AReS

PART1R, L, C Circuit

Experiment 20 :LC Filter

Theory

Inductor(L) and capacitor(C) have characteristics as below for DC and AC in normal state. In DC, L is shorted and C is opened. On the contrary, in AC, L is opened and C is shorted. Above is an extreme example but the filter circuit can be realized using this characteristics. Below are the voltage change by the circuit and frequency of LPF(Low Pass Filter), HPF(High Pass Filter), BPF(Band Pass Filter) using capacitor and inductor.

A. Low Pass Filter

fig1-34

Fig. 1-34Low Pass Filter

In fig.1-34(a), the relationship between v_i and v₀ is as below.

$v_o over v_i = {1 over {j omega C}} over {R + 1over {j omega _0 C}} = 1 over {1 + j omega CR} = K_L$

In the formula above, if ω, that is, f increases and gets bigger than constant value f_c, v₀/v_i becomes smaller and smaller and becomes near to "0", as in fig.(b). Therefore, from the relationship of v₀=K_vi, it can be found that as the frequency of v_i becomes bigger than f_c, v₀ gets near to "0", and only low frequency of v_i is expressed at v₀. Like this, the circuit in fig.(a) functions as low pass filter(LPF) which passes low frequency only.

B. High Pass Filter

fig1-35

Fig. 1-35High Pass Filter

Fig.1-35(a) is a high pass filter(HPF) circuit using R and L, and here, the relationship between v_i and v₀ is as below.

$v_o over v_i = {j omega L} over {R + j omega L} = {j omega L over R} over {1 + j omega L over R} = K_H~$

In the formula above, if ω, that is, f decreases and gets smaller than constant value f_c, v₀/v_i becomes smaller and smaller and becomes near to "0", as in fig.(b). Therefore, from the relationship of v₀=K_vi, it can be found that as the frequency of vi becomes smaller than f_c, v₀ gets near to "0", and only high frequency of vi is expressed at v₀. Using this characteristic, the circuit in fig.(a) functions as high pass filter(HPF).

C. Band Pass Filter

fig1-36

Fig. 1-36Band Pass Filter

Fig.1-36(a) is a band pass filter(BPF) circuit, and here, the relationship between v_i and v₀ is as below.

$v_o over v_i = {{j omega L 1 over {j omega C}} over {j omega L + 1 over {j omega C}}} over {R+ {{j omega L 1 over {j omega C} } over {j omega L + 1over {j omega C}}}} = {{j omega L} over {1- omega ^2 LC}} over {R + {j omega L} over {1 - omega ^2 LC}} = {j omega L} over {R(1- omega ^2 LC) + j omega L} = K_B}$

In the formula above, if ω, that is, f increases and gets bigger than constant value f₁, v₀/v_i becomes bigger and bigger, and if it becomes bigger than f₂, v₀/v_i becomes smaller and smaller again and becomes near to "0", as in fig.(b). Therefore, the frequency of v_i which is bigger than f₁ and smaller than f₂ is expressed at v₀. Using this characteristic, the circuit in fig.(a) functions as band pass filter(BPF).

Experiment Process

fig1-37 fig1-37

Fig. 1-37LPF(CR) Characteristic Experiment

1. In Block k of M01, compose an experiment circuit as in fig.3-36, make the size of input voltage as 2V(rms), change the frequency to find -3dB, -6dB frequency and record the result in the relevant column of table 1-20. Record each calculated frequency in the table.

graph

tab1

Experiment 1-20.1 RC LPF Circuit (In Block k of M01, compose a circuit as in fig.1-37.)

1.Connection

1.Circuit Connection

Connect between right terminal of R16 and right terminal of C6 with yellow line.

2.Measuring Instrument Connection

Function Generator Connection

Connect between A+ terminal of Signal Input CH A on front panel and left terminal of R16 of Block k with red line, and between A- terminal and left terminal of C6 with black line.

Oscilloscope and Voltmeter Connection

Connect between A+ terminal of Signal Input CH A on front panel and left terminal of R16 of Block k with red line, and between A- terminal and left terminal of C6 with black line.

Connect between B+ terminal of Signal Input CH B on front panel and right terminal of C6 of Block k with red line, and between B- terminal and left terminal of C6 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 10v and click button_arrow_bottom to set up the amplitude as amplitude 29%.

Choose Frequency as 1k.frequency 1khz.

