ST AN2131 Application note

AN2131

APPLICATION NOTE

HIGH POWER 3-PHASE AUXILIARY POWER SUPPLY DESIGN BASED ON L5991 AND ESBT STC08DE150

1. INTRODUCTION

This application note deals with the design of a 3- Phase auxiliary power supply for 150W dual output SMPS, using the L5991 PWM driver and the STC08DE150 ESBT as main switch. The combination of these ST's parts aims at obtaining a high efficiency solution for high DC input voltage, typical requirement of any three phase application. The L5991 driver is an upgraded version of the UC384X current mode PWM driver. It boasts some very interesting additional features.

The necessity to handle both high output power and wide input voltage leads to design a flyback stage working in mixed operation mode: discontinuous and continuous. The continuous current mode introduces a right half plan zero in the loop-transfer function which makes the feedback stabilization difficult; the study on the frequency response, reported in the present document, has been carried out using MATLAB.

Furthermore, the slope compensation is implemented and deeply explained. It is necessary to remove sub-harmonic oscillations when the duty cycle is higher than 50%.

Finally the experimental results are analyzed to better understand the benefits given by the use of the ESBT in this application.

2. DESIGN SPECIFICATIONS AND PRELIMINARY REMARKS.

The table 1 lists the converter specification data and the main parameters fixed for the demo board.

If we look at the specs, particularly at the power and at the input voltage range, and after a brief description of the differences between continuous and discontinuous mode, it will soon be clear that it is very difficult and not convenient to design a flyback converter working in discontinuous mode.

Figure 1 shows a simplified schematic diagram of a flyback converter.

The discontinuous mode, shown in figure 2, has no front-end step in its primary current, iT, and at turn-off, the secondary current iD, is a decaying

March 2005

triangle which drops to zero before the next turnon.

In the continuous mode, shown in figure 3, the primary current iT has a front-end step and the characteristic appearance of a rising ramp on a step. During the transistor off time (figure 3), the secondary current has the shape of a decaying triangle sitting on a step with the current still remaining in the secondary at the instant of the next turn-on. There is, therefore, still some energy left in the secondary at the instant of next turn-on.

The two modes show significantly different operating properties and usages. The discontinuous mode responds more rapidly and with a lower transient output voltage spike to sudden changes in load current and input voltage. On the other hand, discontinuous mode provides a secondary peak current in the range of two or three times the continuous mode. This can be easily understood by comparing figure 2 and figure 3.

The secondary current average value is equal to the DC load current, as reported in both the above mentioned figures. Assuming also closely equal off time, it is obvious that the triangle in the discontinuous mode must show a much larger peak than the trapezoid of the continuous mode to get the same average value. Therefore, in the discontinuous mode, the larger secondary peak current, at the beginning of turn-off, will cause a greater RFI problem.

Secondary rms current in the discontinuous mode can be up to twice that in the continuous mode. This requires larger secondary wire size and output filter capacitors with larger ripple current ratings for the discontinuous mode. Rectifier diodes will also have a higher temperature rise in the discontinuous mode because of the larger secondary rms current.

Primary peak currents for the discontinuous mode are about twice those in the continuous mode. As a result, the discontinuous mode requires a higher current rating and possibly a more expensive power transistor. Also, the higher primary current in the discontinuous mode results in a greater RFI problem.

Despite all these relative disadvantages, the discontinuous mode is much more used for low

Rev. 1

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AN2131 - APPLICATION NOTE

power applications. This is due to two reasons. Firstly, as mentioned above, the discontinuous mode, with an inherently lower transformer magnetizing inductance, responds more quickly and with a lower transient output voltage spike to rapid changes in output load current or input voltage. Secondly, because the transfer function of the continuous mode has a right half plane zero, the error amplifier bandwidth must be drastically reduced to stabilize the feedback loop. As a

consequence, the transient response is much slower.

Finally, referring to the power spec of our demo, it is clear that the discontinuous mode cannot be used because it would determine a very high primary and secondary peak current with a higher cost of all the main components involved: power transistor, secondary diode and output capacitor.

