1. Filters Background:. Filters may be classified as either digital or analog. Digital filters. Digital filters are implemented using a digital computer or special purpose digital hardware. Analog filters. Analog filters may be classified as either passive or active and are usually implemented with R, L, and C components and operational amplifiers.

2. Filters Background: active filter. An active filter is one that, along with R, L, and C components, also contains an energy source, such as that derived from an operational amplifier. passive filter. A passive filter is one that contains only R, L, and C components. It is not necessary that all three be present. L is often omitted (on purpose) from passive filter design because of the size and cost of inductors – and they also carry along an R that must be included in the design.

3. Passive Analog Filters Background: Four types of filters - “Ideal” lowpasshighpass bandpassbandstop

4. Background: Realistic Filters: lowpasshighpass bandpassbandstop Passive Analog Filters

5. Low Pass Filter Consider the circuit below. R CVIVI VOVO + _ + _ Low pass filter circuit

6. Passive Analog Filters Low Pass Filter 0 dB 1   0 1/RC Bode Linear Plot. -3 dB x 0.707 Passes low frequencies Attenuates high frequencies

7. Passive Analog Filters High Pass Filter Consider the circuit below. C R ViVi VOVO + _ + _ High Pass Filter

8. Passive Analog Filters High Pass Filter 0 dB.. -3 dB 0   1/RC 1 0.707 Bode Linear Passes high frequencies Attenuates low frequencies x

9. Passive Analog Filters Bandpass Pass Filter Consider the circuit shown below: CL R ViVi VOVO + _ + _ When studying series resonant circuit we showed that;

10. Passive Analog Filters Bandpass Pass Filter We can make a bandpass from the previous equation and select the poles where we like. In a typical case we have the following shapes.   0 0 dB -3 dB  lo  hi.... 1 0.707 Bode Linear  lo  hi

11. A Bandpass Filter

12. RLC Band stop Filter Consider the circuit below: R L C + _ VOVO + _ ViVi The transfer function for V O /V i can be expressed as follows: