3.3. 3.2 3.1 3. 2.7. 2.4. 2.3. 2.2 2.1 2. 1.5. 1.4 1.3 1.2 1.1 1.

2.6. 2.5. P2.3.4.

Introduction
Differential
Equations Exercises2.7.2.2.7.1.
.... Problems Basic 2.3.3.2.3.2. 2.2.1.
2.2.3. Introduction.
2.3.1. Classification
Standard Signals
SIGNALS 1.5.1.
Electrical
Sources
of Exercises1.5.2. 1.4.2.1.4.1.
System
Energy 1.4.7.1.4.6.1.4.5.1.4.4.1.4.3.PropertiesBasic 1.3.3.1.3.2.System Network
Circuit
1.3.1.System and
Initial CIRCUIT LinearDirect2.4.4.2.4.3.2.4.2.2.4.1.Other
System 2.6.2.2.6.1. 2.2.2. INTRODUCTION.

Conditions in Modelling
Mechanical
System
Formula Independent
........
Sources Time-Invariant
Invertibility
Instantaneous
Stability
... Causal Linear
Representation Modelling
Terminology
Systems
Interconnections
Systems. of Some
of
Electrical
System GateSignal
Analysis Time Sinusoidal
Properties Exponential Doublet
Signal
Unit Impulse
Signal
Relationship
Signal SignalContinuous-Time
RampSignal
StepPeriodicEven Dependent Continuous-Time
Signals
ANALYSIS Signals AND
Invariant Signal and
(or and and
in of of K.M. and
or OddWAVEFORM Concepts
or Non-CausalNon-Linear
******t**
Circuits Terms LTI LTI (or Unperiodic
between Singularity and
(LTI) Gate Signals Controlled
Sources and and
BY Systems Inverse
Systems Formula) and and
of Systems Dynamic
Time-Varying for
CLASSICAL Differential Function Standard Discrete-Time Discrete-Time
Functions Systems Systems Linear
Signals Systems
SYNTHESIS
Systems
... ) Signals
Time Contents
....
Equations Systems
METHOD Signals Systems. Invariant

System

SPECIMEN
COPY,Fot

.27-71 8-26
.21 .20 20 15 14 13 13 12 12 12 11 10
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30 28.27 26 25 24 7 5 5 4 4 4 3 3 2 2 1
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 6.8. 3.7. 3.6. 3.5. 3.4. 3.3. 5.2. 3.1. 5.5. 5.4. 5.3. 5.2. 5.1. 5. 4.4. 4.3. 4.2. 4.1. 4. 3.9. 3.8. 3.7. 3.6. 3.5. Responses
Various3.4.
6.8.2.
Relationships 6.7.3.6.7.2.6.7.1. MatrixIncidence
Cut-Set
(Q Matrix 6.2.3.6.2.2.
Introduction Problems
6.8.1, Inter-Relation
Submatrices Elements
Loop [A) 6.2.6.6.2.5.6.2.4.GRAPHTHEORY 6.2.1. Exercises
Representation
Diagram 5.3.2.5.3.1.
Block 5.3.4.5.3.3.
Functions.
Transfer Transformed Solution
Introduction.
CIRCUITProblems Introduction
Definition
Transformation
Laplace
Inverse
Properties
Exercises. TRANSFORM
LAPLACE Transient
Transient
Exercises.
Problems. Transient
Transient
Transient3.4.4. 3.4.3.3.4.2.3.4.1.
Matrix
Relation
RelationRelationRelation
Relation
Cut-setLoopBranch
Tree PathGraphNodeand Inductance
Parameter
Parameter
Resistance
of Capacitance
Parameter
Independent
Sources of
of or Graph Linear of of Response
Response Response
State
Response
ZeroInput
Zero
Transient
Response
Steady
State
among or
(twigs) ANALYSIS Response
Response
Response Response
among A,
Circuit Circuit Circuit Laplace the
between between
between
betweenbetween B,
Theory Laplace
Parameters Various and and Differential
Matrix Components of of of of of
..
Co-tree Transform. SeriesSeriesSeriesSeriesSeries
branch
co-tree B, A A BY Transform
and
and andMatrices
(B] LAPLACE
Equations R-C R-L R-C R-L
voltages
voltages
branch
(ink) B, (links R-L-C
Representation Circuit
Circuit Circuit
Circuit
or circuit
and chords) TRANSFORM having
having having
having
twig having

