Mesh Analysis 2 & Time-arying Signals

Mesh Analysis 2

In this lab, we used another method other than the nodal analysis to solve circuit problems. Mesh analysis uses meshes instead of nodes to form equations. A mesh is a loop that does not contain other loops. we assume every mesh has a certain current running around. For convenience, the directions of the currents are set to be either all clockwise or all counterclockwise. This method can quickly setup a coefficient matrix of all the currents. It saves the time of simplifying the equation. Whenever there is a current source separating two meshes, the two meshes can form a "super-mesh". A "super-mesh" construct one loop equation consisting of multiple currents.

Here is a circuit graph of the lab with theoretical calculations. we used mesh analysis to get the three equations and used matrix to find the solutions. the mesh currents are listed at the top right corner.

we chose four resistances and measured their experimental resistances.

This picture shows the setup of the circuit

We measured the experimental voltages and compared to the given voltages in the circuit graph.

The following table shows the theoretical data, experimental data and percent error.

	V1 (V)	V2 (V)	I1 (mA)	R1 (kΩ)	R2 (kΩ)	R3 (kΩ)	R4 (kΩ)
Experimental	4.99	-3.6	-0.362	6.62	4.57	21.6	9.6
Theoretical	5	-3.22	-0.322	6.8	4.7	22	10
Percent Error	0.20%	11.80%	12.42%	2.65%	2.77%	1.82%	4.00%

Time-varying Signals

In this lab, we used the wavegen to generate time-varying signals. In all previous labs, we have been using the DC input only. We tried sinusoidal, ramp up waves on the wavegen.

sinusoidal wave scope

sinusoidal Wavegen

RampUp Scope

RampUp Wavegen

The amplitudes, frequencies and periods from the oscilloscope perfectly match the settings in the wave gen.

Summary: The mesh analysis is another alternative to Kirchoff's Laws. I believe that it applies to more circuits that nodal analysis. It handles both the voltage source and current source. It also helps to set up the coefficient matrix very fast while nodal analysis still requires one extra step to simply the equations. It is a very useful method and it should be the first choice for most circuit problems.

The time-varying signals allow us to test circuit with an alternating voltage. It is a better way than using the power supply box knob to adjust the voltage. We are going to use this technique in the following experiments.