Flyback Converters
The flyback converter has long been popular for lowpower applications. The major attraction of the flyback topology is its low component count. At higher power levels, the output capacitor ripple current is often too great to deal with using conventional, lowcost capacitors. Dynamic response is also limited in continuous conduction mode, because of a righthalfplane (RHP) zero in the transfer function.
In the flyback topology, energy is stored in a power inductor (which often has multiple windings, as in a transformer) during the ontime of the switch. During the offtime of the switch, the energy is delivered to the load. The flyback topology is often used in both discontinuous and continuous conduction modes and can be successfully controlled using current mode or voltage converters.
A Flyback Subcircuit
A simplified functional schematic diagram of the flyback subcircuit is shown in Fig. 5.1. It is included in the Power IC Model Library for PSpice available from AEi Systems. It is a universal subcircuit that is capable of simulating the flyback regulator in both the continuous and discontinuous modes of operation with either voltage mode or current mode control. The derivation of the model is as follows.
Defined terms
Pin Converter input power VC Offset error amp output
Lm Power transformer NP Power transformer ratio magnetizing
/min Minimum primary Vout Subcircuit output voltage current
Figure 5.1 Flyback subcircuit schematic that can be used in both voltage and current modes with discontinuous and continuous inductor currents.
/max Peak primary current Fsw Switching frequency n
Efficiency factor Propagation delay MOSFET ontime Converter input voltage
I out Average output current Rb Current transformer burden
NC Current transformer ratio D Converter duty cycle Pout Converter output power
Governing equations
Pout = Pnn
Imax is defined by the control Voltage Vc as
Rb Tm
The MOSFET ontime is calculated as
9 UtLAY
During the MOSFET offtime, the primary current falls as
NP Lm Fsw
Substituting equations,
NP \ Vin (Imax — /min) which can be further simplified as
Vout Np V
Substituting equations,
out 2 VVout Vin Np  Vout and the duty cycle can be calculated as
LmFsw (^max Zmin)
The circuit shown in Fig. 5.2 is a simple representation, using the new subcircuit, of a dualoutput flyback converter with a separate transformer winding for voltage regulation. The flyback subcircuit essentially replaces the PWM switch model discussed in Chap. 4.
The results of the gainphase measurement of the flyback converter are shown in Figs. 5.3 and 5.4 for a 30mA load and a 1A load on each output, respectively. The circuit has a bandwidth of 7 kHz with a phase margin of 75° and a 1A load. At a 30mA load, the performance is quite different because of the discontinuous operation. The 34 kHz would likely be a problem for most applications. Either the converter would require a preload or the 1A load bandwidth would have to be reduced. This would sacrifice performance.
Note that L1 and C4 are used to break the loop for the openloop measurement. Voltage source V4 represents the injection signal. This method allows the DC path to be closed via L1, while the AC information is removed (essentially) by the very low frequency filter created by L1 and C4.
Audio Susceptibility
The same SPICE model can be used to evaluate closedloop performance parameters, such as audio susceptibility. To use the model for these
X1 FLYBACK
TURNS
100U> R1 450
X1 FLYBACK
TURNS
C2 450 100U
FLY1: DUAL OUTPUT FLYBACK CONVERTER
.AC DEC 25 100 1MEG
.OPTIONS RELTOL=.01 ITL1=500 ITL2=500 ITL4=500 GMIN=1n
.PROBE
.PRINT AC V(11) VP(11) V(3) VP(3) .PRINT AC V(6)VP(6) .PRINT TRAN V(3) V(18) .PRINT DC V(17)
V1 1 0 28 ; add "AC 1" for Audio Susceptibility Test
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 9 11 DN5806
D2 18 7 DN5806
C1 11 0 100U
C2 0 18 100U
R1 11 0 15 ; 15 ohms for 1A, 450 for 30ma R2 0 18 15 ; 15 ohms for 1A, 450 for 30ma R3 4 0 1MEG
X7 8 21 0 6 16 14 UC1843AS
VEA 6 60 10m ; Added for convergence at low currents
Figure 5.2 Schematic design and netlist for a dualoutput flyback converter.
