INTRODUCTION TO TRANSFORMER

A transformer may bee defined as a static electric device that transfers electrical energy from one circuit to another circuit at the same frequency but with changed voltage(or current or both) through a magnetic circuit.

Principle of Operation

When alternating voltage V

When a load is connected to the secondary side, current will start flowing in the secondary winding. Voltage induced in the secondary winding is responsible to deliver power to the load connected to it.

In this way power is transferred from one circuit (primary) to another (secondary) winding through a magnetic circuit by electromagnetic induction. This is the working principle of the transformer.

OHM's LAW

In general, materials have a characteristics behavior of resisting the flow of electric charge. This physical property or ability to resist current is known as resistance and is represented by the symbol R. In other words, resistance is the capacity of materials to impede the flow of or, more specifically, the flow of electric charge. The circuit element used to model this behavior is the resistor.

Conceptually, we can understand the resistance of material, if we think about moving electrons that make up electric current interacting with and being resisted by the atomic structure of the material through which they are moving. Because of the course of these interactions, some amount of electric energy is converted to thermal energy and dissipated in the form of heat. This effect is not desirable but many useful electrical appliances take advantage of resistance heating, including space heaters, irons, stores and toasters.

Figure below shows a material with uniform cross-sectional area A, length l and resistivity ρ(ohm-meters).

We can represent resistance in mathematical form,

The amount of resistance depends on the material.

Good conductors such as copper and aluminium have low resistivity and hence have small value of resistance. They are good choices for wiring used to conduct electric current. In a circuit diagram, copper or aluminium wiring is not usually modeled as a resistor. The resistance of the wire is so small compared to the resistance of other elements in the circuit that we can neglect the wiring resistance to simplify the diagram. For the purpose of constructing circuits, resistors are usually made from metallic alloys and carbon compound.

The circuit symbol of resistor is shown in figure below:-

It is denoted by R. The resistance is the simplest passive element.

Resistivity of common material is show in table below:-

Material	Resistivity	Usage
Gold	2.45*10-8	Conductor
Silver	1.64*10-8	Conductor
Copper	1.72*10-8	Conductor
Aluminum	2.8*10-8	Conductor
Silicon	6.4*102	Semiconductor
Carbon	4*10-5	Semiconductor
Germanium	47*10-2	Semiconductor
Mica	5*1011	Insulator
Paper	1*1010	Insulator

 Georg Simon Ohm (1784-1854), a German physicist, who established the relationship between current and voltage for a resistor. This relationship is known as ohm's law. Ohm's law is the algebraic relationship between voltage and current for a resistor. Ohm's law states that the voltage "v" across the resistor is directly proportional to the current "i" flowing though the resistor.

 i.e. v ∝ i

or, v=i.R

Above  equation is the mathematical form of ohm's law.

Ohm defined the constant of proportionality to be the resistance R. The resistance can change if the external or internal conditions of the element are altered, for example, if there are changes in the temperature.

If current flows from a higher potential to a lower potential, v=i.R and if a current flows from a lower potential to a higher potential, v=-i.R. Since the value of R can vary from ZERO to INFINITY, we must consider the two extreme possible values of R.

A element with R=∞ is called an open circuit as shown in figure(a).

V-I CHARACTERISTICS OF DIODE USING PSPICE

Inorder to simulate the V-I characteristics of diode the circuit is drawn as shown in figure below. To find the component click get new part option near the search box. Following pop-up windows appears, then add parts.

The starting point is taken 0V and ending point is taken 2V with 0.2V increment, and the sweep type will be Linear. Click OK. So in this way I have set the parameter.

Now lets go for simulation. For simulation press F11 or click on simulate key.

Voltage drop in  the diode can be seen by above simulation.
Current flowing through diode is shown below.

ANALYSIS SETUP

Search PSpice Design Manager in Windows Start Menu. 

Following windows will appear :-

Create new Schematic file named Circuit_1.sch 

 Double-click on Circuit_1.sch file then following window appears in the screen :-

After that click on Analysis on the task bar. After that click on Setup option. Then a window will pop-up.

