PGT 320 Chapter 4 FULLWAVE RECTIFIERS converting ac

FULL-WAVE RECTIFIERS q INTRODUCTION q SINGLE-PHASE FULL-WAVE RECTIFIERS q CONTROLLED FULL-WAVE RECTIFIERS q EXERCISE

INTRODUCTION Objective of a FWR: • converting ac into a voltage or current that

Figure 4. 1 pg 112 SINGLE-PHASE FULL-WAVE RECTIFIERS THE BRIDGE RECTIFIER Copyright © The

Figure 4. 1 pg 112 Notes: • • • D 1, D 2 conducts

Figure 4. 2 pg 113 THE CENTER-TAPPED TRANSFORMER RECTIFIER Copyright © The Mc. Graw-Hill

Figure 4. 2 pg 113 THE CENTER-TAPPED TRANSFORMER RECTIFIER Notes: • • Only contains

Figure 4. 1(b) pg 115 R LOAD R Copyright © The Mc. Graw-Hill Companies,

Figure 4. 3 a pg 116 R-L LOAD Copyright © The Mc. Graw-Hill Companies,

Figure 4. 3 b-c Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for

Example 4. 1: FWR with R-L LOAD The bridge rectifier circuit has an ac

Solution Example 4. 1: FWR with R-L LOAD a) Average output voltage is :

Figure 4. 5 R-L-SOURCE LOAD • • Notes • • Industrial load also modeled

Figure 4. 6 CAPACITANCE OUTPUT FILTER Notes • • Placing a large capacitor in

Figure 4. 7 VOLTAGE DOUBLERS • • Notes Circuit (a) serves as simple voltage

Figure 4. 8 pg 127 L-C FILTERED OUTPUT Notes • • This time, FWR

Figure 4. 9 a PSpice The small capacitors across the diodes help with convergence.

Figure 4. 9 b Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for

Figure 4. 10 pg 131 CONTROLLED FULL-WAVE RECTIFIERS Copyright © The Mc. Graw-Hill Companies,

CONTROLLED FULL-WAVE RECTIFIERS • A versatile method of controlling the output of a full-wave

Figure 4. 10 a , c pg 132 CONTROLLED FULL-WAVE RECTIFIER WITH AN R

Figure 4. 10 a pg 132 EXAMPLE 4. 6: CONTROLLED FULL-WAVE RECTIFIER WITH AN

Figure 4. 11 a CONTROLLED FULL-WAVE RECTIFIER WITH AN R-L LOAD • • •

Figure 4. 11 b DISCONTINUOUS CURRENT Copyright © The Mc. Graw-Hill Companies, Inc. Permission

Figure 4. 11 b-c CONTINUOUS CURRENT Copyright © The Mc. Graw-Hill Companies, Inc. Permission

Figure 4. 12 Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction

Figure 4. 13 Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction

Figure 4. 14 CONTROLLED RECTIFIER WITH AN R-L-SOURCE LOAD Copyright © The Mc. Graw-Hill

Figure 4. 15 CONTROLLED SINGLE-PHASE CONVERTER OPERATING AS AN INVERTER • • • For

EXERCISE #1 1. Design and label a full-wave controlled bridge rectifier has an ac

EXERCISE #2 A controlled full-wave bridge rectifier of Fig. 4 -11 a has a

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FULL-WAVE RECTIFIERS q INTRODUCTION q SINGLE-PHASE FULL-WAVE RECTIFIERS q CONTROLLED FULL-WAVE RECTIFIERS q EXERCISE Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

INTRODUCTION Objective of a FWR: • converting ac into a voltage or current that is purely dc or has some specified dc component. Advantages of FWR: • The average current in the ac source is zero in the full-wave rectifier, thus avoiding problems associated with nonzero average source currents, particularly in transformers. • The output of the full-wave rectifier has inherently less ripple than the half-wave rectifier. Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 4. 1 pg 112 Notes: • • • D 1, D 2 conducts in same pair. D 3, D 4 conducts in same pair. Those pair cannot conduct simultaneously. Max Vd (in r. bias) is peak Vs but in negative polarity. From source, Id 1 4 is symmetric, so cancel each other zero. Irms load is similar with Irms source +ve symmetric with –ve equal.