R4 3 21 8K R5 21 0 2.5K C3 8 12 1N R6 12 21 47K V3 16 0 15
L1 17 60 10 ; 10 for open loop Gain/Phase analysis, 1p for Closed loop
* analysis (Transient or Audio Susceptibility)
C4 15 17 10 ; 10 for open loop Gain/Phase analysis, 1p for Closed loop
* analysis (Transient or Audio Susceptibility) V4 15 0 AC 1
X1 1 0 17 2 5 FLYBACK Params: L=20U NC=100 NP=1 F=250K EFF=1 RB=10
.END
Figure 5.2 (Continued).
evaluations, the inductor, capacitor, and AC voltage source can be left in the circuit. This is accomplished by changing the value of L1 to 1 pH, and C4 to 1 pF. To simulate the audio susceptibility performance, an AC source statement must also be added to the input voltage source, V1.
The results of the audio susceptibility simulation are shown in the graph of Fig. 5.5.
1K 10K 100K
Freqency in Hz
Figure 5.3 Gainphase Bode plot of the dualoutput flyback converter with a 1A load on each output.
1K 10K 100K
Freqency in Hz
Figure 5.3 Gainphase Bode plot of the dualoutput flyback converter with a 1A load on each output.
360.00 80.000
270.00
40.000
270.00
40.000
90.000
90.000
1K 10K 100K
Freqency in Hz
Figure 5.4 Gainphase Bode plot of the dualoutput flyback converter with a 30mA load on each output.
Freqency in Hz
Figure 5.5 Audio susceptibility simulation results, node 11.
Input Voltage in Volts
Figure 5.6 Graph showing the nonlinear relationship between the input voltage and the control voltage.
Input Voltage in Volts
Figure 5.6 Graph showing the nonlinear relationship between the input voltage and the control voltage.
Feedforward Improvements
The flyback converter has a peak input current that varies with input voltage.
This can be seen by sweeping the input voltage and monitoring the control voltage or the output of the error amplifier (see Fig. 5.6).
Although this curve is not linear, the audio susceptibility of the flyback converter can still benefit from feedforward compensation. This is most easily added via a simple resistor connected from the input voltage to the current sense pin of the PWM IC. We can add a feedforward signal in series with the control pin of the subcircuit to accomplish the same effect.
The schematic showing the incorporation of the feedforward signal is shown in Fig. 5.7.
The improvement in audio susceptibility is graphically shown in Fig. 5.8. Note that the feedforward signal improves the audio susceptibility performance by more than 20 dB. In several applications, I have been able to use this feedforward technique, rather than adding a linear regulator, to obtain the necessary attenuation. There are several benefits. There is no reduction in efficiency performance, as would occur with the addition of a linear regulator. Also, the converter can be made smaller and less expensively without the linear regulator.
FLY2: FEEDFORWARD SIGNAL .OPTION GMIN=10N .NODESET V(2) = 15.7
.AC DEC 25 100 1MEG
* ALIAS V(5)=D .PRINT AC V(6)VP(6) .PRINT AC V(11) VP(11) V(3) .PRINT TRAN V(3) V(18) V(5) V1 1 0 28 AC 1
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 9 11 DN5806 D2 18 7 DN5806 C1 11 0 100U C2 0 18 100U
* I1 0 11 pulse 0 0.5 .1u .1u .1u 1m 2m ; use for load step analysis R1 11 0 15
Figure 5.7 Feedforward signal schematic and netlist.
X1 1 0 17 2 5 FLYBACK Params: L=20U NC=100 NP=1 F=250K EFF=1 RB=10
.END
Figure 5.7 (Continued).
Flyback Transient Response
The transient response of the flyback converter is unaffected by the addition of the feedforward signal. The transient response simulation results in Fig. 5.9 show an overlay of a 0.5A step on the +15V output with and without the feedforward signal. To calculate the DC output resistance, we use the following equations:
lout 0.833
VD7 V064
Frequency in Hz
Figure 5.8 Graph showing improvement in audio susceptibility.
