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# POWER SUPPLIES, RECTIFIER CIRCUITS, AND POWER SUPPLY FILTERS

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### Power Supplies

A DC power supply can perform several functions; it can transform line voltages to higher or lower values, rectify AC, filter pulsating DC, or make more than one relatively constant DC voltage available. Each of these functions are integrated into most power supplies. The primary characteristics that must be considered in the selection of a power supply are:

• The DC voltage or voltages required from the power supply.
• The maximum current required by the circuit components to meet their power requirements. The current drawn is termed the load.
• The amount of variation in DC output permitted under constant load; this is referred to as the amount of ripple.
• The amount of variation in DC output permitted with changes in load; this is referred to as the amount of regulation required.
 3.4 Pi Filter

### Rectifier Circuits

Rectification is described as the changing of an alternating current (AC) to a unidirectional or direct current (DC). The normal PN junction diode is well suited for this purpose as it conducts very heavily when forward-biased (low resistance direction) and only slightly when reverse-biased (high resistance direction). Figure 1 is a block diagram of a power supply showing an AC input to, and a DC output from, a block labeled Positive Power Supply and Filter Network. Although Figure 1 shows a power supply that provides a unidirectional current, which causes a positive voltage output, it might well be designed to furnish a negative voltage output.

Figure 1: Positive Voltage Output From an AC Input

Many electronic circuits depend upon DC for proper operation. This is the reason why a change of AC to DC is necessary. As already pointed out, the PN junction diode conducts more easily in one direction than in the other. Transistors are also unidirectional and a constantly alternating source voltage would be undesirable. Before describing how an AC input is converted into a DC output, the definition of "load" as it applies to power supplies must be understood. Load is the current supplied to the power-consuming device or devices connected to the power supply. The power-consuming device needs voltage and current for proper operation and this voltage and current is supplied by the power supply. The power-consuming device may be a simple resistor or one or more electronic circuits using resistors, capacitors, coils, and active devices.

### Half Wave Rectifier

Figure 2 shows the PN junction diode functioning as a half-wave rectifier.

Figure 2: Positive Voltage Output Half Wave Rectifier

A half-wave rectifier is one that uses only half of the input cycle to produce an output.

The induced voltage across L2 (the transformer secondary) will be as shown in Figure 2. The dots (polarity marks) on the transformer indicate points of the same polarity. During the portion of the input cycle that is going positive (solid line), CR1, the PN junction diode, will be forward-biased and current will flow through the circuit. L2, acting as the source voltage, will have current flowing from the top to the bottom. This current then flows up through RL causing a voltage drop across RL equal to the value of current flowing times the value of RL. This voltage drop will be positive at the top of RL, with respect to its other side; and the output will therefore be a positive voltage with respect to ground.

It is common practice for the end of a resistor receiving current to be given a sign representing a negative polarity of voltage, and the end of the resistor through which current leaves to be assigned a positive polarity of voltage. The voltage drop across RL, plus the voltage drop across the conducting diode will equal the applied voltage. Although the output voltage will nearly equal the peak applied voltage, it cannot reach this value due to the voltage drop, no matter how small, across CR1. In a half-wave rectifier circuit the average DC output voltage is 0.318 of the peak value of one half AC cycle.

The broken line illustrates the negative half-cycle of the input. When the negative half-cycle is felt on CR1, the PN junction diode is reverse-biased. The reverse current will be very small, but it will exist. The voltage resulting from the reverse current, as shown below the line in the output is exaggerated to bring out the point of its existence. Although only one cycle of input is shown in Figure 2, it should be realized that the action described above continually repeats itself, so long as there is an AC input.

By reversing the diode connection in Figure 2, having the anode on the right instead of the left, the output would now become a negative voltage. The current would be going from the top of RL toward the bottom, making the output at the top of RL negative with respect to the bottom or ground side.

The same negative output can be obtained from Figure 2 if the reference point (ground) is changed from the bottom (where it is shown) to the top, or cathode-connected end, of the resistor. The bottom of RL is shown as being negative with respect to the top, and reading the output voltage from the "hot" side of the resistor to ground would result in a negative voltage output.

### Full Wave Rectifier

A full-wave rectifier is a device that has two or more diodes arranged so the load current flows in the same direction during each half-cycle of the AC supply. The PN junction diode works just as well in a full-wave rectifier circuit as shown in Figure 3.

