Module 7  Introduction to SolidState Devices and Power Supplies
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E_{avg}) flows through the load resistance. This statement can be clarified by using the formula for X_{C} in a halfwave and fullwave rectifier. First, you must establish some values for the circuit. 421
As you can see from the calculations, by doubling the frequency of the rectifier, you reduce the impedance of the capacitor by onehalf. This allows the ac component to pass through the capacitor more easily. As a result, a fullwave rectifier output is much easier to filter than that of a halfwave rectifier. Remember, the smaller the X_{C} of the filter capacitor with respect to the load resistance, the better the filtering action. Since the largest possible capacitor will provide the best filtering. Remember, also, that the load resistance is an important consideration. If load resistance is made small, the load current increases, and the average value of output voltage (E_{avg}) decreases. The RC discharge time constant is a direct function of the value of the load resistance; therefore, the rate of capacitor voltage discharge is a direct function of the current through the load. The greater the load current, the more rapid the discharge of the capacitor, and the lower the average value of output voltage. For this reason, the simple capacitive filter is seldom used with rectifier circuits that must supply a relatively large load current. Using the simple capacitive filter in conjunction with a fullwave or bridge rectifier provides improved filtering because the increased ripple frequency decreases the capacitive reactance of the filter capacitor. Q14. What is the most basic type of filter? Q15. In a capacitor filter, is the capacitor in series or in parallel with the load? Q16. Is filtering better at a high frequency or at a low frequency? Q17. Does a filter circuit increase or decrease the average output voltage? Q18. What determines the rate of discharge of the capacitor in a filter circuit? 422
Q19. Does low ripple voltage indicate good or bad filtering? Q20. Is a fullwave rectifier output easier to filter than that of a halfwave rectifier? LC ChokeInput Filter The LC chokeinput filter is used primarily in power supplies where voltage regulation is important and where the output current is relatively high and subject to varying load conditions. This filter is used in high power applications such as those found in radars and communication transmitters. Notice in figure 419 that this filter consists of an input inductor (L1), or filter choke, and an output filter capacitor (C1). Inductor L1 is placed at the input to the filter and is in series with the output of the rectifier circuit. Since the action of an inductor is to oppose any change in current flow, the inductor tends to keep a constant current flowing to the load throughout the complete cycle of the applied voltage. As a result, the output voltage never reaches the peak value of the applied voltage. Instead, the output voltage approximates the average value of the rectified input to the filter, as shown in the figure. The reactance of the inductor (X_{L}) reduces the amplitude of ripple voltage without reducing the dc output voltage by an appreciable amount. (The dc resistance of the inductor is just a few ohms.) Figure 419.  LC chokeinput filter. The shunt capacitor (C1) charges and discharges at the ripple frequency rate, but the amplitude of the ripple voltage (E_{r}) is relatively small because the inductor (L1) tends to keep a constant current flowing from the rectifier circuit to the load. In addition, the reactance of the shunt capacitor (X_{C}) presents a low impedance to the ripple component existing at the output of the filter, and thus shunts the ripple component around the load. The capacitor attempts to hold the output voltage relatively constant at the average value of the voltage. The value of the filter capacitor (C1) must be relatively large to present a low opposition (X_{C}) to the pulsating current and to store a substantial charge. The rate of the charge for the capacitor is limited by the low impedance of the ac source (the transformer), by the small resistance of the diode, and by the counter electromotive force (CEMF) developed by the coil. Therefore, the RC charge time constant is short compared to its discharge time. (This comparison in RC charge and discharge paths is illustrated in 423