voltages Sinusoidal DCDC

Sinusoidal
DC
Excitation
Excitation
and Excitation
tree-branch Excitation
Excitation
...

(twig)

voltages

*******l64 .. 148-209
.91-147
.72-90
164 164 163 163 162 162 162 153 152 150 150 150 149 149 148 148 148 148 145 145 122 112
95 95 94 94 94 91 91 89 89 73 73 12 72 69 63 42 46 37 34 31 31 31 31 31.31
 8.1. 8. Compensation
TheoremSubstitution
7.13. Theorem
Tellegen's
Theorem
7.12.7.11. 7.10. 7.9. 7.8. 7.5.
Super-Position
7.7. Theorem7.6. 7.4. 7.3. 7.2. 7.1. 7. 6.11.6.10.
6.9.
duction
TWORKS
O-PORT Problems
Exercise
7.13.2.
7.13.1. 7.12.2. Millman's
Theorem
7.12.1. Mlaximum7.9.2.
7.9.1. 7.8.3.Thevenin's 7.7.2.
7.7.1. 7.6.2.7.6.1. 7.5.4.7.5.3.Kirchhoffs
7.8.2.7.8.1. Reciprocity
Theorem 7.4.3.
8.1.1, 7.4.2.
7.4.1.
Terminology Transformations
Network
7.5.2.7.5.1.LawsTransformations Delta
NETWORK
7.2.2.THEOREMS
7.2.1.
SourceIntroduction. Exercise
Star Problems Network6.9.3.6.9.2.
Duals 6.9.1. 6.8.5.
Analysis
Network .. 6.8.4.6.8.3.

tion Limitations
Limitations
Applications Limitations
Applications Limitations
Applications and
Applications
Limitations
Reciprocity of
Applications
Procedure Limitations
Applications Kirchhoff's
Kirchhoffs
of Super-mesh
Analysis
Super-node
Analysis Junction
Convention
Sign Node
andMesh
Loopand StarDelta Analysis
Analysis
Cut-Set
Power with Analysis. Relation
Relation
NodalLoop Relation
and Duality
to Mutual
Norton's to
Transfer Delta
Star between
between
of to between
of of of of of Voltage
Current
of Millman'sThevenin's
of
Obtain of of
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Conversion Inductance ...
CompensationSubstitution
Substitution Millman'sThevenin's Super-position
Reciprocity
Theorem
of Compensation Theorems Super-position
Theorem branch twig
branch
inear Law Law
V
Theorem and (KVL)(KCL) currents
Theorem and currents voltage
ient Theorem and Theorem
Theorem Theorem Zh
Theorem Norton's Theorem
Theorem
Norton's or
and
Iy and and
and link
Theorems
Theorems link node
Zy currents
(LTI) currentsvoltages

