Frequency Response of R-L network
Author Name: Leandrou Vasilis
OBJECTIVES
This report aims to:
- Pay careful attention the way frequency is affected on the impedance of a series R-L network.
- Make a plan with voltages and current of a series network against frequency.
- Find out and plot the phase angle of the input impedance versus frequency for a series R-L network.
BACKGROUND THEORY
In this experiment will be used a DMM, an Oscilloscope, a function generator, 100Ω resistor and 10mH inductor.
- The DMM read resistance, voltage and current with a digital display.
- The oscilloscope is an instrument that will display the variation of a voltage with time on a flat screen monitor.
- A function generator typically expands on the skills of the audio oscillator by supplying a square wave and triangular waveform with an increased frequency range.
EQUIPMENT
· Digital Multimeter (Brand: Good Will Instruments Co. Ltd, Model: GDM-8135, Serial Number: CF-922334)
· Dual Trace Oscilloscope (Brand: HAMEG, Model: HM 203-6, Serial Number: 46/87 Z33418)
· Function generator (Model: TG 550)
· 100Ω resistor
· 10mH Inductor
EXPERIMENTAL METHOD AND PROCEDURE
Part 1
The function generator was connected in series with the 100Ω resistor and the 10mH inductor. The oscilloscope was connected to the inductor. The input voltage was maintaining at 4V. The voltage across the inductor was measured in different values of frequency (table 1). Then the resistor interchanges position with the inductor. The voltage across the resistor was measured and the current of the circuit was calculated in different values of frequency (table 1). Then the ZΤ was calculated using two different formulas. The VL, VR, I, ZT and θ versus frequency was plot.
OBSERVATIONS
Table 1 VL, VR, I versus Frequency.
Frequency |
VL(p-p) |
VR(p-p) |
Ip-p |
0.1KHz |
0.8V |
3.2V |
31.46mA |
1KHz |
2V |
2.4V |
23.6mA |
2KHz |
3V |
2.1V |
20.6mA |
3KHz |
3.2V |
1.8V |
17.7mA |
4KHz |
3.6V |
1.6V |
15.73mA |
5KHz |
3.8V |
1.4V |
13.76mA |
6KHz |
3.9V |
1.2V |
11.8mA |
7KHz |
3.95V |
1V |
9.8mA |
8KHz |
3.97V |
0.8V |
7.8mA |
9KHz |
3.98V |
0.7V |
6.8m |
10KHz |
4V |
0.6V |
5.9mA |
Table 2 ZT versus Frequency.
Frequency |
E(p-p) |
Ip-p |
ZT= Ep-p / Ip-p |
ΖΤ= RxR+XLxXL |
0.1KHz |
4V |
31.46mA |
127.14Ω |
14.8Ω |
1KHz |
4V |
23.6mA |
169.5Ω |
132.4Ω |
2KHz |
4V |
20.6mA |
194.17Ω |
177.6Ω |
3KHz |
4V |
17.7mA |
226Ω |
207.4Ω |
4KHz |
4V |
15.73mA |
254.3Ω |
250.9Ω |
5KHz |
4V |
13.76mA |
290.7Ω |
294.3Ω |
6KHz |
4V |
11.8mA |
339Ω |
330.5Ω |
7KHz |
4V |
9.8mA |
408.16Ω |
415.7Ω |
8KHz |
4V |
7.8mA |
512.8Ω |
519Ω |
9KHz |
4V |
6.8m |
588.2Ω |
594Ω |
10KHz |
4V |
5.9mA |
678Ω |
685,6Ω |
Table 3 θ versus Frequency.
Frequency |
R(measure) |
XL |
θ=tan (XL/R) |
0.1KHz |
101.7Ω |
25.4Ω |
14 |
1KHz |
101.7Ω |
84.74Ω |
39.8 |
2KHz |
101.7Ω |
145.6Ω |
55 |
3KHz |
101.7Ω |
180.8Ω |
60.64 |
5KHz |
101.7Ω |
276.6Ω |
69.8 |
10KHz |
101.7Ω |
678Ω |
81.47 |
Data discussion
The voltage from one side of coil to the other side will rise with frequency since the inductive reactance increases directly with frequency and the impedance of the resistor is essentially independent of the applied frequency.
The shapes of the curves versus frequency will have the same characteristics since the voltage and current of the resistor are related by the fixed resistance value.
At very low frequency the inductive reactance will be small compared to the series resistive element and the network will be primarily resistive in nature. The phase angle associated with the input impedance approaching 0 fates.
At increasing frequencies XL will drown out the resistive element and the network will be primarily inductive, resulting in an input phase angle approaching 90 fates.
On the table 1 seeing that as the frequency increases the voltage across the inductor increases but the voltage across the resistor and the current decreases. When f= 1 KHz VL=2V, VR=2.4V I=23.6mA and when f=2 KHz VL=3V, VR=2.1V, I=20.6mA.
On the table 2 seeing that as the frequency increases the ZT increases. When f=1 KHz ZT=169.5Ω and when f=3 KHz ZT=226Ω. There is same difference between the two different formulas of ZT.
On the table 3 seeing that as the frequency increases θ increases. When f=0.1 KHz θ=14 and when f=2 KHz θ=55.
Error Analysis
On the table 2 seeing that there is a small difference between the two formulas of ZT. When f=5 KHz ZT=290.7Ω and ZT=294.3Ω. The difference is very small and you can calculate by: difference%= (ZT-ZT)/ZTx100%
Ex. (290.7-294.3)/ 290.7x100%= 1.23% difference.
RECOMMENDATIONS
The voltage from one side of coil to the other side will rise with frequency since the inductive reactance increases directly with frequency and the impedance of the resistor is essentially independent of the applied frequency.
The shapes of the curves versus frequency will have the same characteristics since the voltage and current of the resistor are related by the fixed resistance value.
At very low frequency the inductive reactance will be small compared to the series resistive element and the network will be primarily resistive in nature. The phase angle associated with the input impedance approaching 0 fates.
At increasing frequencies XL will drown out the resistive element and the network will be primarily inductive, resulting in an input phase angle approaching 90 fates.