Table 1. Converter Specification data and Fixed Parameters

Symbol	Description	Values
Vinmin	Rectified minimum Input voltage	250
Vinmax	Rectified maximum Input voltage	850

Vout1	Output voltage 1	24V/6.25A
Vout2	Output voltage 2	5V/0.075A

Vaux	Auxiliary Output voltage	15V/0.01A
Pout	Maximum Output Power	150W

η	Converter Efficiency	>75%
F	Switching frequency	90 kHz

Fsb	Stand-by switching frequency	35 kHz

Vspike	Max over voltage limited by clamping circuit	200V

Figure 1. Simplified Schematic Diagram of a Flyback Converter

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AN2131 - APPLICATION NOTE

Figure 2. Discontinuous Mode Flyback Waveforms

Figure 3. Continuous Mode Flyback Waveforms

	Ton	Ts	t
	Ton

ID
		Toff	t
		Toff
VT			Vin+Vfly

3. FLYBACK CONTINUOS MODE WITH L5991

The minimization of the power drawn from the mains under light load conditions (Stand-by, Suspend or some other idle modes) is an issue that has recently become of great interest, mainly

because new and more severe standards are coming into force.

The key point of this strategy is a low switching frequency. It is well-known that many of the power loss sources in a lightly loaded flyback waste energy proportionally to the switching frequency, hence this should be reduced as much as possible. On the other hand, it is equally well-

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AN2131 - APPLICATION NOTE

known that a low switching frequency leads to bigger and heavier magnetics and makes filtering more troublesome. It is then advisable to make the system operate at high frequency under nominal load condition and to reduce the frequency when the system works in a low-consumption mode. This requires a special functionality of the controller. It should be able to automatically recognize the condition of light or heavy load and then adequate its operating frequency accordingly.

The L5991 PWM controller, with its "Stand-by function", meets exactly this requirement. This application note will deal with the design of a flyback using L5991 PWM driver, while deeper details about the driver itself can be found in the dedicated application note AN1049.

The specifications table reports the two values of the switching frequency, 90kHz for normal mode and 35kHz for stand-by mode.

4. FLYBACK STAGE DESIGN

The continuous mode operation, as any switching topology, is identified by observing the steady state behavior of the energy storage component. In the flyback topology, the storage element is represented by the magnetization transformer inductance, which is charged by the primary winding during the on time, and discharged by the secondary winding during the off time. The flyback topology will hence be working in continuous mode if the secondary winding current does not reach zero at the end of the off time.

As previously said, the mixed mode implies a discontinuous mode operation for low load and/or higher input voltage. The boundary depends on the output power for a given input voltage. The higher is the input voltage the higher is the output power when the continuous mode starts. Theoretically, there isn't any restriction to fix the boundary between continuous and discontinuous mode. It will be given by imposing design equation for others relevant circuit parameters.

The maximum duty cycle, that in a discontinuous mode flyback is imposed to prevent the continuous mode operation, in this case must be fixed establishing a good trade-off between primary and secondary side performance. There are two opposite effects: by increasing the duty cycle the rms current at primary side can be reduced, while the rms current at secondary side will be increased. This means that a higher duty cycle imposes a less stressful condition to any parts in the primary path, and a more stressful condition to the secondary path. In the same way, to decrease the duty cycle causes an optimization of

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secondary side and a deterioration of primary side performances.

The higher duty cycle is a further help to easily design the flyback stage for a wide range voltage input. On the other hand, the higher duty cycle implies a higher reflected voltage to promptly demagnetize the flyback transformer.

For such a high power flyback stage, an important parameter to monitor is the current ripple at secondary side; it is needed either to lower rms current or to reduce RFI. Further consideration concerns the reflected flyback voltage which is imposed in order not to overcome the maximum breakdown of the power switch.

The above consideration plus some cost issues generate a clear figure of how to impose design equations. Moreover, since design specifications imply a high power output only, the following calculation will consider the influence of both low power and auxiliary outputs negligible.

In continuous operation mode the relationship between input and output voltage is only dependent on the duty cycle and not on the frequency. The relationship is given by the following formula:

VOut1	=	N S1		D	Eq. 1
Vin		N P		1 − D

Eq. 1 is ideal and does not take into consideration real effects such as the voltage drops on the power switch and on the output diode. Including these two voltage drops it is possible to get the first design equation and calculate the turn ratio between input and the higher power output (Vout1).