Figure 3: Unfiltered Negative Output Full Wave Rectifier

The circuit shown has a negative voltage output; however, it might just as well have a positive voltage output. This can be accomplished by either changing the reference point (ground side of RL) or by reversing the diodes in the circuit.

The AC input is felt across the secondary winding of T1. This winding is center tapped as shown; the center of the secondary is at ground potential. Ground potential is defined as a reference point that is of no particular polarity.

When the polarity is such that the top of T1 secondary is negative, the bottom is positive. At this time, the center tap, as shown, has two polarities, positive with respect to the top half of the winding, and negative with respect to the bottom half of the winding. When the secondary winding is positive at the top, the bottom is negative and the center tap is negative with respect to the top and positive with respect to the bottom.

For ease of explanation, the negative alternation will be considered when the rectifier current is initially energized by the AC source. CR1 will be forward-biased, with negative voltage felt on its cathode, and CR2 will be reverse-biased, with a positive voltage felt on its cathode. Therefore, the top of T1 secondary must be negative with respect to the bottom. When forward bias is applied to CR1, it conducts heavily from cathode to anode (dashed arrow), down through RL, creating a voltage drop across RL, which is negative at the top with respect to the bottom or ground side of RL. The current passing through RL is returned to CR1 by going through the grounded center tap and up the upper section of the center-tapped secondary winding of T1. This completes the first alternation of the input cycle.

The second alternation of the input now is of such polarity as to forward bias CR2: a negative voltage at the bottom of T1 secondary winding with respect to ground. CR1 is now reverse-biased. As CR2 conducts, current moves in the same direction through RL (solid arrow), from top to bottom, back through the lower half of the center-tapped secondary to CR2.

It can be seen in the output waveform of Figure 3 that there are two pulses of DC out for every cycle of AC input. This is full-wave rectification.

Current flow through RL is in the same direction, no matter which diode is conducting. The positive going alternation of the input allows one diode to be forward-biased and the negative going alternation of the input allows the other diode to be forward-biased. The output, for the full-wave rectifier shown, is a negative voltage measured from the top RL to ground. In a full-wave rectifier, the average DC output voltage is 0.434 of the peak value of the AC input voltage.

It should also be noted that the output voltage is a function of only half the total transformer secondary voltage. This is because the center tap is used to provide the current return path. The forward-biased diode will allow current flow and the load sees this "half of the secondary" voltage.

### Bridge Rectifier

A bridge rectifier makes use of four diodes in a bridge arrangement to achieve full-wave rectification. This is a widely used configuration, both with individual diodes and with single component bridges where the diode bridge is wired internally. Now, the PN junction diode will be described as it is used in a bridge rectifier circuit. Figure 4 shows such a circuit capable of producing a positive output voltage.

Figure 4: Bridge Rectifier Circuit

When the AC input is applied across the secondary winding of T1, it will forward bias diodes CR1 and CR3, or CR2 and CR4. When the top of the transformer is positive with respect to the bottom, as shown in Figure 4 by the designation number 1, both CR1 and CR2 will feel this positive voltage. CR1 will have a positive voltage on its cathode, a reverse bias condition, and CR2 will have a positive voltage on its anode, a forward bias condition. At the same time, the bottom of the secondary winding will be negative with respect to the top, placing a negative voltage on the anode of CR3, a reverse bias condition and a negative voltage on the cathode of CR4, resulting in a forward bias condition.

During the half-cycle of the input designated by the number 1 in Figure 4, we find that CR2 and CR4 are forward biased and will therefore conduct heavily. The solid arrows show the conducting path from the source (the secondary winding of T1) through CR4 to ground, up through RL making the top of RL positive with respect to the grounded end, to the junction of CR2 and CR3. CR2, being forward-biased, offers the path of least resistance to current flow and this is the path current will take to get back to the source.

During the alternation designated by the number 2 in Figure 4 shown by the dashed arrows, the top of the secondary winding is going negative while the bottom is going positive. The negative voltage at the top is felt by both CR1 and CR2, forward biasing CR1 and reverse biasing CR2. The positive voltage on the bottom of T1 secondary is felt by CR3 and CR4, forward biasing CR3 and reverse biasing CR4. Current flow, starting at the source (T1 secondary winding) is through CR1 to ground, up through RL (this is the same direction as it was when CR2 and CR4 were conducting), making the top of RL positive with respect to its grounded end to the junction of CR2 and CR3. This time CR3 is forward-biased and offers the least opposition to current flow, and current takes this path to return to its source.

