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
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. Polyphase Systems
9. Operational Amplifiers
10. Laplace Transforms
11. Time-Dependent Circuits
- Introduction
- Inductors and capacitors
- First-order transients
- Nodal analysis
- Mesh analysis
- Laplace transforms
- Additional techniques
12. Two-Port Networks
Appendix
Current Source Combinations
Series
Current sources should never be combined in series. What would happen if we connect two current sources with different currents 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 $I_i$ points towards the same node as $I_{eff}$ and with $-$ sign if $I_i$ points to the other node. Since all the current sources are connected in parallel, when we replace $I_i$ with $I_{eff}$, the other current sources are removed (i.e. replaced with open circuits).
For instance, consider the circuit in Fig. 1, in which current sources $I_1$, $I_2$, and $I_3$ are connected in parallel. In this circuit, we can keep one current source, say $I_1$, replace its value with $$\begin{equation}I_{1,eff}=I_1-I_2+I_3\end{equation}$$ and remove current sources $I_2$ and $I_3$ from the circuit. Notice that $I_1$ and $I_3$ appear with positive sign in the above equation because both $I_1$ and $I_3$ point towards node $v_3$, just like $I_{1,eff}$. $I_2$ appears with negative sign because it points towards node $v_4$ while $I_{1,eff}$ points towards node $v_3$. If we kept current source $I_2$, we had to replace its value with $$\begin{equation}I_{2,eff}=-I_1+I_2-I_3\end{equation}$$ $I_1$ and $I_3$ appear with positive sign in the above equation because $I_2$ points towards node $v_4$, just like $I_{2,eff}$. $I_1$ and $I_3$ appear with negative sign because they point towards node $v_3$ while $I_{2,eff}$ points towards node $v_4$. Also, if we kept current source $I_3$, we had to replace its value with $$\begin{equation}I_{3,eff}=I_1-I_2+I_3\end{equation}$$