Frequency in Hz
Figure 5.8 Graph showing improvement in audio susceptibility.
15.082 15.060
15.042 a 15.020
15.002 g 14.980
14.962 14.940
14.922 14.900
2.2000M 2.6000M 3.0000M 3.4000M 3.8000M
Time in Secs
Figure 5.9 Transient response simulation results with the unaffected flyback converter.
= 1 (350 nH) (2.07)2 250kHz + (1.04)2 0.1 + (1.15)2 0.03 2
P 0 188
Reff = j^ + Rd = — + 0.12 = 0.483 + 0.12 = 0.603 n
The resulting 0.6 n is a good approximation of the DC output resistance. Based on our example, the load regulation from 10% to 100% load would be
The actual value that was recorded for the converter was 0.49 V. Obviously, the resistance is nonlinear and dependent upon input voltage, but this is a good estimate.
The calculated output resistance was implemented into this SPICE model in order to get the simulation results of Fig. 5.11.
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
The delta inductor current can be calculated on the basis of the output voltage and D':
Ls Fs
The peak secondary current is calculated as
The secondary RMS current can be approximated by
J Tout
The output capacitor RMS ripple current is calculated as
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
The parameters from the power supply design are listed in the following table.
Li 
350 ßH 
Lout 
0.833 A 
L s 
25 ßH 
Fs 
250 kHz 
ESR 
0.03 Œ 
DCR 
0.1 Œ 
D 
0.36 
D ' 
0.64 
N 
1 
R eff 
0.12 Œ 
Simulating Regulation
One of the more difficult simulations to perform is the DC regulation of the flyback converter. The regulation and, more importantly, the crossregulation of a flyback converter is a function of the parasitic leakage
X1 FLYBACK +15
X1 FLYBACK +15
Figure 5.10 Dualoutput 15V power supply schematic.
Figure 5.10 Dualoutput 15V power supply schematic.
inductance of the power transformer, the output rectifier 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 lightload or noload 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 dualoutput 15V 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.
Definitions  
L1 
Power transformer 
/out 
Output DC current 
secondary leakage  
inductance  
Ls 
Power transformer 
Fs 
Switching frequency 
secondary inductance  
ESR 
Output capacitor 
DCR 
Transformer secondary 
ESR 
resistance  
D 
Duty cycle 
D ' 
1 Duty cycle 
N 
power transformer turns ratio 
/rms 
RMS secondary current 
Ipk Peak secondary current
A /1 Secondary inductor current delta Reff Effective average resistance
Rd Effective diode resistance Icap Output capacitor RMS current
The total loss of the secondary can be calculated as floss — 2 T1 If Fs + Ir2ms DCR + Ic2ap ESR
FLY3: FEEDFORWARD SIGNAL
.OPTION RELTOL=.01 ABSTOL=0.1u VNTOL=10u GMIN=10NITL1=500 ITL4=500 .NODESET V(2) = 15.7 .TRAN 10U 4M 2M 1u .PROBE
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 218K
C3 8 12 1N
R6 12 21 47K
V3 16 0 15
X1 1 0 17 2 5 FLYBACK Params: L=20U NC=100 NP=1 F=250K EFF=1 RB=10
.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.
2.2000M 2.6000M 3.0000M 3.4000M 3.8000M
Time in Sees
Figure 5.11 Transient analysis that shows the effect of the output resistance.
2.2000M 2.6000M 3.0000M 3.4000M 3.8000M
Time in Sees
Figure 5.11 Transient analysis that shows the effect of the output resistance.
Time Domain Model
The next simulation shows the basic configuration for a transient model of an offline flyback 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 simplified, it can easily be upgraded even further. Upgrades could include a nonlinear core model for the power transformer, an input EMI filter, 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 final 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.
350V
R14 10K
16.6 
r"'  
Tran  
R13 
VOUT6.2 
I  
50K 
DIODE

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