description here
  • but aside from the collector output current being defined by the level of beta and IB , we do not have a good representation for the output impedance of the device.
  • In reality the characteristics do not have the ideal appearance of parallel straight line.
  • Rather, they have a slope that defines the output impedance of the device.
  • The steeper the slope, the less the output impedance and the less ideal the transistor.
  • In any event, an output impedance can now be defined that will appear as a resistor in parallel with the output as shown in the equivalent circuit.
enter image description here

Common Base Configuration

  • For the common emitter configuration the use of a diode to represent the connection from base to emitter is same for the common base configuration.
  • The pnp transistor employed will present the same possibility at the input circuit.
  • The result is the use of a diode in the equivalent circuit as shown in Fig.
    enter image description here
  • For the output circuit, we find that the collector current is related to the emitter current by alpha.
  • In this case, however, the controlled source defining the collector current is opposite in direction to that of the controlled source of the common emitter configuration.
  • The direction of the collector current in the output circuit is now opposite that of the defined output current.
  • For the ac response, the diode can be replaced by its equivalent ac resistance determined by re = 26mV/IE.
  • An additional output resistance can be determined from the characteristics in much the same manner as applied to the common emitter configuration.
  • In general, common base configurations have very low input impedance because it is essentially simply re .
  • Typical values extend from a few ohms to perhaps 50 ohm.
  • The output impedance ro will typically extend into the megaohm range.
  • Because the output current is opposite to the defined Io direction, you will find in the analysis to follow that there is no phase shift between the input and output voltages.
  • For the common emitter configuration there is a 180 degree phase shift.
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Common Collector Configuration

  • For the common collector configuration, the model defined for the common emitter configuration is normally applied rather than defining a model for the common collector configuration.

COMMON EMITTER FIXED BIAS CONFIGURATION

  • The input signal Vi is applied to the base of the transistor, whereas the output Vo is off the collector.
  • In addition, the input current Ii is not the base current, but the source current.
  • The output current Io is the collector current.
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  • The small signal ac analysis begins by removing the dc effects of VCC and replacing the dc blocking capacitors C1 and C2 by short circuit equivalents, resulting in the network of Fig.
enter image description here
  • Substituting the re model for the common-emitter configuration results in the network of Figure shown below.
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  • The negative sign in the resulting equation for Av reveals that a 180 degree phase shift occurs between the input and output signals.
Categories
Types of powers: Active, Reactive, Apparent & complex power

Types of powers: Active, Reactive, Apparent & Complex Power

  • We can take Impedance triangle idea one step further by converting the impedance triangle into a power triangle representing the three elements of power in an AC circuit.
  • Ohms Law tells us that in a DC circuit, power (P), in watts, is equal to the current squared times the resistance.
  • So, we can multiply the three sides of our impedance triangle above by square of current to obtain the corresponding power triangle as shown below.
  • Real Power=P=I2 R Watts,(W)
  • Reactive Power Q=I2 X Volt Ampere Reactive(VAR)
  • Apparent Power S=I2 Z Volt Ampere (VA)
  • Z=R+jX and S=P+jQ
  • AC apparent Power is a complex quantity made up of Real Active Power & Imaginary Reactive Power.
  • It is the real resistance that leads to the dissipation of real active power.
  • It is the imaginary reactance that leads to the reactive power.
  • The sum of the real power and the reactive power yields the apparent power.

Real Power in AC Circuits:

  • Real power (P), also known as true or active power, performs the real work within an electrical circuit.
  • Real power, measured in watts, defines the power consumed by the resistive part of a circuit.
  • As resistances do not produce any phasor difference (phase shift) between voltage and current waveforms, all the useful power is delivered directly to the resistance and converted to heat, light and work.
  • The power consumed by a resistance is real power which is fundamentally the circuits average power.
  • P=VI cos φ, Where V & I are RMS values of Voltage & current
  • φ is the Power Factor angle, i.e. the angle between V & I

Reactive Power in AC Circuits:

