2020 Linear Circuits

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Academic unit or major
Undergraduate major in Information and Communications Engineering
Nakamoto Takamichi 
Course component(s)
Mode of instruction
Day/Period(Room No.)
Mon5-6(S421)  Thr5-6(S421)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

This course focuses on analyses both in time and frequency domains indispensable for circuit analysis. Topics are Fourier and Laplace transforms, linearity and time-invariant circuit, frequency response of linear time-invariant circuit, nodal and mesh analyses and two-port circuit network. Furthermore, this course includes distributed constant circuit as well as lumped constant circuit and the concept of impedance matching. Students will be able to understand analysis methods of lumped constant and distributed constant circuits both in time and frequency domains and to obtain fundamental knowledge of linear circuits.
Knowledge of linear circuit is required for designing electronic circuits indispensable for realizing a modernized information system. Moreover, its concept is widely applicable to designs of various linear systems beyond circuit fields.

Student learning outcomes

By the end of this course, students will be able to
1) analyze circuits using Fourier and Laplace transforms.
2) analyze linear time-invariant circuits.
3) understand impulse and step responses.
4) analyze two-port networks.
5) understand distributed-constant circuits and utilize them.
6) understand the concept of impedance matching and consider it for circuit designs.


Linear time-invariant circuit, Laplace transform, Impulse response, Convolution integral, Distributed-constant circuit, Impedance matching

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Review the content of previous class, explain the content of each class using many examples and then describe the advanced content. Students are sometimes given exercise problems at the end of class.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Basic mathmatics and linear circuits Explain basic mathematics for linear circuits (1)
Class 2 Fourier series and Fourier transform Explain basic mathematics for linear circuits (2)
Class 3 Laplace transform and its properties Explain basic mathematics for linear circuits (3)
Class 4 Linearity and time invariance of circuit Explain the concept of linearity and time invariance.
Class 5 Convolution integral and frequency response of linear time-invariant circuit Explain concept of convolution integral and frequency response of linear circuit.
Class 6 Nodal analysis and mesh analysis Explain methods of nodal analysis and mesh analysis using example circuits.
Class 7 Stability and temporal response of linear time-invariant circuit (impulse response and step response) Explain stability of linear time-invariant circuit, its impulse response and its step response.
Class 8 Two-port networks (Z matrix, Y matrix, F matrix, S matrix, Combination of 2-port networks) Explain Z, Y, F and S matrices using examples.
Class 9 Properties of two-port networks (Reciprocal theorem, Properties of two-port reactance network) Explain reciprocal theorem and two-port reactance networks.
Class 10 Structures of two-port networks (Fundamentals of filters) Explain various types of filters as a representative of two-port networks.
Class 11 Synthesis of filter circuits (LC two-port networks) Explain how to synthesize filter circuits.
Class 12 Distributed-constant circuits and lumped-constant circuits, network analyzer Derive differential equation of distributed constant circuits.
Class 13 Reflection and transmission of distributed-constant circuits, standing wave Explain reflection and trasmission of distributed-constant circuit and their analogies with other physical phenomena.
Class 14 Maximum power transfer theorem and impedance matching Explain the concept of impedance matching and its applications to other physical phenomena.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


Disitrbute course materials through OCW-i during classes if neccesary.

Reference books, course materials, etc.

Linear circuit theory, Shigetaka Takagi, Asakura shoten, ISBN 978-4-254-22163-3 C3055(Japanese)
Fundamentals of circuit theory, Ken Yanagisawa, Denki gakkai, ISBN4-88686-204-7 C3054(Japanese)

Assessment criteria and methods

Students' ability of analysis methods for linear and time-invariant cirucuits will be assessed by assignments and final examinations. Assignments 40% and final examination 60%.

Related courses

  • ICT.I203 : Electric Circuits
  • ICT.I312 : Linear Electronic Circuits

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed Electric circuits (ICT .I203) or have equivalent knowledge.

Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Takamichi Nakamoto nakamoto[at]nt.pi.titech.ac.jp (Ex. 5017),

Office hours

Contact by e-mail or phone in advance to sckedule an appointment.

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