AReS

PART1R, L, C Circuit

Experiment 19 :Parallel Resonant Circuit

Theory

fig1-32

As in fig.1-32(a), when R, L, C elements are connected in parallel, the size and phase of their AC combined resistance, that is, the impedance Z are as below.

Impedance :
Z = R + j( omega L - 1 over omegaC )

Size :
$vert Z vert = sqrt {R^2 + ( omegaL - 1 over omegaC )^2}$

Phase :
$theta = tan^-1 {{( omegaL - 1 over omegaC )} over R}$

In L-C parallel circuit, at the frequency of ω₀C = 1/ ω₀L, the impedance Z has pure resistance only, and the frequency here becomes resonant frequency. The angular frequency satisfying this condition becomes ω₀ = 1/ √ LC, and this ω₀ is resonant angular frequency, and the resonant frequency f₀ is f₀ = 1/ 2π√ LC. Q(quality factor) at parallel resonant circuit is defined as Q = f₀ / (f₂ - f₁) just as serial resonant circuit, and expressed as Q = ω₀CR = R₁(ω₀L). That is, Q is proportional to R. Fig.1-32(b) shows the graph expressing the relationship between resonant frequency and the current at parallel resonant circuit.

Experiment Process

fig1-33

Fig. 1-33RLC Parallel Resonant Experiment Circuit

1. In Block j of M01, connect Function Generator, oscilloscope or AC voltmeter as in fig.1-33(a).

2. Make the sine wave output of Function Generator as 20Vp-p, and change the frequency from 2kHz to 10kHz by 200Hz interval to record the output voltage V in table 1-19.

Find the frequency that becomes 0dB(resonant frequency), -3dB and -6dB and record the result in the relevant column.

Make R15 resistance shorted and measure the voltage value applied to R14 and record the result in the relevant column of table 1-19.

tab1

Experiment 1-19.1 Process RLC Parallel Resonant Circuit (Compose as in fig.1-33)

1.Connection

1.Function Generator Connection

Connect between A+ terminal of Signal Input CH A on front panel and SW3 left terminal of Block j with red line, and between A- terminal and left terminal of C5 with black line.

2.Measuring Instrument(Voltmeter) Connection

V1 Measurement: Connect between A+ terminal of Signal Input CH A on front panel and lower terminal of R15 of Block j with red line, and between A- terminal and upper terminal of R15 with black line.

V2 Measurement: Connect between B+ terminal of Signal Input CH B on front panel and right terminal of R14 of Block j with red line, and between B- terminal and left terminal of R14 with black line.

2.Wiring Diagram

flash

3.Measurement

1Choose analog output at left menu of front panel.
In Function Generator window, set up Amplitude as 20vpp , Frequency as 100 , Signal as sine and click button_arrow to set up as 2kHz. Click on to output 2KHz 20Vp-p.
2Click analog input at left menu of Touch LCD panel.
Choose Volt & Ampere Meter tab and click voltage, pp, ac for CH A, CH B and then the measured value is indicated. Record in the relevant column of table 1-19. CH A is V1(voltage between R15’s both ends), and CH B is V2(voltage between R14’s both ends)

Make R15 resistance shorted and measure and record the voltage value applied to R14.
3Change the frequency as in table 1-19 and measure and record the result in the relevant column.
Choose quick launch at lower part of left menu on Touch LDC panel and click Analog Output.

Click arrow right on the right of Frequency 100Hz and increase the frequency by 200Hz and record the measured value in CH A and CH B of Volt & Ampere Meter in the relevant column of table 1-19.

Make R15 resistance shorted and measure and record the voltage value applied to R14.
4After the measurement, click on red2 to cut off the output of function generator.

Experiment Result Report

result
Title	Parallel Resonant Circuit	Date
Department		Id Number		Name

1. Experiment Result Table

Table 1-19

result_table
V \| F	2㎑	2.2㎑	2.4㎑	2.6㎑	2.8㎑	3.0㎑	3.2㎑	3.4㎑	3.6㎑	3.8㎑
V1
V2
V2’
V \| F	4.0㎑	4.2㎑	4.4㎑	4.6㎑	4.8㎑	5.0㎑	5.2㎑	5.4㎑	5.6㎑	5.8㎑
V1
V2
V2’
V \| F	6.0㎑	6.2㎑	6.4㎑	6.6㎑	6.8㎑	7.0㎑	7.2㎑	7.4㎑	7.6㎑	7.8㎑
V1
V2
V2’
V \| F	8.0㎑	8.2㎑	8.4㎑	8.6㎑	8.8㎑	9.0㎑	9.2㎑	9.4㎑	9.6㎑	9.8㎑
V1
V2
V2’

※ V2’is the V2 voltage when R15 is shorted.

2. Review and Explanation

1) Calculate the resonant frequency using table 1-19 above and draw the graph below and compare it with the resonant frequency.

section paper

Level	-f ← 0 → +f					BW (3㏈)
Level	-6㏈	-3㏈	0㏈	-3㏈	-6㏈	BW (3㏈)
Frequency