Experiment 3 Research on RLC Circuits PDF

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Experiment3ResearchonRLCCircuits 1. Objective You will observe the resonance and the related fact that such circuits respond better to signals of certain frequencies (called selectivity). 2. Preparation (1) Review the RLC series resonant circuit in your textbook. (2) In Circuit shown in Figure 3-1, if the output voltage of the function generator is Vrms = 2V, and R=51Ω, C = 33nF, L = 9mH, the resistance of the coil rL=0.7Ω, respectively, try to calculate the following parameters: Resonant Frequency f0=____________Hz Quality Factor (rL need to considering) Q=____________ Voltages across the capacitor and the inductor when the circuit in resonance VL ≈ VC = ______________V (3) When output voltage v0 is in phase with the input vi in frequency selective network shown in Figure 3-2, try to obtain the resonant frequency f0 = __________Hz, and Vo/Vi = ________________. 3. Instruments and Equipment No.

Name

Model

Quantity

1

Circuit Lab Kit

EEL-DL2

1

2

Function Generator

DF 1631

1

3

Single Channel AC Milli-voltmeter

HG2172

1

4

Dual Trace Oscilloscope

V-212

1

4. Contents and requirements i

Red

L(rL)

Red Power output

  vi 



Red R

Black

Black Function Generator

CH1

C

 vR  

Scope CH2

Black Figure 3-1

RLC series circuit

(1) Measurement of the frequency characteristic of RLC series circuit ★ Construct the circuit shown in Figure 3-1, in which R=51Ω, C = 33nF. The power output terminals of the function generator supply the sinusoidal voltage whose amplitude and frequency can be changed. By Oscilloscope, Channel 1 displays the waveform of the signal source voltage vi, and Channel 2 displays the

voltage across the resistor R. ★ Measure the resonance frequency f0 in resonance state Try to make the voltage vi in phase with vR by adjusting the function generator’s output frequency. We observe the two voltage in phase by Lissajous figure method. Lissajous Figure Method Setting the Oscilloscope in “X-Y” mode by rotation the “scan frequency button”(TIME/DIV), in which the Channel 1 is set as X axis, and Channel 2 is set as Y axis. When in resonance, the waveform becomes a skew line. Recording the function generator’s output frequency as the resonance frequency, measure the maxim voltage VR. NOTE: “VOLTS/DIV” of Channel 1 and 2 should be used the same (1V desirable) ★ Measure the current resonant curve of RLC series circuit Adjust the output frequency of the function generator according to Tab 3-1, measure and record the voltages VR by AC milli-voltmeter. In Tab 3-1, you can choose any frequency between fL and fH as you want. Tab 3-1 R = 51，C = 33nF，L = 9mH，rL = 0.7， Vi = 2V(unchanging) f / kHz

6

7

8

fL =

f0 =

fH =

10

11

13

VR / V Calculation I/mA (= VR /R)

NOTE: In Tab 3-1, the frequencies, fH and fL, are the high and low half-power frequency, respectively, which is found by adjusting the frequency to make the voltage vR=0.707(VR at f0). ★ In resonant state, measure the voltages VL, VC, and VR, then, record in Tab 3-4. ★ Adjusting the output frequency of the function generator, try to observe the phase relationship between the input vi and vR by restoring the scope’s setting in X-T mode. Recording the waveforms of vi and vR in Tab 3-2. Tab 3-2 Frequency f

f < f0

f = f0

f > f0

Waveforms of vi and vR Phase difference  v, i Inductive or capacitive

★ In Figure 3-1, substitute R = 100Ω for R = 51Ω, repeat the above steps, recording the measurement in Tab 3-3. ★ In resonant state, measure the voltages VL, VC, and VR, then, fill in Tab 3-4.

Tab. 3-3 R = 100，C = 33nF，L = 9mH，rL = 0.7，Vi = 2V(unchanging) f / kHz

6

7

7.5

f0 =

f1 =

f2 =

10.5

11.5

13

VR / V Calculation I/mA (= VR /R)

★ changing C = 10nF and R = 51Ω, measure the resonant frequency f0, voltages VL, VC, and VR, then, fill in Tab 3-4. Tab 3-4

Circuit parameters

Resonance frequency f0 / kHz Theoretical Measured value value

Voltage across

Voltage across

Voltage across

the resistor

the inductor

the capacitor

VR /V

VL /V

VC /V

R2 = 51, C = 33nF R2 = 100, C = 33nF R2 = 51, C = 10nF

(2) Measurement of the frequency selective characteristic of RC series-parallel circuit C R ★ Construct the circuit shown in Figure 3-2, in which R = 300Ω and C + + = 1μF. The input voltage vi with rms C R vi value Vi = 3V is a sinusoidal signal vo _ supplied by the function generator. _ ★ Using the method of measuring Fig. 3-2 the resonant frequency in step (1) as mention before, adjust the output frequency of the function generator. Observe the waveforms of the voltage vi and vo, record the frequency in Tab 3-5 when these two signals are in phase. ★ Measure the voltages Vo at frequency f =100Hz and f=2000Hz, fill in the Table 3-5. Then, calculate the value Vo/Vi. Table 3-5 R = 300，C = 1μF， Vi = 3V(unchanging) f / Hz

100

f0 =

2000

Vi / V Vo /Vi

5. Questions (1) Draw I(f) curves in same coordinate system according to Table 3-1 and 3-3. Try to explain the relationship between the quality factor Q and the resonance

characteristics. (2) According to experimental data, complete Table 3-6. L = 9mH，rL = 0.7

Tab. 3-6 R = 51，C = 33nF

R = 100，C = 33nF

R = 51，C = 10nF

Theoretical f0

value Measured value Theoretical

Q

value Measured value Theoretical

Bandwidth

value

fBW

Measured value

(3) According to the experimental data f0, Q, fBW, VL and VC in resonance, summarize the effect of circuit element R, L and C on the frequency characteristics....