Two
Port
orks

279-350 .23-278
.222 .222 .222 221 .219 .219 218 218 .218 217 .215
- .214 214 213 213 .213 .213 213 213 212 211 211 210 210
2 272 271 258 258 257 256 256 255 241 226 226 226 223 206 206 198 171 171 165 165 165 164 164 164
 9.4. 9.3. 9.2. 9.1. T-Transformation
9. 8.15. Impedances
Image
8.14. 8.13.
y-Domain
esponse 9.8. 9.7. 9.6. Stability9.5. 8.12. 8.11. S.10. 8.9. 8.8. 8.7. 8.6. 8.5. 8.4 8.3.
8.2.
Time-Domain
Natural 9.5.3.9.5.2. 9.4.2.Functions
9.4.1.Network 9.2.1.
Poles Introduction
Concept
NETWORK Problems
Exercise
Transformation.
8.15.2.o
Tt8.15.1.
9.5.1. 8.14.3. 8.14.1.
8.14.2.
Impedance
Output
8.13.2.
Impedance
8.13.1. Parallel-Series
InputInput Connection
8.12.2. Connection
Cascade
Open8.11.5.
8.12.1.
Series-Parallel
Connection. 8.11.3.
Connection
Parallel
8.11.2.
Connection
8.11.4. 8.11.1.
Interconnections 8.10.5.
Series 8.10.6. 8.10.4. 8.10.2.
8.10.3. 8.10.1.
Symmetry
Conditionfor
Relationships Inverse
Parameters
Reciprocity
Condition Inverse
Hybrid(h)
forTransmissionShortOpen 8.1.2.
and
Response and Circuit
Routh-Hurwitz
Criterion
Stability Terminal of
Necessary Zeros
RelationshipNecessary
Relationship TImageImageImage T-parameters Open g-Parameters
h-Parameters Circuit
Circuit
Complex to T'-Parameters
Z-parameters
Y-parameters
T-parameters Hybrid
Transmission
Output Relationship
Response FUNCTIONS TTransformation.
of impedances
impedances
impedances Circuit and Between (7)
Admittance
Impedance
and Network Pairs Short (g)
Conditions
Conditions ...
Impedances of or
Frequency Two Parameters
Natural between
between and Chain
from or in
Circuit in in in in in
in Parameter (7) of
Functions Ports
terms Short
Porttermsterms terms
terms termsterms Two
Pole-zero in in in Parameters or () (2)
from
requencies impulse for for AND termstermsterms Networks Port
pole Impedances
of ABCD
Paramneters
Parameters..
Transfer
Driving Circuit of of of of of of
Pole- positions Open otherotherother otherotherother Sets Variables
RESPONSES of of of Parameters
-zeroPlot response T-parametersinput
open-circuit Impedances
Circuit parameters
parameters parameters
parameters.
parametersparameters
Functions Point
Plot and and
stabilityandImmittance and
stability. output
and Short in
short-circuit terms
impedances
Circuit
Functions of
T-parameters
Impedances
impedances

.351-425

377 374 374 369 366 366 366 362 362 359 352 352 351 .351 .346 345 326 326 325 .323 322 .322 .322 321 320 .320 .320 .319 319 304 303 302 299 299 .298 297 296 295 293 292 291 291 288 286 285 284 283 .282.281 .280 280
 11.5. Introduction
Difference
Equations
11.4. 11.3. 11.2. 11.1. 11. 10.6. 10.5. 10.4.10.3. Introduction
10.2. 10.1. 10. 9.17.9.16. Bode
9.13.
Plot 9.9.
9.15. 9.14. Convolution
Frequency
Response
9.12. 9.11. 9.10.

11.5.3. Properties
11.5.2. 11.4.4.
11.5.1. 11.4.5. 11.4.1.
11.4.3.11.4.2. TheBlock Problems
Exercise R-L Synthesis10.2.3.
R-C L-CPolynomial
HurwitzElements
10.2.2 SYNTHESIS
NETWORK
10.2.1. Exercise
Problems 9.17.5.
9.17.4. 9.17.2.
9.17.3. MeasureSteps
Quadratic
Factors
9.15.4. 9.9.1.
z-TRANSFORMS 9.17.1. 9.15.3.9.15.2.9.15.1.
Standard Magnitude
Bode 9.13.3. 9.13.1.
9.13.2. Plot Angle 9.9,2.
Relation
z-Transform Immittance
Impedance
Impedance
Diagram to Plots and
Time
tiplication Definition
Relationship
..*********
Linearity The
Definition
Properties Positive
Causality DeterminationPhae Gain GainPhase Sketch System
Simple Poles LogarithmicPhase Response
Time
of of of of Form Frequency
ResponseBetween
Region One Realizability Relative of Magnitude
Shifting the Integral
Margin
MarginCrossover or Basic
z-Transform Representation
... or or
Function Real
Crossover the Poles ofAngle
of of of R-C R-L Port and Zeros Gain H(Go) Time
the the ofthe Stability Bode Factors *******.