- Choose Signal as sine and click on to output 1kHz 2Vrms.
2Click analog input at left menu of Touch LCD panel.
Choose Volt & Ampere Meter tab and click voltage, rms, ac for CH A, CH B.

Check out if the value of CH A is 2Vrms and record the value of CH B in table 1-20.
3Choose quick launch at lower part of left menu on Touch LDC panel and click Analog Output .

Click arrow right on the right of Frequency 1.00kHz and increase the frequency as much as 1kHz and record the measured value in CH B and CH B of Volt & Ampere Meter in the relevant column of table 1-20. (CH B is EC1)

Change the frequency up to 20KHz and measure and record the result.

4.Calculation

1. Calculate the frequency that becomes 3dB, -6dB and record the result in table 1-20.

Process

fig1-38 fig1-38

Fig. 1-38HPF(CR) Characteristic Experiment

1. In the circuit of fig.1-38(a), make the size of input voltage as 2V(rms), change the frequency to find -3dB, -6dB frequency and record the result in the relevant column of table 1-20. Record each calculated frequency in the table.

tab2

Experiment 1-20.2 RC HPF Circuit (In Block k of M01, compose a circuit as in fig.1-38.)

1.Connection

1.Circuit Connection

Connect between right terminal of R16 and right terminal of C6 with yellow line.

2.Measuring Instrument Connection

Function Generator Connection

Connect between A+ terminal of Signal Input CH A on front panel and left terminal of C6 of Block k with red line, and between A- terminal and left terminal of R16 with black line.

Oscilloscope and Voltmeter Connection

Connect between A+ terminal of Signal Input CH A on front panel and left terminal of C6 of Block k with red line, and between A- terminal and left terminal of R16 with black line.

Connect between B+ terminal of Signal Input CH B on front panel and right terminal of R16 of Block k with red line, and between B- terminal and left terminal of R16 with black line

2.Wiring Diagram

flash

3.Measurement

1Execute the measurement of Experiment LPF Circuit above.
2(CH B is ER2)

4.Calculation

1. Calculate the frequency that becomes 3dB, -6dB and record the result in table 1-20.

Experiment Process

fig1-39 fig1-39

Fig. 1-39LPF(LC) Characteristic

1. In the circuit of fig.1-39(a), make the size of input voltage as 2V(rms), change the frequency to find -3dB, -6dB frequency and record the result in the relevant column of table 1-22. Connect C6 and R17 in parallel and connect the load, and find the frequency that becomes -3dB and -6dB and record the result. Record each calculated frequency in the table 1-23.

tab3

Experiment 1-20.3 LC LPF Circuit (In Block k of M01, compose a circuit as in fig.1-39.)

1.Connection

1.Circuit Connection

In Block k, connect between right terminal of L5 and right terminal of C6 with yellow line.

2.Measuring Instrument Connection

Function Generator Connection

Connect between A+ terminal of Signal Input CH A on front panel and left terminal of L5 of Block k with red line, and between A- terminal and left terminal of C6 with black line.

Oscilloscope and Voltmeter Connection

Connect between A+ terminal of Signal Input CH A on front panel and left terminal of L5 of Block k with red line, and between A- terminal and left terminal of C6 with black line.

Connect between B+ terminal of Signal Input CH B on front panel and right terminal of C6 of Block k with red line, and between B- terminal and left terminal of C6 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 10v and click button_arrow_bottom to set up the amplitude as amplitude 29%.

Choose Frequency as 1k. frequency 1khz.

Choose Signal as sineand click onto output 1kHz 2Vrms.
2Click analog input at left menu of Touch LCD panel.
Choose Volt & Ampere Meter tab and click voltage, rms, ac for CH A, CH B.

Check out if the value of CH A is 2Vrms and record the value of CH B in table 1-22.
3Choose quick launch at lower part of left menu on Touch LDC panel and click Analog Output .
Click arrow right on the right of Frequency 1.00kHz and increase the frequency as much as 1kHz and record the measured value in CH B and CH B of Volt & Ampere Meter in the relevant column of table 1-22 (LPF) No Load.
4Connection and Measurement of Resistance Load R17
In Block k, connect between left terminal of R17 and left terminal of C6, and between right terminal of R17 and right terminal of C6 with yellow lines.

