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.
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, Distributed-constant circuit, Impedance matching
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
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 | |
---|---|---|
Class 1 | Concept of linear circuit | Explain what a linear circuit is. |
Class 2 | Fourier transform and its properties | Explain the concept of frequency space. |
Class 3 | Laplace transfrom and its properties | Explain the method of solving differential equations using Laplace transform and its application to analysis of LCR circuit. |
Class 4 | Linearity and time invariance of a circuit | Explain the concept of linearity and time invariance. |
Class 5 | Frequency response of linear time-invariant circuit (Convolution integral, Amplitude characteristic, Phase characteristic) | Explain convolution integral and derive relationship between convolution integral and frequency response. |
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 | Test level of understanding with exercise problems | Test level of understanding for classes 1–7. |
Class 9 | Two-port networks (Z matrix, Y matrix, F matrix, S matrix, Combination of 2-port networks) | Explain Z, Y, F and S matrcies using examples. |
Class 10 | Properties of two-port networks (Reciprocal theorem, Properties of two-port reactance network) | Explain reciprocal theorem and two-port reactance networks. |
Class 11 | Synthesis of two-port networks | Explain various types of filters as a representative of two-port networks. |
Class 12 | Distributed-constant circuits and lumped-constant circuits | Derive differential equation of distributed canstant circuits. |
Class 13 | Frequency responses of distrbuted-constant circuits | Explain frequency responses of distributec constant circuits. |
Class 14 | Reflection and transmission of distributed-constant circuits | Explain reflection and trasmission of distributed-constant circuit and their analogies with other phyhsical phenomona. |
Class 15 | Maximum power transfer theorem and impedance matching | Explain the concept of impedance matching and its applications to other physical phenomena. |
Disitrbute course materials during classes if neccesary.
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)
Students' ability of analysis methods for linear and time-invariant cirucuits will be assessed by midterm and final examinations. Midterm examation 50% and final examination 50%.
Students must have successfully completed Electric circuits (ICT .I203) or have equivalent knowledge.
Takamichi Nakamoto nakamoto[at]nt.pi.titech.ac.jp (Ex. 5017),
Shigetaka Takagi takagi[at]ict.e.titech.ac.jp
Contact by e-mail or phone in advance to sckedule an appointment.