(or byBetween AND Admittance

AdmittanceNetworks
FunctionsStability (PM) (GM) of
of
Convergence or at 'K Scales Plot
Real a Unilateral z-Transform
ROC Frequency Plot Zeros a Response
Theory GM Frequency the Function
Constant ITS of
(Semilog
lation) the and Origin
(1 H(jo).
with
z-Transform APPLICATIONS. PM + and
z-Transform Function
Function Tjo)tl (jo
Two
from Papers), Frequency
Kinds
Bode
and of Plot Response
the Elements
Laplace

Transform

.474-507 426-473
....415
480 480 480 480 478 478 478 476 475 475 474 474 474 472 472 444 440 436 435 431 426 426 426 426 423 423 416 415 415 415 414 409 406 403 401 400 .399 399 398 398 398 398 397 397 381 380 379 .378
 11.5.4, Scaling inthez-IDomain (or Complex Translation 481
11.5.5. Time Expansion 481
11.5.6. Time Reversal 481
11.5.7. Conjugation 482
11.5.8. Initial Value Theorem 482
11.5.9. Final Value Theorem
482
11.5.10. Differentiation in the z-Domain (or Multiplication by n) 482
11.5.11. Convolution Theorem 483
11.6. Inverse z-Transform 486
11.7. The System Function of aLinear Time Invariant System 489
11.7.1. Causality .... 489
11.7.2. Stability 490
11.7.3. Interconnections of the Systems 498
11.7.4. Systems Block-Diagrams 498
Exercise 504
Problems 504

