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
Series Connections
Two or more components (each with two terminals) are connected in series when they are part of the same two minor meshes, or, to one minor mesh and the outside mesh. For instance, in Fig. 1:
- Voltage source $V_1$ and resistor $R_1$ are connected in series because they both belong to minor mesh $i_1$ and the outside mesh.
- Current source $I_1$ and capacitor $C_1$ are connected in series because they both belong to minor mesh $i_3$ and the outside mesh.
- However, resistor $R_3$ and inductor $L_1$ are not connected in series because they belong to different pair of minor meshes (resistor $R_3$ belongs to $i_1$ and $i_2$, while inductor $L_1$ belongs to the outside mesh and $i_2$.
In Fig. 2:
- Voltage source $V_1$ and inductor $L_1$ are connected in series because they both belong to minor mesh $i_2$ and the outside mesh.
- Capacitor $C_1$, current source $i_1$ and capacitor $C_2$ are connected in series because they all belong to minor mesh $i_3$ and the outside mesh.
- Resistor $R_2$ and inductor $L_2$ are connected in series because they both belong to minor meshes $i_2$ and $i_3$.
If one component is connected in series with a second component, and the second component is connected in series with the third component, then, the first component is also connected in series with the third component.
Parallel connections
Two or more components (each having two terminals) are connected in parallel when they are connected between the same two nodes. For instance, looking at the circuit in Fig. 2:
- Capacitor $C_3$ and resistor $R_1$ are connected in parallel because they are both connected between nodes $v_2$ and $v_3$.
- However, inductors $L_1$ and $L_2$ are not connected in parallel because they are not connected between the same two nodes (inductor $L_1$ is connected between $v_3$ and $v_6$, while inductor $L_2$ is connected between $v_4$ and $v_6$.
If one component is connected in parallel with a second component, and the second component is connected in parallel with the third component, then, the first component is also connected in parallel with the third component.