|Laplace Transform 12|
1.1 Laplace Transform (LT) of Standard Functions: Definition.
unilateral and bilateral Laplace Transform, LT of sin(at), cos(at),
eat ,tn , sinh(at), cosh(at), erf(t), Heavi-side unit step, dirac-delta
function, LT of periodic function
1.2 Properties of Laplace Transform: Linearity, first shifting theorem,
second shifting theorem, multiplication by t n , division by t ,
Laplace Transform of derivatives and integrals, change of scale,
convolution theorem, initial and final value theorem, Parsavel’s
1.3 Inverse Laplace Transform: Partial fraction method, long division
method, residue method
1.4 Applications of Laplace Transform: Solution of ordinary
2.0 Fourier Series 10
2.1 Introduction: Definition, Dirichlet’s conditions, Euler’s formulae
2.2 Fourier Series of Functions: Exponential, trigonometric functions,
even and odd functions, half range sine and cosine series
2.3 Complex form of Fourier series, orthogonal and orthonormal set of
functions, Fourier integral representation
3.0 Bessel Functions 08
3.1 Solution of Bessel Differential Equation: Series method, recurrence
relation, properties of Bessel function of order +1/2 and -1/2
3.2 Generating function, orthogonality property Bessel Fourier series of functions
4.0 Vector Algebra 12
4.1 Scalar and Vector Product: Scalar and vector product of three and
four vectors and their properties
4.2 Vector Differentiation: Gradient of scalar point function, divergence
and curl of vector point function
4.3 Properties: Solenoidal and irrotational vector fields, conservative
4.4 Vector Integral: Line integral, Green’s theorem in a plane, Gauss’
divergence theorem, Stokes’ theorem
5.0 Complex Variable 10
5.1 Analytic Function: Necessary and sufficient conditions, Cauchy
Reiman equation in polar form
5.2 Harmonic function, orthogonal trajectories
5.3 Mapping: Conformal mapping, bilinear transformations, cross ratio,
fixed points, bilinear transformation of straight lines and circles
1. P. N. Wartikar and J. N. Wartikar, “A Text Book of Applied Mathematic”, Vol. I & II,
Vidyarthi Griha Prakashan
2. A. Datta, “Mathematical Methods in Science and Engineering”, 2012
3. B.S. Grewal, “Higher Engineering Mathematics”, Khanna Publication
1. B. S. Tyagi, “Functions of a Complex Variable,” Kedarnath Ram Nath Publication
2. B. V. Ramana, “Higher Engineering Mathematics”, Tata Mc-Graw Hill Publication
3. Wylie and Barret, “Advanced Engineering Mathematics”, Tata Mc-Graw Hill 6th Edition
4. Erwin Kreysizg, “Advanced Engineering Mathematics”, John Wiley & Sons, Inc
5. Murry R. Spieget, “Vector Analysis”, Schaum’s outline series, Mc-Graw Hill Publication
|Internal Assessment (IA):|
Two tests must be conducted which should cover at least 80% of syllabus. The average marks of
both the tests will be considered for final Internal Assessment.
End Semester Examination:
1. Question paper will comprise of 6 questions, each carrying 20 marks.
2. The students need to solve total 4 questions.
3. Question No.1 will be compulsory and based on entire syllabus.
4. Remaining question (Q.2 to Q.6) will be selected from all the modules.
Term Work/ Tutorial:
At least 08 assignments covering entire syllabus must be given during the ‘class wise tutorial’.
The assignments should be students’ centric and an attempt should be made to make assignments
more meaningful, interesting and innovative.
Term work assessment must be based on the overall performance of the student with every
assignment graded from time to time. The grades will be converted to marks as per ‘credit and
grading system’ manual and should be added and averaged. Based on above scheme grading
and term work assessment should be done.
|Electrical Network Analysis and|
Synthesis – Instrumentation Engineering Semester 3 syllabus
Analysis of networks with dependent sources, mesh analysis, nodal
analysis, source transformation technique, superposition theorem,
Thevenin’s theorem, Norton’s theorem, maximum power transfer
theorem, solution of networks with AC sources. Analysis of coupled
circuits (self inductance, mutual inductance, and dot convention)
2 Graph Theory
Introductory definition – Graph of a network, trees, co-trees, loops.
Incidence matrix, loop matrix and cutest matrix. Network equilibrium
3 Time and Frequency response of circuits
Voltage/current relations for R, L, C and their equations in time domain.
Initial and final conditions, first and second order differential equations,
steady state and transient response. Analysis of transient and steady state
responses using Classical technique as well as by Laplace transforms.
Steady state response to step, ramp, impulse and sinusoidal input
4 Network Functions: poles and zeros
Network functions for one port and two port networks, Driving point and
transfer functions, ladder network, general network, poles and zeros of
network functions, restrictions on Pole and zero locations for driving
point functions and Transfer functions, time domain behavior from polezero
5 Two-Port parameters
Open circuit, Short circuit, transmission and hybrid parameters,
relationship between parameter sets, reciprocity and symmetry conditions,
parallel connections, parallel connection of two port networks.
6 Fundamentals of Network Synthesis.
Causality and stability, Hurwitz polynomials, positive real functions,
synthesis of one port networks with two kinds of elements. Properties and
synthesis of L-C, R-C, R-L driving point impedances, synthesis of R-L-C
Properties of transfer functions, zeros of transmission, synthesis of Y21
and Z21 with a 1-Ohm termination, synthesis of constant – resistance
1. Question paper will comprise of 6 questions, each carrying 20 Marks.
2. Total 4 questions need to be solved.
3. Question No. 1 will be compulsory and based on entire syllabus wherein sub questions of
4 to 5 marks will be asked.
4. Remaining questions will be mixed in nature.
5. In question paper weightage of each module will be proportional to number of respective
lecture hours as mentioned in the syllabus.
Term work shall consist of minimum three simulations and four tutorials from the above list.
The distribution of marks for term work shall be as follows:
Laboratory work (Tutorials) : 10 Marks
Laboratory work (programs / journal) : 10 Marks
Attendance (Theory and Practical) : 5 Marks
The final certification and acceptance of term work ensures the satisfactory performance of
laboratory work and minimum passing in the term work.
Internal Assessment consists of two tests out of which, one should be compulsory class test (on
minimum 02 Modules) and the other is either a class test or assignment on live problems or
End Semester Examination: Some guidelines for setting the question papers are as, six questions
to be set each of 20 marks, out of these any four questions to be attempted by students. Minimum
80% syllabus should be covered in question papers of end semester examination.
1. Kuo Franklin F., Network analysis and synthesis, 1st ed., Wiley International, 1962.
2. Van Valkenburg M.E., Network analysis, 3rd ed., Eastern Economy Edition, 1983.