# Frequency Response of R-L network

20/07/2013 13:02

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.