Download Experiment # 1 - GWU`s SEAS - The George Washington University

The George Washington University
School of Engineering and Applied Science
Department of Electrical and Computer Engineering
ECE 2110 - LAB
Experiment # 3
Voltage Division, Circuit Reduction, and Node Voltage Analysis (1)
Equipment:
Lab Equipment
(2 Sets) Digital Multimeter (DMM)
(2 Pairs) Test Leads
(1 Set) Bread Board
(1 Set) DC Power Supply
Equipment Description
Keithley Model 175 Digital Multimeter (DMM)
Banana to mini-grabber test leads
Prototype Bread Board
Agilent E3631A Triple Output DC Power Supply
Table 1.1
Components:
Kit Part #
Spice Part
Name
Resistor (R1)
Resistor (R2)
Resistor (R3)
Resistor (R4)
Resistor (R5)
Resistor (R6)
Resistor
Mystery Resistor
Potentiometer
R
R
R
R
R
R
R
R
POT
Symbol Name
Part Description
(used in schematics
throughout this lab manual)
470 Ω Resistor
560 Ω Resistor
680 Ω Resistor
750 Ω Resistor
820 Ω Resistor
910 Ω Resistor
1 k Ω Resistor (2)
? Ω Resistor
10 k Ω Potentiometer
Table 1.2
R1
R2
R3
R4
R5
R6
Objectives:






To calculate and measure the total resistance in a series/parallel circuit.
To calculate and measure the total current in a series/parallel circuit for a given applied
voltage.
To calculate the expected total power dissipated in a series/parallel circuit from nominal
and measured values.
To calculate and measure the voltage drop across and the current through all
components of a series/parallel circuit.
To calculate the power dissipated by each component of a series/parallel circuit from
measured data.
Design, build and test a voltage ladder and a particular non series/non parallel circuit
known as a Wheatstone Bridge Circuit.
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 1 of 6
Prelab: (Submit electronically prior to lab meeting, also have a printed copy for yourself during lab)
1. Based on the class notes, you should be familiar with the concept of resistors in series and
resistors in parallel. For this prelab, you are asked to simplify circuits to find their equivalent
resistance. Read prelab part 2, before working out parts a,b, & c.
a.
Find REQ in the circuit in Fig. 1A. DO NOT substitute values for the resistors. Leave
your answers in terms of R1, R2, R3, and R4. Show the detailed steps of how you
simplified the circuit to find REQ.
b.
Find REQ in the circuit in Fig. 1A. DO NOT substitute values for the resistors. Leave
your answers in terms of R1- R6. Show the detailed steps of how you simplified the
circuit to find REQ.
c.
For the figure shown in Fig.1C, the resistors are not in series or parallel, thus REQ
cannot be found through circuit reduction. Instead, (1) use node voltage analysis to
determine VA and VB in terms of R1-R5 and V1. Then, (2) use KCL to determine current
I1 in terms of VA, VB, and the necessary resistors. Finally, (3) use Ohm’s law to determine
REQ in terms of V1, VA, VB, and R1-R5. For Extra Credit solve REQ in terms of R1-R5
only. Matlab may be used for the extra credit, but not parts 1-3. Show all work and
clearly label equations.
I1
I1
REQ
REQ
Fig. 1B – Series / Parallel Circuit
Fig. 1A – Voltage Ladder Circuit
I1
VB
VA
REQ
Fig. 1C – Wheatstone Bridge Circuit
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 2 of 6
2. For this problem, you will find numerical values for REQ for the circuit and numerical values
for the voltage, current and power dissipation of each resistor in the three circuits given. To
do calculations, using the nominal values of resistors given in the “components” section and
also use V1 = 6 Vdc.
a. For the circuit in Fig. 1A:
1) Find the equivalent resistance (REQ).
2) Find the expected voltage drop across each resistor.
3) Find the expected current through each resistor.
4) Find the total current (I1) delivered by the voltage source to the circuit
5) Calculate the power dissipated by each resistor.
6) Create Data Table 1.2A with the calculated values from 1-5.
b. For the circuit in Fig. 1B:
1) Find the equivalent resistance (REQ).
2) Find the expected voltage drop across each resistor.
3) Find the expected current through each resistor.
4) Find the total current (I1) delivered by the voltage source to the circuit
5) Calculate the power dissipated by each resistor.
6) Create Data Table 1.2B with the calculated values from 1-5.
c.
For the circuit in Fig. 1C:
1) Using your formulas above, find the numerical values for VA, VB, I1, and then REQ.
2) Find the expected voltage drop across each resistor.
3) Find the expected current through each resistor.
4) Find the total current (I1) delivered by the voltage source to the circuit
5) Calculate the power dissipated by each resistor.
6) Create Data Table 1.2C with the calculated values of from 1-5.
3. Cadence Simulation: using PSPICE to simulate circuit in Fig. 1A, Fig. 1B, and Fig. 1C. For
each circuit find a) all node voltages, b) current through each resistor, and c) power
dissipated by each resistor. Compare the simulation results with your calculations.
