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
The $V_{test}/I_{test}$ method
Have you ever wondered how an ohmmeter works (an ohmmeter is an instrument that measures the resistance or impedance of a circuit)? In order to measure the resistance of a network the ohmmeter applies a small voltage at the terminals of the network and measure the current going through the terminals. Then, it uses Ohm's law to compute the resistance of the circuit. This principle stays at the basis of the $V_{test}/I_{test}$ method that is often used in electronics to measure or compute the resistance of a network. Depending on the type of the source that is used to energize the network, we distinguish two methods.
The test voltage source method
When using the test voltage source method we apply a test voltage (in theoretial calculations often taken equal to $1 \: {\textcolor{gray}V}$) and compute the value of the current injected by this source. Then, the resitance of the network is comptued using
$$\begin{equation}R=\frac{V_{test}}{I_{test}}\end{equation}$$The test current source method
When using the test current source method we apply a test current (in theoretial calculations often taken equal to $1 \: {\textcolor{gray}A}$) and compute the value of the voltage at the terminals of the network. Then, the resitance of the network is comptued using the same equation as above.
Notes
- Whenever you use the $V_{test}/I_{test}$ method to determine the resistance of a circuit, you need to make sure your circuit does not have any independent sources that could affect your measurements (in practice they can demage your ohmmeter).
- The $V_{test}/I_{test}$ method is often used to determine the Norton and Thévenin resistance (or impedance in the case of AC circuits) of a network.