  • Reactive power (Q), (sometimes called wattless power) is the power consumed in an AC circuit that does not perform any useful work.
  • But it has a big effect on the phase shift between the voltage and current waveforms.
  • Reactive power is linked to the reactance produced by inductors and capacitors and counteracts the effects of real power.
  • Reactive power does not exist in DC circuits.
  • Q=VI sin φ, Where V & I are RMS values of Voltage & current
  • φ is the Power Factor angle, i.e. the angle between V & I

Apparent Power in AC Circuits:

  • The product of the rms voltage, V applied to an AC circuit and the rms current, I flowing into that circuit is called the volt-ampere product (VA) given the symbol S and whose magnitude is known generally as apparent power.
  • As apparent power is made up of two parts, the resistive power which is the in phase power or real power in watts and the reactive power which is the out of phase power in volt amperes(VA).
  • We can show the vector addition of these two power components in the form of a power triangle.
  • A power triangle has four parts: P, Q, S and power factor angle or phase angle.
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Concept of power factor

Concept of Power Factor

AC Impedance:

  • AC circuits contain both resistance and reactance that are combined together to give a total impedance (Z) that limits current flow around the circuit.
  • Impedance is not equal to the algebraic sum of the resistive and reactive ohmic values as a pure resistance and pure reactance are 90 degree out of phase with each other.
  • But we can use this 90 degree phase difference as the sides of a right angled triangle, called an impedance triangle, with the impedance being the hypotenuse as determined by Pythagoras theorem.
  • This geometric relationship between resistance, reactance and impedance can be represented visually by the use of an impedance triangle as shown.
enter image description here
  • Impedance, which is the vector sum of the resistance and reactance, has not only a magnitude (Z) but it also has a phase angle, which represents the phase difference between the resistance and the reactance.

Power Factor in AC Circuits:

The power factor is calculated as the ratio of the real power to the apparent power because this ratio equals to cosine of phase angle.

Power factor, is an important part of an AC circuit that can also be expressed in terms of circuit impedance or circuit power.

Power factor is defined as the ratio of real power (P) to apparent power (S), and is generally expressed as either a decimal value, for example 0.95, or as a percentage: 95percentage.

Power factor angle defines the phase angle between the current and voltage waveforms, were I and V are the magnitudes of rms values of the current and voltage.

Power Factor is also defined as the ratio of Resistance & Magnitude of Impedance.

cos φ= PowerFactor=R/Z

If the phase angle is positive then voltage leads the current and Power factor becomes lagging.

If the phase angle is negative then current leads the voltage and Power factor becomes leading.

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Categories
AC Fundamentals

AC Fundamentals

Alternating currents (ac) are currents that alternate in direction (usually many times per second).

Alternating currents

  • Alternating currents (ac) are currents that alternate in direction (usually many times per second).
  • Such currents are produced by voltage sources whose polarities alternate between positive and negative.
  • By convention, alternating currents are called ac currents and alternating voltages are called ac voltages.
  • One complete variation is referred to as a cycle.
  • If a waveform repeats itself at regular intervals, it is called a periodic waveform.

Generation of AC Signal:

  • Alternating voltage may be generated by rotating a coil in a magnetic field.
  • The value of the voltage generated depends on the (a)number of turns in the coil, (b)strength of the field and (c)the speed at which the coil or magnetic field rotates.
  • Michael Faraday discovered the fundamental relationship between the voltage and magnetic flux in a circuit.
  • If the flux linking a conductor changes with time, a voltage is induced at its terminal.
  • The magnitude of the induced voltage is proportional to the rate of change in the magnetic flux.
  • The arrangement of coil & magnet can be understood by the following figure.
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  • The generated emf is always in the form of sinusoidal voltage.

