This article discusses the role and function of capacitor-input (C-input) filters in converting pulsating DC into a smoother DC output for electronic devices. It explains how these filters operate, the factors influencing their effectiveness, and compares their performance in half-wave and full-wave rectifiers.
Power Supply Filters
The output of a half-wave or full-wave rectifier is pulsating direct current. This type of output is generally not usable for most electronic circuits. A rather pure form of DC is usually required. This form of DC is achieved through a filter.
The filter of a power supply is designed to change pulsating DC into a rather pure form of DC. Filtering takes place between the output of the rectifier and the input to the load device.
Figure 1. Filter as a Component in a Power Supply Circuit
The pulsating DC output of a rectifier contains two components. One of these deals with the DC part of the output. This component is based on the combined average value of each pulse. The second part of the output refers to its AC component. Pulsating DC, for example, occurs at 60 or 120 Hz, depending on the rectifier employed. This part of the output has a definite ripple frequency. Ripple must be minimized before the output of a power supply can be used by most electronic devices.
Power supply filters fall into two general classes according to the type of component used in its input. If filtering is first achieved by a capacitor, it is classified as a Capacitor-input filter, or capacitor filter. When a coil of wire or inductor is used as the first component, it is classified as an L-input filter, or inductive filter.
Capacitor-input filters develop a higher value of DC output voltage than L-input filters. The output voltage of a C-input filter usually drops in value when the load increases. L-input filters, by comparison, tend to keep the output voltage at a rather constant value. This is particularly important when large changes in the load occur. However, the output voltage of an L-input filter is somewhat lower than that of a C-input filter. Figure 2 shows a graphic comparison of output voltage and load current for C-input and L-input filters.
Figure 2. Load current versus output voltage comparisons for L-input and C-input filters.
Characteristics of Capacitor-Input Filter
The AC component of a power supply can be effectively reduced by a C-input filter. A single capacitor is simply placed across the load resistor, as shown in Figure 3. For alternation 1 of the circuit, Figure 3(a), the diode is forward biased. Current flows according to the arrows of the schematic. The capacitor (C) charges quickly to the peak voltage value of the first pulse. At the same point in time, current is also supplied to $R_{L}$. The initial surge of current through a diode is usually quite large. This current is used to charge C and supply $R_{L}$ at the same time. A large capacitor, however, responds somewhat like low resistance when it is first being charged. Note the amplitude of the $I_{D}$ waveform during alternation 1.
When alternation 2 of the input occurs, the diode is reverse-biased. Figure 3(b) shows how the circuit responds to this alternation. Note that there is no current flow from the source through the diode. The charge acquired by C during the first alternation now finds an easy discharge path through $R_{L}$. The resulting discharge current flow is indicated by the arrows between C and $R_{L}$. In effect, $R_{L}$ has supplied current even when the diode is not conducting. The voltage across $R_{L}$ is, therefore, maintained at a much higher value. See the $V_{RL}$ waveform for alternation 2 in Figure 3(c).
Figure 3: C-input filter action. (a) Alternation one. (b) Alternation two. (c) Waveforms for AC input, diode voltage ($V_{D}$) and current ($I_{D}$), and load resistor voltage ($V_{RL}$) and current ($I_{RL}$).
Discharge of C continues for the full time of alternation 2. Near the end of the alternation, there is somewhat of a drop in the value of $V_{RL}$. This is due, primarily, to a depletion of capacitor charge current. At the end of this time, the next positive alternation occurs. The diode is again forward-biased. The capacitor and $R_{L}$ receive current from the source at this time. With C still partially charged from the first alternation, less diode current is needed to recharge C. In Figure 3(c), note the amplitude change in the second 1, pulse. The process from this point on is a repeat of alternations 1 and 2.
The effectiveness of a capacitor as a filter device is based on a number of factors. Three very important considerations are:
- the size of the capacitor;
- the value of the load resistor, $R_{L}$;
- the time duration of a given DC pulse.
These three factors are related to one another by the following formula:
$$T = R \times C$$
Where,
- T is the time in seconds,
- R is the resistance in Ohms,
- and C is the capacitance in farads.
The product of RC is an expression of the filter circuit’s time constant. RC is a measure of how rapidly the voltage and current of the filter respond to changes in input voltage. A capacitor will charge to 63.2% of the applied voltage in one time constant. A discharging capacitor will have a 63.2% drop of its original value in one time constant. It takes five time constants to charge or discharge a capacitor fully.
The filter capacitor of Figure 3 charges quickly during the first positive alternation. Essentially, there is very little resistance for the RC time constant during this period. The discharge of C, however, is through $R_{L}$. If $R_{L}$ is small, C will discharge very quickly. A large value of $R_{L}$ will cause C to discharge rather slowly. For good filtering action, C must not discharge very rapidly during the time of one alternation. When this occurs, there is very little change in the value of $V_{RL}$. A C-input filter works very well when the value of $R_{L}$ is relatively large. If the value of $R_{L}$ is small, as in a heavy load, more ripple will appear in the output.
Comparison of Half-Wave and Full-Wave Capacitor-Input Filtering
A rather interesting comparison of filtering occurs between half-wave and full-wave rectifier power supplies. The time between reoccurring peaks is twice as long in a half-wave circuit as it is for a full-wave. The capacitor of a half-wave circuit, therefore, has more time to discharge through $R_{L}$.
The ripple of a half-wave filter will be much greater than that of a full-wave circuit. In general, it is easier to filter the output of a full-wave rectifier. Figure 4 compares half-wave and full-wave rectifier filtering with a single capacitor.
Figure 4: Comparison of C-input filtering with half-wave and full-wave rectifiers. (a) Half-wave. (b) Full-wave.
The DC output voltage of a filtered power supply is usually a great deal higher than that of an unfiltered power supply. In Figure 3, the waveforms show an obvious difference between outputs.
In the filtered outputs, the capacitor charges to the peak value of the rectified output. The amount of discharge action that takes place is based on the resistance of $R_{L}$. For a light load or high resistance $R_{L}$, the filtered output remains charged to the peak value. For example, the peak value of 10-$V_{RMS}$ is 14.14 V.
For an unfiltered full-wave rectifier, the DC output is approximately 0.9 × RMS, or 9.0 V. Comparing 9 V to 14 V shows a rather decided difference in the two outputs. For the half-wave rectifier, the output difference is even greater. The unfiltered half-wave output is approximately 45% of 10 $V_{RMS}$, or 4.5 V. The filtered output is 14 V less 20% for the added ripple, or approximately 11.2 V. The filtered output of a half-wave rectifier is nearly 2.5 times more than that of the unfiltered output. These values are only rough generalizations of power supply output with a light load.
Review Questions
- The purpose of a filter circuit is to increase _____ and decrease _____.
- A capacitor filter places a single capacitor in with the load.
Answers
- DC voltage, ripple
- parallel
Key Takeaways
Capacitor-input filters play a critical role in improving the quality of power supply outputs by minimizing ripple and maintaining a higher and more stable DC voltage. They are especially important in applications such as in audio, communication, and digital electronics.