NP		=		Vin − Vcson		D	Eq. 2

N	S1		Vout1 + Vd1			1− D
					fw

Where, VCSon and Vd1fw are respectively the voltage drop on the power switch and on the

secondary side diode. Eq. 2 is valid for any input voltage. The second design equation comes from the maximum power switch breakdown, defining first Vfly, the flyback reflected voltage, and then calculating the maximum switch breakdown voltage.

Vfly	=	NP	(Vout1+ Vd1fw )	Eq. 3

		NS1

AN2131 - APPLICATION NOTE

BV = Vfly + Vspike + Vin max + m arg in

Eq. 4

Eq. 4 also includes the safe design margin and the allowed voltage spike fixed by clamping network design. By combination of Eq. 3 and Eq. 4, the maximum primary/secondary turn ratio is finally obtained.

Vfly		≤ BV − Vspike − Vin max − m argin
N P			BV − Vspike − Vin max − m arg in	Eq. 5
N P		≤	BV − Vspike − Vin max − m arg in
N S	1		VOut1 + Vd1 fw

For 150W power output, the proposed power switch is STC08DE150, with BV=1500V. Assuming Vspike=200V, margin=200V and Vd1fw=1V. From Eq. 5 results:

NP	≤ 10	Eq. 6

NS1

From Eq. 2, imposing Vin=Vinmin=220V, Np/Ns = 10, and considering the normal mode switching

frequency, the maximum duty cycle and the maximum on time are:

Dmax = 52.8% Ton max = 5.87 s

Eq. 7

NP			Vfly
		=			=15.8	Eq. 10
N
	aux	Vaux +Vd
				fw

The next transformer design step is to fix the primary and/or secondary magnetization inductances. There are several criteria: the first one is to select the primary inductance in order to ensure continuous mode operation from full load to minimum load. This method, since a bigger primary magnetization inductance is requested, assures a very low output current ripple, increasing transformer primary turns. Furthermore, it makes the RHP zero lower, so that the loop stabilization will be more complicated. The second alternative criterion is to calculate primary and secondary inductances by defining maximum secondary ripple current. This last method fixes a limit for the rms current and does not require such a high primary magnetization inductance, but it may lead to a transition mode operation.

It is worth noticing that the value of the duty cycle calculated by Eq. 7 is a good trade-off to optimize both primary and secondary side performances. By the way, it must be pointed out that being Dmax>50%, slope compensation may be necessary. This subject will be deeply analyzed in paragraph 7.

Once fixed the turn ratio between input and the higher power output, the flyback reflected voltage is fixed by Eq. 3 as well.

Vfly	=	N P	(Vout1 + Vd1fw )= 250V	Eq. 8

		N S1

It is now possible to calculate the two turn ratios referred to the slave Vout2 and to the auxiliary outputs.

N P			Vfly
		=			= 33	Eq. 9
N		=			= 33	Eq. 9
N	S 2	Vout2 + Vd
	S 2			fw

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AN2131 - APPLICATION NOTE

Figure 4. Waveforms and Nomenclature of the Continuous Mode Flyback Design

Ipcs

∆Ips

	Ton	Ts	t
	Ton		Is1cs


Is1		∆Is1
Is1			Iout1
			Iout1
		Toff	t
		Toff
VT			Vin+Vfly

Figure 4 reports the most significant waveforms and relevant nomenclature to further proceed in the flyback design. From figure 4, we define IPCS the primary average current value and ∆IPS the primary current variation during the on time, IS1CS the secondary average current value and ∆IS1 the secondary current variation during the off time and IOut1 the secondary average current.

