Laboratory Experiment #3 - Technical Memorandum
TO:
(GTA’s Name Here)
FROM: (Student’s Name Here)
CC:
(Professor’s Name Here)
DATE: (Date of Memorandum Submission Here)
RE:
Lab #3: Voltage Division, Circuit Reduction, and Node Voltage Analysis
ORANIZATION OF MEMORANDUM:
On 9/23/2010, this student performed the GWU - ECE 11 Lab Experiment #3. The following three experiments were carried out:
EXPERIMENT #3.1: (3) circuits were analyzed by hand, built and measured in lab, to explore voltage division, circuit reduction,
and node-voltage analysis.
EXPERIMENT #3.2: (1) Voltage Ladder circuit was designed to a given specification, built, measured and demonstrated to the
GTA, to explore voltage division.
EXPERIMENT #3.3: (1) Wheatstone bridge circuit was built to serve as a detector circuit to determine an unknown resistance.
MEMORANDUM FORMAT:
This memo is broken into 3 sections; one section per experiment (3.1 – 3.3). For experiment #3.1, PSPICE schematics are
shown, followed by the hand calculations and data collected during the experiment in tabulated form. Hand calculations are
compared to collected data using percentage error in each of the associated tables.
The section for experiment #3.2, discusses the design specifications the procedure this student used to implement the
specifications. PSPICE schematics are shown verifying design specifications were met.
For experiment #3.3, the experimental setup is shown. The formulas required to determine the unknown resistance value using
the supplied schematic are discussed and plotted.
Laboratory Experiment #3 – Technical Memorandum
Page 1 of 5
EXPERIMENT #3.1 – Schematics, Calculations, Measured Results, and Percentage Error
Figure 1a – Voltage Ladder
Circuit
Figure 1b – Series / Parallel Circuit
Figure 1c – Wheatstone Bridge Circuit
Tabulated voltages, currents, power, for individual resistors in circuits from Figures 1a-c:
Voltage (V)
Current (mA)
Power (mW)
Calc.
Mes.
P.E. (%)
Calc.
Mes.
P.E. (%)
Calc.
Mes.
P.E. (%)
R1
1.13
1.14
1.06
2.40
2.45
2.08
2.71
2.79
3.17
R2
1.34
1.37
1.93
2.40
2.45
2.08
3.23
3.36
4.06
R3
1.63
1.65
1.10
2.40
2.45
2.08
3.92
4.04
3.21
R4
1.80
1.82
1.11
2.40
2.45
2.08
4.32
Table 1a – Calculated and Measured Data for Circuit in Figure 1a
4.46
3.22
Voltage (V)
Current (mA)
Power (mW)
Calculated
Measured
% Error
Calculated
Measured
% Error
Calculated
Measured
% Error
R1
1.22
1.20
1.53
2.59
2.60
0.27
3.16
3.12
1.27
R2
1.45
1.44
0.83
2.59
2.60
0.27
3.77
3.74
0.56
R3
1.42
1.41
0.97
2.09
2.09
0.18
2.98
2.95
1.15
R4
2.67
2.66
0.40
3.56
3.59
0.81
9.51
9.55
0.41
R5
3.33
3.35
0.62
4.06
4.09
0.74
13.52
13.70
1.36
R6
1.91
1.94
1.81
2.09
2.09
0.18
3.99
Table 1b – Calculated and Measured Data for Circuit in Figure 1b
4.05
1.63
Laboratory Experiment #3 – Technical Memorandum
Page 2 of 5
Tabulated voltages, currents, power, for individual resistors in circuits from Figures 1a-c (con’t):
Voltage (V)
Current (mA)
Power (mW)
Calculated
Measured
% Error
Calculated
Measured
% Error
Calculated
Measured
% Error
R1
2.34
2.34
0.00
5.00
4.98
0.40
11.70
11.65
0.40
R2
2.40
2.41
0.42
4.29
4.29
0.00
10.30
10.34
0.42
R3
0.06
0.07
2.95
0.10
0.09
4.21
0.01
0.01
1.38
R4
3.66
3.65
0.27
4.88
4.91
0.61
17.86
17.92
0.34
R5
3.60
3.59
0.28
4.38
4.38
0.00
15.77
Table 1c – Calculated and Measured Data for Circuit in Figure 1c
15.72
0.28
Tabulated equivalent resistances and total currents for circuits in figures 1a-c:
Req (Ω)
Circuit
Calculated
Total Current (mA)
Measured
% Error
Calculated
Measured
% Error
1a
2460
2420
1.63
2.40
2.45
2.08
1b
975
964
1.13
6.15
6.17
0.26
9.23
0.75
1c
645
638
1.11
9.30
Table 1d – Calculated data, Measured Data, % Error for Circuits in Figures 1a-c
Laboratory Experiment #3 – Technical Memorandum
Page 3 of 5
EXPERIMENT #3.2 – Design Discussion, SPICE Simulations, Results
Figure 2 – Voltage Ladder Designed, Measured, and Simulated
Design Specification:
In the second experiment, this student designed a voltage ladder according to following specifications:






5 V DC power supply
Voltage drop across resistor 1 (R1) of 0.2 V (±5%)
Voltage drop across resistor 2 (R2) of 0.2 V (±5%)
Voltage drop across resistor 3 (R3) of 1.6 V (±5%)
Voltage drop across resistor 4 (R4) of 3.0 V (±5%)
Total consumed power less than or equal to 80 mW
Design Discussion:
This student used the following procedure to implement the voltage ladder to the specifications given:
1.