views A and B of figure 420.) Consequently, when the pulsating voltage is first applied to the LC chokeinput filter, the inductor (L1) produces a CEMF which opposes the constantly increasing input voltage. The net result is to effectively prevent the rapid charging of the filter capacitor (C1). Thus, instead of reaching the peak value of the input voltage, C1 only charges to the average value of the input voltage. After the input voltage reaches its peak and decreases sufficiently, the capacitor C1) attempts to discharge through the load resistance R_{L}). C1 will only partially discharge, as indicated in view B of the figure, because of its relatively long discharge time constant. The larger the value of the filter capacitor, the better the filtering action. However, because of physical size, there is a practical limitation to the maximum value of the capacitor. Figure 420A.  LC chokeinput filter (charge and discharge paths). CHARGE PATH Figure 420B.  LC chokeinput filter (charge and discharge paths). DISCHARGE PATH The inductor (also referred to as the filter choke or coil) serves to maintain the current flow to the filter output (R_{L}) at a nearly constant level during the charge and discharge periods of the filter capacitor. The inductor (L1) and the capacitor (C1) form a voltage divider for the ac component (ripple) of the applied input voltage. This is shown in views A and B of figure 421. As far as the ripple component is concerned, the inductor offers a high impedance (Z) and the capacitor offers a low impedance (view B). As a result, the ripple component (E_{r}) appearing across the load resistance is greatly attenuated (reduced). The inductance of the filter choke opposes changes in the value of the current flowing through it; 424
therefore, the average value of the voltage produced across the capacitor contains a much smaller value of ripple component (E_{r}) than the value of ripple produced across the choke. Figure 421.  LC chokeinput filter. Now look at figure 422 which illustrates a complete cycle of operation for a fullwave rectifier circuit used to supply the input voltage to the filter. The rectifier voltage is developed across the capacitor (C1). The ripple voltage at the output of the filter is the alternating component of the input voltage reduced in amplitude by the filter section. Each time the anode of a diode goes positive with respect to the cathode, the diode conducts and C1 charges. Conduction occurs twice during each cycle for a fullwave rectifier. For a 60hertz supply, this produces a 120hertz ripple voltage. Although the diodes alternate (one conducts while the other is nonconducting), the filter input voltage is not steady. As the anode voltage of the conducting diode increases (on the positive half of the cycle), capacitor C1 chargesthe charge being limited by the impedance of the secondary transformer winding, the diode's forward (cathodetoanode) resistance, and the counter electromotive force developed by the choke. During the nonconducting interval (when the anode voltage drops below the capacitor charge voltage), C1 discharges through the load resistor (R_{L}). The components in the discharge path have a long time constant; thus, C1 discharges more slowly than it charges. 425
Figure 422.  Filtering action of the LC chokeinput filter. The choke (L1) is usually a large value, from 1 to 20 henries, and offers a large inductive reactance to the 120hertz ripple component produced by the rectifier. Therefore, the effect that L1 has on the charging of the capacitor (C1) must be considered. Since L1 is connected in series with the parallel branch consisting of C1 and R_{L}, a division of the ripple (ac) voltage and the output (dc) voltage occurs. The greater the impedance of the choke, the less the ripple voltage that appears across C1 and the output. The dc output voltage is fixed mainly by the dc resistance of the choke. Now that you have read how the LC chokeinput filter functions, it will be discussed with actual component values applied. For simplicity, the input frequency at the primary of the transformer will be 117 volts 60 hertz. Both halfwave and fullwave rectifier circuits will be used to provide the input to the filter. Starting with the halfwave configuration shown in figure 423, the basic parameters are: With 117 volts ac rms applied to the T1 primary, 165 volts ac peak is available at the secondary [(117 V) x (1.414) = 165 V]. You should recall that the ripple frequency of this halfwave rectifier is 60 hertz. Therefore, the capacitive reactance of C1 is: 426
