Design Considerations

10.6.3 Design Considerations

In the design of rectifier circuits, it is necessary for the designer When a practical transformer (with leakage inductance) is used to determine the voltage and current ratings of the diodes. in the flyback converter circuit shown in Fig. 10.38, there will The idealized waveforms and expressions for the maximum

10.6.2.2 Practical Circuit

be large ringings. In order to reduce these ringings to prac- diode voltages and currents given under the heading of “Ideal tically acceptable levels, snubber and clamping circuits have circuit” above (for both forward and flyback converters) are to be added. Figure 10.40 shows a practical flyback converter

a good starting point. However, when parasitic/stray compo- circuit where a resistor–capacitor snubber (R 2 C 2 ) is used to nents are also considered, the simulation results given under

10 Diode Rectifiers 177

0V V1(VPULSE)

DT

1.0A 0A –1.0A

I(DM) 4.0A

0A –4.0A

ID(M1) 100V

0V –100V

V(100) 200V

0V –200V

V(3) 20V

0V –20V

V(6) 20V

0V –20V

V(9) 20V

0V –20V

V(6,9) 20A

0A –20A

I(DR) 20A

0A –20A

I(DF) 15.0A

12.5A 10.0A

I(L1) 4.2V 4.1V

FIGURE 10.36 Waveforms of practical forward converter for continuous-mode operation.

178 Y. S. Lee and M. H. L. Chow

0V V1(VPULSE)

DT

500mA 0A –500mA

I(DM) 2.0A

0A –2.0A

ID(M1) 100V

0V –100V

V(100) 200V

0V –200V

V(3) 20V

0V –20V

V(6) 20V

0V –20V

V(9) 40

0V –40V

V(6,9) 4.0A

0A –4.0A

I(DR) 4.0A

0A –4.0A

I(DF) 4.0A

0A –4.0A

I(L1) 7.6V

7.5V 7.4V

0s

20us V(99)

Time FIGURE 10.37 Waveforms of practical forward converter for discontinuous-mode operation.

10 Diode Rectifiers 179

P :N S =1:2

Pulse

FIGURE 10.38 Basic circuit of flyback converter.

0V V1(VPULSE)

DT

4.0A 0A –4.0A

ID(M1) 200V

0V –200V

V(3) 200V

0V –200V

V(6) 109.2V

109.1V 109.0V

V(9) 400V

0V –400V

V(6,9) 2.0A

0A –2.0A

0s

20us I(DR) or I(LS)

(D+D 2 )T T

Time

FIGURE 10.39 Idealized steady-state waveforms of flyback converter for discontinuous-mode operation.

180 Y. S. Lee and M. H. L. Chow

R 2 C 2 V IN = 60 V, D S = MUR460

9 D R = MUR460,M 1 = IRF640

L = 0.05 W

L P = 100 mH, L S = 400 mH V IN 2 3 0 R L = 400 W

M 1 N 5 P :N S Effective winding resistance of L =1:2 = 0.025 W

Pulse

Effective winding resistance of L S = 0.1 W Coupling coefficient K = 0.992

FIGURE 10.40 Practical flyback converter circuit.

0V V1(VPULSE)

DT

4.0A 0A –4.0A

ID(M1) 200V

0V –200V

V(3) 200V

0V –200V

V(6) 98.8V

98.7V 98.6V

V(9) 400V

0V –400V

V(6,9) 1.0A

0A –1.0A

I(DR) 2.0A

0A –2.0A

I(DS) 200V

0V –200V

0s

20us V(3,2)

(D+D 2 )T T

Time FIGURE 10.41 Waveforms of practical flyback converter for discontinuous-mode operation.

10 Diode Rectifiers 181 “Practical circuit” are much more useful for the determina- better damping. However, a large C (and a small R) will result

tion of the voltage and current ratings of the high-frequency in a large switching loss (which is equal to 0.5CV 2 f ). As rectifier diodes.

a guideline, a capacitor with five to ten times the junction Assuming that the voltage and current ratings have been capacitance of the rectifier may be used as a starting point determined, proper diodes can be selected to meet the require- for iterations. The value of the resistor should be chosen to ments. The following are some general guidelines on the provide a slightly underdamped operating condition. selection of diodes:

• For low-voltage applications, Schottky diodes should be

10.6.4 Precautions in Interpreting Simulation

used because they have very fast switching speed and low

Results

forward voltage drop. If Schottky diodes cannot be used, either because of their low reverse breakdown voltage In using the simulated waveforms as references for design or because of their large leakage current (when reversely purposes, attention should be paid to the following: biased), ultra-fast diodes should be used.

