## 3.3 Analysis with Mesh or Loop Equations

In writing mesh or loop equations, we follow these steps:

1. For a circuit containing M = L = B ? N + 1 meshes (or loops), we assign a mesh or loop current i 1, i 2, , i n ? 1 for each mesh or loop.

2. If the circuit does not contain any current sources, we apply KVL around each mesh or loop.

3. If the circuit contains a current source between two meshes or loops, say meshes or loops j and k denoted as mesh variables i j and i k, we replace the current source with an open circuit thus forming a common mesh or loop, and we write a mesh or loop equation for this common mesh or loop in terms of both i j and i k. Then, we relate the current source to the mesh or loop variables i j and i k.

Example 3.3

For the circuit of Figure 3.8, write mesh equations in matrix form and solve for the unknowns using matrix theory, Cramer's rule, or Gauss's elimination method. Verify your answers with Excel or MATLAB. Please refer to Appendix A for procedures and examples. Then construct a table showing the voltages across, the currents through, and the power absorbed or delivered by each device.

Figure 3.8: Circuit for Example 3.3

Solution:

For this circuit we need M =

##### Products & Services
Loop Powered Devices

Loop powered devices are electronic devices that can be connected in a transmitter loop, normally a current loop, without the need to have a separate or independent power source. Typical loop powered devices include sensors, transducers, transmitters, isolators, monitors, PLCs, and many field instruments.

Mesh
Mesh consists of wires or fibers woven or knitted into a grid or screen pattern to create a semi-permeable barrier.
Current Loop Converters
Current loop converters convert an analog or digital signal to a current loop output such as 4-20 mA or 0-20 mA.
IC Phase-locked Loops (PLL)
IC phase-locked loops (PLL) are closed-loop frequency controls that are based on the phase difference between the input signal and the output signal of a controlled oscillator.
Mesh Generators
Mesh generators are software systems that generate a mesh in order to simulate a geometric field. They use various algorithms such as the finite element method (FEM).

##### Topics of Interest

3.4 Transformation between Voltage and Current Sources In the previous chapter we stated that a voltage source maintains a constant voltage between its terminals regardless of the current that flows...

3.3 Analysis with Mesh or Loop Equations In writing mesh or loop equations, we follow these steps: For a circuit containing M = L = B ? N + 1 meshes (or loops), we assign a mesh or loop current i 1,...

This chapter begins with nodal, loop and mesh equations and how they are applied to the solution of circuits containing two or more node-pairs and two or more loops or meshes. Other topics included in...

This chapter begins with nodal, loop and mesh equations and how they are applied to the solution of circuits containing two or more node-pairs and two or more loops or meshes. Other topics included in...

3.2 Analysis with Nodal Equations In writing nodal equations, we perform the following steps: For a circuit containing N nodes, we choose one of these as a reference node assumed to be zero volts or...

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