EE3301 Experiment 5 A BRIDGE RECTIFIER POWER SUPPLY

Transcription

1 Fall 2000 Releant sections of textbook: Chapter 10 Output Stages and Power Supplies 10.5 inear oltage regulators 10.6 inear-power-supply design EE3301 Experiment 5 A BRIDGE RECTIFIER POWER SUPPY 1 Introduction Most electronic systems require a nonarying current and oltage ( dc ) for their power source. If the power supplied by an electric utility is to be used, it is necessary to conert the utility s alternating oltage (an ac quantity) to that required by the electronic system. Frequently the alternating oltage is transformed with an iron-core transformer to a potential appropriate for the electronic equipment. In this experiment, a full-wae bridge rectifier and a capacitor filter will be used to produce a nearly constant load oltage,, as shown in Fig. 1. If it is assumed that the transformer secondary oltage, trans, is unaffected i 120Vac trans C Figure 1: Full-wae rectifier using 4 diodes. by the capacitor (this assumption is alid only for large alues of load resistance), the load oltage,, and diode current, i, result, as shown in Fig. 2. τ c τ d t T/2 T Figure 2: Output (load) oltage as a function of time, indicating the charging interal, t c and discharging interal, t d, of the capacitor (shown in Fig. 1). 1

2 The capacitor is alternately charged by the diode current (increasing its stored energy) and discharged by the load resistance, modeled with the equialent circuit shown in Fig. 3. During the discharge interal (labeled τ d ), the diode current, i, is zero; that is, none of the diodes are conducting since they are all reerse biased. The ariation of the load oltage during this interal is readily determined since it corresponds to m C min t τ d Figure 3: Output (load) oltage as a function of time, indicating the charging interal, t c and discharging interal, τ d, of the capacitor (shown in 1). the discharge of a capacitance by a resistance. A new time scale, t, has been introduced (at the start of discharge, t = 0). The initial oltage, m, is approximately equal to the secondary oltage of the transformer minus two diode forward oltages. The oltage at the end of the discharge interal, min, depends on the time constant of the circuit, C, as gien in Eq. 1. min = m exp τ d/( C) (1) To minimize the ariation in the load oltage, the time constant of the circuit must be much larger than the discharge interal, τ d. For most applications, relatiely large alues of capacitance are required. During the charging interal (labeled τ c ), two diodes are conducting tand the diode current, i, depends on both the capacitance and the load resistance. i = C d dt (2) To obtain a solution for oer an entire period, the indiidual solutions for the charging and discharging interals must be joined together, taking into account both the oltage and the current. The transformer oltage, howeer, is an unknown. During the charging interal when the diodes are conducting, the diode current, and hence the transformer current, is large. As a result of the transformer s inductance and resistance, its terminal oltage is reduced. Furthermore, a nonlinear effect, a saturation of the transformer s core, generally occurs. As indicated in the preceding diagram, the maximum alue of load oltage is somewhat less than the oltage that occurs without a capacitie filter. In addition, the current pulses tend to be somewhat longer than that which results for an undistorted transformer oltage. An analytical determination of is generally not possible. As a result, a set of approximations are normally used to predict the behaior of the power supply load oltage. Of particular interest is the peakto-peak ariation (the ripple) in the load oltage. To calculate this quantity, it is assumed that the discharge interal of a full-wae rectifier circuit continues for one-half of a period (τ d = T /2). The peak-to-peak ripple oltage, ripple shown in Fig. 4, may readily be calculated for these assumptions. ripple = m min ( ) = m 1 exp T /(2C) (3) 2

3 T/2 m min t Figure 4: Peak-to-peak ripple oltage, m min, as a function of time. If the time constant of the circuit, C, is large compared to T /2, the exponential may be approximated by the first two terms of its Taylor series expansion. exp T /(2C) 1 T /(2 C) fort /(2 C) 1 (4) The fractional ariation in the load oltage is therefore gien by a relatiely simple expression, Eq. 5: ripple m T 2 C = 1 2 f C (5) The Hertizan frequency, f, is that of the power-line oltage. It should be noted that the approximate expression obtained for the ripple oltage tends to predict a somewhat greater oltage than that which actually occurs. Hence, if this expression is used when designing a power supply, it assures that the actual ripple oltage is less than that used for the calculations. The aerage alue of load oltage (its dc alue) falls between min and m. The aerage oltage depends on the characteristics of the transformer and the oltage across the diodes when they are conducting. 2 Experimental Procedure A transformer that has a secondary oltage of 24 V (rms alue) and a current rating of one ampere is required. Either four indiidual power diodes or an integrated circuit bridge rectifier may be used. The indiidual diodes or the bridge rectifier should hae a current rating of at least one ampere and a peak inerse oltage (PIV) of at least 50 olts. If indiidual diodes are used for the bridge circuit, it is imperatie i 120Vac trans C Figure5: Full-waerectifier using4diodes,withr=1kωandc=470µf. that they be connected correctly, otherwise two diodes will be destroyed when the supply is turned on. An electrolytic capacitor (500 mf) with a oltage rating of at least 50 olts is required. It is important that the 3

