1. Passive filters A frequency selective circuit, or filter, enables signals at certain frequencies to reach the output, and it attenuates (weaken or lessen the effect of) signals at other frequencies to prevent them from reaching the output. The transfer function is

2. Ideal frequency response plots of the four types of filter circuits

3. Low-Pass Filters

4. General form for the transfer functions of these two lowpass filters:

5. Example: Solution

7. Problem :

8. High Pass Filters

9. Example

12. Band pass Filters

16. Band pass filter – Quantitative analysis

18. The bandwidth of a bandpass filter is defined as the difference between the two cutoff frequencies.

19. The quality factor Q, is defined as the ratio of center frequency to bandwidth We can also rewrite the equations for the cutoff frequencies in terms of the center frequency and the bandwidth or the quality factor

20. Example : A graphic equalizer is an audio amplifier that allows you to select different levels of amplification within different frequency regions. Using the series RLC circuit in, choose values for R, L,and C that yield a bandpass circuit able to select inputs within the 1-10 kHz frequency band. Such a circuit might be used in a graphic equalizer to select this frequency band from the larger audio band (generally 0-20 kHz) prior to amplification. Choose C = 1 microFarad. Solution : We compute the center frequency as the geometric mean of the cutoff frequencies: Convert the center frequency to radians per second to calculate L, To check whether these component values produce the bandpass filter we will, substitute them into

21. Bandreject Filters A bandreject filter attenuates voltages at frequencies within the stopband, which is between w c1 and w c 2. It passes frequencies outside of the stopband

23. ……………………………………………………… Formulae for both filters