Execute XMeasurement 1)~3)Execute Measurement 1)~3) and record the measured value in CH B in the relevant column of table 1-22 (LPF) Load. and record the measured value in CH B in the relevant column of table 1-22 (LPF) Load.\
5Change the frequency up to 20KHz and measure and record the result.

4.Calculation

1. Calculate the frequency that becomes 3dB, -6dB and record the result in table 1-23.

Experiment Process

fig1-40 fig1-40

Fig. 1-40HPF(LC) Characteristic

1. In the circuit of fig.1-40(a), make the size of input voltage as 2V(rms), change the frequency to find -3dB, -6dB frequency and record the result in the relevant column of table 1-22. Connect L5 and R17 in parallel and connect the load, and find the frequency that becomes -3dB and -6dB and record the result. Record each calculated frequency in the table 1-23.

tab4

Experiment 1-20.4 LC HPF Circuit (In Block k of M01, compose a circuit as in fig.1-40.)

1.Connection

1.Circuit Connection

In Block k, connect between right terminal of L5 and right terminal of C6 with yellow line.

2.Measuring Instrument Connection

Function Generator Connection

Connect between A+ terminal of Signal Input CH A on front panel and left terminal of C6 of Block k with red line, and between A- terminal and left terminal of L5 with black line.

Oscilloscope and Voltmeter Connection

Connect between A+ terminal of Signal Input CH A on front panel and left terminal of C6 of Block k with red line, and between A- terminal and left terminal of L5 with black line.

Connect between B+ terminal of Signal Input CH B on front panel and right terminal of L5 of Block k with red line, and between B- terminal and left terminal of L5 of Circuit-5 with black line.

2.Wiring Diagram

flash

3.Measurement

1Execute Measurement 1)~3) of Experiment LPF Circuit and record the measured value in CH B in the relevant column of table 1-22 (HPF) No Load.
2Connection and Measurement of Resistance Load R17
In Block k, connect between left terminal of R17 and left terminal of L5, and between right terminal of R17 and right terminal of L5 with yellow lines.

Execute Measurement 1)~3) and record the measured value in CH B in the relevant column of table 1-22 (HPF) Load.
3the frequency up to 20KHz and measure and record the result.
Wiring Diagram

flash

4.Calculation

1. Calculate the frequency that becomes 3dB, -6dB and record the result in table 1-23.

Experiment Result Table

result
Title	LC Filter	Date
Department		Id Number		Name

1. Experiment Result Table

Table 1-20(LPF)

result_table
V \| F	1㎑	2㎑	3㎑	4㎑	5㎑	6㎑	7㎑	8㎑	9㎑	10㎑
EC1(V)
V \| F	11㎑	12㎑	13㎑	14㎑	15㎑	16㎑	17㎑	18㎑	19㎑	20㎑
EC1(V)

(HPF)

result_table
V \| F	1㎑	2㎑	3㎑	4㎑	5㎑	6㎑	7㎑	8㎑	9㎑	10㎑
ER2(V)
V \| F	11㎑	12㎑	13㎑	14㎑	15㎑	16㎑	17㎑	18㎑	19㎑	20㎑
ER2(V)

1. Draw the measurement value of table 1-20 in the graph below.

section paper (LPF)

section paper (HPF)

2. If the point of 2V is 0 dB and point of 1.5V is –3dB, record the Y axis value of the point that meets the graph in table 3-20. Also, if the point of 1.0V is -6dB, record the Y axis value of the point that meets the graph in table 1-21.

Table 1-21

result_table
Circuit \| Measurement		Input Level	Frequency [㎐]		Reduction Ratio [㏈/oct.]
Circuit \| Measurement		Input Level	(-3㏈)	(-6㏈)	Reduction Ratio [㏈/oct.]
Fig. 1-36 (LPF)	Calculated Value	2 Vrms
Fig. 1-36 (LPF)	Measured Value
Fig. 1-37 (HPF)	Calculated Value	2 Vrms
Fig. 1-37 (HPF)	Measured Value

2. Review and Explanation

1) In the given circuits of fig.1-37, 1-38, calculated the cutoff frequency(fC) and the frequency at the point of –6dB, record the result in table 1-21 and compare it with the measured result.

2) Explain why measured fC and calculated fC are different..