As can be seen, the diodes in the bridge circuit operate in pairs; first one pair (CR1 and CR3) conducts heavily and then the other pair (CR2 and CR4) conducts heavily. As shown in the output waveform, we get one pulse out for every half-cycle of the input or two pulses out for every cycle in. This is the same as for the full-wave rectifier circuit explained previously.

### Three-Phase Bridge Rectifier

A three-phase full-wave bridge rectifier is used where a higher ripple frequency is desired. A higher ripple frequency will represent the smoother DC output that may be required in closely regulated power supplies. Figure 5 shows a basic three-phase rectifier.

Figure 5: Three-Phase Full Wave Bridge Rectifier

Conduction of CR1- CR4 depends on the phase polarity at any given instant in time. A minimum of two diodes or a maximum of four diodes may be in conduction simultaneously.

### Power Supply Filters

As previously indicated, the operation of most electronic circuits is dependent upon a direct current source. It has been shown how alternating current can be changed into a pulsating direct current; that is, a current that is always positive or negative with respect to ground. Although this current is not of a steady value, it has "ripple." Ripple can be defined as "the departure of the waveform of a rectifier from pure DC." Ripple is the amplitude excursions, positive and negative, of a waveform from the pure DC value the alternating component of the rectifier voltage. Ripple contains two factors that must be considered: frequency and amplitude. Ripple frequency, in the rectifiers that were presented, are either the same as line frequency for a half-wave rectifier, or twice the line frequency for full-wave rectifiers. In the half-wave rectifier, one pulse of DC output was generated for one cycle of AC input; the ripple frequency is the same as the input frequency. In the full-wave rectifiers (center-tapped and bridge), two pulses of DC output were produced for each cycle of AC input: the ripple frequency is twice that of the line frequency. With a 40Hz input frequency, there is a 40Hz ripple frequency in the output of the half-wave rectifier and an 80Hz ripple frequency in the output of the full-wave rectifier. The purpose of power supply filters is to smooth out the ripple contained in the pulses of DC obtained from the rectifier circuit while increasing the average output voltage or current. Filter circuits used in power supplies are of two general types: Capacitor input and Choke input. There are several combinations that may be used, although they are referred to by different names (Pi, RC, L section, etc). The closest element electrically to the rectifier determines the basic type of filter being used. Figure 6 depicts the basic types. In the capacitor input filter, a capacitor is placed in parallel with the load resistor. Rapid variations in voltage are shunted to ground by the capacitor. This provides a smoother overall output for the output.

Figure 6: Filter Circuits

The choke input filter uses an inductor in series with the load resistor. The inductor opposes changes in current to provide smoother output for the load. The capacitor input filter will keep the output voltage at a higher level compared to a choke input. The choke input will provide a steadier current under changing load conditions. From this, it can be seen that a capacitor input filter would be used where voltage is the prime factor and the choke input filter is used where a steady flow of current is required.

### Capacitor Input Filter

First, an analysis will be made of the simple capacitor input filter depicted in Figure 7.

Figure 7: Power Supply With Simple Capacitor Filter

The output of the rectifier, without filtering, is shown in Figure 7B, and the output, after filtering, is shown in Figure 7C. Without the capacitor, the output across RL will be pulses as previously described. The average value of these pulses would be the EDC output of the rectifier. With the addition of the capacitor, the majority of the pulse changes are bypassed through the capacitor and around RL. As the first pulse appears across the capacitor, changing it from negative to positive, bottom to top, the peak voltage is developed across the capacitor. When the first half-cycle has reached its peak and starts its negative going pulse, the capacitor will start to discharge through RL maintaining the current through RL in its original direction, thereby holding the voltage across RL at a higher value than its unfiltered load. Before the capacitor can fully discharge, the positive pulse of the next half cycle is nearing its peak, recharging the capacitor. As the pulse again starts to go negative, the capacitor starts to discharge once again. The positive going pulse of the next half cycle comes in and recharges the capacitor; this action continues as long as the circuit is in operation. The charge path for the capacitor is through the transformer secondary and the conducting diodes, and the discharge path is through the load resistor. The reactance of the capacitor, at the line frequency, is small compared to RL, which allows the changes to bypass RL and, effectively, only pure DC appears across RL.