Fundamental quantities of Sinusoidal Waveform:

  • Cycle: One complete set of positive and negative values of alternating quantity is known as cycle.
  • one complete cycle is said to spread over 360 degree.
  • Time Period: The time taken by an alternating quantity to complete one cycle is called its time period T.
  • Frequency: The number of cycles/second is called the frequency of the alternating quantity. Its unit is hertz(Hz).
  • frequency is given by the reciprocal of the time period of the alternating quantity.(f=1/T)
  • Amplitude: The maximum value, positive or negative, of an alternating quantity is known as its amplitude
  • Peak to Peak Value: It is measured between minimum and maximum peak.
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  • Angular Velocity: The rate at which the coil of generator rotates to produce the AC signal is known as Angular Velocity.
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  • Phase: Phase of an alternating current means the fraction of the time period of that alternating current which has elapsed since the current last passed through the zero position of reference.
  • If a sinewave does not pass through zero at t=0, it has a phase shift.
  • Waveforms can be shifted to left or right.
  • Waveform shifted left can be understood as given. It is also known as leading wave with respect to reference zero point.
    enter image description here
  • Waveform shifted right can be understood as given. It is also known as lagging wave with respect to reference zero point.
    enter image description here
  • When we compare two different wave forms, then a leading alternating quantity is one which reaches its maximum (or zero) value earlier as compared to the other quantity.
  • Similarly a lagging alternating quantity is one which reaches its maximum or zero value later than the other quantity.
  • A plus sign when used in connection with phase difference denotes lead whereas a minus sign denotes lag.

Root Mean Square (RMS) Value:

  • The r.m.s. value of an alternating current is given by that steady (d.c.) current which when flowing through a given circuit for a given time produces the same heat as produced by the alternating current when flowing through the same circuit for the same time.
  • It is also known as the effective or virtual value of the alternating current.
  • The r.m.s. value of a complex current wave is equal to the square root of the sum of the squares of the r.m.s. values of its individual components.
  • Irms=I=Im / √2 or Vrms=V=Vm / √2

Average Value:

  • The average value of an alternating current is expressed by that steady current which transfers across any circuit the same charge as is transferred by that alternating current during the same time.
  • In the case of a symmetrical alternating current (i.e. one whose two half cycles are exactly similar, whether sinusoidal or non sinusoidal), the average value over a complete cycle is zero.
  • Hence, in their case, the average value is obtained by adding or integrating the instantaneous values of current over one half cycle only.
  • But in the case of an unsymmetrical alternating current (like half wave rectified current) the average value must always be taken over the whole cycle.
  • Vavg=2Vm/π or Iavg=2Im/π
Form Factor:
  • It is the ratio of RMS value of alternating signal to the average value is known as Form factor.
  • For a sinusoidal signal the value is 1.11.
  • FF=Vrms/Vavg=Vm / √2/2Vm/π = 1.11

Crest or Peak or Amplitude Factor:

  • It is defined as the ratio of maximum value to the r.m.s. value of an alternating signal.
  • For a sinusoidal signal the value is 1.414.
  • The information of this factor helps to find dielectric stress and iron loss as they both are proportional to maximum value.
  • PF=Vm/Vm / √2=√2=1.414

Representation of sinusoidal signal in Phasor form:

  • The alternating voltages and currents are represented by phasors rotating counter clockwise with the same frequency as that of the alternating quantity.
  • A sine wave can be represented by a phasor with the phase angle amount shifted from reference axis and the radius being the rms value of the signal.
  • The angle shift of radius from reference is considered as clockwise if phase angle is positive & anticlockwise if phase angle is negative.
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Important Concepts of Electrical Technology

Important Concepts of Electrical Technology

Basic Properties of Electric Charge:

  • The fundamental electric quantity is charge.
  • Atoms are composed of charge carrying particles: electrons and protons, and neutral particles, neutrons.
  • The smallest amount of charge that exists is carried by an electron and a proton.
  • Basic Properties of Electric Charge:
    – Additivity: If a system contains two-point charges q1 and q2, the total charge of the system is obtained simply by adding algebraically q1 and q2, i.e., charges add up like real numbers or they are scalars like the mass of a body.
    – Charge is conserved: Total charge of the isolated system is always conserved.
    – Quantization: all free charges are integral multiples of a basic unit of charge denoted by e.

