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

Ideal frequency response plots of the four types of filter circuits

Low-Pass Filters

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

Example:

Solution

Problem :

High Pass Filters

Example

Band pass Filters

Band pass filter – Quantitative analysis

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

• 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

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 geometricmean 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 theminto

Bandreject FiltersA bandreject filter attenuates voltages at frequencies within the stopband, which is between wc1 and wc2. It passes frequencies outside of the stopband

………………………………………………………Formulae for both filters