Filters

• By combining resistor, capacitor, inductor in special ways we can design circuits that are capable of passing certain frequency while rejecting others.

• Some example of filters are low pass filter, high pass filters and band pass filters.

• Low pass filter circuits pass only the low frequencies but rejects high frequencies.

Low pass filter• Combination of R and C.• It has a frequency sensitive

voltage divider.• Frequency sensitive part

comes from the C.• At high frequency capacitors

reactance decreases. Output voltage decreases too.

• At low frequency capacitor reactance increases. Output voltage increases too.

Attenuation Vs Frequency• From the circuit we can find that

• The magnitude or attenuation

• When ω is 0, attenuation is 1 which means low frequency passes through the circuit.

• When ω is infinity, attenuation is 0, which means high frequency cannot pass the circuit.

• The cut-off frequency is the frequency at which attenuation is i.e. |Vout|= |Vin|

• At cutoff frequency

Attenuation in dB• Attenuation is expressed in dB• Decibel / non-decibel conversion

• Notice that when =0.707 (half power condition), AdB=-3dB • Notice that at the points where dB values are minus are true attenuation; If

dB value is positive can be considered as gain.

Phase shift vs frequency• For any filter we should consider

phase shift as well as the attenuation.• Phase shift is a measurement to determine

how much output signal has been shiftedin phase related to the input voltage.

• Phase shift is • As ω goes 0, phase shift goes 0° (i.e no phase shift). When ω goes to

infinity phase shift goes to -90°.• Phase shift also can be written in terms of cut off frequency:

Where

• Notice that when ω=ωc , phase shift is -45°

Rectifier

7805 IC120VAC5VDC

• A step down transformer reduces the 120VAC to 12VAC• Diodes passes only the positive portion of the signal.• The filter capacitor smoothes the signal.• 7805 outputs a regulated +5V