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Flyback Converters
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From the previous simulation, we can obtain the nominal duty cycle of 0.36 with an input voltage of 28 V, or we could calculate it as D=1 Vin Vout
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The delta inductor current can be calculated on the basis of the output voltage and D : Il = Vout D Ls Fs
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The peak secondary current is calculated as Ipk = Iout Il + D 2
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The secondary RMS current can be approximated by Iout Irms = D The output capacitor RMS ripple current is calculated as Icap = Iout 1 +D D
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The effects of the diode forward drop can best be approximated by evaluating the difference in forward voltage at two output currents of interest as Rd = Vf Iout
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The parameters from the power supply design are listed in the following table. L1 Ls ESR D N 350 H 25 H 0.03 0.36 1 Iout Fs DCR D R eff 0.833 A 250 kHz 0.1 0.64 0.12
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Simulating Regulation One of the more dif cult simulations to perform is the DC regulation of the yback converter. The regulation and, more importantly, the crossregulation of a yback converter is a function of the parasitic leakage
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X1 FLYBACK FLYBACK
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V(11) +15 X3 TURNS OUT
2 13
X4 TURNS
D1 DN5806
VINV
V1 28 VC
15 17
C1 100U RTN DUTY
R1 450
+C4 10
V4 AC L1 10
V(5) D
V(6) FDBCK X7 UC1843AS
14 16 VC 6 OUT GND REF COMP FDBK 8 21
C2 100U R6 47K R4 8K
R2 450
C3 1N
V(3) SENSE
X5 TURNS
D2 DN5806 V(18) -15
V3 15
R5 2.5K R3 1MEG
X6 TURNS
Dual-output 15-V power supply schematic.
inductance of the power transformer, the output recti er characteristics, and the output capacitor equivalent series resistance (ESR). In simple terms, these losses can be viewed as linear power losses. Although this is not entirely true, it will generally provide reasonably accurate results. The one characteristic that will not show up is the large voltage at the output under light-load or no-load conditions. This does not generally pose a problem because there is a protection or limiting device (such as a zener diode) present to make this voltage predictable. The following example is from an actual dual-output 15-V power supply that was designed recently (see Fig. 5.10). Given the following parameters, we will calculate the regulation for incorporation into our SPICE model.
De nitions
Power transformer secondary leakage inductance Power transformer Ls secondary inductance ESR Output capacitor ESR D Duty cycle N power transformer turns ratio
Iout
Output DC current
Switching frequency
DCR Transformer secondary resistance 1 Duty cycle D Irms RMS secondary current
Flyback Converters
Ipk Rd Icap
Peak secondary current Effective diode resistance Output capacitor RMS current
I1 Reff
Secondary inductor current delta Effective average resistance
The total loss of the secondary can be calculated as Ploss = 1 2 2 2 L1 IP Fs + Irms DC R + Icap ESR 2
FLY3: FEEDFORWARD SIGNAL .OPTION RELTOL=.01 ABSTOL=0.1u VNTOL=10u GMIN=10N ITL1=500 ITL4=500 .NODESET V(2) = 15.7 .TRAN 10U 4M 2M 1u .PROBE V(11)=+15 V(3)=SENSE V(6)=FDBCK V(18)=-15 V(5)=D .PRINT TRAN V(3) V(18) V(5) V1 1 0 28 X3 2 0 13 4 TURNS Params: NUM=18 X4 9 0 13 4 TURNS Params: NUM=18 X5 0 7 13 4 TURNS Params: NUM=18 X6 3 0 13 4 TURNS Params: NUM=12 D1 10 11 DN5806 D2 18 15 DN5806 C1 11 0 100U C2 0 18 100U I1 0 11 pulse 0 0.5 .1u .1u .1u 1m 2m R1 11 0 15 R2 0 18 15 R3 4 0 1MEG X7 8 21 0 6 16 14 UC1843AS R4 3 21 8K R5 21 0 2.5K C3 8 12 1N R6 12 21 47K V3 16 0 15 EB1 6 17 Value= { .005*V(1)} R7 9 10 .6 R8 7 15 .6 X1 1 0 17 2 5 FLYBACK Params: L=20U NC=100 NP=1 F=250K EFF=1 RB=10 + TS=.25U .END
The simulation results are shown in Fig. 5.11 along with the previous transient simulation results in order to see the effect of the output resistance.
Five
Wfm1, Wfm2: +15 in Volts
Wfm3: +15 in Volts
14.180 14.076
2.2000M
2.6000M
3.0000M
3.4000M
3.8000M
Time in Secs
Transient analysis that shows the effect of the output resistance.
Time Domain Model The next simulation shows the basic con guration for a transient model of an off-line yback converter (see Fig. 5.12). The transient model allows us to investigate details within the converter, such as peak switch current, harmonic content, output ripple voltage, and many other phenomena that would not be observable using a state space model. Although this model is somewhat simpli ed, it can easily be upgraded even further. Upgrades could include a nonlinear core model for the power transformer, an input EMI lter, multiple outputs, transformer leakage inductance, etc. In most cases, it is recommended that you start with a basic power supply representation such as this and then add the required details. In fact, each piece can be simulated separately before they are all put together. Using this approach you will have more assurance that the nal model will converge, and you can make any necessary changes to the subsections by taking advantage of the superior simulation speed. Obviously, as the model complexity increases, the run time will also increase, thus making investigation of the behavior of each subsection more costly. The simulation results of the transient model are shown in Fig. 5.13.
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