Coulomb Law:

Force between two-point charges varies inversely as the square of the distance between the charges and is directly proportional to the product of the
magnitude of the two charges and acted along the line joining the two charges.
– Thus, if two point charges q1 , q2 are separated by a distance r in vacuum, the magnitude of the force (F) between them is given by:

Electric Field:

  • Charge q produces an electric field everywhere in the surrounding
  • When another charge q is brought at some point P, the field there acts on it and produces a force.
  • Units are newtons per coulomb, equivalent to volts per metre
  • The electric field produced by the charge q at a point r is given as:

Current:

  • Current is rate of flow of negatively-charged particles, called electrons, through a predetermined cross-sectional area in a conductor. Flow of electrons in an electric circuit leads to the establishment of current.
  • Current always flows from positive to negative.
  • Unit of Current is Ampere.
  • Amp = C/sec

Voltage:

  • A Voltage is the force applied to a conductor which causes electric current to flow.
  • It is the work done in moving a positive charge of 1 coulomb from one terminal through an element to another terminal.
  • The force required to make electricity flow through a conductor is called a difference in potential, electromotive force (emf), or more simply referred to as voltage.

Resistance:

  • Resistance (also known as ohmic resistance or electrical resistance) is a measure of the opposition to current flow in an electrical circuit.
  • The amount of resistance depends upon composition, length, cross-section and temperature of the resistive material.
  • Resistance of a conductor increases with an increase of length or a decrease of cross section.
  • Resistance is designated by the symbol R and unit is Ohm.
  • V=IR
Electric Circuit:
  • Interconnection of electrical elements linked together in a closed path so that an electric current may continuously flow.

Elements in Electric Circuit:

  • Linear Elements: Elements which satisfy the principle of superposition and homogeneity theorem are Linear Elements.
    – If the principle of superposition is true, then the excitation i1 + i2 must produce a response v1 + v2
    – If principle of homogeneity is true, the response of the element must be kv2, for an excitation ki.
    – Network consisting of linear elements is known as Linear Circuit.
  • Passive Circuit Elements: Elements which cannot supply any energy (voltage or current), can only absorb a positive or zero energy
    • Current enters at positive(+ve) & leaves at negative(-ve) terminal.
    • Examples of passive elements are resistors, capacitors and inductors.
    • Active Circuit Elements: Elements which supply energy to a circuit or is a source of energy.
    • Current is supplied from +ve terminal & enters at -ve terminal.
    • Examples: Voltage & Current sources
  • Unilateral network: An Unilateral network is one whose properties or characteristics change with the direction.
    • An example of unilateral network is the semiconductor diode, which conducts only in one direction.
  • Bilateral network: A bilateral network is one whose properties or characteristics are same in either direction.
    • For example, a transmission line is a bilateral network, because it can be made to perform the function equally well in either direction.

Electrical Energy:

  • The electrical energy is the amount of charge q moved through voltage V in a time interval t.
  • The voltage across an element is the work done in moving a positive charge of 1 coulomb from first terminal through the element to second
    terminal.
  • Unit of energy Joule, KWh(Kilowatt hour)

Electrical Power:

  • It is the time rate of change of energy.
  • P=dw/dt
  • P=VI (For DC)
  • AC Power:
    • p=vi(instantaneous AC Power)
    • P = VI cos ϕ (Real Power/Active Power/Consumed Power)
    • Unit: Watt
    • Q = VI sin ϕ (Reactive Power/Imagine Power)
    • Unit: Volt Ampere Reactive (VAR)
    • S=VI* (Total Power)
      – Unit is Volt Ampere(VA)
Categories
Conventional & Non-Conventional Ways of Electricity Generation Uncategorized

Conventional & Non-conventional ways of Electricity Generation

Electrical technology is used for generating, storing, regulating, transferring, and using electrical energy for solving different purpose in real life. Example: power plant generators, Air Conditioners, electric light bulb, Electric Fan, Electric Heater etc.

