1. 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.

2. 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.

3. 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

4. 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.

5. 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 shifted in 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°

6. Rectifier 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
120VAC
5VDC