• The voltage/current spikes that appear in the practically • The reverse breakdown-voltage rating of the diode should

measured waveforms may not appear in the simulated

be reasonably higher (e.g. 10 or 20% higher) than waveforms. This is due to the lack of a model in the com- the maximum reverse voltage, the diode is expected to

puter simulation to simulate unwanted coupling among encounter under the worst-case condition. However, an

the practical components.

overly-conservative design (using a diode with much • Most of the computer models of diodes, including those higher breakdown voltage than necessary) would result

used in the simulations given above, do not take into in a lower rectifier efficiency, because a diode having

account the effects of the forward recovery time. (The

a higher reverse-voltage rating would normally have a forward recovery time is not even mentioned in most larger voltage drop when it is conducting.

manufacturers’ data sheets.) However, it is also interest- • The current rating of the diode should be substan-

ing to note that in most cases the effect of the forward tially higher than the maximum current the diode is

recovery time of a diode is masked by that of the effec- expected to carry during normal operation. Using a diode

tive inductance in series with the diode (e.g. the leakage with a relatively large current rating has the following

inductance of a transformer).

advantages: • It reduces the possibility of damage due to tran-

sients caused by start-up, accidental short circuit, or Further Reading

random turning on and off of the converter. • It reduces the forward voltage drop because the diode

1. Rectifier Applications Handbook, 3rd ed., Phoenix, Ariz.: Motorola, Inc., is operated in the lower current region of the V–I

characteristic. 2. M. H. Rashid, Power Electronics: Circuits, Devices, and Applications, In some of the “high-efficiency” converter circuits, the cur- 2nd ed., Englewood Cliffs, NJ: Prentice Hall, Inc., 1993. rent rating of the output rectifier can be many times larger 3. Y.-S. Lee, Computer-Aided Analysis and Design of Switch-Mode Power Supplies, New York: Marcel Dekker, Inc., 1993.

than the actual current expected in the rectifier. In this way, a 4. J. W. Nilsson, Introduction to PSpice Manual, Electric Circuits Using higher efficiency is achieved at the expense of a larger silicon

OrCAD Release 9.1, 4th ed., Upper Saddle River, NJ: Prentice Hall, Inc., area.

In the design of R–C snubber circuits for rectifiers, it should 5. J. Keown, OrCAD PSpice and Circuit Analysis, 4th ed., Upper Saddle

be understood that a larger C (and a smaller R) will give

River, NJ: Prentice Hall, Inc., 2001.

This page intentionally left blank

Single-phase Controlled Rectifiers

José Rodríguez, Ph.D.,

11.1 Introduction .......................................................................................... 183

Pablo Lezana, Samir

11.2 Line-commutated Single-phase Controlled Rectifiers ..................................... 183

Kouro, and Alejandro

11.2.1 Single-phase Half-wave Rectifier • 11.2.2 Bi-phase Half-wave Rectifier

• 11.2.3 Single-phase Bridge Rectifier • 11.2.4 Analysis of the Input Current • 11.2.5 Power Department of Electronics,

Weinstein

Factor of the Rectifier • 11.2.6 The Commutation of the Thyristors • 11.2.7 Operation in the Universidad Técnica Federico

Inverting Mode • 11.2.8 Applications

Santa María, Valparaíso, Chile

11.3 Unity Power Factor Single-phase Rectifiers .................................................. 192

11.3.1 The Problem of Power Factor in Single-phase Line-commutated Rectifiers • 11.3.2 Standards for Harmonics in Single-phase Rectifiers • 11.3.3 The Single-phase Boost Rectifier • 11.3.4 Voltage Doubler PWM Rectifier • 11.3.5 The PWM Rectifier in Bridge Connection • 11.3.6 Applications of Unity Power Factor Rectifiers References ............................................................................................. 203

11.1 Introduction

11.2 Line-commutated Single-phase Controlled Rectifiers

This chapter is dedicated to single-phase controlled rectifiers, which are used in a wide range of applications. As shown in

11.2.1 Single-phase Half-wave Rectifier

Fig. 11.1, single-phase rectifiers can be classified into two big categories:

The single-phase half-wave rectifier uses a single thyristor to control the load voltage as shown in Fig. 11.2. The thyristor

(i) Topologies working with low switching frequency, will conduct, on-state, when the voltage v T is positive and a also known as line commutated or phase controlled firing current pulse i G is applied to the gate terminal. The rectifiers.

control of the load voltage is performed by delaying the firing (ii) Circuits working with high switching frequency, also pulse by an angle α. The firing angle α is measured from the

known as power factor correctors (PFCs). position where a diode would naturally conduct. In case of Line-commutated rectifiers with diodes, covered in a pre- Fig. 11.2 the angle α is measured from the zero-crossing point

vious chapter of this handbook, do not allow the control of of the supply voltage v s . The load in Fig. 11.2 is resistive and power being converted from ac to dc. This control can be therefore the current i d has the same waveform of the load achieved with the use of thyristors. These controlled rectifiers voltage. The thyristor goes to the non-conducting condition, are addressed in the first part of this chapter.

off-state, when the load voltage, and consequently the current, In the last years, increasing attention has been paid to the reaches a negative value. control of current harmonics present at the input side of the

