Introduction to ElectronicsTheory Notes:

Dr.Yatindra Nath Singh Electrical Engineering Department

IIT Kanpur-208016

Lab material: Dr.Joseph John

Electrical Engineering Department IIT Kanpur-208016

Reviwed by: Dr.S.P.Das

Electrical Engineering Department IIT Kanpur-208016

Copyright 2003-2005,2007 Yatindra Nath Singh, 2005, 2007 Joseph John All rights for this work is reserved with the authors. No part of this work can be reproduced by any means without the prior written permission from the author. Author provided the limited rights to the instructors at academic institutions for using this work for teaching in their classes.

The authors permit this work to be used by NPTEL initiative of all IITs and MHRD, Govt. of India for non-profit distribution, conditioned on that this copyright notice is reproduced as it is.

This document contains the notes which have been used for teaching this course. The updated course notes can always be checked at Brihaspati.

Basic idea of the course will be to introduce the basic concepts required to understand the electronic circuits.

Prerequisites: There are no prerequisites as such for the course. The course has been built for first year undergraduate students and targeted as general course for all branches of engineering.

Course Website: http://brihaspati.ee.iitk.ac.in/ Use login 'guest' password 'guest'.

Books and references

1. Ralph J.Smith, R.C.Dorf, Circuits, devices and systems, John Wiley, 1992 2. R.L.Boylestad, L. Nashelsky, Electronic devices and circuit theory, Prentice Hall, 2002 3. A.S.Sedra, K.C.Smith, Microelectronic circuits, Oxfort University Press, 1998 4. R.A.Gayakwad, Op-amps and linear integrated circuits, Prentice Hall of India 5. Millman, Grabel, Microelectronics, McGraw-Hill. 6. DeCarlo, and Lin, Linear circuit analysis, Oxford Univesity Press, 2001 (second edition). 7. Hayt, Kammerly and Durbin, Engineering Circuit Analysis, Tata McGrawHill, sixth edition

Contents o course outline

System Passive elements Sources

o Dependent Sources

Lecture 3: DC Circuit Analysis Lecture 4: More on Dependent Sources

o Thevenin's Theorem o Norton Theorem o Example: Analysing circuits using Thevenin's and Norton's equivalents

Using Thevenin's equivalent Using Norton's equivalent

Transient response of RL circuit R-C Circuits Sinusoidal Steady State Response Power Supply

o Full Wave rectifier o Full wave rectifier without center tapped transformer o LM 317: Regulator

Bipolar Junction Transistor o CE Characteristics o Constant current source o Constant voltage source

Operational Amplifiers Digital Circuits

o Universality of certain gates Using NAND gates

o Boolean Expressions

Other ways of realizing logic functions

o Multiplexers (MUX) o Flip-Flops and Latches o Sequential circuits

Master Slave Flip-Flop (S-R) Edge triggered Flip-Flop

Lab schedule About this document ...

System Each system will have inputs and output. Example of an input can be battery which is connected to a circuit. The output is some entity which we want to measure in a circuit element.

In the example below, the input is the battery supplying voltage . Since, we are interested in current flowing in the resistor, the output is current .

Figure 1.1: Resistance

The process of predicting the output for given inputs in a electronic system is circuit analysis. The inputs can be of various forms e.g, mic converts audio to electrical signal. Alternatively, the output can also be a non-electrical entity e.g., speaker converting the electrical signal to audio. In general the electronic system will have multiple inputs (can be signal inputs or power sources) and multiple outputs.

We need to understand the basic elements to do circuit analysis.

Passive elements Most of the Circuit elements have at least two leads (electrical terminals). They are characterized by voltage across the terminals and current flowing through the device (see Fig.2.1); this is V-I characterization of device.

Figure 2.1: Simple element

Resistance: Across this element, if we applied a voltage source and observe the current, then we will observer that , that is, , where R is the resistance measured in Ohms (Fig.1.1, 2.2).

Figure 2.2: Graph of V vs I for a Resistance

Higher the value of R, larger the voltage required to achieve the same current. Voltage proportional to current - is Ohm's law (It was deduced hueristically by experiments for metals, by George Simon Ohm). For lamp, this law is not true, as with increase in current, temperature of bulb increases, causing the

increase in resistance. Hence Ohms law is not strictly true for lamp. But for most of the practical purposes and for this course the Ohm's law holds true for the resistive circuit elements.

The resistive elements (resistances) can be fixed or variable. Commonly use resistor types are carbon film and wirewound. The example of variable resistor is potentiometer.

For a material with length and cross-sectional area , the resistance will be , where is

specific resistivity (property of material). Inverse of resistance is conductance. , measured in mhos or Seimens.

