Linear Circuit Analysis
1. Introduction
2. Basic Concepts
- Currents and voltages
- Linear circuits
- Linear components
- Loops and nodes
- Series and parallel
- R, L & C combinations
- V & I combinations
- Power and energy
3. Simple Circuits
- Ohm's law
- Kirchhoff's current law
- Kirchhoff's voltage law
- Single loop circuits
- Single node-pair circuits
- Voltage division
- Current division
4. Nodal and Mesh Analysis
5. Additional Analysis Techniques
- Superposition
- Source transformation
- The $V_{test}/I_{test}$ method
- Norton equivalent
- Thévenin equivalent
- Max power transfer
6. AC Analysis
7. Magnetically Coupled Circuits
8. Operational Amplifiers
9. Laplace Transforms
10. Time-Dependent Circuits
- Introduction
- First-order transients
- Nodal analysis
- Mesh analysis
- Laplace transforms
- Additional techniques
11. Two-Port Networks
Appendix
3-Quarter Courseplan
Quarter 1
Below are the recommended assignments (HW1-HW11) that are generated by default when the instructor creates a new Linear Circuit Analysis course and choses Quarter 1 in a 3-quarter course. The table shows the proposed due dates for each HW set but each instructor can set his or her own time schedule. The instructor can also re-organize the content and change the type, difficulty, and number of homework problems in each set.
| Week numbera | HW number | HW | Assignment numberb | Due | Description |
|---|---|---|---|---|---|
| Week 1 | Series/Parallel | HW 1 | 1 | End of 2nd week | Identify R, L, C, voltage and current sources, nodes, and loops, series and parallel connections. |
| Week 2 | Resistor simplification | HW 2 | 1 | End of 2nd week | Simplify a network of resistors using series and parallel transformations. |
| Week 3 | Simple circuits (I) | HW 3 | 2 | End of 3rd week | Compute currents, voltages, and powers (dissipated and generated) in circuits with one source and one resistor. |
| Week 4 | Simple circuits (II) | HW 4 | 3 | End of 4th week | Compute currents, voltages, and powers in circuits with 3 or more components, using KVL, KCL, resistor simplifications, current and voltage division. |
| Week 4 | DC nodal analysis (eqs.) | HW 5 | 3 | End of 4th week | Write the system of nodal analysis equations (but do not solve it). |
| Week 5 | DC nodal analysis (num.) | HW 6 | 4 | Beginning of 6th week | Write and solve the system of nodal analysis equations to compute currents, voltages and powers. |
| Week 5 | DC mesh analysis (eqs.) | HW 7 | 4 | Beginning of 6th week | Write the system of mesh analysis equations (but do not solve it). |
| Week 6 | Review session or optional midterm | ||||
| Week 7 | DC mesh analysis (num.) | HW 8 | 5 | Beginning of 8th week | Write and solve the system of mesh analysis equations to compute currents, voltages and powers. |
| Week 7 | DC superposition | HW 9 | 6 | Beginning of 9th week | Use the superposition method to compute currents and voltages in DC networks. |
| Week 8 | DC Source transformation | HW 10 | 6 | Begining of 9th week | Simplify a circuit using successive source transformations. |
| Week 9 | DC Norton/Thévenin | HW 11 | 7 | Beginning of 10th week | Compute the Norton and Thévenin equivalent circuits or DC networks. |
| Week 10 | Final exam | ||||
| Analyze circuits containing one or more operational amplifiers. | |||||
aThe week when the topic is covered.
bHomeworks that have the same assignment number have the same deadlines. For instance, Assignment number 1 containts HW1, HW2, and HW3, which are all due at the end of the second week of classes.