Figure 4. 2 pg 113 THE CENTER-TAPPED TRANSFORMER RECTIFIER Notes: • • Only contains 2 diodes (cost saving) but need center tapped transformer. Each diode cannot conduct simultaneously. Iload can be +ve or zero but cannot be –ve. Vo = +Vs 1 when D 1 conducts while –Vs 2 when D 2 conducts. So Vs 1=Vs 2=Vs(Nsec/2 Npri) Transformer provide electrical isolation between source and load. Lower peak diode high voltage application Only one diode voltage drop suitable for low V and high I application. Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Example 4. 1: FWR with R-L LOAD The bridge rectifier circuit has an ac source with Vm =100 V at 60 Hz and a series RL load with R=10 Ω and L=10 m. H. (a) Determine the average current in the load. (b) Estimate the peak-to-peak variation in load current based on the first ac term in the Fourier series. (c) Determine the power absorbed by the load and the power factor of the circuit. (d) Determine the average and rms currents in the diodes. Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Solution Example 4. 1: FWR with R-L LOAD a) Average output voltage is : - c) Power absorbed by load, P=Irms² Average output current is : - b) Amplitudes of the ac voltage terms are determined from previous Vn equation. For n =2 and n = 4, Power in the load, Irms source is similar with Irms load and power factor, pf In equation for amplitudes of first two ac current terms: - d) Each diode conducts for one-half of the time, so Noted I 2 larger, so variation of Io, △Io = 2 (3. 39) = 6. 78 A Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 4. 5 R-L-SOURCE LOAD • • Notes • • Industrial load also modeled as series resistance, inductance and dc source such as AC motor drive and battery charger. 2 possible modes: - continuous and discontinuous. • • • Load current, Io always positive for steadystate operation (after a few periods). One pair of diodes is always conducting and Vo is a FW rectified sine wave. Unchanged by DC source continuous. Load current, Io returning to zero during every period. Analyzed like HWR. Vo is not FW rectified sine wave. Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 4. 6 CAPACITANCE OUTPUT FILTER Notes • • Placing a large capacitor in parallel with Rload Vo essentially becomes a DC. Time that C need to discharge in FWR is smaller compared to HWR; because of rectified sine wave in second half of each period. Noted HWR is zero (unrectified) for its second half in one period. The Vo ripple for FWR is one half of HWR. The peak for Vo will be less in FWR because 2 diodes voltage drops rather than one in HWR. For small ΔVo: Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 4. 7 VOLTAGE DOUBLERS • • Notes Circuit (a) serves as simple voltage doubler Vo is twice the Vs peak. +ve supply C 1 charges to Vm through D 1. -ve supply C 2 charges to Vm through D 2. Thus Vo = sum of capacitors C 1, C 2 voltages = 2 Vm. Advantage of voltage doubler(V/Do. ): This circuit avoid using a transformer to step up its voltage saving expense, volume and weight. Circuit (b) comes with capacitance output filter. When switch open: circuit acts as FWR output approximately Vm when C large. When switch closed: circuit acts as V/Do. +ve supply: C 1 charges to Vm through D 1, -ve supply C 2 charges to Vm through D 4. Vo = 2 Vm. Diodes D 1, D 3 remains reverse biased in this mode. Application: 120 V to 240 V traveller AC adaptor system. (UK system US) Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 4. 8 pg 127 L-C FILTERED OUTPUT Notes • • This time, FWR output has an LC filter to produce Vo that close to purely DC. C holds Vo at constant level L smooths current from rectifier and reduces peak current in the diodes. Can work in continuous current discontinuous current Continuous current mode inductor current always +ve Discontinuous current mode inductor current returns to zero in each cycle. However, continuous case is easy to analyze is considered first. Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

CONTROLLED FULL-WAVE RECTIFIERS • A versatile method of controlling the output of a full-wave rectifier is to substitute diodes with controlled switches such as thyristors (SCRs). Output is controlled by adjusting the delay angle of each SCR, resulting in an output voltage that is adjustable over a limited range. • Controlled full-wave rectifiers are shown in Fig. 4 -10. For the bridge rectifier, SCRs S 1 and S 2 will become forward-biased when the source becomes positive but will not conduct until gate signals are applied. Similarly, S 3 and S 4 will become forward-biased when the source becomes negative but will not conduct until they receive gate signals. • For the center-tapped transformer rectifier, S 1 is forward-biased when vs is positive, and S 2 is forward-biased when vs is negative, but each will not conduct until it receives a gate signal. • The delay angle, α is the angle interval between the forward biasing of the SCR and the gate signal application. If the delay angle is zero, the rectifiers behave exactly as uncontrolled rectifiers with diodes. The discussion that follows generally applies to both bridge and centertapped rectifiers. Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 4. 10 a pg 132 EXAMPLE 4. 6: CONTROLLED FULL-WAVE RECTIFIER WITH AN R LOAD • Solution Average output voltage, • Average load current, • Power absorbed by load is, ***(convert α=40° radian 0. 698) • Rms current in source also 5. 80 A so that the apparent power of the source is: - • Power factor, Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 4. 11 a CONTROLLED FULL-WAVE RECTIFIER WITH AN R-L LOAD • • • Notes Can be either continuous or discontinuous and each of them have separate analysis. For discontinuous, starting the analysis at ωt =0 with zero load current, SCRs S 1 and S 2 forward-biased and S 3 and S 4 reverse-biased as +Vs. Gate signals are applied to S 1 and S 2 at t, turning S 1 and S 2 on Vo = Vs. Identical to that of the controlled HWR. • • Current functions zero at ωt = β. If β < π+α , current remains zero until ωt = π+α when gate signal is applied to S 3 and S 4 becomes f/biased and begin to conduct. • Analysis of the controlled FWR operating in the discontinuous current mode identical to controlled HWR except period for the output current is π rather than 2π rad. For continuous, the load current is still positive at ωt= π+α when gate signals are applied to S 3 and S 4, both are turned on and S 1 and S 2 are forced to off. Second half cycle, initial current condition not zero current function not repeat. • • Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 4. 15 CONTROLLED SINGLE-PHASE CONVERTER OPERATING AS AN INVERTER • • • For inverter operation of the converter in Fig. 4 -14, power is supplied by the dc source, and power is absorbed by the bridge and is transferred to the ac system. The load current must be in the direction shown because of the SCRs in the bridge. For power to be supplied by the dc source, Vdc must be negative. For power to be absorbed by the bridge and transferred to the ac system, the bridge output voltage Vo must also be negative. So a delay angle larger than 90 will result in a negative output voltage. Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

EXERCISE #1 1. Design and label a full-wave controlled bridge rectifier has an ac input of 240 V at 50 Hz and a 20 Ω load resistor. The firing angle, α is 40°. 2. Determine the average current in the load, the power absorbed by the load, the source voltamperes and power factor. • ANSWER: - 20 Ω Vs=240 V f= 50 Hz S 1, S 2, S 3, S 4 = SCR α = 40° Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

EXERCISE #2 A controlled full-wave bridge rectifier of Fig. 4 -11 a has a source of 120 V rms at 60 Hz, R =10Ω, L =20 m. H, and α=60°. Determine (a) an expression for load current, (b) the average load current, and (c) the power absorbed by the load. Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.