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:
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