### Choke Input Filter

The next filter to be analyzed is the choke input filter, or the L section filter. Figure 8 shows this filter and the resultant output of the rectifier after filtering has taken place.

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Figure 8: L Section (Choke Input) Filter

The series inductor of Figure 8 will oppose rapid changes in current. The output voltage of this filter is less than that of the capacitor input filter since the choke is in series with the output impedance. The parallel combination of RL and C in connection with L smoothes out the peaks of the pulses and results in a steady, although reduced, output. The inductance "chokes" off the peaks of the alternating components of the rectified waveform and the DC voltage is the average, or DC value, of the rectified wave. The choke input filter allows a continuous flow of current from the rectifier diodes rather than the pulsating current flow as seen in the capacitor input filter. The XL of the choke reduces the ripple voltage by opposing any change in current caused by the positive and negative pulses of the rectifier output voltage. This keeps a steady current flowing to the load throughout the entire cycle. The pulsating voltage developed across the capacitor is maintained at a relatively constant value approaching the average value of input voltage because of this steady current flow.

### Multiple Section Choke Input Filter

Using more than one section can enhance the filtering action provided by the choke input filter. Figure 9 shows two sections with representative waveforms approximating the shape of the voltage with respect to ground at different points in the filter networks.

Figure 9: Multiple Section Choke Input Filter

While Figure 9 shows two choke input sections being used as a multiple section filter, more sections may be added as desired. While the multiple section filter does reduce the ripple content, and they are found in applications where only a minimum ripple content can be tolerated in the output voltage, they also result in reduced regulation. The additional sections add more resistance in series with the power supply, which results in increased voltage variations in the output when the load current varies.

### Pi Filter

The Pi filter, named because of its resemblance to the Greek letter Pi is a combination of the simple capacitor input filter and the choke input filter. This filter is shown in Figure 10.

Figure 10: Pi Filter

The resistor, R, is known as a bleeder resistor and is found in practically all power supplies. The purpose of this resistor is two-fold: when the equipment has been working and is then turned off, it provides a discharge path for the capacitor, preventing a possible shock to maintenance personnel; it also provides a fixed load, no matter what equipment is connected to the power supply. The Pi filter is basically a capacitor input filter with the addition of an L section filter. The majority of the filtering action takes place across C1, which charges through the conducting diode(s) and discharges through R, L, and C2. As in the simple capacitor input filter, the charge time is very fast compared to the discharge time. The inductor smoothes out the peaks of the current pulses felt across C2, thereby providing additional filtering action. The voltage across C2, since C2 is in parallel with the output, is the output voltage of the power supply. Although the voltage output is lower in this filter than it would be if taken across C1 and the load, the amount of ripple is greatly reduced. Even though C1 will charge to the peak voltage of the input when the diodes are conducting, and discharge through R when they are cut off, the inductor is also in the discharge path and opposes any changes in load current. The voltage dividing action of L and C2 is responsible for the lower output voltage in the Pi filter when compared to the voltage available across C1. As shown in Figure 10 the charge path for both C1 and C2 is through the transformer secondary, and, in the case of C2, through L. Both charge paths are through the conducting diode. However, the discharge path for C1 is through R and L while the discharge path for C2 is through R only.

### RC Capacitor Input Filter

While the Pi filter previously discussed had an inductor placed between two capacitors, a resistor can replace the inductor, as shown in Figure 11.

Figure 11: Capacitor Input Filter

The main difference in operation between this Pi filter and the one previously discussed is the reaction of an inductor to AC when compared to the resistor. In the former filter the combination of the reactance of L and C2 to AC provides better filtering, giving a relatively smooth DC output. In Figure 11, both the AC and DC components of the rectified current pass through R1. The output voltage is reduced due to the voltage drop across R1 and the higher the current, the greater this voltage drop. This filter is effective in high voltage, low current applications. As in choke input filters, the capacitor input filters shown may be multiplied; i.e., identical sections may be added in series. The choice of a filter for a particular use is a design problem, but the purpose and operation of filters should be understood by all, because of their importance to the proper operation of equipment following the power supply.