12. FILTER SYNTHESIS 508-550

12.1. Introduction 508
12.2. Parameters of a Filter. 508
12.2.1. Characteristic Impedance 508
12.2.2. Pass Band. 508
12.2.3. Stop Band 508
12.2.4. Cut-off Frequency 508
12.2.5. Units of Attenuation 508
12.3. Classification of Filters. 509
12.3.1. Low Pass Filters 509
12.3.2. High Pass Filters 509
12.3.3. Band Pass Filters 509
12.3.4.Band Stop or Band Elimination Filters 509
12.4. Block diagram Representative of the Filters 510
12.5. Filter Networks 511
12.6. Characteristic of Filter Networks 512
12.6.1. Characteristic Impedance 512
12.6.2. Propagation Constant () 514
12.6.3. Classification of Pass-Band and Stop-Band ... 515
12.6.4. Cut-off Frequency 517
12.7. Summary of Relations for Filter Networks 518
12.8. Constant-K Low Pass Filters 518
12.9. Constant-K High Pass Filters. 521
12.10. Constant-K Band Pass Filters 526
529
12.11. Constant-K Band Stop Filters 532
12.12. m-derived Filters
532
12.12.1. m-derived T-networks 533
12.12.2. m-derived r-networks
534
12.13. m-derived Low Pass Filters 534
12.13.1. m-derived T-network Low Pass Filter 535
12.13.2. m-derived -network Low Pass Filter 536
12.14. m-derived High Pass Filters 536
12,14.1. m-derived T-network High Pass Filter 537
12.14.2. m-derived -network High Pass Filter 539
12.15.m-derived Band Pass Filters ...541
12.16. Composite Filters
 551-561 562562562563563563563564566568569570570572572 574-598
551551551552553553555556557557559559559560560561 562-573 574576576580582582E2
574.574
545545546546547548550550
Signal.
Periodic
Coefficients
Conditions
Series
a Series
Filter
Filter Noise of
Connections. Feedbacks Representation.
Series
Fourier
Spectra
Pass Fourier Fourier
Pass and Dirichlet
Feedback.
Voltage-Series
Feedback
Current-Shunt
Current-Series
Feedback
HighFilterFilter
Low in DistortionFeedback
Increase
Bandwidth
Voltage-Shunt Oscillators.
Undamped Phase
FEEDBACK
AMPLIFIERS Oscillators
Oscillators
Damped the Frequency
Time
FiltersActive
Active Negative
Fedback
PositiveFeedback. Feedback
Feedback. Various
Oscillators
Classification
of of Series:
PassStop and
Determination
Gain
Stability Oscillator
Phase-shift
RC Continuous
PassiveOrder Band
Band in .
Oscillator SERIES
FOURIER Magnitude
Order Oscillator
Operation. Fourier
Feedback.
ofConcept Reduction
Negative Negative
Between
OSCILLATORS
Oscillator
Sinusoidal
Sinusoidal Oscillator
Colpitts
Oscillator
Hartley of Negative
Effect
Symmetry
....... . Oscillator
Crystal
14.11.
Oscillator
Active
Active
of FirstFirst Series
Fourier of
Bridge Introduction
Filters
Limitations Introduction Comparison Introduction of of Properties
Existence
Problems of of Problems
Exercise of Problems
Exercise Concept
12.18.1.
12.18.2. Exercise
12.18.3.
12.18.4. Efects 13.3.3. 13.4.3.
13.4.1. 13.4.4. 14.5.1.
Types 14.5.2.Wien Clapp 15.2.1.15.2.3.
15.2.2.
Active 13.2.2.
13.2.1. 13.3.2.
13.3.1. Types 13.4.2.
12.17. 14.10. 15.4.
15.5.15.6.
12.18.
13. 13.1.13.2. 13.3. 13.4. 13.5. 14. 14.1.14.2.14.3.14.4.14.5. 14.6.14.7.
14.8.14.9. 15. 15.1.15.2. 15.3.
 18.4. 18.3. 18.2.18.1. 18. 17.9.17.8. 17.7. 17.5. 17.4. 17.3.
17.6. Mechanical
Systems.
17.2.
ntroduction
17.1. 17. 16.5. 16.4.16.3. 16.2.16.1. 16.
entationIntroduction
Terminology
Variable
Space
StateState
Approach
Variable Exercises
Thermal
System
System
Liquid
Level
Electro-Mechanical
System17.6.2. D'Alembert's
VARIABLE
ANALYSIS
State STATEProblems Force-Crrent
MechanicalAnalogy
Force-Voltage
17.6.1. Analogy 17.2.1.
ANALOGOUS
Principle17.2.2. SYSTEMSProblems
Exercise 16.4.9.
16.4.10.
Systems 16.4.7.
16.4.8. 14.4.5.
16.4.6. 14.4.4. 16.4.2. Existence
Introduction Problems
16.4.1.Fourier
16.4.3.Properties
FOURIERTRANSFORM Exercise 15.6.8.
15.6.10.15.6.9. 15.6.7. 15.6.5.
15.6.4. 15.6.2.
15.6.1.
15.6.6. 15.6.3.

Mechanical
Lever
Friction
Transform Parseval's
Rotational
Systems
Translation
Systems Characterized Parseval's
MultiplicationRelation
Convolution
Property Reversal
Duality
Differentiation
Integration and Sbifting
TimeTime Conjuge Time
Linearity of of Convolution
Periodic
Differentiation
Coupling Integration
Conjugation
Multiplication Reversal
..Scaling
Time Time
Fourier Fourier Linearity
Shifting
Time
ad
Wheels tion of
Frequency Transform Relation
Devices Transform
Periodic
by and
or Property
Linear
Gears Conjugate for
Signals AND
Scaling Continuous
Constant-Coefficient or
Modulation ITS
Symmetry
APPLICATIONS
Time

