Resistor-Capacitor (RC) Filters
The RC capacitor-input filter is limited to applications in which the load current is small. This type of filter is used in power supplies where the load current is constant and voltage regulation is not necessary. For example, RC filters are used in high-voltage power supplies for cathode-ray tubes and as part of decoupling networks for multistage amplifiers.
The figure below shows an RC capacitor-input filter and its associated waveforms. Both half-wave and full-wave rectifiers are used to provide the inputs.
RC filter and waveforms.
The RC filter above consists of an input filter capacitor (C1), a series resistor (R1), and an output filter capacitor (C2). Although not part of the RC filter, RL is shown to help explain the circuit. This filter is sometimes referred to as an RC pi-section filter because its schematic symbol resembles the Greek letter pi.
Although the single capacitor filter is suitable for many noncritical, low-current applications, when the load resistance is very low or when the percent of ripple must be held to an absolute minimum, the capacitor must have an extremely large value. While electrolytic capacitors are available in sizes up to 10,000 µF or greater, the larger sizes are quite expensive. A more practical approach is to use a more sophisticated filter that can do the same job but that has lower capacitor values, such as the RC filter.
The waveforms shown in the figure represent the unfiltered output from a typical rectifier circuit. Note that the dashed line, which indicates the average value of output voltage (Eavg) for the half-wave rectifier, is less than half the amplitude of the voltage peaks (approximately 0.318). The average value of output voltage (Eavg) for the full-wave rectifier is greater than half (approximately 0.637), but is still much less than, the peak amplitude of the rectifier-output waveform. With no filter circuit connected across the output of the rectifier circuit (unfiltered), the waveform has a large value of pulsating component (ripple) as compared to the average (or dc) component.
An RC filter, such as a pi-section filter, does a much better job than a single capacitor filter.
The picture above illustrates an RC filter connected across the output of a rectifier. C1 performs the same function that it did in the single capacitor filter. It is used to reduce the percentage of ripple to a relatively low value. Thus, the voltage across C1 might consist of an average dc value of +100 volts with a ripple voltage of 10 volts. This voltage is passed on to the R1-C2 network, which reduces the ripple even further (view C).
C2 offers an infinite impedance (resistance) to the dc component of the output voltage. Thus, the dc voltage is passed to the load, but reduced in value by the amount of the voltage drop across R1. However, R1 is generally small compared to the load resistance. Therefore, the drop in the dc voltage by R1 is not a drawback.
Component values are designed so that the resistance of R1 is much greater than the reactance of C2 at the ripple frequency. C2 offers a very low impedance to the ac ripple frequency. Thus, the ac ripple senses a voltage divider consisting of R1 and C2 between the output of the rectifier and ground. Therefore, most of the ripple voltage is dropped across R1. Only a trace of the ripple voltage can be seen across C2 and the load.
In extreme cases where the ripple must be held to an absolute minimum, a second stage of RC filtering can be added. In practice, the second stage is rarely required. The RC filter is extremely popular because smaller capacitors can be used with good results.
The RC filter has some disadvantages, however. First, the voltage drop across R1 takes voltage away from the load. Second, power is wasted in R1 and is dissipated in the form of unwanted heat.
Finally, if the load resistance changes, the voltage across the load will change. Even so, the advantages of the RC filter overshadow these disadvantages in many cases.
The resistor-capacitor (RC) filter is also subject to problems that can cause it to fail. The shunt capacitors (C1 and C2) are subject to an open circuit, a short circuit, or excessive leakage. The series filter resistor (R1) is subject to changes in value and occasionally opens. Any of these troubles can be easily detected.
The input capacitor (C1) has the greatest pulsating voltage applied to it and is the most susceptible to voltage surges. As a result, it is frequently subject to voltage breakdown and shorting. The remaining shunt capacitor (C2) in the filter circuit is not subject to voltage surges because of the protection offered by the series filter resistor (R1). However, a shunt capacitor can become open, leaky, or shorted.
A shorted capacitor or an open filter resistor results in a no-output indication. An open filter resistor results in an abnormally high dc voltage at the input to the filter and no voltage at the output of the filter. Leaky capacitors or filter resistors that have lost their effectiveness, or filter resistors that have decreased in value, result in an excessive ripple amplitude in the output of the supply.
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