LAB #09: Thevenin's Theorem

OVERVIEW:
The purpose of this lab was to sketch, analyze, and build a circuit with independent sources. Our primary technique for solving this circuit is Thevenin's Theorem.

PROCEDURE:
Pre-Lab:
As instructed in the ENGR 44 Lab book, use Thevenin's theorem to find the Thevenin equivalent of the circuit in Figure 1. Our goal is to find Vth and Rth.

Lab:

1. Construct the circuit given in the lab book, and measure Voc and Rth.
2. Calculate the percent difference between your predicted values and measured values for Vth and Rth respectively.

Original Circuit

Thevenin Equivalent Circuit

ANALYSIS:
Pre-Lab:
Ideal Resistance Values:
R1 = 1k
R2 = 2.2k
R3 = 1.5k (or 1.3k)
R4 = 4.7k
R5 = 6.8k (side)
R6 = 6.8k (bottom)
RL = 10k

Predicted Voltage and Resitance Values:
A) Voc = Vth =  0.4565 V
B) Rth = Req = 7.4k

Rth Calculation

Voc Calculation

Lab:
Measured Resistance Values:
R1 = 1.11k
R2 = 2.2k
R3 = 1.2k
R4 = 4.69k
R5 = 6.63k (side)
R6 = 6.79k (bottom)
RL = 5.62k

Actual Voltage and Resistance Values:
A) VL = 0.4395V ==> Vth = 0.4395V
B) Req = Rth = 7.39k

Voc on OG circuit

Voc on Thevenin Equivalent Circuit

Maximum Power Transfer to Load Resistor:
Pmax ==> Rth = RL
==> Pmax = V^2/(RL)
==> Pmax = 0.25*(Vth)^2/Rth
==> Pmax = _______

Part 2:
Percent error between predicted and measured voltage:
Error in Vth: (|0.4565 - 0.4395| / 0.4565)* 100 = 3.72%
Error in Rth: (|7.4 - 7.39| / 7.4)* 100 = 0.135%

CONCLUSION:
Our measured values for voltage difference Vth and the Thevenin Resistance Rth matched relatively close to their corresponding predicted values. During the pre-lab, we used Thevenin's to predict the values of Vth and Rth and we found these values to be 0.4565 V and 7.4k, respectively. For the actual lab, we measured Vth = 0.4595 V and Rth = 7.39k, which corresponds to a percent error of 3.72% and 0.135%  respectively. This uncertainty is likely due to the internal resistance of the DMM, which may have caused our measured voltage values to be slightly off. Another possible source of error is the fact that many of our resistance values did not match up perfectly with their ideal values. Another source of uncertainty to consider is that we did not directly measure Vth, but calculated it using the voltage divider rule--- utilizing measured values of VL, RL, and Rth.

MATLAB PROBLEM:
Our professor gave us this Thevenin problem to complete in Matlab.

Thevenin Equivalence problem

Since I don't currently own Matlab, I have worked the problem out by hand. Here are my results:

Vth = Voc = 10.67 V

Rth = Req = 8.889 ohms

Mesh Analysis to find Voc

Wye-Delta Transformation to find Req