Ideal Circuit

10.6.1.1 Ideal Circuit

The voltage induced at node 6 of the secondary Figure 10.29 shows the idealized steady-state waveforms for

winding L S is

continuous-mode operation (the current in L 1 being continu-

ous). These waveforms are obtained from PSpice simulations, based on the following assumptions:

V (6) =V IN

s /N p (10.83)

This voltage drives a current I(DR) (current through clamping diode D M are ideal diodes with infinitely fast

• Rectifier diode D R , flywheel diode D F , and magnetic-reset

rectifier diode D R ) into the output circuit to produce switching speed.

the output voltage V o . The rate of increase of I(DR) is • Electronic switch M1 is an idealized MOS switch with

given by

infinitely fast switching speed and

1 On-state resistance

d I (DR)

= V IN

−V o (10.84)

L 1 Off-state resistance

dt

where V o is the dc output voltage of the converter. It should be noted that PSpice does not allow a switch

The flywheel diode D F is reversely biased by V(9), to have zero on-state resistance and infinite off-state

the voltage at node 9.

resistance. • Transformer T 1 has a coupling coefficient of 0.99999999.

0 < t < DT (10.85) PSpice does not accept a coupling coefficient of 1.

V (9) =V IN ( N S /N P ) for

• The switching operation of the converter has reached a The magnetic-rest clamping diode D M is reversely steady state.

biased by the negative voltage at node 100. Assuming that L M and L P have the same number of turns, we

Referring to the circuit shown in Fig. 10.28 and the wave-

have

forms shown in Fig. 10.29, the operation of the converter can

be explained as follows:

V (100) = −V IN for 0 < t < DT (10.86)

1. For 0 < t < DT (D is the duty cycle of the MOS switch M 1 and T is the switching period of the converter. M 1 A magnetizing current builds up linearly in L P . This is turned on when V1(VPULSE) is 15 V, and turned off

magnetizing current reaches the maximum value of when V1(VPULSE) is 0 V).

1 6 I(DR) 9 L 1 99 I o

V IN = 50 V

D I(L1)

L P = 0.576 mH

V IN

3 L M = 0.576 mH

0 0V L

S = 0.036 mH

Pulse

R L = 0.35 W N P :N M :N S =4:4:1

0V 0 FIGURE 10.28 Basic circuit of forward converter.

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

0V V1(VPULSE)

DT

500mA 0A –500mA

I(DM) 5.0A

0A –5.0A

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) 20A

15A 10A

I(L1) 5.1V

5.0V 4.9V

0s

20us V(99)

Time FIGURE 10.29 Idealized steady-state waveforms of forward converter for continuous-mode operation.

10 Diode Rectifiers 169

2. For DT < t < 2DT • The maximum current in the forward rectifying diode

The switch M 1 is turned off at t = DT .

D R and flywheel diode D F is

The collapse of magnetic flux induces a back emf in L M , which is equal to L P , to turn-on the clamp-

I (DR) max = I (DF) max

ing diode D M . The magnetizing current in L M drops (from the maximum value of (V IN DT )/L P , as men-

( 1 − D) T (10.94) tioned above) at the rate of V IN /L P . It reaches zero at

=I o +

t = 2DT . where V o = DV IN (N S /N P ) and I o is the output loading The back emf induced across L P is equal to V IN . The

current.

voltage at node 3 is • The maximum reverse voltage of D R and D F is

V (3) = 2V IN for DT < t < 2DT

V (DR) max = V (DF) max

The back emf across L S forces D R to stop conducting. N S

The inductive current in L 1 forces the flywheel diode

= V (6, 9) max =V IN (10.95) N P

D F to conduct. I(L1) (current through L 1 ) falls at the

rate of • The maximum reverse voltage of D M is

d I (L1)

−V o

V (DM ) max =V IN (10.96)

dt

• The maximum current in D M is The voltage across D R , denoted as V(6,9) (the voltage

at node 6 with respect to node 9), is

V IN

I (DM ) max = DT (10.97) L

V (DR)

= V (6, 9) P = −V IN ( N S /N P ) for DT < t < 2DT

• The maximum current in the switch M1, denoted as

ID(M1), is

3. For 2DT < t < T

ID(M 1) max =

I (DR) max + I (DM) max

D M stops conducting at t

N = 2DT . The voltage across P

L M then falls to zero.

V IN The voltage across L P is zero.