Figure 2.3: Bulb as a resistive load

In Fig. 2.4, property of interest is resistance between A and B. It is dependent on details of wire, connector, filament, material, and shape. It can be abstracted as simple resistance (Fig.2.4).

Figure 2.4: Bulb abstracted as a simple resistance

Inductance:

It another important basic circuit element. Current flowing in a wire causes generation of magnetic field intensity ( ). is independent of material medium surrounding the current carrying wire. The

leads to magnetic flux density . Here is absolute permeability of vaccum. is relative permeability of material where is measured. The flux flowing around wire links with the conducting wire. And if the flux linkage changes it lead to generation of EMF (electromotive force) which try to oppose the change in flux. This means it tries to nullify the change in current.

The current causes production of magnetic flux. is the EMF of a single turn. Here, .

Thus, the total EMF , where is the number of turns.

Defining the inductance - , is inductance and measured in Henry. See the output current of sinusoidal applied across an inductor in Fig.2.5

Figure 2.5: V and I as function of t for an Inductor

Figure 2.6: Physical Implementation of an inductor

In lumped model, inductance is considered only due to element. The inductance due to wires connecting it to other elements is neglected (Fig.2.6)

Analysis of circuit: To find voltage or currents in an element of interest. One can also find voltage and current in all the elements of circuit.

Lumped simplified model of resitance, inductance and capacitance.

Capacitance: , capacitance. The magnitude of charge on either plate is given by .

Figure 2.7: Symbols for resitance, inductance and capacitance

Lumped model: Shape, material, wire, connectors - effect of each is assumed to be due to single entity shown by the symbols in the diagram. In actual resistance, inductance and capacitance are distributed all across the circuits. For most practical purpose, lumped model- satisfactory.

Series and Parallel connections

Figure 2.8: A series connection of resistors

Kirchoff's volatage law: In a circuit, if your start from a point A and tranverses the circuit in any fashion and reaches back to point A, the total sum of potential changes should be zero. This has to be true since, same point cannot have two different potentials.

Kirchoff's current law: At any point in the network, total amount of current entering and leaving the point has to be equal to rate of accumulation of charge at the point. Since, in the circuits ordinarily the points where one circuit element is connected to other circuit element (these points are called nodes) do not store charge sum of incomming current has to be equal to sum of outgoing currents.

Thus, for series model, we get relations:

     

     

     

Thus equivalent resistance of series connection is .

For parallel connection, we get the relations:

     

     

     

     

Thus, equivalent resistance here is: . Similarly, we calculate equivalent inductance and capacitance for series and parallel cases.

Inductances in series:

     

     

     

Inductances in parallel:

     

     

     

     

     

Figure 2.9: Series connection of capacitances

Capacitances in series:

     

     

     

     

Capacitances in parallel

     

     

     

     

Inductance of a Solenoid (Coil)

Figure 2.10: A Solenoid diagram showing magnetic circuit path lengths

Define =magnetic circuit path length A=magnetic circuit crossectional area. Inductance: (Assuming that is same in the closed path of length .)

     

     

     

     

     

     

     

     

     

Here is magnetomotive force (equivalent of eletromotive force - EMF in magnetic domain),

and flux is equivalent of current in magnetic domain. The Magnetic reluctance= is then equivalent of resistance in magentic domain.

Linearity: when elemental change in cause , always leads to same elemental change in effect i.e., , then the system is said to be linear.

In general, for a system let input lead to output , and a small perturbation in causes a

small perturbation in output. If perturbation alwasy leads to same perturbation of in

the output irrespective of any , then the system is linear.

The implication of the above is that if input causes output , and causes , then

will cause an output of . This is principal of superposition.

Sources

Figure 3.1: A DC source (Ideal Voltage Source) with a circuit element

Ideal voltage source: Whatever amount of current is drawn from it the voltage at the terminals is always same. Whenever the terminals are short circuited (resistance of between the terminals) the infinite amount of current flows to maintain voltage. This is hypothetical condition, why?

Figure 3.2: Ideal Current Source

Ideal current source: Whatever load or network of elements is connected to source, the current pumped by the source into the load always remains same. Whenever the terminals are open circuits (Terminals are not connected to any thing) the voltage across the terminals becomes to maintain the same amount of current through terminals. This is also hypothetical condition, why?

Can I leave a current source as shown in figure 3.3?

Figure 3.3: Current Source left open

In this case, voltage across the terminals will be .

Non Ideal Voltage Source: See the circuit in figure 3.4. A non ideal voltage source is modeled with an

internal resistance of source . Thus battery terminal voltage changes with the load current.

Figure 3.4: Non Ideal Voltage Source

Under no load, i.e. for zero current, . When a load current flows, . For a

new battery, generally, is negligible, and it increases as the battery gets discharged. is a function of electrolyte and terminal materials.