3. Discuss the experiment result.

Experiment Result Report

result
Title	LC Filter	Date
Department		Id Number		Name

1. Experiment Result Table

Table 1-22 (LPF)

result_table
V \| F	1㎑	2㎑	3㎑	4㎑	5㎑	6㎑	7㎑	8㎑	9㎑	10㎑
No Load
V \| F	11㎑	12㎑	13㎑	14㎑	15㎑	16㎑	17㎑	18㎑	19㎑	20㎑
No Load

(HPF)

result_table
V \| F	1㎑	2㎑	3㎑	4㎑	5㎑	6㎑	7㎑	8㎑	9㎑	10㎑
No Load
V \| F	11㎑	12㎑	13㎑	14㎑	15㎑	16㎑	17㎑	18㎑	19㎑	20㎑
No Load

1) Draw the measured value of table 1-22 in the graph below. (Red - Load, Green - No Load)

section paper (LPF)

section paper (HPF)

2) If the point of 2V is 0 dB and point of 1.5V is –3dB, record the Y axis value of the point that meets the graph in table 1-22. Also, if the point of 1.0V is -6dB, record the Y axis value of the point that meets the graph in table 1-23.

Table 1-23 (LPF, HPF Characteristic Experiment by LC)

result_table
Circuit \| Measurement		Input Level	Frequency [㎐]		Reduction Ratio [㏈/oct.]
Circuit \| Measurement		Input Level	(-3㏈)	(-6㏈)	Reduction Ratio [㏈/oct.]
Fig. 1-38 (LPF)	No Load	2 Vrms
	Load
	Calculated Value
Fig. 1-39 (HPF)	No Load	2 Vrms
	Load
	Calculated Value

2. Review and Explanation

1) In the given circuits of fig.1-39, 1-40, calculated the cutoff frequency(_C) and the frequency at the point of –6dB, record the result in table 1-23 and compare it with the measured result.

PART1R, L, C Circuit

Experiment 20 :LC Filter

Theory

Experiment Process

Experiment 1-20.1 RC LPF Circuit (In Block k of M01, compose a circuit as in fig.1-37.)

1.Connection

1.Circuit Connection

2.Measuring Instrument Connection

2.Wiring Diagram

flash

3.Measurement

4.Calculation

Process

Experiment 1-20.2 RC HPF Circuit (In Block k of M01, compose a circuit as in fig.1-38.)

1.Connection

1.Circuit Connection

2.Measuring Instrument Connection

2.Wiring Diagram

flash

3.Measurement

4.Calculation

Experiment Process

Experiment 1-20.3 LC LPF Circuit (In Block k of M01, compose a circuit as in fig.1-39.)

1.Connection

1.Circuit Connection

2.Measuring Instrument Connection

2.Wiring Diagram

flash

3.Measurement

4.Calculation

Experiment Process

Experiment 1-20.4 LC HPF Circuit (In Block k of M01, compose a circuit as in fig.1-40.)

1.Connection

1.Circuit Connection

2.Measuring Instrument Connection

2.Wiring Diagram

flash

3.Measurement

flash

4.Calculation

Experiment Result Table

1. Experiment Result Table

1. Draw the measurement value of table 1-20 in the graph below.

2. If the point of 2V is 0 dB and point of 1.5V is –3dB, record the Y axis value of the point that meets the graph in table 3-20. Also, if the point of 1.0V is -6dB, record the Y axis value of the point that meets the graph in table 1-21.

2. Review and Explanation

1) In the given circuits of fig.1-37, 1-38, calculated the cutoff frequency(fC) and the frequency at the point of –6dB, record the result in table 1-21 and compare it with the measured result.

2) Explain why measured fC and calculated fC are different..

3. Discuss the experiment result.

Experiment Result Report

1. Experiment Result Table

1) Draw the measured value of table 1-22 in the graph below. (Red - Load, Green - No Load)

2) If the point of 2V is 0 dB and point of 1.5V is –3dB, record the Y axis value of the point that meets the graph in table 1-22. Also, if the point of 1.0V is -6dB, record the Y axis value of the point that meets the graph in table 1-23.

2. Review and Explanation

1) In the given circuits of fig.1-39, 1-40, calculated the cutoff frequency(C) and the frequency at the point of –6dB, record the result in table 1-23 and compare it with the measured result.

2) Explain why measured fC and calculated fC are different..

3. Discuss the experiment result.

1) In the given circuits of fig.1-39, 1-40, calculated the cutoff frequency(_C) and the frequency at the point of –6dB, record the result in table 1-23 and compare it with the measured result.

2) Explain why measured f_C and calculated f_C are different..