Mechatronics Engineering
Power Electronics
Class: IELC 4303
NRC: 50938
Lab Practice #1
Impedance 1: Phasor Relationships
Ricardo Villanueva Canto
00328323
Luis Andrés Alemán Sánchez
00369774
Hector Hiram Moore Navarro
00368365
Sonja Katri Helena Henttinen
00535909
Professor
Héctor Pacheco Martínez
Due Date
26/08/2023
Experiment
Calculating the magnitude and phase of the series RC impedance over at least the
frequency range 200Hz through 200kHz.
To determine current:
𝑉(𝑡) = 4 𝑉𝑝𝑝 ∠ 0°
𝐼𝑅 =
𝑉𝑅
4𝑉
=
= 18.18 𝑚𝐴
𝑍𝑅
220Ω
𝑰𝑹 = 𝑰𝑪
To determine Impedance:
𝑍𝑅 = 220Ω ∠ 0°
𝜔 = 2𝜋𝑓
𝑍𝑇 = 𝑍𝑅 + 𝑍𝐶
𝑍𝑇 = 𝑅 +
|𝑍𝑇 | = √𝑅2 + (
1
𝑗𝜔𝐶
𝜃 = tan−1 (−
1
𝑍𝑇 = 𝑅 − 𝑗
𝜔𝐶
R = 220Ω
Frequency
f (Hz)
Vin
peak-peak (V)
Vout
peak-peak (V)
200
4.24
500
4.16
1000
|
1 2
)
𝜔𝐶
1
)
𝜔𝐶𝑅
C =0.1µF
Impedance Calculated
Current
Impedance
Phase Measured
Measured (mA) Measured ( Ω)
(Degrees)
(Ω)
(Degrees)
4.12
7960.79
-88.42
0.545
7773.33
-85.68
4.00
3190.69
-86.05
0.727
5720.00
-82.44
3.92
3.62
1606.68
-82.13
1.364
2874.67
-78.18
2000
4.04
3.68
825.63
-74.55
1.636
2468.89
-71.42
5000
3.68
2.88
386.94
-55.35
3.636
1012.00
-52.42
10000
3.52
1.96
271.53
-35.88
7.091
496.41
-38.05
20000
3.44
1.20
233.95
-19.89
10.182
337.86
-23.30
50000
3.28
0.60
222.29
-8.23
12.182
269.25
-14.18
100000
3.28
0.48
220.57
-4.14
12.727
257.71
-14.38
200000
3.28
0.28
220.14
-2.07
13.636
240.53
-14.50
Table 1. Results for the 220Ω resistor circuit.
R = 1kΩ
Frequency
f (Hz)
V (in)
peak-peak
V(out)
peak-peak
200
4.08
500
4.00
1000
|
C =0.1µF
Impedance (Calculated)
Current
Impedance
Phase Measured
Measured (mA) Measured ( Ω)
(Degrees)
(Ω)
(Degrees)
3.92
8020.33
-82.84
0.164
24888.00
-80.10
3.60
3336.48
-72.56
0.410
9760.00
-73.50
3.92
2.88
1879.64
-57.86
1.066
3678.77
-57.60
2000
3.92
1.84
1277.99
-38.51
2.131
1839.38
-41.10
5000
3.84
0.92
1049.44
-17.66
2.992
1283.51
-24.00
10000
3.84
0.56
1012.59
-9.04
3.361
1142.63
-10.00
20000
3.92
0.40
1003.16
-4.55
3.607
1086.91
-8.60
50000
3.92
0.24
1000.51
-1.82
3.775
1038.52
-4.00
100000
3.92
0.17
1000.13
-0.91
3.842
1020.25
5.00
200000
3.92
0.14
1000.03
-0.46
3.871
1012.68
15.00
Table 2. Results for the 1kΩ resistor circuit.
Results
(a)
Prepare a plot of the impedance phase measurements made in part 1 of the
experiment. Show the data as a semi-log plot: phase in degrees (linear scale) versus
frequency (logarithmic scale). On the same plot, show the mathematical prediction for
the phase, (i.e., determine the impedance of the series RC circuit). Discuss the results.
Which of the phase measurements seemed to work the best for you? Why?
PHASE VS FREQUENCY 220Ω
PHASE (DEGREES)
Mathematical Approach
0.00
-10.00
-20.00
-30.00
-40.00
-50.00
-60.00
-70.00
-80.00
-90.00
-100.00
200
Oscilloscope
2000
20000
FREQUENCY F (HZ)
200000
PHASE VS FREQUENCY 1KΩ
Mathematical Approach
Oscilloscope
20.00
PHASE (DEGREES)
0.00
-20.00
-40.00
-60.00
-80.00
-100.00
200
2000
20000
200000
FREQUENCY F (HZ)
(b)
Prepare two plots of the impedance magnitude measurements made in part 1. For
the first plot, show the magnitude measurements along with the mathematical prediction
as a semi-log plot: magnitude in ohms (linear scale) versus frequency (log scale). For the
second plot, again show the measured and calculated magnitude values but use a log-log
plot: magnitude (log scale) versus frequency (log scale). Discuss the results and compare
the features of the two data plots.
(c)
Prepare a plot of the impedance phase measurements (semi-log) and a plot of the
impedance magnitude measurements (log-log) from part 2. On the same plots show the
mathematical predictions for the impedance. Discuss the differences between the plots
for part 1 and the plots for part 2.
(d)
What would you change about the procedures of this experiment?
We wouldn’t