Property Periodic
Differential
Signal

Equations

658-681 633-657 .599-632

.....651 .....585
.....585
659 .658 .658 658 .655 655 .653 648 .646 .642 .642 .640 637 636 .635 .634 .634 .633 .631 .630 .617 .616 .615 .614 613 .612 .612 611 611 .611 610 .610 608 .601 599 597 597 585 585 .585 585 584 584 .583 583
 INDEX
ANSWERS APPENDICES 19.7. 19.6. 19.5.19.4. 19.3. 19.2.19.1. 19. 18.9.
18.8. 18.7. 18.6.18.5.
D: Appendix
AppendixAppendix Problems 19.7.2.
Exercises 19.7.1. 19.6.2.
Inductive Transformer
19.6.1. Linear
Inductive Mutual
Introduction
TheInductance
Conventions
Energy Dot Problems
Exercises 18.8.3. 18.8.1.
18.8.2.
Miscellaneous.
Appendix C: MAGNETICALLYCOUPLED
CIRCUITS State-Transition
Advantages Matrix 18.7.2.
(STM)18.7.3. 18.7.1.
Derivation
Linear State
TO Model
in or
UNSOLVED B: A Coupling
Parallel
Aiding.
Opposing
Parallel Coupling
Aiding
Series
Opposing
Series a Invariance
Transfer
Similarity
Experiments Pair Properties
Solution
Signifacance
Diagonalization
Eigen-Values
Invariance
of of of
Manuals Introduction : of TransferFrom
Complex State
of
in Mutually
in the
Parallel Series Variable the of of Transformation
Transfer
Number the of Function
PROBLEMS to Non-Homogeneous the
Matrix Coupled STM
System Analysis. STM
Function
From
Function
Algebra
Inductors State

and State Model

Determinants. Equation

(Forced

System)

.761-769
737-760 697-736 682-696
708-712
713-736 705-707
699-704

695 695 692 692 692 691 691 691 689 687
683...
682 682 .678 .678 .675 672 672 .672 671 668 668 668 667 666 663
 elements
electrícnot task. component the example,
Usually, output we
bOX
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desired hand systems
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NTRODUCTION characterised systems.
TIME and
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On as
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interest
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FOR will
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CONCEPTS input
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Therefore, each
as ...,
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interest 1.1. and
systems a
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MODELING automobile. visualize(0), referred Fig. analyse
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NETWORK or
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 4 00Cìrcuts and Systems Introduction J 5

1.4.5. Causal and Non-CausalSystems 1.5.1. Independent Sources

A
system is said to be causal or non-anticipative if the output of the system at any time depends is assumed to deliver energy with a terminal
onlw on values of the inputtheatinput.
the present time and in the past, i.e., the system output does not A. The voltage source : The voltage source
anticipate future values of voltage.
a constant terminal voltage v(t) regardless of
For example, (i) An ideal voltage source :Which maintains shown in figure 1.6(a) and (b). A U-i plot of the
Y() =x) + x(t- 1) or y[n] =x[n] +x[n -1] is the value of the current through its terminals as
source, is shown in figure 1.6 (c).
causal, while terminal voltage-current relationship for an idealvoltage
y(0) = x() +x{t + 1)or y[n] =y[n] +y[n + 1] is
non-causal systems.
1.4.6. Invertibility and Inverse Systems
Asystem is said to be invertible if distinct inputs lead to distinct outputs. Ifa system is invwea:a y
then an inverse system exists that, when cascaded with the original system, yields an ontoe,
oln] equal to the input x(t) or x[n] to the first system, as illustrated in figure 1.4(a)
An example of an invertible continuous-time system is illustrated in figure 1.4(h) (a) (b) (c)

