Home www.play-hookey.com Thu, 04-15-2021

Filters

### Overview

As we have already seen, the rectifier circuitry takes the initial ac sine wave from the transformer or other source and converts it to pulsating dc. A full-wave rectifier will produce the waveform shown to the right, while a half-wave rectifier will pass only every other half-cycle to its output. This may be good enough for a basic battery charger, although some types of rechargeable batteries still won't like it. In any case, it is nowhere near good enough for most electronic circuitry. We need a way to smooth out the pulsations and provide a much "cleaner" dc power source for the load circuit.

To accomplish this, we need to use a circuit called a filter. In general terms, a filter is any circuit that will remove some parts of a signal or power source, while allowing other parts to continue on without significant hinderance. In a power supply, the filter must remove or drastically reduce the ac variations while still making the desired dc available to the load circuitry.

Filter circuits aren't generally very complex, but there are several variations. Any given filter may involve capacitors, inductors, and/or resistors in some combination. Each such combination has both advantages and disadvantages, and its own range of practical application. We will examine a number of common filter circuits on this page.

### A Single Capacitor

If we place a capacitor at the output of the full-wave rectifier as shown to the left, the capacitor will charge to the peak voltage each half-cycle, and then will discharge more slowly through the load while the rectified voltage drops back to zero before beginning the next half-cycle. Thus, the capacitor helps to fill in the gaps between the peaks, as shown in red in the first figure to the right.

Although we have used straight lines for simplicity, the decay is actually the normal exponential decay of any capacitor discharging through a load resistor. The extent to which the capacitor voltage drops depends on the capacitance of the capacitor and the amount of current drawn by the load; these two factors effectively form the RC time constant for voltage decay.

As a result, the actual voltage output from this combination never drops to zero, but rather takes the shape shown in the second figure to the right. The blue portion of the waveform corresponds to the portion of the input cycle where the rectifier provides current to the load, while the red portion shows when the capacitor provides current to the load. As you can see, the output voltage, while not pure dc, has much less variation (or ripple, as it is called) than the unfiltered output of the rectifier.

A half-wave rectifier with a capacitor filter will only recharge the capacitor on every other peak shown here, so the capacitor will discharge considerably more between input pulses. Nevertheless, if the output voltage from the filter can be kept high enough at all times, the capacitor filter is sufficient for many kinds of loads, when followed by a suitable regulator circuit.

### RC Filters

In order to reduce the ripple still more without losing too much of the dc output, we need to extend the filter circuit a bit. The circuit to the right shows one way to do this. This circuit does cause some dc loss in the resistor, but if the required load current is low, this is an acceptable loss.

To see how this circuit reduces ripple voltage more than it reduces the dc output voltage, consider a load circuit that draws 10 mA at 20 volts dc. We'll use 100 µf capacitors and a 100Ω resistor in the filter.

For dc, the capacitors are effectively open circuits. Therefore any dc losses will be in that 100Ω resistor. for a load current of 10 mA (0.01 A), the resistor will drop 100 × 0.01 = 1 volt. Therefore, the dc output from the rectifier must be 21 volts, and the dc loss in the filter resistor amounts to 1/21, or about 4.76% of the rectifier output. This is generally quite acceptable.

On the other hand, the ripple voltage (in the USA) exists mostly at a frequency of 120 Hz (there are higher-frequency components, but they will be attenuated even more than the 120 Hz component). At this frequency, each capacitor has a reactance of about 13.26Ω. Thus R and C2 form a voltage divider that reduces the ripple to about 13% of what came from the rectifier. Therefore, for a dc loss of less than 5%, we have attenuated the ripple by almost 87%. This is a substantial amount of ripple reduction, although it doesn't remove the ripple entirely.

If the amount of ripple is still too much for the particular load circuit, additional filtering or a regulator circuit will be required.

### LC Filters

While the RC filter shown above helps to reduce the ripple voltage, it introduces excessive resistive losses when the load current is significant. To reduce the ripple even more without a lot of dc resistance, we can replace the resistor with an inductor as shown in the circuit diagram to the right.

In this circuit, the two capacitors store energy as before, and attempt to maintain a constant output voltage between input peaks from the rectifier. At the same time, the inductor stores energy in its magnetic field, and releases energy as needed in its attempt to maintain a constant current through itself. This provides yet another factor that attempts to smooth out the ripple voltage.

In some cases, C1 is omitted from this filter circuit. The result is a lower dc output voltage, but improved ripple removal. The choice is a trade-off, and must be made according to the specific requirements in each individual case.

For dc, the inductance has only the resistance of the wire that comprises the coil, which amounts to a few ohms. Meanwhile, the capacitors still operate as open circuits at dc, so they do not reduce the dc output voltage. However, at the basic ripple frequency of 120 Hz, a 10 Henry inductance has a reactance of:

XL = 2πfL = 7540Ω

At the same time, a 100 µf capacitor at the same ripple frequency has a reactance of:

XC = 1/2πfC = 13.26Ω

Thus, L and C2 form a voltage divider that drastically reduces the ripple component (to less than 0.2%) while leaving the desired dc output nearly alone. This configuration may provide sufficiently pure dc for some applications, without the need for any following regulator at all.

The drawback of this approach is that a 10 Henry inductor is as large as some power transformers, with a heavy iron core. It takes up a lot of space and is relatively expensive. This is why the RC filter circuit may be preferred to the LC filter, provided the ripple reduction is sufficient and the power loss in the resistor is not excessive.

 Prev: Basic Rectifier Circuits Next: Regulators