Conventional & Non-conventional ways of Electricity Generation:

Most electricity in the world is conventionally generated. Example: using coal, oil, natural gas, nuclear energy, or hydropower

  • Electricity is normally generated in Power plants.
  • Capacity of a Powerplant is the amount of electricity it can produce when it is running at full blast. It is other wise known as name plate capacity.
  • Name plate capacity or the maximum amount of power is typically measured in megawatts (MW) or kilowatts (KW).
  • The energy produced is defined in the units of KWh (Kilowatt Hour) or MWh(megawatts hour). It can be defined as:
  • Total KWh energy consumed= KWh rating X Number of hours it worked.
  • Capacity factor (net) of a Power plant: The ratio of the net electricity generated, for the time considered, to the energy that could have been generated at continuous full-power operation during the same period.
  • Example: Let a Powerplant has nameplate capacity of 3,942 MW & its annual generation was 31,200,000 MWh

Hydropower plants

  • Hydropower plants use water to generate electricity. When flowing water is captured and turned into electricity, it is called hydroelectric power or hydropower.
  • There hydroelectric facilities are powered by the kinetic energy of flowing water as it moves downstream.
  • Turbines and generators convert this kinetic energy into electricity, which is then fed into the electrical grid to be used in homes, businesses,
  • and by industry.
  • Tehri Hydropower Complex in Uttarakhand is the largest hydroelectric power plant in India with a capacity of 2400MW (Mega Watt)

Thermal Power station

  • A thermal power station is a power station in which heat energy is converted to electricity.
  • Water is heated into steam, which is used to drive the turbine of electrical generator.
  • After it passes through the turbine the steam is condensed in a steam condenser and recycled to where it was heated.
  • This is known as a Rankine cycle.
  • Coal has been used widely in thermal power station to heat the water & steam generation for decades.
  • Use of Gases have also increased now a days as an alternative of Coal because of its low price.
  • Vindhyachal Thermal Power Station in Madhya Pradesh is the biggest thermal power plant in India, with an installed capacity of 4,760MW.

Nuclear powerplants

  • Nuclear powerplants are also a type of Thermal Power plant.
  • Nuclear Power plant satisfies both economic and environmental protection goals.
  • So, the energy produced from Nuclear Power plant is a clean & green
    energy.
  • Heat source for a Nuclear Power plant is the fission reaction of radioactive elements in a nuclear reactor.
  • This heat of nuclear reactor heats the reactor coolant which may be water or gas, or even liquid metal, depending on the type of reactor.
  • The reactor coolant then goes to a steam generator and heats water to produce steam.
  • The pressurized steam is then fed to a multi-stage steam turbine for electricity generation.
  • Uranium-238 (U-238) and Uranium-235 (U-235) are normally used as fuel for fission reaction
  • Kudankulam Nuclear Power Plant in Tamil Nadu is the highest capacity nuclear plant in India with an installed capacity of 2000 MW.
Nuclear powerplants
  • There are various Renewable Energy Sources also present which contributes for electricity generation.
  • The conversion of solar radiation directly into electrical power is done in Solar Power Plants.
  • Thermal energy is transformed into electrical energy using photovoltaic panels.
  • Large number of panels are installed in an optimal configuration and harvest light energy from the sun and convert it into electrical energy
    which feeds into the grid.
  • Harvested thermal energy is converted into direct current (DC) electricity using solar panels.
  • To convert this direct current (DC) electricity to alternating current (AC) electricity, an essential component inverter is used.
  • Inverter is a component which converts direct current (DC) electricity to alternating current (AC) electricity.
  • Bhadla Solar Park of 2,250MW is India’s biggest solar power plant in the state of Rajasthan.
  • Wind mill converts the kinetic energy of moving air into mechanical energy that can be either used directly to run the machine or to run the
  • Induction generator to produce electricity.
  • Electricity produced from Tides of sea is known as Tidal Energy.

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