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. Operational Amplifiers
8. Laplace Transforms
9. Time-Dependent Circuits
- Introduction
- First-order transients
- Nodal analysis
- Mesh analysis
- Laplace transforms
- Additional techniques
10. Two-port networks
Current Source Combinations
Series
Current sources should never be combined in series.
Parallel
If two or more current sources $I_1$, $I_2$, ... $I_n$ are connected in parallel they can be replaced with a single current source with $$I_{eff}=\pm I_1 \pm I_2\pm...\pm I_n$$ where the terms in the right hand side are taken with $+$ sign if the corresponding current source $I_i$ is oriented in the same direction with $I_{eff}$ and with $-$ sign if $I_i$ is oriented in opposite direction with $I_{eff}$. Since all the current sources are connecte in parallel, when we replace $I_i$ with $I_{eff}$, we need to remove the other current sources.
For instance, considering the circuit in Fig. 1, current sources $I_1$, $I_2$, and $I_3$ are connected in parallel. Therefore, we can keep one the current sources, say $I_1$, replace its value with $I_{eff}=I_1-I_2+I_3$, and remove current sources $I_2$ and $I_3$ from the circuit.