Then you will see various option appear in pop-up window. The most important option in  the analysis setup is AC Sweep and DC Sweep, which is described below :-

AC Sweep :- AC Sweep is a frequency response analysis. PSpice 

Click on the AC sweep then following window will pop-up.

DC Sweep :- 

Click on the DC sweep then following window will pop-up.

Here you have to type the name of the element you want to analyze, for example for voltage source "V", for current source"I" and so on.

You have add Start Value, End Value & Increment. After that you are ready to analyze the element within that range with the Increment you want.

HOW TO INSTALL PSPICE 9.1 STUDENT VERSION IN WINDOWS 10

Introduction :-

• Spice (Simulation Program for Integrated Circuits Emphasis)is a general purpose analog circuit simulator and is used to verify circuit designs and also to predict the circuit behavior.
• PSpice is a PC version of SPICE.
• And HSpice is a version which runs on workstations and also on larger computers.
• PSpice has standard components (such as NAND, NOR, Flip-Flop, and other digital gates, OP Amps etc.) in Analog and Digital libraries which makes it a useful tool for a wide range of Analog and Digital application.
• PSpice is a product of OrCAD Corporation and we are using the student version here.
• The Simulation using PSpice is also included in the syllabus of Purbanchal University for Electrical Engineering
• The student PSpice version had circuit simulation limited.

Let's install the software :-

Link to the software

You will get this type of file. After that extract the file.

You need to make a folder and copy the link of folder and paste in the Unzip To Folder Option. In my case I have paste 

C:\Users\dell\Downloads\Programs\PSPICE here.

After that click on the setup.exe file.

Press OK.

After clicking Finish the setup is finished

ACTIVE AND PASSIVE CIRCUIT ELEMENTS

An electric circuit is simply an interconnection of the element. Circuit analysis is the process of determining the current through the elements or voltages across the elements of the circuit.
There are two types of elements found in electric circuits :- Active element and Passive elements, by considering the energy delivered to or by them.
A circuit element is said to be passive if the total energy delivered to it from the rest of the circuit is always non-negative i.e.

w=∫p dt=∫v.i dt ≥ 0

Of course, an active element is one that is not passive. That is equation (1.10) does not hold good for all time. In general, an active element is capable of generating energy while a passive element is not. Examples of passive elements are resistors, inductors, and capacitors. Examples of active elements are generators, batteries, and operational amplifiers.
The most important active elements are voltage or current sources that generally delivers power to the circuit connected to them. There are two types of sources :- Independent and Dependent sources.

An independent voltage source is a two-terminal element that maintains a specified voltage between its terminals. The voltage is completely independent of current through the element. Physical sources such as generator and batteries may be regarded as approximations to ideal voltage source. 

Note that both symbols of above figure can be used to represent DC voltage source, but the symbol of figure(a) can be used for a time varying voltage source.

 An independent current source is a two-terminal element that provides a specified current completely independent of the voltage across the source.

Independent sources are usually meant to deliver power to the external circuit. Symbol above is true for both DC and AC current source. For example i=2Amp is DC current source and i=2sin(100Πt) is AC current source.



Dependent sources are usually designated by diamond-shaped symbols.

A dependent or controlled voltage source is similar to an independent source expect that the voltage across the source terminals is a function of other voltage or currents in the circuit.

A voltage-controlled voltage source is a voltage source having a voltage equal to a constant times the voltage across a pair of terminals elsewhere in the network. This is shown in figure (c).
A current-controlled voltage source is a voltage source having a voltage equal to a constant times the current through some other element in the circuit. This is shown in figure (d). The factor multiplying the current is called the gain parameters.
The current flowing through a dependent current source is determined by a current or voltage elsewhere in the circuit. Two example of current controlled current sources are shown below :-

A current-controlled current source is shown in figure (e). In this case it is assumed that current through the source is 2-times the value of iₓ. A voltage-controlled current source is shown in figure (f). The current through the source is 3-times the voltage vₓ. The factor multiplying the voltage is called the gain parameter.
Controlled-voltage sources and controlled-current sources are useful in constructing circuit models for many types of real-world devices, such as transistor,transformers,electrical machines and electronics amplifiers.
In summary, there are four kinds of controlled sources,

