Thevenin Equivalent

Introduction
           If we have a power system with multiple sources and loads, we sometimes get into a really complex circuit. In order to be able to easily calculate a complicated circuit, thevenin equivalents is used. This experiment serves the purpose of be able to make a complicated circuit and do some calculation on the thevenin equivalent.

Experimental

We first use a nodal analysis to calculate the open circuit voltage using the information given:
R_C1 = 100 ohm
R_C2 = R_C3 = 39ohm
R_L1 = 680ohm
V_S1 = V_S2 = 9V
V_load2 min = 8V

calculation to obtain V_x

Based on the calculation using nodal analysis, V_x is calculated to be 8.644V


Once V_x is obtained, another calculation is done for finding V_y:

calculation to obtain V_y

V_y of 5.112V is obtained

Once the V_y is obtained, the smallest permissible for R_L2 and short circuit current is calculated as follow:

Calculation for R_L2 and I

I = 9.77 mA

R_L2 = 819ohm

Once the calculation part is done, each components were measured and the circuit for the thevenin equivalent was built

Component	Nominal Value	Measured Value	Power or Current Rating
R_TH	65.9ohm	66.2 ± 0.1 ohm	0.3W
R_L2	819 ohm	819 ± 1 ohm	0.3W
V_TH	8.644V	8.66 ± 0.02 V	2A

The data taken is tabulated below:

Config	Theoretical	Measured	%error
R_L2 = R_L2 min	V_L2 = 8V	7.99 ± 0.01 V	0.125
R_L2 = infinity	V_L2 = 8.64V	8.66 ± 0.02V	0.231

Once the thevenin equivalent circuit is done, the actual complicated circuit will be built after the component was measured:

Component	Nominal Value	Measured Value	Power or Current Rating
RC1	100Ω	98 ± 1Ω	0.25W
RC2	39 Ω	38 ± 0.5 Ω	0.25W
RC3	39 Ω	38 ± 0.5 Ω	0.25W
RL1	680 Ω	680 ± 1 Ω	0.25W
VS1	9V	9.12 V	2A
VS2	9V	9.21V	2A

The breadboard for the circuit

Other setup like the resistor box that can't be put into the breadboard

The result was taken and tabulated as follow:

Config	Theoretical Value	Measured Value	Percent Error
RL2 = RL2, min	Vload2 = 8V	8.15 V	1.875
RL2 = ∞	Vload2 = 8.644V	8.81 V	1.920

 \

Once the data is obtained, we want to find maximum power through experiment. Theoretically, maximum power is obtained when R_L2 is equal to the thevenin resistance. In this case, we will try to see it by varying resistance of R_L2 to be 0.5 R_TH, R_TH , and 2 R_TH. The calculation for power is shown below:

Power = V^2 / R

The data is tabulated as follow:

Configuration	V­Load 2	PLoad 2
RL2 = 0.5RTH = 33.4 ± 0.1 Ω	2.93 ± 0.01 V	257 ± 2.52 mW
RL2 = R­TH = 66.4 ± 0.1 Ω	4.39 ± 0.01 V	290 ± 1.76 mW
RL2 = 2RTH = 131.9 ± 0.1 Ω	5.87 ± 0.01 V	261 ± 1.09 mW

Conclusion
            As we seen on the table above, the maximum power of 290 mW is obtained when the load resistance is equal to the thevenin resistance. The percent error of the actual circuit is larger than the thevenin circuit which can be expected. The reason for this is in the actual circuit has more component on it which will build up error from the discrepancy in the components value. This also contributes to the uncertainty in the power calculation.