Quarter 2
Below are the recommended assignments (HW1-HW10) that are generated by default when the instructor creates a new Linear Circuit Analysis course and choses Quarter 2 in a 3-quarter course.
| Week number | HW number | HW | Assignment number | Due | Description |
|---|---|---|---|---|---|
| Week 1 | L/C simplification | HW 1 | 1 | End of 2nd week | Simplify networks of capacitors and inductors using series and parallel transformations. |
| Week 2 | Impedance simplification | HW 2 | 1 | End of 2nd week | Compute the effective impedance of an AC network of R, L, and C using series and parallel combinations. |
| Week 2 | AC nodal analysis | HW 3 | 2 | Beginnig of 4th week | Write the system of nodal analysis equations (but do not solve it). |
| Week 3 | AC nodal analysis | HW 4 | 3 | Beginnig of 4th week | Write and solve the system of nodal analysis equations compute currents and voltages. |
| Week 4 | AC mesh analysis | HW 5 | 3 | End of 5th week | Write the system of mesh analysis equations (but do not solve it). |
| Week 5 | AC mesh analysis | HW 6 | 4 | End of 5th week | Write and solve the system of mesh analysis equations to compute currents and voltages. |
| Week 6 | Review session or optional midterm | ||||
| Week 7 | AC superposition | HW 7 | 4 | End of 7th week | Use the superposition method to compute currents and voltages in DC networks |
| Week 8 | AC Norton/Thévenin | HW 8 | 5 | End of 8th week | Compute the Norton and Thévenin equivalent circuits or AC networks. |
| Week 9 | AC analysis | HW 9 | 6 | End of 9th week | Use a.c techniques to solve general AC circuits. |
| Week 9 | AC OpAmps | HW 10 | 7 | End of 10th week | Single OpAmp inverters and followers containing AC sources, resistors, inductors, and capacitors. |
| Week 10 | Final exam | ||||
| Compute y, z, h, and t parameters of DC and AC two-port networks. | |||||
| Derive transfer function from a Bode magnitude plot and draw the Bode magnitude plot of a transfer function. | |||||
Quarter 3
Below are the recommended assignments (HW1-HW10) that are generated by default when the instructor creates a new Linear Circuit Analysis course and choses Quarter 3 in a 3-quarter course.
| Week number | HW number | HW | Assignment number | Due | Description |
|---|---|---|---|---|---|
| Week 1 | AC power | HW 1 | 1 | End of 2nd week | Compute real power, reactive power, complex power, and power factor in AC circuits. |
| Week 1 | AC maximum power transfer | HW 2 | 2 | End of 2rd week | Compute maximum power transferred in AC circuits; AC power factor correction. |
| Week 2 | Laplace transforms | HW 3 | 3 | End of 3th week | Compute the direct Laplace transform of various functions. |
| Week 3 | Inverse Laplace transforms | HW 4 | 4 | Beginning of 4th week | Compute the inverse Laplace transform of various functions. |
| Week 5 | First-order transient circuits | HW 6 | 6 | Beginning of 6th week | Use the time relaxation approach to compute current and voltages in first-order transient circuits. |
| Week 4 | Review session or optional midterm | ||||
| Week 5 | ODE nodal analysis (eqs.) | HW 7 | 7 | Beginning of 6th week | Write the system of nodal analysis ODEs for first, second and higher-order transient circuits (zero and non-zero initial conditions). |
| Week 6 | ODE mesh analysis (eqs.) | HW 8 | 8 | Beginning of 7th week | Write the system of mesh analysis ODEs for first, second and higher-order transient circuits (zero and non-zero initial conditions). |
| Week 4 | Laplace impedance simplification | HW 5 | 5 | Beginning of 4th week | Tranform a circuit to s-domain and compute its equivalent s-domain impedance. |
| Week 6 | Laplace transform nodal analysis (num.) | HW 9 | 9 | End of 7th week | Convert circuits to s-domain, then write and solve the system of nodal analysis equations for first and second-order transient circuits (zero initial conditions). |
| Week 6 | Laplace transform mesh analysis (num.) | HW 10 | 9 | End of 7th week | Convert circuits to s-domain, then write and solve the system of mesh analysis equations for first and second-order transient circuits (zero initial conditions). |
| Week 7 | Laplace analysis (num.) | HW 11 | 10 | Beginning of 8th week | Source transformations, Norton/Thévenin equivalent circuits and superposition in the s-domain (zero initial conditions). |
| Week 8 | Magnetically coupled systems | NYI | 11 | Beginning of 9th week | |
| Week 8 | Two-port networks | NYI | 12 | End of 9th week | |
| Week 9 | Three-phase systems | NYI | 13 | End of 9th week | |
| Week 10 | Final exam | ||||