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
Power factor correction
Why do we need power factor correction?
Consider the circuit in Fig. 1 and assume that the load is operating at a specific power factor, which can be calculated using the equations from the previous section. Also assume that the red capacitor is removed (this capacitor which will be later to increase the power factor of the load). If the wires are ideal (i.e. have zero internal resistance) the power supplied by the voltage source is equal to the power consumed by the load. However, if the wire are not ideal and have some internal resistance (as it is always the case in practical applications) the power supplied by the voltage source is larger than the power consumed by the load because of the losses in the wires. Therefore, it is useful to ask the question if it is possible to decrease the power losses in the wires without changing the power delivered to $Z_L$.
In DC circuits the answer to the above question is negative. However, it turns out that in AC circuits, if the power factor is less than one as it is often the case in practical applications, it is possible to decrease the power loses in wires (and, in this way, the power supplied by the voltage source) by increasing the power factor of the load. This can be achieved by connecting a reactive element in parallel with $Z_L$ and located very closed to the load. The new reactive element should be of opposite type than the reactivity of the load itself. For instance, if the load is inductive (like in Fig. 1 the reactive element that we need to connect to the load should be a capacitor. If the load is capacitive (like in Fig. 2 the reactive element that we need to connect to the load should be am inductor. In the optimum case, the power factor of the new "load" made by the reactive element and $Z_L$ or $Z_C$ should be as closed to 1 as possible.
In typical industrial applications, the power is delivered over long transmission lines. To decrease the power loses in these lines regulations often requires companies to improve their power factor above a certain minimum limit.
Most often, industrial consumers have larger motors and other electromagnetic systems that are inductive in nature. Therefore, the most common case is when we need to connect , the power is delivered over long transmission lines. To decrease the power loses in these lines regulations often requires companies to improve their power factor above a certain minimum limit.