Linear Circuit Analysis
1. Introduction
2. Basic Concepts
- Charge, current, and voltage
- Power and energy
- Linear circuits
- Linear components
- Nodes and loops
- Series and parallel
- R, L & C combinations
- V & I combinations
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 (DC)
5. Additional Analysis Techniques (DC)
- Superposition
- Source transformation
- The $V_{test}/I_{test}$ method
- Norton equivalent
- Thévenin equivalent
- Max power transfer
- DC analysis of L & C
6. AC Analysis
7. Magnetically Coupled Circuits
8. Polyphase Systems
9. Operational Amplifiers
10. Laplace Transforms
11. Time-Dependent Circuits
- Introduction
- Inductors and capacitors
- First-order transients
- Second-order transients
-
Parallel RLC circuits
Series RLC circuits - Nodal analysis
- Mesh analysis
- Laplace transforms
- Additional techniques
12. Two-Port Networks
Appendix
Additional Analysis Techniques in Time-Dependent Circuits
As discussed earlier in this chapter, in addition to the nodal and mesh analysis methods, most of the techniques used for DC and AC circuits can also be applied to time-dependent circuits:
- Ohm's law
- Current division
- Voltage division
- Impedance simplification
- Superposition
- Source transformation
- Norton and Thévenin equivalent circuits
Click the links in the Examples of Solved Problems section to see how these methods are applied to solve different problems in linear circuits.
Examples of Solved Problems
-
Impedance simplification in the s-domain
Circuit with 0 loops, 1 resistor, 1 inductor, 1 capacitor
Circuit with 1 loop, 2 resistors, 1 inductor, 1 capacitor
Circuit with 3 loops, 2 resistors, 2 inductors, 2 capacitors
-
Superposition
Circuit with 2 loops, 1 voltage source, 1 current source, 1 resistor, 1 inductor/capacitor (numerical in s-domain)
Circuit with 3 loops, 1 voltage source, 1 current source, 2 resistors, 1 inductor, 1 capacitor (numerical in s-domain)
Circuit with 4 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor, 1 dependent (numerical in time/s-domain)
-
Source transformation
Circuit with 2 loops, 2 sources, 2 resistors, 1 inductor/capacitor (numerical s-domain simplification)
Circuit with 3 loops, 2 sources, 2 resistors, 1 inductor/capacitor (numerical s-domain simplification)
Circuit with 2 loops, 2 sources, 2 resistors, 1 inductor/capacitor (numerical time/s-domain Norton, source transformation)
Circuit with 4 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor (numerical time/s-domain Norton, source transformation)
Circuit with 4 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor (numerical time/s-domain Thévenin, source transformation)
-
Norton and Thévenin equivalent circuits
Circuit with 3 loops, 2 sources, 2 resistors, 1 inductor/capacitor (numerical time/s-domain Norton, source transformation)
Circuit with 4 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor (numerical time/s-domain Thévenin, source transformation)
-
Impedance simplification in the s-domain
Circuit with 0 loops, 1 resistor, 1 inductor, 1 capacitor
Circuit with 1 loop, 2 resistors, 1 inductor, 1 capacitor
Circuit with 3 loops, 2 resistors, 2 inductors, 2 capacitors
Circuit with 8 loops, 6 resistors, 3 inductors, 3 capacitors
-
Superposition
Circuit with 2 loops, 1 voltage source, 1 current source, 1 resistor, 1 inductor/capacitor (numerical in s-domain)
Circuit with 3 loops, 2 voltage sources, 2 resistors, 1 inductor, 1 capacitor (numerical in s-domain)
Circuit with 3 loops, 2 current sources, 2 resistors, 1 inductor, 1 capacitor (numerical in s-domain)
Circuit with 3 loops, 1 voltage source, 1 current source, 2 resistors, 1 inductor, 1 capacitor (numerical in s-domain)
Circuit with 3 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor (numerical in s-domain)
Circuit with 4 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor (numerical in s-domain)
Circuit with 3 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor, 1 dependent source (numerical in s-domain)
Circuit with 4 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor, 1 dependent source (numerical in s-domain)
-
Source transformation
Circuit with 2 loops, 2 sources, 2 resistors, 1 inductor/capacitor (numerical s-domain simplification)
Circuit with 3 loops, 2 sources, 2 resistors, 1 inductor/capacitor (numerical s-domain simplification)
Circuit with 3 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor (numerical s-domain simplification)
Circuit with 5 loops, 3 sources, 2 resistors, 2 inductors, 2 capacitors (numerical s-domain simplification)
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Norton equivalent circuits
Circuit with 2 loops, 2 sources, 2 resistors, 1 inductor/capacitor (numerical time/s-domain Norton, source transformation)
Circuit with 3 loops, 2 sources, 2 resistors, 1 inductor/capacitor (numerical time/s-domain Norton, source transformation)
Circuit with 4 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor (numerical time/s-domain Norton, source transformation)
Circuit with 5 loops, 3 sources, 2 resistors, 2 inductors, 2 capacitors (numerical time/s-domain Norton, source transformation)
-
Thévenin equivalent circuits
Circuit with 2 loops, 2 sources, 2 resistors, 1 inductor/capacitor (numerical time/s-domain Thévenin, source transformation)
Circuit with 3 loops, 2 sources, 2 resistors, 1 inductor/capacitor (numerical time/s-domain Thévenin, source transformation)
Circuit with 4 loops, 3 sources, 2 resistors, 1 inductor, 1 capacitor (numerical time/s-domain Thévenin, source transformation)
Circuit with 5 loops, 3 sources, 2 resistors, 2 inductors, 2 capacitors (numerical time/s-domain Thévenin, source transformation)