Non Ideal Current Source: See the circuit in figure 3.5.

Figure 3.5: Non-ideal Current Source

A non ideal current source is modeled by an internal conductance in parallel with the source.

.

From the figure, we see that: . Ideal current source has , i.e., .

Non-ideal voltage source and current source analysis: The source is non-ideal, hence v is not constant. If

it is linear circuit, and are linearly related. is cause, and is effect. Thus we get:

Figure 3.6: Battery

    (3.1)

    (3.2)

Figure 3.7: Model

This equation is equivalent to fig.3.7. Thus a battery can be represented by 3.8:

Figure 3.8: Battery Model

Similarly, for a nonideal current source (fig.3.9), if it is linear,

    (3.3)

    (3.4)

For ideal current source, always. Thus .

Figure 3.9: Current Source

Figure 3.10: Current Source Model

In the above, the sources are modelled using ideal voltage (current) sources whose voltage (current) remains constant.

We can also have source whose output can be controlled. These can be used to model certain real life devices (e.g., transistor) We will study transistor later during the course.

Dependent Sources Output of source depends on some other variable. These are of four types depending on the controlling variable and output of the source.

Voltage controlled voltage sources: This is a voltage source whose output can be controlled by

changing the controlling voltage (Fig.3.11). This is a voltage amplifier if we consider the VCVS to be a box which takes the input as voltage and then at the output generated the amplified voltage. In the figure, 20 will be the gain of voltge amplifier.

Figure 3.11: Voltage controlled voltage source

Voltage controlled current sources: In case the control variable is voltage and the output of the source is current, it is VCCS. The unit of gain factor (20 in the Fig.3.12) will of siemens. This is transconductance amplifier.

Figure 3.12: Voltage controlled current source

Output current can be modified by changing . .

Current controlled voltage sources: shown in figure 3.13.

Figure 3.13: Current controlled voltage source This is a transimpedence amplifier since the ratio of output to input has units of resistance (more general term is impendance). The gain factor for this type of source has units of ohm, measured as

.

Current controlled current sources (Fig. 3.14 : A current amplifier, the gain is current gain (dimensionless, as in voltage amplifier).

Figure 3.14: Current controlled current source

Lecture 3: DC Circuit Analysis A network of passive elements and sources is a circuit. Analysis: To determine currents or voltages in various elements (effects) due to various sources (cause).

Figure 4.1:

In circuit 4.1 all the time. Expected that all current (voltage) in (across) the elements is constant. Inductor:

(4.1)

implies constant. Hence

Inductors act as a short cicuit for DC inputs. This would not be the case if I put a switch across a source.

Capacitor:

(4.2)

as (expected), . Thus capacitor acts as open circuit for DC analysis.

Figure 4.2:

The resultant circuit will be as shown in Fig.4.2.

Analysis: To find currents in all branches, voltage across all branches. We can use Kirchoff's law (voltage and current). For as many independent equations as number of unknown variables. Solve the simultaneous equations, and get the result.

Voltage drop from 'a' to 'b'. Therefore,

Current in branch ab in the direction from 'a' to 'b'. Here . Hence:

     

     

     

     

     

     

     

     

     

     

     

     

     

     

Note: In a circuit with nodes, the number of branches will alwasy be , where are maximum number of independent closed paths possible in the circuit.

Hence, we can always form equations using Ohm's law, equations using KCL, equations using KVL. Hence in total equations can be formed, which are sufficient to solve for variables (voltage and current in each branch).

Can we simplify the situation? Loop currents method: We do away with branch currents and define loop currents. The branch currents can be written in terms of loop currents once all the loop currents passing through the branch and their directions are known. The branch voltages can always be written using Ohm's law and branch current written in terms of loop currents. So now our objective is to find loop currents. For this we choose maximum number of independent loops (Fig.4.3) and apply KVL in them.

Figure 4.3:

If and are known, voltages across all elements can be found. Make two independent equations: For loop abef

    (4.3)

    (4.4)

For loop bcde:

    (4.5)

    (4.6)

Use any technique to solve these (such as using matrices). We get:

    (4.7)

    (4.8)

Nodal Voltage Method

Figure 4.4: Nodal Voltage method

Considering Fig.4.4.

Independent Nodes: One of the nodes in circuit need to be considered as reference node. Hence its node potential is zero. For other nodes, nodal voltage is potential differetial w.r.t. to reference node. The

nodes are called independent nodes. In general for node network, nodes will be independent.