By adopting the second design method, we now fix the maximum secondary ripple current ∆Ιs% in the following equations:

∆IS1max	= 2 ∆I S IS1CS	= 2 ∆IS		IOut1max	Eq. 11

			1− Dmax

where ∆Ιs1max is the maximum secondary current variation and ∆Ιs is the ripple current. Therefore we have:

	=	(VOut1 − Vd fw ) (TS	− TON max )
LS1				Eq. 12
		∆I S!max

where LS1 is the secondary magnetization inductance. Imposing ∆Ιs%= ±30% from Eq. 11 and Eq. 12 results:

LS1 = 16.17µH

Eq. 13

while the primary magnetization inductance is:

	N	P	2
L =				L	=1617 H	Eq. 14

P	NS1			S1

Once fixed turn ratios and the primary inductance value, some extra calculation is needed to choose either the transformer or the external components for flyback stage. Since design specifications request one high power output only, while the slave and the auxiliary outputs need a very small power, for designing the transformer we can only consider a single output. Based on this supposition the relevant design parameters are here below reported.

Fixed Np/Ns = 10 and Lp = 1.6 mH.

Primary Winding:

∆Ip =

(Vin min − Vcson ) *Ton max

0.8A Eq. 15

Ipcs =

Po max

1.48A Eq. 16

(Vinmin − Vcson ) η D max

Ippk

= Ipcs

∆Ip

1.88A

Eq.

Iprms

∆I P

−

∆IP

Dmax Ippk Ipcs −

Ippk

Ipcs

1.08A

Eq. 18

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AN2131 - APPLICATION NOTE

Master Secondary Winding:

Is1CS

IOut1max

13.24A

Eq. 19

− D max

∆Is1 =

(Vout1+ VdFW ) (T − TON max )

9.7A Eq. 20

Ls1

Is1

= Is1

+ ∆Is1 =

18.9A

Eq. 21

Is1rms

−

∆Is1

−

∆Is1

= (1 − Dmax ) Is1pk Is1cs

Is1pk

− Is1cs

= 9.29A

Eq. 22

Above calculation have been made considering a continuous mode operation. This condition is assured by imposing ∆Is% < 100%. According to the reported design parameters, the transformer has been designed by Cramer and all remaining power parts have been chosen as reported in ST's application note AN1889.

5. BASE DRIVING CIRCUIT DESIGN

In practical applications, such as SMPS, where the load is variable, the collector current is variable as well.

As a consequence, it is very important to provide a base current to the device which is related to the collector one. In this way, it is possible to avoid the device over saturation at low load and to optimize the performance in terms of power dissipation.

The best and simplest way to do this is the proportional driving method provided by the current transformer, in figure 5.

At the same time, as already stated, it is very useful to provide a short pulse to the base to make the turn-on as fast as possible and to reduce the dynamic saturation phenomenon.

The pulse is achieved by using the capacitor and the zener in figure 5.

Figure 5. The Proportional Driving Schematic

and its Equivalent Circuit

The driving network guarantees a zone with fixed IC/IB ratio that results imposed once the current transformer turn ratio has been chosen. From the ESBT STC08DE150 datasheet, and in particular looking at the storage time characterization, it is clear that a turn ratio equal to 5 is a good value to ensure the right saturation of ESBT at Ic = 2A, so that in the current transformer we can fix at first:

N P	=	1	Eq. 23

NS 5

The core magnetic permeability of the current transformer has to be as high as possible in order to minimize the magnetization current Im (that is not transferred to the secondary side but only drives the core into saturation). On the contrary, too high a permeability core may lead the core into saturation even with a very small magnetization current. To avoid that it is necessary to increase the number of primary turns and the size of the core as well. On the other hand, if a core with a very small magnetic permeability is chosen, it is possible to reduce the number of primary turns and the core size, but if the permeability is too small we may not have current on the secondary side because almost all the collector current

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AN2131 - APPLICATION NOTE

becomes magnetization current. As a compromise a ferrite material with a relative permeability in the range of 4500 ÷ 7000 is the best choice.

When a ferrite ring with some diameter has been selected, the minimum primary turns is determined to avoid the core saturation from the preliminarily fixed turn ratio N with 0.2. By applying the Faraday’s law and imposing the maximum flux Bmax equals to Bsat/2:

= N

dϕ

∆B

= 2

V1 Ton max

∆t

TP dt

A B

sat

Eq.

Where, Bsat is the saturation flux of the core and it depends on the magnetic permeability.