4 polarity markings of the capacitor correspond to the polarity of its terminal oltage. If the capacitor should happen to be connected to the circuit with its leads reersed, it will be destroyed (ery likely accompanied by a noticeable bang and obnoxious odor). A power resistor capable of dissipating at least one watt is necessary for. Since the leads of the components that are likely to be used are larger than those intended for use with an experimenter board, a suitable experimental bread-board designed for large leads or a prewired assembly is necessary for this experiment. 1. Assemble the circuit omitting the capacitor for this part of the experiment. Note that neither side of the transformer s secondary winding is connected to the common ground connection of the circuit (that to which the ground lead of the oscilloscope is connected). Using an oscilloscope, obsere and sketch. Determine the peak alue of the load oltage from the oscilloscope trace. If the circuit is working properly, the amplitude of adjacent peaks will be the same. Using a digital multimeter (AC range), determine oltage across the secondary winding of the transformer. A meter that does not hae one of its inputs connected to a common ground, such as a hand-held, battery-powered instrument, is necessary. Using a multimeter, determine the aerage alue of the load oltage,. For this oltage measurement a DC range should be used. 2. Before proceeding, it should be established that the data of the preious part is reasonable. Using the ac reading of the digital multimeter, calculate the corresponding peak transformer oltage, V trans. Compare this oltage with the peak alue of obtained from the oscilloscope trace. For no instrument and reading errors, a difference of about 1.4 olts, a oltage corresponding to the forward oltage of two diodes, would be expected. If the difference is considerably greater than this, the circuit is not operating properly. 3. Connect the 470uF capacitor to the circuit (being sure to obsere its polarity markings). Using an oscilloscope, obsere and sketch. An accurate determination of the peak-to-peak alue of the ripple oltage may be accomplished by using the AC input of the oscilloscope. For this condition, the aerage alue of the load oltage is, in effect, subtracted from the actual oltage. The sensitiity setting of the oscilloscope may then be increased to produce a magnified display of the arying oltage component. A multimeter may be used to determine the aerage alue of the load oltage. 4. The dependence of the aerage load oltage and the corresponding ripple oltage on the aerage load current is to be determined. A set of load resistors (fie or more) with alues of 30 to 500 ohms is needed. These resistors should hae a power rating of at least 2 Watts. Since these resistors will become fairly hot when dissipating een a few watts of electrical power, care should be exercised in handling the resistors. Aoid exceeding the 2-Watt rating by ensuring that the DC oltage neer exceeds roughly 8 olts by adjusting the ariac oltage, as P = V 2 /R, and R is at least 30Ω. Using the procedure of section 2.3, determine, for each alue of load resistance, the peak-to-peak ripple of the load oltage and its aerage alue. The aerage load current is the aerage load oltage diided by the resistance. 5. In the preious part, the ripple load oltage ( ripple ) for small alues of load resistance was greater than that generally acceptable for an electronic power supply. To reduce the ripple oltage, a larger capacitance is required. For the smallest alue of load resistance used (a alue of approximately 30 ohms), obsere the effect of connecting asecond 470uF capacitance in parallel with that of the circuit (resulting in aalue of 940uF for C). Determine the aerage and ripple oltage for this circuit. Increase the circuit capacitance to 2000 mf and again determine the aerage and ripple load oltage. 6. If a current probe is aailable for the oscilloscope, it may be used to determine the instantaneous diode current, i. Simultaneously obsere the current and the ripple oltage for the load resistance 4

5 and capacitances of the preious part. Carefully sketch the resultant current noting both its peak amplitude and its duration. 7. Using a suitable instrument, obtain measured alues for the resistances and capacitances used in this experiment. 8. Now connect the M7805 oltage regulator as shown in Fig. 6. Use the 10 ohm, 10 Watt, resistor 120Vac trans i 0.22µ F M µ F 1000 µ F Figure 6: Use of a M7805 regulator. for, monitor with an oscilloscope, and measure the ripple oltage as a function of the transformer secondary oltage, trans from 8-9 olts-rms to 3.5 olts-rms. Be careful when making these measurements to monitor the temperature of the load resistor... it can get ery warm. 3 Conclusion In section 2.1 of the experimental procedure, the rectified oltage of a power supply with no filter was determined. Based on the peak alue of (determined from the oscilloscope display) and the multimeter measurement of the transformer oltage, what was the oltage across the diodes when they were conducting? Using the peak alue of, calculate, assuming that it is a full-wae rectified oltage, the aerage alue of. Compare this alue with that measured with the multimeter. In sections 2.3 and 2.4 (capacitie filter) the dependence of the aerage and peak-to-peak ripple oltage on the load resistance,, was determined. Plot the measured alues of ripple and aerage load oltage as a function of the aerage load current (aerage oltage diided by ). Also plot a theoretical cure of ripple oltage (it may be assumed that m is equal to the aerage alue of the load oltage). If the ripple oltage is large, the exponential relationship will need to be used in calculating its theoretical alue. In section 2.5 of the experimental procedure, the dependence of the ripple oltage on the filter capacitance (for a fixed alue of ) was determined. Plot, as a function of capacitance, the experimentally determined ripple oltage an that predicted by the theoretical expressions. The diode current was determined in section 2.6 with an oscilloscope current probe (if one was aailable). The aerage alue of the diode current is equal to the aerage load current since the aerage alue of the capacitor s current is zero. Using the sketches of current, i, estimate the aerage currents by performing a graphical integration. Using an appropriate table, compare the aerage alues of current with the measured alues of the load current. The peak diode current is of importance when selecting a diode rectifier. ist these alues in the table. Often the rms alue rather than the peak-to-peak alue of the ripple oltage of a power supply is specified. This is the oltage indicated by a true rms oltmeter. These type meters generally ignore the aerage alue of their input oltage. An appropriate theoretical rms alue of the ripple oltage may be obtained by assuming that it has a triangular waeform, as shown in Fig. 7: 2 r = ripple. (6) 5

6 T/2 r T /2 T t r Figure 7: Approximate theoretical rms alue of the ripple oltage, assuming a triangular waeform. For full-wae rectification, the period of this oltage is one half that of the sinusoidal transformer oltage. What is the rms alue of the oltage expressed in terms of its peak amplitude, r? Obtain an expression for the ratio of this oltage and m. Concerning the use of the 7805 regulator, from your plot of ripple s. AC input oltage, what can you conclude about the alue of using such a regulator in the design of a power supply? 6