1. Voltage-Controlled Voltage Sources (VCVS)
2. Current-Controlled Voltage Sources (CCVS)
3. Current-Controlled Current Sources (CCCS)
4. Voltage-Controlled Current Sources (VCCS)

POWER AND ENERGY

Power and energy calculation are very important in circuit analysis. Although voltage and current are useful variables in an electric circuit, they are not sufficient by themselves. One reason is that the useful output of the system often is non-electrical, and this output is conveniently expressed in terms of power and energy. Another reason is that all practical devices have limitations on the amount of power that they can handle. For example, we all know from our experience that a 60-watt bulb gives more light than 40-watt bulb. We also know that when we pay our electricity bills, we are paying for the electrical energy (watt-hour) consumed over a certain period of time.
We now relate power and energy to voltage and current, we recall from physics that: power is the time rate of expending or absorbing energy.
Power is measured in watts(W). Mathematically we write this relationship as,
p=dw/dt..................................... (1.6)
where,
p=power in watts
w=the energy in joule
t=time in second
Thus, 1 watt=1 joule/sec
p=dw/dt=(dw/dq)*(dq/dt)=v*i.......... (1.7)
Above equation shows the power associated with a basic circuit element is simply the product of the current in the element and the voltage across the element. Therefore, power is a quantity associated with a pair of terminals, and we have to be able to tell from our calculation whether power is being delivered to the element or supplied by the element. If the power has a (+)ve sign, power is being delivered to or absorbed by the element. But,how do we know when the power has a positive or a negative sign.
Polarity of voltage and direction of current play a major role in determining the sign of power.

In order to have power a positive sign, the direction of current and polarity of voltage must Conform with those shown in figure (a). By the passive sign convention, current enters through the positive polarity of the voltage and in this case p=+vi or vi>0 implies that the element is absorbing power. But if p=-vi or vi<0, as in figure (b), the element is releasing or supplying power.
Passive sign convention is satisfied when the current enters through the positive terminal of an element and p=+vi. However, if the current enters through the negative terminal, p=-vi.
In general we can write,
+power absorbed=-power supplied.

For any electric circuit, law of conservation of energy must be obeyed. For this reason, at any instant of time, the algebraic sum of power in a circuit must be zero. Therefore, we can write,

∑p=0................ (1.8)

Equation (1.8) confirms the fact that the total power supplied to the circuit must balance the total power absorbed.
To calculate the energy w supplied or absorbed by a circuit element between time instant t0 and t, we get integrate power. Therefore,

w=∫p dt=∫v.i dt................ (1.9)

Thus,energy is the capacity to do work. Energy is measured in joules.
The electric power utility companies measure energy in watt-hour (Wh).
Where, 1 Wh=3600 joules.

VOLTAGE

As explained in the previous section, to move the electron in a conductor in a conductor in a particular direction requires some work or energy transfer. This work is done by an external electromotive force (emf), typically represented by battery. This emf is also known as potential difference or voltage. Actually, whenever positive and negative charges are separated, energy is expanded.
Voltage is the energy per unit charge created by the separation. Thus, the voltage V₁₂ between two point 1 and 2 in an electric circuit is the energy or work needed to move a unit charge from 1 to 2. We express this ratio in differential form as :-
v=V₁₂=dw/dq................ (1.3)

where, 

w=the energy in joule

q=the charge in coulombs

v=V₁₂=the voltage in volts

From equation (1.3) it is evident that
 1 volt=1 joule/coulomb=1 newton-meter/coulomb

Thus, voltage or potential difference is the energy required to move a unit charge through an element.

Figure below shows the voltage across a lamp connected between point 1 and 2.

The plus (+) and minus (-) sign s are used to represent reference direction or voltage polarity. The voltage V₁₂ can be interpreted in two ways. 

1. Point 1 is at a potential of V₁₂ volts higher than point 2.
2. The potential at point 1 with respect to potential 2 is V₁₂.