Calculated ratio of voltage across each resistor to the supply voltage:
a. (R1 / 5 V) = 0.04V, (R2 / 5 V) = 0.04 V, (R3 / 5 V) = 0.32 V, (R4 / 5V) = 0.6 V
2.
Divide each ratio from step 1, by 0.4
a. Ratio 1 = 0.04 / 0.04 = 1, Ratio 2 = 0.04 / 0.04 = 1, Ratio 3 = 0.32 / .04 = 8, Ratio 4 = 0.32 / .6 = 15
3.
Assume kilo-ohm range for resistors
a. R1 = Ratio 1 (kΩ) = 1 kΩ, R2 = Ratio 2 (kΩ) = 1 kΩ, R3 = Ratio 3 (kΩ) = 8 kΩ, R4 = 15 kΩ
4.
Voltage ladder assembled in PSPICE, shown in figure 2.
a. Figure shows specified voltage drops were achieved
5.
Total power consumed (1mW), far less than specified:
a. 𝑃 =
𝑉2
∑4
𝑖=1 𝑅𝑖
=
52
25000
= 1 𝑚𝑊
Laboratory Experiment #3 – Technical Memorandum
Page 4 of 5
EXPERIMENT #3.3 – Design Discussion, SPICE Simulations, Results
Figure 3a – Wheatstone Bridge Detection Circuit Schematic
Experiment Setup:
Figure 3a shows the experimental setup of the Wheatstone bridge. Potentiometer (R2) was inserted into the bridge to estimate
the resistance of an unknown resistor (R5). The potentiometer was adjusted until the voltmeter (V) displayed VBA = 0, indicating a
balanced bridge. The ammeter (A) was used to measure current through (R2), so its value could be determined without
removing it from the circuit.
Analysis of Data:
The collected data is shown in table 3a. The formula used to determine R2: (𝑅2 =
𝑉𝑆−(𝑉𝐵𝐴 + 𝑉𝑆
𝑅4
)
𝑅1 +𝑅4
𝐼𝑅2
). Figure 3b shows this
formula plotted. Finding the tangent to the curve at the point where the curve crosses the VBA = 0 axis, the unknown resistor can
be estimated as 5.05 kΩ. The unknown resistance was actually 5.1kΩ. This reveals a < 1 % percentage error indicating that the
Wheatstone bridge is a very accurate detection circuit.
3.5
VBA (V)
IR2 (mA)
VR2 (V)
R2 (Ω)
2.99
1.19
0.01
10
2.5
2.49
1.09
0.51
471
2
1.29
0.85
1.71
2009
1.5
0.44
0.68
2.56
3761
0.21
0.64
2.79
4393
0.5
0.04
0.60
2.96
4910
0
-0.31
0.53
3.31
6195
-0.5 0
-0.73
0.45
3.73
8264
-1
-1.03
0.39
4.03
10297
-1.5
-1.12
0.37
4.12
11005
Table 3a - Measured Data
Laboratory Experiment #3 – Technical Memorandum
3
VBA (V)
1
2000
4000
6000
8000
10000
12000
R2 (Ω)
Figure 3b – Estimation of unknown resistance from measured data
Page 5 of 5