The load average voltage is given by rectifiers, originating from a very important development in

1 the so-called PFC. These circuits use power transistors work- π

V max

V max sin(ωt )d(ωt ) ing with high switching frequency to improve the waveform

quality of the input current, increasing the power factor. High (11.1) power factor rectifiers can be classified in regenerative and non-regenerative topologies and they are covered in the second where V max is the supply peak voltage. Hence, it can be seen part of this chapter.

from Eq. (11.1) that changing the firing angle α controls

184 J. Rodríguez et al.

Single Phase Rectifiers

Line Commutated

Power factor Correction (PFC)

Regenerative (AFE)

Boost

Voltage Doubler

Others

Bridge

FIGURE 11.1 Single-phase rectifier classification.

i ,v

FIGURE 11.2 Single-thyristor rectifier with resistive load.

both the load average voltage and the amount of transferred

11.2.2 Bi-phase Half-wave Rectifier

power. The bi-phase half-wave rectifier, shown in Fig. 11.4, uses a Figure 11.3a shows the rectifier waveforms for an R–L center-tapped transformer to provide two voltages v 1 and v 2 . load. When the thyristor is turned on, the voltage across the These two voltages are 180 ◦ out of phase with respect to the inductance is mid-point neutral N. In this scheme, the load is fed via thyris-

tors T 1 and T 2 during each positive cycle of voltages v 1 and v 2 ,

v L =v s −v R =L (11.2) respectively, while the load current returns via the neutral N.

di d

dt

As illustrated in Fig. 11.4, thyristor T 1 can be fired into the on-state at any time while voltage v T1 >

0. The firing pulses are where v R is the voltage in the resistance R, given by v R = R·i d . delayed by an angle α with respect to the instant where diodes If v s −v R >

0, from Eq. (11.2) holds that the load current would conduct. Also the current paths for each conduction increases its value. On the other hand, i d decreases its value state are presented in Fig. 11.4. Thyristor T 1 remains in the on- when v s −v R <

0. The load current is given by state until the load current tends to a negative value. Thyristor T 2 is fired into the on-state when v T2 >

0, which corresponds

in Fig. 11.4 to the condition when v 2 > 0.

The mean value of the load voltage with resistive load is

determined by

V max to zero when A 1 =A 2 , maintaining the thyristor in conduction

Graphically, Eq. (11.3) means that the load current i d is equal

= (1 + cos α) state even when v s < 0.

V diα =

V max sin(ωt )d(ωt )

π When an inductive–active load is connected to the rectifier,

(11.4) as illustrated in Fig. 11.3b, the thyristor will be turned on

if the firing pulse is applied to the gate when v s > E d . Again, The ac supply current is equal to i T1 (N 2 /N 1 ) when T 1 is in the the thyristor will remain in the on-state until A 1 =A 2 . When on-state and −i T2 (N 2 /N 1 ) when T 2 is in the on-state, where

the thyristor is turned off, the load voltage will be v d =E d .

N 2 /N 1 is the transformer turns ratio.

11 Single-phase Controlled Rectifiers 185

Area A 1 v d

Area A 2

v R ,v d

(a)

Area A 1

i d v d Area A 2

0 2π ω t

(b)

FIGURE 11.3 Single-thyristor rectifier with: (a) resistive-inductive load and (b) active load.

The effect of the load time constant T L = L/R, on the rectifier behaves like a current source. With continuous load normalized load current i d (t)/î R (t) for a firing angle α =0 ◦ is current, thyristors T 1 and T 2 remain in the on-state beyond the shown in Fig. 11.5. The ripple in the load current reduces as positive half-wave of the source voltage v s . For this reason, the load inductance increases. If the load inductance L → ∞, the load voltage v d can have a negative instantaneous value. then the current is perfectly filtered.

The firing of thyristors T 3 and T 4 has two effects: (i) they turn-off thyristors T 1 and T 2 and

(ii) after the commutation, they conduct the load current. Figure 11.6a shows a fully controlled bridge rectifier, which This is the main reason why this type of converters are called

11.2.3 Single-phase Bridge Rectifier

uses four thyristors to control the average load voltage. In addi- “naturally commutated” or “line commutated” rectifiers. The tion, Fig. 11.6b shows the half-controlled bridge rectifier which supply current i S has the square waveform, as shown in uses two thyristors and two diodes.

Fig. 11.9, for continuous conduction. In this case, the average The voltage and current waveforms of the fully controlled load voltage is given by bridge rectifier for a resistive load are illustrated in Fig 11.7.

Thyristors T π

1 and T 2 must be fired on simultaneously during

2V max

V max sin(ωt )d(ωt ) = cos α (11.6) the positive half-wave of the source voltage v s , to allow the

V diα =

conduction of current. Alternatively, thyristors T 3 and T 4 must

be fired simultaneously during the negative half-wave of the

source voltage. To ensure simultaneous firing, thyristors T 1 and