( 1 − D) T + DT

2 L 1 L P (10.98)

V (3) =V IN

It should, however, be understood that, due to the non-ideal The voltage across L S is also zero.

characteristics of practical components, the idealized wave- forms shown in Fig. 10.29 cannot actually be achieved in the

V (6) =0

real world. In the following, the effects of non-ideal diodes and Inductive current I(L1) continues to fall at the rate of transformers will be examined.

d I (L1)

−V o

10.6.1.2 Circuit Using Ultra-fast Diodes

dt

1 Figure 10.30 shows the waveforms of the forward converter (circuit given in Fig. 10.28) when ultra-fast diodes are used as

The switching cycle restarts when the switch M 1 is

D M ,D R , and D . (Note that ultra-fast diodes are actually much turned on again at t

=T. F

slower than Schottky diodes.) The waveforms are obtained by From the waveforms shown in Fig. 10.29, the following PSpice simulations, based on the following assumptions: useful information (for continuous-mode operation) can be

• D M is an MUR460 ultra-fast diode. D R and D F are found:

MUR1560 ultra-fast diodes.

• The output voltage V o is equal to the average value of • M 1 is an IRF640 MOS transistor. V(9).

• Transformer T 1 has a coupling coefficient of 0.99999999 (which may be assumed to be 1).

• The switching operation of the converter has reached a

steady state.

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

V1(VPULSE)

DT

500mA 0A –500mA

I(DM) 40A

0A –40A

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) 100A

0A –100A

I(DR) 100A

0A –100A

I(DF) 15A

10A 5A

I(L1) 3.8V

3.7V 3.6V

0s

20us V(99)

Time FIGURE 10.30 Waveforms of forward converter using “ultra-fast” diodes (which are actually much slower than Schottky diodes).

10 Diode Rectifiers 171 It is observed that a large spike appears in the current wave-

The resultant waveforms shown in Fig. 10.32 indicate that forms of diodes D R and D F (denoted as I(DR) and I(DF) there are large voltage and current ringings in the circuit. in Fig. 10.30) whenever the MOS transistor M 1 is turned These ringings are caused by the resonant circuits formed by on. This is due to the relatively slow reverse recovery of the the leakage inductance of the transformer and the parasitic flywheel diode D F . During the reverse recovery time, the pos- capacitances of diodes and transistor. itive voltage suddenly appearing across L S (which is equal to

A practical converter may therefore need snubber circuits to

V IN (N S /N P )) drives a large transient current through D R and damp these ringings, as described below.

D F . This current spike results in large current stress and power

dissipation in D R ,D F , and M 1 .

A method of reducing the current spikes is to use Schottky

10.6.1.5 Circuit with Snubber Across the

diodes as D R and D F , as described below.

Transformer

In order to suppress the ringing voltage caused by the res- onant circuit formed by transformer leakage inductance and

10.6.1.3 Circuit Using Schottky Diodes

the parasitic capacitance of the MOS switch, a snubber circuit, In order to reduce the current spikes caused by the slow reverse shown as R 1 and C 1 in Fig. 10.33, is now connected across the

recovery of rectifiers, Schottky diodes are now used as D R and primary winding of transformer T 1 . The new waveforms are

D F .The assumptions made here are (referring to the circuit shown in Fig. 10.34. Here the drain-to-source voltage wave- shown in Fig. 10.28):

form of the MOS transistor, V(3), is found to be acceptable. However, there are still large ringing voltages across the output

• D R and D F are MBR2540 Schottky diodes.

rectifiers (V(6,9) and V(9)).

• D M is an MUR460 ultra-fast diode. In order to damp the ringing voltages across the output • M 1 is an IRF640 MOS transistor.

rectifiers, additional snubber circuits across the rectifiers may • Transformer T 1 has a coupling coefficient of 0.99999999. therefore also be required in a practical circuit, as described

• The switching operation of the converter has reached a below. steady state.

The new simulated waveforms are given in Fig. 10.31. It is

found that, by employing Schottky diodes as D R and D F , the

10.6.1.6 Practical Circuit

amplitudes of the current spikes in ID(M1), I(DR), and I(DF) Figure 10.35 shows a practical forward converter with snubber can be reduced to practically zero. This solves the slow-speed circuits added also to rectifiers (R 2 C 2 for D R and R 3 C 3 problem of ultra-fast diodes.

for D F ) to reduce the voltage ringing. Figures 10.36 and

10.37 show the resultant voltage and current waveforms. Figure 10.36 is for continuous-mode operation (R L

where I(L1) (current in L 1 ) is continuous. Figure 10.37 is The simulation results given above in Figs. 10.29–10.31 (for for discontinuous-mode operation (R L

10.6.1.4 Circuit with Practical Transformer

the forward converter circuit shown in Fig. 10.28) are based becomes discontinuous due to an increased value of R L . These on the assumption that transformer T1 has effectively no leak- waveforms are considered to be acceptable. age inductance (with coupling coefficient K = 0.99999999).

The design considerations of diode rectifier circuits in It is, however, found that when a practical transformer high-frequency converters will be discussed later in Sub-

(having a slightly lower K ) is used, severe ringings occur. section 10.6.3. Figure 10.32 shows some simulation results to demonstrate this phenomenon, where the following assumptions are made: