Linear Circuit Analysis

1. Introduction
2. Basic Concepts
3. Simple Circuits
4. Nodal and Mesh Analysis
5. Additional Analysis Techniques
6. AC Analysis
7. Operational Amplifiers
8. Laplace Transforms
9. Time-Dependent Circuits
10. Two-port networks

Topics convered in CircuitsU

Below is the list of chapters, for which CircuitsU can generate random problems. The instructor can re-organize the content of the chapters and topics covered in each chapter, and change the type, difficulty, and number of homework problems that the site will generate in each homework assignment. The instructor can also build homework assignments covering problems from different chapters (for instance, to design a midterm or a final exam).

Chapter 1 is an introduction to electric components and circuit diagrams and is the homework associated with it is usually assigned in the first week of classes for students to get used with the website. Chapters 2-9 focus on DC circuits; chapters 10-21 focus on AC circuits; chapters 22-27 focus on Laplace transforms and first and second-order transient circuits. These homework assignments cover most of the topics that are usually covered in a college-level, introductory course on linear circuit analysis. For instance, if the Linear Circuit Analysis course is taught as a:

  • year-long course sequence: most topics could be covered throughout the course
  • two-semester course sequence: chapters 1-16 could be offered during the first semester and chapters 17-26 are offered during the second semester
  • three-quarter course sequence: chapters 1-9 could be offered during the first quarter, chapters 10-17 are offered during the second quarter, and chapters 18-26 are offered in the third quarter
Some chapters and the corresponding recommended homework assignments, such as superposition methods, operational amplifiers, or Bode plots can be omitted without any loss of continuity.

Types of problems
CircuitsU can generate a large range of problems such as:
  • General problems, in which students need to answer simple questions such as identifing different components in a circuit, or series and parallel connections.
  • Numerical problems, (ℕ), in which the known variables in the problem are given numerically and students need to compute the shought variable or variables numerically.
  • Analytical problems, (Ⓐ), in which the known variables are given symbolically and the students need to compute the analytically.
  • Design problems, (ⅅ), in which students need to comptute specific elements in a circuit in order for some conditions to be satisfied (e.g. what are the values of specific resistors such that the gain of an amplifier to be equal to 10).
The instructor has much flexibility in selected the number, type, and difficulty of problems in each chapter.

1. Nodes and loops, series and parallel connections

  • Identify resistors, capacitors, inductors, voltage and current sources in electric circuit diagrams
  • Identify nodes and loops in electric circuits
  • Identify series and parallel connections

2. R, L, C combinations

  • Compute the equivalent resistance of a resistor network
  • Compute the equivalent capacitance/inductance of a network of capacitors/inductors

3. Simple circuits

  • Use KVL and KCL to analyze single loop and single node-pair circuits
  • Use voltage and current division to solve simple circuits
  • Compute the power generated/dissipated by a component

4. DC nodal analysis

  • Write and solve the system of nodal equations in DC circuits
  • Compute DC currents, voltages, and powers using nodal analysis
  • Use nodal analysis to solve design problems

5. DC mesh analysis

  • Write and solve the system of mesh equations in DC circuits
  • Compute DC currents, voltages, and powers using mesh analysis
  • Use mesh analysis to solve design problems

6. DC superposition

  • Analyze DC circuits using the method of superposition

7. DC source transformation

  • Use source transformation to compute currents, voltages and powers in DC circuits

8. DC Norton and Thévenin equivalent circuits

  • Compute the Norton and Thévenin equivalent circuits of a DC network
  • Simplify DC circuits by making successive source transformations (not yet implemented)

9. Operational amplifiers (DC)

  • Analyze DC circuits with operational amplifiers

10. Impedance simplification (AC)

  • Compute the equivalent (complex) impedance of a network containing resistors, capacitors and inductors

11. AC nodal analysis

  • Write and solve the system of nodal equations in AC circuits
  • Compute AC currents and voltages using nodal analysis

12. AC mesh analysis

  • Write and solve the system of mesh equations in AC circuits
  • Compute AC currents and voltages using mesh analysis

13. AC superposition

  • Analyze AC circuits using the method of superposition

14. AC source transformation

  • Use source transformation to compute currents and voltages in AC circuits

15. AC Norton and Thévenin equivalent circuits

  • Compute the Norton and Thévenin equivalent circuits of an AC network
  • Simplify AC circuits by making successive source transformations

16. Operational amplifiers (AC)

  • Analyze AC circuits with operational amplifiers

17. AC power analysis

  • Calculate instantaneous and average power in AC circuits
  • Calculate real power, reactive power, complex power, and power factor in AC circuits
  • Find maximum power transfer

18. Magnetically coupled networks

  • Solve problemes with magnetically coupled inductors
  • Solve problems with ideal transformers
  • To be implemented in Spring 2024

19. Polyphase circuits

  • Three phase circuits
  • Not yet implemented

20. Two-port networks

  • Calculate the admittance ($y$), impedance ($z$), hybrid ($h$ and $g$), and transmission ($t$ and $t'$) parameters for two-port networks
  • Convert from one type of network parameters to another type (e.g. $y$-parameters to $z$-parameters,...)

21. Frequency Selective Circuits

  • Compute voltage gain ($G_v$), current gain ($G_i$), transimpedance ($Z$), and transadmittance ($Y$) of AC filters
  • Make Bode plots; derive the transfer function from the Bode plot
  • Compute the resonant frequency and bandwidth
  • Partly implemented (to be finished in Spring 2024)

22. Laplace transforms

  • Compute the direct and inverse Laplace transforms of different functions using the linearity of Laplace transforms, time-shifting, frequency shifting, etc.

23. Laplace impendance simplification

  • Transform a circuit from time domain to s-domain
  • Compute the impedance of a circuit in the s-domain

24. First-order transient circuits

  • Compute time-dependent currents and voltages in first-order transient circuits using:
    1) the time relaxation approach (aka step-by-step approach)
    2) the Laplace transform method
    3) the method of integro-differential equations (for nodal and mesh analysis)

25. Second-order transient circuits

  • Compute time-dependent currents and voltages in second-order transient circuits using:
    1) the Laplace transform method
    2) the method of integro-differential equations (nodal and mesh) analysis

26. Other applications of Laplace transforms

  • Superposition in the s-domain
  • Source transformation in the s-domain
  • Norton and Thévenin equivalent circuits in the s-domain
  • Higher-order transient circuits