a) y(t) o(t) = xt) Fig. 1.6 (a-c) Ideal voltage source and v-icharacteristic.
Inverse System keeps
(ii) A practical voltage source : In which the voltage across the terminals of the source
System
x{n] y[n] on] = xn)
falling as the current through it increases. This behaviour can be explained by connecting a resistance
(a) rin series with an ideal voltage source, as in figure 1.7(a) and (b). Then we have the terminal voltage
U, as
it) v() U, =U- i,r
Resistance, R Conductance, G -i() Where i, is the current flowing and r the internal resistance of the ideal voltage source. Av-i
(b) relationship for a practical voltage source, is shown in figure 1.7(c).
Fig. 1.4 (a) Ageneral invertible system (b) an example of invertible system. i, r
1.4.7. Stability
Stability is another important system property. Astable system is one that will remain at rest u)
unless excited by an external source and will return to rest if all the excitations are removed. The
necessary condition for the continuous-time system to be stable is that the roots of the characteristic
equation have negative real parts (or lie in the left-halfof s-plane), while for the discrete-time svstem (a) (b) (C
the roots of the characteristic equation are inside the unit circle as shown in figure 1.5(a) and (b)
respectively. Fig. 1.7 (a-c) Practical voltage source and v-i characteristic.
jImz B. The current source :The current source is assumed to deliver energy through its terminals.
A
J0 Unstable Unstable (i) An ideal current source: Which maintains a constant current i(t) regardless of the value
region regionoanatnete of the terminal voltage as shown in figure 1,.8(a). The v-i characteristic of an ideal current source, is
Stable Unstable shown in figure 1.8(6).
-Unit Circle
region region Stable Stable
region region
+Real z
0
Stable Stable
region region v(t)
Stable Unstable
region region Unstable Unstable
region region
(a) (b (a) (6)
Fig. 1.5. Stable and Unstable regions (a) For continuous time system in the s-plane Fig. 1.8 (a-b) Ideal current source and v-i
(b) For discrete-time system in the z-plane. characteristic.
(ii) A practical current source: In which the current
1.5. ELECTRICAL ENERGY SOURCES keeps falling as the terminal voltage across it increases. This through thebeterminals of the source
a resistance R in parallel with an ideal current source, as inbehaviour can explained by connecting
There are two types of sources of electrical energy. the voltage source and the current source. They , as
igure l1.9(a). Then the terminal current
are two-terminals element either independent or dependent as follows:
 Introduction 7
600Circuits and Systems

y, =(4, +1y) 4, +ty - 1) =(4, +)-4, +4,

Where , is the terminal voltage and Athe internal resistance of theideal current source. Av-irelatin.. Therefore, y(t) = t2 (t-1) is non-linear system.
for a practical current soure, is shown in fgure l.9 (%).
EXERCISES

1.1. Differentiate a network and a circuit.

1.2. Define a system.
(a)
>i, 1.3. What are the different interconnections of the systems.
(6
1.4. Describe the different types of the systems.
Fia, l.9 (a-b) Practical current source and v-i characteristic.
1.5. What are the basic system properties.
1.5.2. Dependent or Controlled Sources 1.6. Describe all the types of electrical enérgy sources.
They are of the following types:
) Voltage controlled voltage source (VCVS) as in figure 1.10(@),
() Current controlled voltage source (CCVS) as in figure 1.10(b),
(n) Current controlled current source (CCCS) as in figure 1.10(c),
(iv) Voltage controlled current source (VCCS) as in figure 1.10(d).

U,=0

(a)
(6)
i, =0
+o

t,=0

(c) (d)
Fig. 1.10. Controlled sources (a) VCVS, (b) CCVS, (c) CCCS, and (d) VCCS.
In a controlled source the source voltage or current (depending upon the type of source) is not
constant but is dependent on a voltage or current at some other location in the network.
EXAMPLE 1.1 What are the properties of continuous time linear system? Consider a
continuous time system , the input and output is related by y(t) = t' (t- 1). Determine
whether the system is linear or non-linear.
Solution: Continuous Time Linear Systems
(1) The system in which continuous time input signals are applied and result in continuous
output signals.
(2) The system that holds the principle of additivity and
homogeneity.
y(t) = 1 (t-1)
y,=44, -1) =4-4?