Figure 423.  Halfwave rectifier with an LC chokeinput filter. This means that the capacitor (C1) offers 265 ohms of opposition to the ripple current. Note, however, that the capacitor offers an infinite impedance to direct current. The inductive reactance of L1 is: The above calculation shows that L1 offers a relatively high opposition (3.8 kilohms) to the ripple in comparison to the opposition offered by C1 (265 ohms). Thus, more ripple voltage will be dropped across L1 than across C1. In addition, the impedance of C1 (265 ohms) is relatively low with respect to the resistance of the load (10 kilohms). Therefore, more ripple current flows through C1 than the load. In other words, C1 shunts most of the ac component around the load. Let's go a step further and redraw the filter circuit so that you can see the voltage divider action. Refer to view A of figure 424. Remember, the 165 volts peak 60 hertz provided by the rectifier consists of both an ac and a dc component. This first discussion will be about the ac component. From the figure, you see that the capacitor (C1) offers the least opposition (265 ohms) to the ac component. Therefore, the greater amount of ac will flow through C1. (The heavy line in view B indicates the ac current flow through the capacitor.) Thus the capacitor bypasses, or shunts, most of the ac around the load. 427
Figure 424.  Ac component in an LC chokeinput filter. By combining the X_{C} of C1 and the resistance of R_{L} into an equivalent circuit (view B), you will have an equivalent impedance of 265 ohms. As a formula; You now have a voltage divider as illustrated in figure 425. You should see that because of the impedance ratios, a large amount of ripple voltage is dropped across L1, and a substantially smaller amount is dropped across C1 and R_{L}. You can further increase the ripple voltage across L1 by increasing the inductance (X_{L} = 2πfL). Figure 425.  Equivalent circuit of an LC chokeinput filter. 428
Now let's discuss the dc component of the applied voltage. Remember, a capacitor offers an infinite (∞) impedance to the flow of direct current. The dc component, therefore, must flow through R_{L} and L1. As far as the dc is concerned, the capacitor does not exist. The coil and the load are therefore in series with each other. The dc resistance of a filter choke is very low (50 ohms average). Consequently, most of the dc component is developed across the load and a very small amount of the dc voltage is dropped across the coil, as shown in figure 426. Figure 426.  Dc component in an LC chokeinput filter. As you may have noticed, both the ac and the dc components flow through L1. Because it is frequency sensitive, the coil provides a large resistance to ac and a small resistance to dc. In other words, the coil opposes any change in current. This property makes the coil a highly desirable filter component. Note that the filtering action of the LC chokeinput filter is improved when the filter is used in conjunction with a fullwave rectifier, as shown in figure 427. This is due to the decrease in the X_{C} of the filter capacitor and the increase in the X_{L} of the choke. Remember, ripple frequency of a fullwave rectifier is twice that of a halfwave rectifier. For 60hertz input, the ripple will be 120 hertz. The X_{C} of C1 and the X_{L} of L1 are calculated as follows: 429
Figure 427.  Fullwave rectifier with an LC chokeinput filter. When the X_{C} of a filter capacitor is decreased, it provides less opposition to the flow of ac. The greater the ac flow through the capacitor, the lower the flow through the load. Conversely, the larger the X_{L} of the choke, the greater the amount of ac ripple developed across the choke; consequently, less ripple is developed across the load and better filtering is obtained. Q21. In an LC chokeinput filter, what prevents the rapid charging of the capacitor? Q22. What is the range of values usually chosen for a choke? Q23. If the impedance of the choke is increased, will the ripple amplitude increase or decrease? FAILURE ANALYSIS OF AN LC CHOKEINPUT FILTER.  The filter capacitors are subject to open circuits, short circuits, and excessive leakage; the series inductor is subject to open windings and, occasionally, shorted turns or a short circuit to the core. 430
NEETS Table of Contents
 Introduction to Matter, Energy,
and Direct Current
 Introduction to Alternating Current and Transformers
 Introduction to Circuit Protection,
Control, and Measurement
 Introduction to Electrical Conductors, Wiring
Techniques, and Schematic Reading
 Introduction to Generators and Motors
 Introduction to Electronic Emission, Tubes,
and Power Supplies
 Introduction to SolidState Devices and
Power Supplies
 Introduction to Amplifiers
 Introduction to WaveGeneration and WaveShaping
Circuits
 Introduction to Wave Propagation, Transmission
Lines, and Antennas
 Microwave Principles
 Modulation Principles
 Introduction to Number Systems and Logic Circuits
 Introduction to Microelectronics
 Principles of Synchros, Servos, and Gyros
 Introduction to Test Equipment
 RadioFrequency Communications Principles
 Radar Principles
 The Technician's Handbook, Master Glossary
 Test Methods and Practices
 Introduction to Digital Computers
 Magnetic Recording
 Introduction to Fiber Optics
