Unit Converter

The time constant is determined as

where τ is the time constant in seconds, R is the resistance in ohms and C is the capacitance in farads. The time constant of an RC circuit is defined as the time it takes for the capacitor to reach 63.2% of its maximum charge capacity provided that it has no initial charge. Note that the capacitor will be 63.2% charged after τ and almost fully charged (99.3%) after approximately 5τ.

Energy stored E in the capacitor when it is fully charged to voltage U (charging time T >> τ) is determined as follows:

where C is the capacitance in farads and V is the voltage in volts.

Maximum current I is determined from Ohm’s law:

Maximum charge Q is determined as follows:

where C is the capacitance in farads and U — voltage in volts.

Filter electrolytic capacitors on a computer motherboard

Applications

The main part of the ADSL splitter is a low-pass filter

Capacitors are often used in various electronic and electrical devices and systems. You will probably not be able to find an electronic device without at least one capacitor. Capacitors are used for energy storage, providing pulse power, for power conditioning, for power factor correction, for AC coupling and DC blocking, in electronic frequency filters, in noise filters, for motor starting, for information storage, in tuned circuits, in various sensing devices, in mobile phone capacitive touch screens, and for many other purposes.

Resistor–capacitor (RC) circuits can be used as simple low-pass and high-pass filters, integrators, and differentiators.

RC Low-Pass Filters

An example of a second-order two-stage RC low-pass filter with a non-inverting unity amplifier, which is used as a buffer between the two filter stages.

Low-pass filters pass only low-frequency signals and attenuate high-frequency signals. The cutoff frequency is determined by the components in the filter circuit.

Such filters are widely used in electronics. One example is using them in subwoofers to block high frequencies that they cannot reproduce. They are also used in radio transmitters to block unwanted harmonic emissions. Those who use ADSL Internet connection have these filters installed in DSL splitters that prevent interference between telephones and DSL equipment connected to the telephone line.

Low-pass filters are used for conditioning signals prior to analog-to-digital conversion and are called anti-aliasing filters. They are necessary for rejecting the high-frequency components of a signal above the Nyquist frequency to satisfy the sampling theorem.

A simple low-pass filter is shown in the picture above. Only passive components are used in it; therefore it is referred to as a passive low-pass filter. More complex passive low-pass filters also use inductors.

Unlike passive low-pass filters, active filters use some gain devices, for example, transistors or operational amplifiers. Passive filters are also often accompanied by amplifiers. Depending on the number of capacitors and inductors, which affect the steepness of the filter’s frequency response, they are often referred to as “first-order”, “second-order”, etc. filters. A filter consisting of only one resistor and one capacitor is called a first-order filter.

A simple passive first-order RC high-pass filter

RC High-Pass Filters

High-pass filters pass only high-frequency signals and attenuate low-frequency signals. High-pass filters are used, for example, in audio crossovers to block low frequencies of signals sent to tweeters that usually are not capable of handling large power signals at low frequencies.

An active high-pass filter with an operational amplifier

High-pass filters are often used to block DC from circuitry sensitive to it. For example, they are very common in microphone circuits because microphones need DC power, which is supplied through the microphone cable. At the same time, they record only AC signals such as human voice and music. The DC voltage should not appear in the microphone output and to block it a high-pass filter is used.

A simple band-pass filter made by cascading together a low-pass filter (C2, R2) and a high-pass filter (C1, R1)

If high-pass and low-pass filters are used together, they form a band-pass filter, which passes frequencies only within a certain range and attenuates frequencies outside of that range. Such filters are widely used in wireless receivers and transmitters. In receivers, the band-pass filters only allow signals within a selected range of frequencies to pass and to be heard, while rejecting signals at unwanted frequencies. Transmitters must always transmit power only in the range of frequencies allocated to them; therefore, band-pass filters are used in them to limit the bandwidth of the output signal to their transmission band.

This article was written by Anatoly Zolotkov