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 3 of 6
Lab:
Part I – DC Measurements
In this section, you will construct the circuits in Fig. 1A, Fig. 1B, and Fig. 1C. You will then
measure the voltage and current and calculate the power dissipation of each resistor in the three
circuits given. Use V1 = 6 Vdc.
a) For the circuit in Fig. 1A:
1) Construct the circuit in Fig. 1A using a breadboard. DO NOT connect the power
supply (V1) to the circuit yet. Use the DMM to measure the equivalent resistance
(REQ) of Fig. 1A.
2) Connect the power supply (V1 = 6 Vdc) to the circuit. Use the DMM to measure the
voltage drop across each resistor.
3) Measure the current through each resistor in the circuit. Note, it is impossible to
measure the current ‘across’ a resistor, you must use the DMM differently
when measuring current. Ask you GTA how if you do not remember.
4) Measure the total current (I1) used by the circuit.
5) Find the power dissipated by each resistor.
6) Add the measured values from the above information onto Data Table 1.2A.
b) For the circuit in Fig. 1B:
1) Construct the circuit in Fig. 1B. DO NOT connect the power supply (V1) to the circuit
yet. Use the DMM to measure the equivalent resistance (REQ) of Fig. 1B.
2) Connect the power supply (V1 = 6 Vdc) to the circuit. Use the DMM to measure the
voltage drop across each resistor.
3) Measure the current through each resistor in the circuit.
4) Measure the total current (I1) used by the circuit.
5) Find the power dissipated by each resistor.
6) Add the measured values from the above information onto Data Table 1.2B.
c) For the circuit in Fig. 1C:
1) Construct the circuit in Fig. 1C. DO NOT connect the power supply (V1) to the circuit
yet. Use the DMM to measure the equivalent resistance (REQ) of Fig. 1C.
2) Connect the power supply (V1 = 6 Vdc) to the circuit. Use the DMM to measure the
voltage drop across each resistor.
3) Measure the current through each resistor in the circuit.
4) Measure the total current (I1) used by the circuit.
5) Find the power dissipated by each resistor.
6) Add the measured values from the above information onto Data Table 1.2C.
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 4 of 6
Part II – Design, Build and Test the Voltage Ladder
In this section, you are asked to design a voltage ladder using the concept of Voltage Division.
Use the circuit in Fig. 1A and find the appropriate values for R1, R2, R3, and R4 to build a voltage
ladder with the following specifications:
Total Power Consumed (Ptotal): ≤ 0.08 Watts (DC)
Power Supply (V1): 5 Vdc±5%
VAB: 0.2 Volts (DC)±5%
VBC: 0.2 Volts (DC)±5%
VCD: 1.6 Volts (DC)±5%
VDE: 3.0 Volts (DC)±5%
Demonstrate this circuit to your GTA.
Part III – Wheatstone Bridge
Remove resistor R3 from the circuit in Fig. 1C to produce what is commonly known as a
Wheatstone Bridge.
a) What is the expression for Va, the voltage across R5?
b) What is the expression for Vb, the voltage across R4?
c) What conditions do R1, R2, R4 and R5 have to meet so that Va is equal to Vb? (When
Va=Vb the bridge is said to be ‘balanced’)
d) Build a Wheatstone Bridge:
 R1 = R4 = 1 kΩ
 R2 = 10 kΩ potentiometer
 R5 = mystery resistor provided by your instructor (do not measure its resistance
with a multimeter)
 Voltmeter (DMM 175) to measure voltage drop between nodes B and A, Vba
 Ammeter (DMM 178) to measure current through R2
Figure 3: Wheatstone Bridge
e) Set the potentiometer (R2) = 0 Ω (verify with an ohmmeter) by rotating the dial of the
potentiometer in one direction until it can no longer rotate. Insert R2 into the circuit.
Measure and record Vba and the current through R2. Compute the resistance of R2
using Ohm’s Law (VS-Va can be computed using the measured Vba and the constant
Vb).
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
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Adjust the resistance of R2 by rotating the dial on the potentiometer (the direction will
depend upon which two pins you are using) and repeat the measurements.
Acquire 6-8 measurements for Vba and the resistance of R2 (acquire at least two
measurements near Vba = 0V).
f)
Use the data from step e to estimate the resistance of R5.
g) In your lab report, identify which mystery resistor that you used. Describe your method for
determining the resistance of the mystery resistor. Also, provide a plot of your measured
Vba values versus the resistances of R2.
Part IV - Analysis to consider in Lab write-up
Compare and contrast the calculated results from your prelab, to your SPICE simulations and
finally to the DC measurements made in the lab itself. Show the percentage error in each case.
Explain the differences between the calculated, measured, and simulated results then include a
discussion on the reason for the discrepancies. Also explain the concept of tolerance in all the
devices and equipment and how to compensate for the problem of inaccurate measurements.
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
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