Lab Data Sheet ENGR-43 Lab-08

ENGINEERING-43
ThéveninNorton Equivalents
Lab-08 /

Lab Data Sheet – ENGR-43 Lab-08

Lab Logistics

Experimenter: Bruce Mayer, PE
Recorder:
Date: Mar06
Equipment Used (maker, model, and serial no. if available)
Fluke 8050A DMM; S/N 4630210
Tektronix PS280 DC Power Supply; S/N TW527171

Special Note

This laboratory exercise entails a significant amount of circuit construction & measurement effort/time. For this reason:

Please COMPLETE ALL MEASUREMENTSin Table I, Table II, Table III, and Table VIIBEFOREcompleting any of the calculations

Directions

Check out a DMM and Power/Probe Leads for the Power-Supply and DMM

Go to the side counter, collect resistors, “bread board”, and leads required to construct the circuit shown inFigure 1. Configure the Power Supply Outputs to the INDEPENDENT mode as indicated in Figure 2.

Make the Measurement and Calculations needed to complete Table I, Table II, Table III, Table IV, Table V, and Table VI.

Table I– Component Actual-Values by DMM Measurement

Vs1 = / 13.035 V
Vs2 = / 5.009 V
R1 = / 2.089 kΩ
R2 = / 3.803 kΩ
R3 = / 7.584 kΩ
R4 = / 11.472 kΩ
RL = / 3.478 kΩ

Table II–NodeVoltages: Calculations & DMM-Measurements

Value
Determination / V1 / V2 / V3
Calculated / 8.368 V / 13.035 V / 3.456 V
Measured / 8.466 V / 13.057 V / 3.459 V
% / 1.17% / 0.0153% / 0.0868%

Calculate Node Voltages using the component actual-values from Table I
%J = 100x(VJ,meas – VJ,calc)/VJ,calc

Table III– Branch Currents: Calculations & DMM-Measurements

Value
Determin. / I1 (mA) / I2 (mA) / I3 (mA) / I4 (mA) / Is1 (mA) / Is2 (mA) / IL (mA)
Calculated / -2.234 / 3.428 / -0.456 / 0.729 / -5.662 / 1.505 / 1.049
Measured / -2.182 / 3.419 / -0.453 / 0.733 / -5.573 / 1.442 / 0.992
% / 2.33% / 0.263% / 0.658% / 0.549% / 1.57% / 4.19% / 5.43%

Calculate Branch Currents using the component actual-values from Table I
%J = 100x(IJ,meas – IJ,calc)/IJ,calc

Table IV– Power Absorbed by Voltage Supplies: Component and VI Calculations

Value
Calculations / PVs1 / PVs2 / ΣPVsj
Component: Calc1 / -73.804 mW / 7.539 mW / 66.265 mW
Measured VI: Calc2 / -72.655 mW / 7.223 mW / 65.432 mW
% / 1.557% / 4.192% / 1.257%

For ALL power calculations assume that the PASSIVE Sign convention relates component voltage-polarities and current-directions
Calculation-1: Use the component actual-values from Table I
Calculation-2: Use the measured values of V-across, and I-thru for the two supplies from Table II and Table III
%J = 100x(PJ,meas – PJ,calc)/PJ,calc

Table V– Power Absorbed by Resistors: Component and VI Calculations

Value
Calcs / PR1 (mW) / PR2 (mW) / PR3 (mW) / PR4 (mW) / PRL (mW) / ΣPRj (mW)
Component:
Calc1 / 10.426 / 44.69 / 1.577 / 6.097 / 3.827 / 66.617
Measured
VI: Calc2 / 9.946 / 44.455 / 1.556 / 6.164 / 3.423 / 65.544
% / 4.603% / 0.526% / 1.33% / 1.099% / 10.56% / 1.611%

For ALL power calculations assume that the PASSIVE Sign convention relates component voltage-polarities and current-directions
Calculation-1: Use the component actual-values from Table I
Calculation-2: Use the measured values of V-across, and I-thru for the two supplies from Table II and Table III
%J = 100x(PJ,meas – PJ,calc)/PJ,calc

Table VI– Power Balance

Value
Calculations / ΣPVsj / ΣPRj / % Out of Balance, ΔOB%
Component: Calc1 / -66.265 mW / 66.617 mW / 0.265%
Measured VI: Calc2 / -65.432 mW / 65.544 mW / 0.0855%

Calculation-1: Use the component-calculations from Table IV and Table V
Calculation-2: Use the measured VI calculations from Table IV and Table V
OB% by this Equation:

Directions (continued)

Remove the Load Resistor, RL, from the circuit to leave OPEN that branch of the circuit as shown in Figure 3

Make the measurements and calculations need to complete Table VII

Table VII– Thevenin Component Determination

Value / Quantity, and Determination-Method
4.884 V / = Voc By DMM Measurment
3.383 mA / = Isc By DMM Measurment

Hint: The DMM itself acts as the Short Circuit

1.444 kΩ / = RTH,VI = Voc/Isc

Use DMM Measured Voc and Isc

1.4317 kΩ / = RTH,SD by Source Deactivation

DeActivate the Voltage Sources by REMOVING them from the Ckt, and REPLACING them with a wire
Measure using the DMM the resulting Resistance as seen from the Voc terminals

1.4379 kΩ / = RTH,avg = [RTH,VI + RTH,SD]/2

Directions (continued)

In the Space Below Neatly Draw the THEVENIN Equivalent for the Circuit shown in Figure 3 with the Load Resistor REATTACHED. Use RTH,avg from Table VII.

For the Thevenin Equivalent Circuit calculate the Load Current, IL, and mark its magnitude and direction on the circuit Diagram.

Directions (continued)

In the Space Below Neatly Draw the NORTON Equivalent for the Circuit shown in Figure 3 with the Load Resistor REATTACHED. Use RTH,avg from Table VII.

For the NORTON Equivalent Circuit calculate the Load Current, IL, and mark its magnitude and direction on the circuit Diagram.

Directions (continued)

Return all lab hardware to the “as-found” condition

Directions (continued)

QUESTION: How does IL by the Thevenin and Norton Equivalents compare to the DMM-Measured value from Table III?

Using the Single-Loop-Circuit method on the Thevenin form find IL as

Using the Current-Divider method on the Norton form find IL as

From Table III note the measured Load Current of 0.992 mA. Using the MEASURED Value as the BASELINE, find the Δ% for both equivalent Circuits

The Thevenin and Norton equivalents provide estimated Load Currents that are within less than ¼% of the measured value. For this experiment the Equivalent-Circuits Models yield excellent estimates for the physical quantities.

Run Notes/Comments

The Thevin/Norton Equivalents are very accurate for this circuit. This indicates that the BOTH the resistors and Volage-Source very closely approximate the LINEAR Circuit-Component ideal forms