During the conduction time, the junction baseemitter of ESBT can be seen as a forward biased diode. To complete the secondary side load loop the voltage drop on both diode D and resistor RB must be added in series with the base of the ESBT. The equivalent secondary side voltage source is given by:

VS = VBEon + VD + VRB 2.5V

Eq. 25

Since the magnetization inductance cannot be neglected, only IP, a fraction of the total collector current, will be transferred to the secondary. As a result, the magnetization current has to be first as low as possible. Meanwhile, the value of the magnetization inductance must be taken into account for a proper calculation of transformer primary turns and turns ratio. The magnetization voltage drop, that is, the voltage at the primary of the current transformer, can be now easily calculated:

		N1T			1		[V ]	Eq. 26
V1 = VS		N2T		= 2.5 5		= 0.5

The magnetization current will be:
IM max	=		V1TON max					Eq. 27

				LTP

The number of primary turns should be increased

if IMmax is relatively high. But the core must have window area enough to hold all primary and

secondary windings. Otherwise it is necessary to choose a bigger core size. Once both core material and size are fixed, the turn ratio must be

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adjusted to get the desired IC/IB ratio according to the equation below:

Neff	=	I P	=	IC max − I M max	Eq. 28
		I B		IC
			5

where IMmax is the maximum magnetization current.

The insulation between primary and secondary should be considered since the voltage on the primary side during the off time can overstep 1500V.

Next step is to select the zener diode, the capacitor Cb and the resistor Rb. The turn-on performance of ESBT is related to the initial base

peak current and its duration tpeak that is approximately given by:

tpeak = 3RbCb

Eq. 29

A suitable value for Rb is 0.56. It can eliminate the ringing on the base current after the peak, and at the same time, it generates negligible power dissipation.

The value tpeak can be determined once the minimum on time is set based on the operation

frequency. Bear in mind that in practical applications it should never be lower than 200ns. The value of Cb can be counted since the values of tpeak and Rb are known.

Ipeak must be limited in order to avoid an extra saturation of the device. This action is made by the

zener diode Dz that clamps the voltage across the small capacitor Cb. The zener must be chosen according to the following empirical formulas and inside the range of VZmin and VZmax:

VZ max = 2(I peak Rb + 1)

Eq. 30

VZ min = 2(I peak Rb )

The base peak current will be higher with higher clamp voltage (Dz) or smaller capacitance (Cb), which in turn will lead to a shorter duration of the peak time.

The higher and longer the base peak current, the lower the power dissipation during turn-on. But you need to limit the Ib peak both in terms of amplitude and time duration otherwise at low load a very high saturation level may result. If the device is over-saturated the storage time is too long with higher power dissipation during turn-off. Moreover a long storage time can also cause output oscillation especially at high input voltage.

AN2131 - APPLICATION NOTE

To overcome the above mentioned problems it is recommended to fix the peak duration to 1/3 the minimum duty cycle.

6. CONTINUOS CURRENT MODE LOOP STABILIZATION

It is well known from literature that the transfer function of the continuous current mode (CCM) flyback converter is given by:

G1		(s) =	vout1 (s)		=	N R (1− D)
G1		(s) =	vcomp (s)		=
			vcomp (s)			3 RS (1+ D)
						sLp D
	(1+ sCRC ) 1−						Eq. 31
	(1+ sCRC ) 1−						Eq. 31
				N 2 R(1− D)2

1+ sCR

1+ D

where N = Np/Ns, R is the load, RC is the electrolytic capacitor series resistance.

It is worth noticing that the transfer function has one pole and two zeros, whose one on the right half plane. The RHP zero is very difficult if not

impossible to compensate and therefore must be kept well beyond the closed-loop bandwidth. As a result, the transient response of such system will be not extremely fast.

Considering now, the transfer function in the following form:

−

vout1 (s)

z11

z12

(s) =

= k

vcomp (s)

−

Eq. 32

p11

Substituting the values of this design in case of low input voltage (worst case), we obtain the frequency response reported in the following figure 6. Poles and zeros are reported in the below equations:

P11= -202/rad=-32.1Hz
Z11= -23Krad/s=-3.79KHz	Eq. 33
Z12= 88Krad/s=14.1KHz

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