At node b: . Similarly, other equations are:

    (4.9)

    (4.10)

    (4.11)

    (4.12)

    (4.13)

    (4.14)

These are six equations, in six unknowns. Thus can be solved for a unique solution. One can make a supernode and use KCL combining the nodes nodes a and f. We also make extra equations for potential difference between two nodes. With supernode, no. of equations is equal to no. of independent nodes whose voltage w.r.t. reference needs to be determined.

Current Sources in Loop Current Analysis

Figure 4.5: Current sources in Loop current analysis

Using KVL for loop 1 in Fig.4.5:

(4.15)

The other equations are:

(4.16)

(4.17)

The first and the third equation can be combined for taking care of . This can be done by making superloop for writing KVL.

Graph For analysing circuits efficiently. Loop current method

One can form a spanning tree from graph such that current sources are in links (Those elements which do not form part of the tree). Each link when added to the tree gives a loop. All voltage sources should be kept in branches of tree. For example, refer to the following two figures (Fig.4.6 , Fig.4.7)

Figure 4.6: Loop Current method

Figure 4.7: Loop current method

Node voltages

Figure 4.8: Node Voltage method

In the above figure, . There are five unknown node voltages in the above circuit, namely,

, , , and . Correspondingly, we have five equations. Note that we can merge into one supernode

     

     

     

     

     

The second equation follows from looking at node , while the third one from doing the same at node .

Lecture 4: More on Dependent Sources

Figure 5.1: A dependent Source

All dependent sources are linear elements if (see figure 5.1) K=constant and the output is proportional

to controlling variable. Here, in figure 5.1, effect, and V= cause. If K is constant, always

gives same for all values of . . In general all the measured variables can be written as linear combination of all the causes, since nodal voltage or loop current method leads to linear equations. This is true for network with linear elements, and linear dependent sources.

For measuring effect of many sources (also called forcing functions), the effect due to one source at a time is computed (assuming all others to be null). For the sources to be nullified means that if they are voltages sources, they are short circuited (making the voltage of source zero), and if they are current sources, they are open circuited (making the current from the source zero). Effects of all individual independent sources are added to get effect due to presence of all the independent sources. This is known as Superposition Theorem and is valid because of linearity in the circuit (as explained above).

While applying superposition theorm, depenendent sources are retained as any other circuit element. They should not be nullified to get their effect separately on the quantity of interest.

Example: Consider the circuit shown in figure 5.2

Figure 5.2: Example Circuit

Using loop analyis, as shown in fig5.3, we apply KVL. For .

Figure 5.3: Tree for the example circuit

     

     

     

Solving the same circuit using superposition theorem

There are two sources. We will take one at a time and find the contribution in shown in figure which is quantity of interest for us. Taking Voltage source first (as in figure 5.4)

Figure 5.4: Taking Voltage source

(5.1)

Taking current source only, (as in figure 5.5), making tree (as in figure 5.6)

Figure 5.5: Taking Current Source only

Figure 5.6: Making Tree for the circuit considering current source only

     

     

     

     

     

     

When one is finding effect of an independent source, other independent sources are nullified. Let's take an example having dependent source (Fig.7.5).

Figure 5.7: Circuit for analysis with dependent source

Taking voltage source first (Fig.7.6)

Figure 5.8: Taking only voltage source

Using KVL:

(5.2)

Taking Current source (Fig.7.7), and making a tree (Fig.7.8), we write KVL and solve

Figure 5.9: Taking Current Source

Figure 5.10: Making a tree

     

     

     

     

     

     

Now we verify the solution from loop current method directly (Fig.7.9). Making tree (Fig.7.10).

Figure 5.11: Direct Verification

Figure 5.12: Making Tree

     

     

     

     

     

     

which is correct answer.

Thevenin's Theorem and will vary linearly in Fig.5.13.

Figure 5.13: Network (having sources also)

     

     

     

     

     

This implies that voltage across load in figure 5.14 should be

This implies: (see 5.15) , that is, .

Figure 5.14:

Figure 5.15: Getting an equivalent network

Hence, equivalent of network at terminal AB is shown in figure 5.16.

Figure 5.16: Equivalent Network

Here,

open circuit voltage

The two figures shown in figure 5.17 are equivalent. When the source inside the network is neglected (if voltage source, short ckted, if current source, open ckted)

Figure 5.17: Thevenin's Theorem: the two figures are equivalent

The same could be done with equivalent circuit. hence, we get 5.18.

Figure 5.18:

Norton Theorem

If the network shown in figure 5.19 is linear, . The network can then be replaced by a Norton equivalent, as shown in steps in figures 5.20 5.21 5.22 5.23 and 5.24.

Figure 5.19: The Linear Network

Figure 5.20:

Figure 5.21:

Figure 5.22:

Figure 5.23:

Figure 5.24: