## Wednesday, August 13, 2008

### Capacitor

The capacitor's function is to store electrical energy. The capacitor also functions as a filter, passing alternating current (AC) signals but blocking direct current (DC) signals. They are used with resistors in timing circuits because it takes time for a capacitor to fill with charge.
When DC is applied to the capacitor, an electric charge is stored. While capacitor is charging up, current flows. The current will stop flowing when the capacitor has fully charged.
A large capacitance means that more charge can be stored. Capacitance is measured in farads(F).
There are many types of capacitor but they can be split into two groups: polarised (large value, 1uF+) and unpolarised(small values, up to 1uF).
i = C dv/dt
$$i = C \frac{dv}{dt}$$
differentiators: CR : V(t) = RC d/dt V_in(t)
$$V(t)=RC\frac{d}{dt} V_{in}$$Intergrators: RC: V(t) = 1/RC \int V_in(t) dt + constant
$$V(t) = \frac{1}{RC}\int V_{in}(t)dt + constant$$
High pass filter: CR, cutoff freq: 1/RC
V_out = R/(R^2 + (1/w^2 C^2))^(1/2) V_in
$$V_{out} = \frac{R}{\sqrt{R^2+\left(\frac{1}{w^2C^2}\right)}}V_{in}$$Low pass filter: RC, cutoff freq: 1/RC,
V_out = 1/(1+w^2 R^2 C^2)^(1/2) V_in
$$V_{out}=\frac{1}{\sqrt{1+W^2R^2}}V_{in}$$
Other applications:
• Bypass capacitor. In circuit where you want to allow a dc (or slowly varying) voltage. Often the ac is removed from an ac/dc mixture, the dc being free to pass through the bypass component. So the bypass capacitor is to filter the ac or the electrical noise out of the circuit. They do this by removing the alternating current caused by ripple voltage.
• Power-supply filtering. The dc voltage used in electronics are usually generated from the ac line by a processing called rectification, with a large capacitor.
• Timing and waveform generation.