AReS

PART3AC Circuit

Experiment 5 :Filter Circuit

Theory

In normal state, inductor(L) and capacitor(C) has characteristics as below regarding AC and DC. In DC, L becomes short and C becomes open. In contrary, in AC, L becomes open and C becomes short. Though extreme examples, these characteristics can be used in realizing filter circuit. Below is the circuits of LPF(Low Pass Filter), HPF(High Pass Filter), BPF(Band Pass Filter) using capacitor and inductor and the voltage change according to the frequency.

LPF

fig3-18

Fig. 3-18LPF(Low Pass Filter)

In Fig. 3-18 (a), the relationship between υ_i and υ_o is as below.

υ_o/υ_i =(1/(jΩC))/(R+1/(jΩ_oC))=1/(1+jΩ∁R)=K_L

In the formula above, if ω, that is, f increases to become bigger than certain value f_c, υ_o/υ_i gets smaller and becomes near to “0”, as in Fig. 3-18(b). Therefore, in the formula υ_o=Kυ_i, it can be assumed that when the frequency of υ_i gets bigger than f_c, υ_o gets near to "0" and at υ_i, only low frequency is expressed to υ_o. Like this, the circuit in Fig. 3-18(a) works as Low Pass Filter which passes low frequency only.

HPF

fig3-19

Fig. 3-19HPF(High Pass Filter)

Fig. 3-19(a) shows a high pass filter using R and L, and here, the relationship between υ_i and υ_o is as below.

υ_o/υ_i =jΩL/(R+jΩL)=(jΩ L/R)/(1+jΩ L/R)=K_H

In the formula above, if ω, that is, f decreases to become smaller than certain value f_c, υ_o/υ_i gets smaller and smaller and becomes near to “0”, as in Fig. 3-19(b). Therefore, from the relationship of υ_o=Kυ_i, the more the frequency of υ_i becomes smaller than f_c, the more υ_o gets near to “0”, so only higher frequency of υ_i can be expressed in υ_o. Using this characteristic, the circuit in Fig. 3-19(a) can be used as high pass filter(HPF).

BPF

fig3-20

Fig. 3-20BPF(Band Pass Filter)

Fig. 3-20(a) shows a band pass filter(BPF) circuit and here υ_i and υ_o have relationship as below

υ_o/υ_i =((jΩL 1/jΩC)/(jΩL+1/jΩC))/(R+(jΩL 1/jΩC)/(jΩL+1/jΩC))=(jΩL/(1-Ω^2 LC))/(R+jΩL/(1-Ω^2 LC))=jΩL/(R(1-Ω^2 LC)+jΩL)=K_B

In the formula above, if ω, that is, f increases to become bigger than certain value f₁, υ_o/υ_i gets bigger and bigger, and if it becomes bigger than f₂, υ_o/υ_i becomes smaller again to become near to "0", as in Fig. 3-20 (b). Therefore, if the frequency of υ_i is bigger than f₁, then the frequency smaller than f₂ can be expressed in υ_o. Using this characteristic, the circuit in Fig. 3-20(a) can be used as band pass filter(BPF).

Experiment Process

fig3-21

Fig. 3-21Characteristic of LPF(CR)

fig3-22

Fig. 3-22Characteristic of HPF(CR)

tab1

Experiment 3-5.1 RC LPF Circuit (Compose Circuit-5 of M-03 as in Fig. 3-21)

1.Connection

1.Set up R1 as 20㏀

Connect between Multimeter High terminal of front panel and 5a terminal with red line, and connect Low terminal to 5c terminal.

Choose dmm at Touch LCD window, click ohm, and adjust R1 to become 20㏀.

DigitalMultiMeter

Remove the connection line.

2.Circuit Connection

Function Generator Connection

Connect between A+ terminal of Signal Output on the front panel and 5a terminal of Circuit-5 with red line, and between A- terminal and 5d terminal with black line.

Oscilloscope and Voltmeter Connection

Connect between A+ terminal of Signal Output CH A on the front panel and 5a terminal of Circuit-5 with red line, and between A- terminal and 5d terminal with black line.

Connect between B+ terminal of Signal Output CH B on the front panel and 5c terminal of Circuit-5 with red line, and between B- terminal and 5e terminal of Circuit-5 with black line.

2.Wiring Diagram

flash

3.Measurement

1Choose analog output at the left menu of front panel.
In Function Generator window, choose Amplitude as 10v and click arrowto set up the amplitude as amplitude 28% .

Choose Frequency as 1k frequency 1.0khz

Choose Signal as sine and click on to output 1kHz 2Vrms.
2Choose signal input at the left menu of front panel.
Choose Volt & Ampere Meter and choose voltage, rms , acat CH A and CH B each

Check out if the value of CH A is 2Vrms and record the value of CH B in table 3-9.
3Choose quick launch at the left menu of front panel and click analog output

Click arrow right on the right of Frequency 1.00kHz to increase the frequency 1kHz, and record the measured value indicated in CH B of Volt & Ampere Meter in the Relevant Frequency column of table 3-9. (CH B is EC1)

Measure and record with changing the frequency to 20 kHz.

4.Calculation

1. Calculate the frequencies of -3dB, -6dB and record the values in table 3-10.

tab2

Experiment 3-5.2 RC HPF Circuit (Compose Circuit-5 of M-03 as in Fig. 3-22)