Therefore, logically it follows that,

In figure (a), point 1 is +10V above point 2; in figure (b), point 2 is -10V above point 1. We can say that in figure (a) there is a 10V voltage drop from point 1 to 2 or equivalently a 10V voltage rise from point 2 to 1. In general, a voltage drop from 1 to 2 is equivalent to a voltage rise from 2 to 1.

CHARGE AND CURRENT

The concept of electric charge is the underlying principle for explaining all electrical phenomena. The most basic quantity in an electric circuit is the electric charge. Important characteristics of electric charge are :-

1. The charge is bipolar, meaning the electrical effects are described in terms of positive and negative charges.
2. According to experimental observation, the only charges that occurs in nature are integral multiple of electronic charge e=-1.602*10-19 coulomb.
3. Electrical effects are attributed to both the separation of charge and charges in motion.
4. The law of conservation of charges states that charge can neither be created nor destroyed, only transferred. Thus, the algebraic sum of electric charges in a system does not change.

Effect of electric charge can be experienced when we try to remove our woolen sweater and have it stick to our body or walk across a carpet and receive shock.

Charge is an electric property of the atomic particles and is measured in coulombs(C).

Now, consider the flow of electric charges. A unique feature of electric charge is that it can be transferred from one place to another, that means it is mobile, where it can be converted to another form of energy. The motion of charge creates an electric fluid(current).

We know that a conducting wire consists of several atoms and a battery is a source of electromotive force. When a conducting wire is connected to a battery, the charges are compelled to move. Positive charges move in one direction while negative charges move in opposite direction.

This motion of charges creates electric current. Convention is to take the current flow as the movement of positive charges, that is, opposite to the flow of negative charges as shown in figure below: -

The electric effects caused by charges in motion depends on the rate of charge flow. The rate of charge flow is known as the electric current.

Mathematically, the relationship between current, charge and time is,

                                        
$\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;$

where, 
i=the current in Ampere

q=the charge in Coulomb

t=the time Second

The charge transferred between time t₀ and t is obtained by integrating both sides of equation (1.1) we get;

Equation (1.1) suggests that current need not be a constant valued function.

When a current is constant with time, we say that we have direct current (dc). Thus, a direct current (dc) is a current that remains constant with time.

On the other hand, a current that varies with time, reversing direction periodically is called alternating current (ac). Thus, an alternating current is a current that varies with time periodically. Alternating current is used in our household, to run the refrigerator, toaster, air conditioner and other electrical appliances.

 As mentioned earlier, direction of current flow is conveniently taken as the direction of positive charge movement. Based on this convention, a current of 4Amp may be represented positively or negativity. This is shown in figure below where a lamp is connected in series with a battery.

In above figure i₁₂ =4Amp, this means the current through the lamp with its reference direction pointing from 1 to 2. Similarly, i₂₁ is the current with its reference directed from 2 to 1. Of course, i₁₂ and i₂₁, are the same in magnitude and opposite in sign, because they denote the same current but with opposite direction. Thus, we have,

SYSTEM OF UNITS

System of Units

We all electrical engineers deals with several measurable quantities. However, our measurement must be communicated in standard language such that an engineering professional can understand, irrespective of the country where the measurement is conducted.

Such an international measurement language is the International System of Units (SI), adopted by the General Conference on weights and measures in 1960. In this international system there are six principle units from which the units of all the other physical quantities can be obtained. One major advantage of the SI unit is that it uses prefixes based on the power of 10 to relate smaller and larger units to the basic unit.

Quantity	Basic Unit	Symbol
Luminous Intensity	Candela	Cd
Thermodynamics Temperature	Kelvin	K
Length	Meter	m
Mass	Kilogram	Kg
Time	Second	s
Electric Current	Ampere	A

The SI unit Prefix are: -

Multiplier	Prefix	Symbol
1018	exa	E
1015	penta	P
1012	tera	T
109	giga	G
106	mega	M
103	kilo	K
102	hecto	H
10	deka	da
10-1	deci	d
10-2	centi	c
10-3	milli	m
10-6	micro	µ
10-9	nano	n
10-12	pico	p
10-15	femto	f
10-18	atto	a